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Assessing adult learner's numeracy as related to gender and performance in arithmetic/Evaluacion de habilidades aritmeticas de alumnos adultos con relacion al genero y desempeno en aritmetica.

1 INTRODUCTION

The concept of numeracy could be said to have originated from the report for the United Kingdom Ministry of Education (Crowther Report, 1959) and the concept of adult numeracy has gained more popularity in the developed countries such as the United States, Australia, New Zealand and the UK (Cockcroft, 1982; Goyen, 1977; McLennan, 1996; Wickert, 1989). Adult numeracy was initially taken as part of adult literacy (Goyen, 1977) with no visible scale to measure it. Goyen (1977) measured adult literacy with a unidimensional scale and "some five years after the British report (Cockcroft, 1982), although told little about adult numeracy, provided a landmark framework to researching and reporting on the mathematical needs of adult life". The report proposed a definition of numeracy:

We would wish the word 'numerate' to imply the possession of two attributes. The first of these is an 'at-homeness' with numbers and an ability to make use of mathematical skills which enables an individual to cope with the practical mathematical demands of his everyday life. The second is to have some appreciation and understanding of information which is presented in mathematical terms, for instance in graphs, charts or tables or by reference to percentage increase or decrease. (Cockcroft, 1982, p. 11)

Wickert (1989) introduced three literacy dimensions: document literacy, prose literacy, and quantitative literacy. Literacy is defined as using printed information to function in society, to achieve one's goals, and to develop one's knowledge and potential. Document literacy is defined as the ability to use and identify information contained in documents or materials such as tables, schedules, charts, graphs, maps, forms and memos. Prose literacy is the ability to read and interpret prose in newspaper, articles and books while the quantitative literacy is seen as the ability to apply numerical or arithmetic operations to information contained in print materials, such as menus (ABS Aspects of Literacy website; McLennan, 1996; Wickert, 1989). Adult numeracy has been variously used to mean quantitative literacy, quantitative reasoning and statistical literacy (Smit & Mji, 2012). In addition, a plethora of similar and loosely related terms such as mathematical literacy, techno-mathematical literacy, functional mathematics, and mathemacy compete for attention (Condelli, Safford-Ramus, Sherman, Coben, Gal & Hector-Mason, 2006) but numeracy in its real sense is more than any one of these concepts.

Quantitative literacy is a subset of numeracy (Johnston, 2002). Although numeracy and literacy are related, they are not the same. Wickert (1989) in his report noted that when people have poor literacy skills, they have even worse numeracy skills and the need to upgrade numeracy skills in the context of literacy must be taken account of in all decisions to raise the levels of adult literacy. Steen (1991) defined numeracy as being "...to mathematics as literacy is to language" (p. 1). A great number of characterisations of numeracy have been postulated in recent times by different authors whose fundamental themes gyrate around numeracy being the understanding and application of mathematical principles in order to resolve life's day-to-day challenges (Best, 2008; Evans, 2000; Lindenskov & Wedege, 2001; Paulos, 1989). Broadly defined, numeracy is taken as mathematical literacy (De Lange, 2003) involving an individual's capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgments, and to engage in mathematics in ways that meet the needs of that individual's current and future life as a constructive, concerned and reflective citizen (OECD, 2000).

Numeracy covers the ability to understand, use, calculate, manipulate, interpret results, and communicate mathematical information. In the adult context, numeracy refers to the practical or functional use of mathematics. According to Ginsburg, Manly & Schmitt (2006) the term "numeracy" is used in the adult education community to include an array of mathematically related proficiencies that are evident in adults' lives and worthy of attention in adult education settings. They maintained that while there are various definitions of the term numeracy (Coben, 2000; Cockcroft, 1982; Crowther, 1959; Gal, van Groenestijn, Manly, Schmitt & Tout, 2003; Johnston, 1994; Lindenskov & Wedege, 2001; and Steen, 2001), all recognise that mathematics and numeracy are related but are not synonymous. Unlike pure mathematics which leads upward in an ascending pursuit of abstraction and is context-free (Ginsburg et al., 2006), numeracy has a distinctive personal life element in which mathematical topics are woven into the context of work and community for richer engagement (Orrill, 2001) in the democratic process (Johnston, 1994) and utility in the competitive global economy (Wedege, 2003). Condelli, et al., (2006) in a study, reviewed the definitions of numeracy using the Maguire & O'Donoghue's (2002) organizing framework in which numeracy concepts were considered as a continuum of increasing levels of sophistication: formative, mathematical, and integrative. Thus, numeracy is viewed as the basic arithmetic skills (formative phase), situated in context with explicit recognition of importance of mathematics in everyday life (mathematical phase) and gradually incorporating the mathematics, communication, cultural, social, emotional, and personal aspects of each individual in context (integrative phase).

Adult numeracy is an important area of large scale research in many developed countries (Benseman & Sutton, 2011; EU Skills Panorama, 2012; Johnston, 2002; Lowden, Powney, Gardner & Mark, 1995; Tett, Hall, Maclachlan, Thorpe, Edwards & Garside, 2006) including South Africa (Coben, 2000; Smit & Mji, 2012), but in Nigeria the topic is not yet a corner stone of education research as little or no studies have investigated adult numeracy in general. This is incongruence to the expectations of the Nigerian government at all levels that the society be ridden off innumeracy to the point that an average Nigerian should be able to at least perform basic mathematical computations which are needed in today's 21st century work place.

In general, innumeracy has been found to have both short and long term effects on people's lives (Steen, 1991; Paulos, 1989) including mine workers (Smit & Mji, 2012) such as inability to control personal finances, inability to make adequate risk assessments, daily activities, and restricted employment opportunities. Without basic numeracy skills, the large numbers of innumerate adult Nigerians cannot be hopeful of securing jobs with better pay. Adults need higher levels of numeracy to function effectively in their roles as workers, parents, and citizens when one considers the increasingly importance of quantitative and technical aspects of human life in making the world more digitalised. More often than not, numeracy is a key attribute in gaining and retaining employment (Bynner, 2004) with the number of jobs and occupations requiring low-level skills shrinking world-wide and individuals with low level numeracy skills are expected to find it increasingly difficult to compete in the competitively digitalised labour market.

The EU High Level Group of Experts on Literacy (2012) classifies numeracy into three distinct categories: baseline, functional and multiple. Multiple Numeracy--is the ability and willingness to use mathematical modes of thought (logical and spatial thinking) and presentation (formulae, models, graphs, charts) that enable a person to fully function in a modern society, Functional Numeracy--is the ability to apply basic mathematical principles and processes in everyday contexts at home, school and work (as needed for banking, payments, reading timetables, etc.)--, and Baseline Numeracy--is having a sound knowledge of numbers, measures and structures, basic operations, basic mathematical presentations and the ability to use appropriate aids that enable further development.

Ginsburg et al. (2006) through a field-and research-based synthesis of the components required for adults to be numerate, to act numerately, and to acquire numeracy skills, identified three fundamental elements each with different subcomponents that are inherent in proficient numeracy practice. These components form the construct of adult numeracy and each component can be described separately and is different in nature. In actuality they interact, are intertwined, and have little meaning in isolation (Ginsburg et al., 2006).

1. Context--The use and purpose for which an adult takes on a task with mathematical demands (Akinsola & Awofala, 2008). The context has four subcomponents: Family or Personal, as a parent, household manager, consumer, financial and health-care decision maker, and hobbyist. Workplace, as a worker able to perform tasks on the job and to be prepared to adapt to new employment demands. Further Learning, as one interested in the more formal aspects of mathematics necessary for further education or training. And Community, as a citizen making interpretations of social situations with mathematical aspects such as the environment, crime and politics.

2. Content. The mathematical knowledge that is necessary for the tasks confronted. The content is organised into four strands: Number and Operation Sense, a sense of how numbers and operations work and how they relate to the world situations that they represent. Patterns, Functions and Algebra, an ability to analyze relationships and change among quantities, generalize and represent them in different ways, and develop solution methods based on the properties of numbers, operations and equations. Measurement and Shape, knowledge of the attributes of shapes, how to estimate and/or determine the measure of these attributes directly or indirectly, and how to reason spatially. And Data, Statistics and Probability, the ability to describe populations, deal with uncertainty, assess claims, and make decisions thoughtfully.

3. Cognitive and Affective. The processes that enable an individual to solve problems, and thereby, link the content and context. The cognitive and affective component is divided into five subcomponents: Conceptual Understanding, an integrated and functional grasp of mathematical ideas (Kilpatrick, Swafford & Findell, 2001) and the two aspects of conceptual understanding--integrated and functional--frame the ability to think and act numerately and effectively (Ginsburg et al., 2006). Adaptive Reasoning, the capacity to think logically about the relationships among concepts and situations (Kilpatrick et al., 2001). Strategic Competence, the ability to formulate mathematical problems, represent them, and solve them (Kilpatrick et al., 2001) and problem solving represents the heart of numeracy (Ginsburg et al., 2006). Procedural Fluency, the ability to perform calculations efficiently and accurately by using paper and pencil procedures, mental mathematics, estimation techniques, and technological aids (Kilpatrick et al., 2001). And Productive Disposition, the beliefs, attitudes, and emotions that contribute to a person's ability and willingness to engage, use, and persevere in mathematical thinking and learning or in activities with numeracy aspects (Ginsburg et al., 2006). Productive disposition has been identified as a necessary component of mathematical proficiency which should be developed during the course of K-12 mathematics education (Kilpatrick et al., 2001) in both male and female students.

As in advanced mathematics (Akinsola & Awofala, 2009; Awofala, 2011b; Rogers & Kaiser, 1995; Sommers, 2008; Stoeger, 2004; Willis, 1989), gender differences permeate numeracy skills (Beilock, Gunderson, Ramirez & Levine, 2010; Coben et al., 2003; Murray, Clermont & Binkley, 2005; Parsons & Bynner, 2005; Satherley & Lawes, 2009a) and these differences have been ascribed to attitudes, feelings, stereotype threat and the consequences of affective issues as much as to actual cognitive differences (Beaton, Tougas, Rinfret, Huard & Delisle, 2007; Coben et al., 2003; Hyde & Mertz, 2009; Mendick, 2005; Rivardo, Rhodes, Camaione & Legg, 2011; Tomasetto, Alparone & Cadinu, 2011).

It is evident that the effects of poor numeracy skills seem greater on women than on men (Parsons & Bynner, 2005; Reder & Bynner, 2009) with literature suggesting that the gender differences in mathematics performance may be an outcome of teaching approaches that do not relate to preferred learning styles (Awofala, 2011a; Awofala, Balogun & Olagunju, 2011; Zohar, 2006). More so, literature suggests that gender differences in approaches to mathematics have both biological (Awofala, 2008)-an example being differences in spatial processing (Maloney, Waechter, Risko & Fugelsang, 2012) and cultural bases (Awofala, 2008)-an example being spatial processing aspects of intelligence tests being culturally defined (Clifford, 2008). In this new millennium and across cultures, the cultural explanation to gender differences in mathematics performance seems to be gaining more prominence in gender literature with biological explanation waning. However, current research is yet to provide unquestionable answers to gender differences in mathematics performance being underlined by biological factors since inconsistently non-similar patterns of gender differences in mathematics ability are found from cross-cultural studies (Awofala, 2011b; Kane & Mertz, 2012).

Meta-analyses of studies on gender difference in mathematics performance across the United States and the United Kingdom (Luckenbill, 1995) revealed that while a very minute gender difference in early mathematics skills was perceptible at elementary school levels, a gender difference in favour of male students appeared in high schools (Hyde & Mertz, 2009) with the conclusion that differential patterns of course-taking accounted for this difference, with socialisation and discrimination as lesser factors. Although meta-analytic studies on gender difference in mathematics performance is yet to be conducted on the Nigerian sample, international findings regarding gender difference in mathematics performance other than the US and UK showed that females had the same or better performance in mathematics when compared with the males. This is corroborated by the declining gender gaps in mathematics performance in the European Union (EU) with only 2% difference on average between low achievers boys (21%) and low achievers girls (23%) (EU Skills Panorama, 2012). This finding has had to the argument by Hyde & Mertz (2009) that gender differences in mathematical performance were due to changeable socio-cultural factors rather than innate biological differences.

Many studies had supported the socio-cultural origin of gender differences in mathematics performance (Ceci & Williams, 2010, 2011; Lindberg, Hyde, Petersen & Linn, 2010; York & Clark, 2007), with ample research indicating that self-confidence (Carr, Steiner, Kyser & Biddlecomb, 2008), sexism (Sommers, 2008), and stereotype threat (Steffens & Jelenec, 2011; Tomasetto et al., 2011) caused or contributed to these disparities. Stereotype threat occurs when the "motivational, affective, psychological, and cognitive processes interact to impair performance in a stereotype-relevant context" (Schmader, Johns & Forbes, 2008, p. 336) and has been shown to affect numeracy test results through interfering with concentration and co-ordinating information processing.

Bynner and Parsons (2006) found that among individuals born in England and Wales in 1970, males and females had nearly identical levels of literacy skill but there was significantly more gender variation in numeracy, in which skill levels were lower than literacy for both sexes, but especially for women. A 2005 report from the United Kingdom on two longitudinal studies into numeracy and literacy skills using cohorts from 1958 and 1970 found that men had stronger numeracy skills than women (Parsons & Bynner, 2005). For women, the United Kingdom research reports that "while the impact of low literacy and numeracy skills is substantial, low numeracy has greater negative effect (than for men) even when it is combined with competent literacy" (Parsons & Bynner, 2005, p. 7). Between 1996 and 2006, inconsistent findings had been found regarding gender differences on the quantitative literacy scores among New Zealand population. The International Adult Literacy Survey (IALS) conducted in 1996 in New Zealand showed a gender difference on the quantitative literacy scores (which covered a subset of numeracy skills rather than the range of numeracy skills covered in the ALLS (Adult Literacy and Life Skills Survey) but the difference (around 5%) was not statistically significant (Culligan, Sligo, Arnold & Noble, 2004), whereas the more recent New Zealand ALL survey (2006) showed small, but statistically significantly higher numeracy scores for men than women (Satherley & Lawes, 2008a, 2008b). The zero-tolerance gender difference in mathematics performance (Fatade, Nneji, Awofala & Awofala, 2012) was comparable with the much more recent IALS data from Scotland which found no significant gender differences in quantitative literacy scores (St Clair et al., 2010).

In summary, mathematics had for long created social stereotypes and gender inequalities into the educational sector and since its introduction into schools, mathematics had been seen as a male domain or something for boys. This old stereotypic gender differences in cognitive and affective outcomes that formerly subsisted in mathematics were extrapolated to the area of numeracy. Although canonical gender differences in mathematics are declining world-wide and, perhaps, do not have any practical importance for the future, the inconsistent findings regarding gender differences in numeracy have shown the need for more investigations. Unlike the developed countries of the world, where researches into adult learner numeracy had reached an appreciable level, there were paucity of studies in Nigeria on adult learner numeracy and numeracy gender related issues. In addition, the not too straightforward findings on gender differences in arithmetic have further provided the needed impetus for the study.

2 PURPOSE OF THE STUDY

Therefore, the present study investigated Nigerian adult learner numeracy, the differences in numeracy between men and women, and the relationship between numeracy and performance in arithmetic.

3 RESEARCH QUESTIONS

Specifically in this study, the following research questions were addressed:

1. What is the factor structure of the numeracy self-assessment scale?

2. What is the level of perception of numeracy skills among Nigerian adult learners?

3. Is gender a factor in performance in Arithmetic and perception of Numeracy among Nigerian adult learners?

4. What are the composite and relative contributions of dimensions of numeracy (numeracy in everyday life, numeracy in workplace, and numeracy in mathematical tasks) and gender to the explanation of the variance in the adult learners' performance in arithmetic?

4 METHODOLOGY

The study made use of quantitative research method within the blueprint of descriptive survey design. The participants in this study were 32 adult learners (16 men and 16 women) from one accredited adult literacy centre in Lagos State, Nigeria. Their age ranged from 18 to 57 years with mean age of 37.8 years. The participants could also be categorised as 3(9.4%) with age group below 20 years and 29(90.6%) within the age group 20 years and above. For the purpose of data collection, one instrument tagged Numeracy Self-Assessment Scale (NSAC) adopted from the Human Resources and Skills Development Canada was used to collect primary data relating to adult learners' numeracy skills while secondary data relating to their performance in arithmetic were retrieved from their records in the Adult Learners Literacy Centre. The NSAC consisted of 24 items anchored on a 3-point scale ranging from: Yes--3, Somewhat--2, to No--1. The internal consistency reliability coefficient of the NSAC was computed using the Cronbach alpha (a) with a value of 0.87. The second author personally administered the NSAC to the whole sample and in a regularly schedule class and equally retrieved records pertaining to the adult learners' performance in Arithmetic from the centre for the purpose of this study. Data collected were summarized and analysed using percentages, means, standard deviations, independent samples t-test, principal components factor analysis, Pearson moment correlation, and multiple regression analysis.

5 RESULTS

5.1 Research Questions One: What is the factor structure of the numeracy self-assessment scale?

Findings from research question 1 shows the responses of the participants to the 24 items of numeracy self-assessment scale were subjected to principal components factor analyses (PCA) to identify their underlying dimensions.

The data screening processes were carried out and showed missing values for three out of 35 participants and these were discarded. Subsequently, further screening showed no concern about normality, linearity, multicollinearity, and singularity. For example, subscale scores were normally distributed with skewness and kurtosis values within acceptable ranges (e.g. skewness ranged from -2.24 to 0.43, kurtosis ranged from -0.94 to 6.65) as Kline (1998) suggested using absolute cut-off values of 3.0 for skewness and 8.0 for kurtosis. The correlation matrix of the 24 items revealed that the correlations when taken overall were statistically significant as indicated by the Bartlett's test of sphericity, [chi square] = 2204.08; df=276; p < .001 which tests the null hypothesis that the correlation matrix is an identity matrix. The Kaiser-Meyer-Olkin measure of sampling adequacy (MSA) fell within acceptable range (values of .60 and above) with a value of .871. Each of the variables also exceeded the threshold value (.60) of MSA which ranged from .646 to .882. Finally, most of the partial correlations were small as indicated by the anti-image correlation matrix. These measures all led to the conclusion that the set of 24 items of numeracy self-assessment scale was appropriate for PCA and since no particular number of components was first hypothesized (although not unmindful of a priori criterion of four-factor) the criterion was set to eigenvalues greater than one (Kaiser, 1960; Tabachnick & Fidell, 2001).

The initial unrotated PCA resulted in a factor model of seven dimensions as indicated by the eigenvalues exceeding unity but the scree plot showed a factor model of three dimensions. However, based on its pattern of factor loadings, this unrotated factor model was theoretically less meaningful and as such was difficult to interpret. Therefore, the analysis proceeded to rotate the factor matrix orthogonally using varimax rotation to achieve a simple and theoretically more meaningful solution. The rotation resulted in a factor model of three dimensions as suggested by the scree plot and eigenvalues exceeding unity.

In this study, all the communalities for the factor analysis satisfied the minimum requirement of being larger than 0.50, in fact these ranged from 0.697 to 0.982. Figure 1 below is the scree plot which graphs the eigenvalue against the component number and is suggestive of a three component model.

Table 1 displayed the factor loadings for the orthogonal three-factor model of numeracy self-assessment scale. All items loaded .587 and above on their primary factor; none of the secondary loadings exceeded .35. Together the three factors accounted for 60.65% of the total variance. The first factor accounted for 30.37% of the variance (eigenvalue= 7.29) and consisted of five numeracy in everyday life items. The second factor accounted for 16.93% of the variance (eigenvalue = 4.06) and consisted of ten numeracy in workplace tasks items. The third factor accounted for 13.34% of the variance (eigenvalue = 3.20) and consisted of nine numeracy in mathematical tasks items. The internal consistency reliabilities for the subscales are: numeracy in everyday life ([alpha] = .72), numeracy in workplace tasks ([alpha] = .78), and numeracy in mathematical tasks ([alpha] = .83), and the internal consistency reliability for the entire scale ([alpha] = .87) was considered very high and conceptually meaningful (Curtis & Singh, 1997). Thus, the three measures represent empirically separable and internally consistent numeracy self-assessment constructs.

5.2 Research Questions Two: What is the level of perception of numeracy skills among Nigerian adult learners?

Table 1 above showed the overall perception of numeracy skills among Nigerian adult learners. Actual numbers and percentages for responses to each statement were shown in the table. The percentages were in parenthesis. Table 1 showed that the adult learners in the present study had average numeracy strength (Mean=2.470, SD= 0.780). In relation to numeracy in everyday life dimension, more than 90 percent of the adult learners said yes to such numeracy skills, as I can perform simple calculations such as addition and subtraction (item 1), receive cash payments and make change (item 2), calculate the cost of items on a bill (item 3), make comparisons (e.g. taller or shorter, heavier or lighter, greater than or less than) (item 4) while more than 75 percent of the adult learners said yes to numeracy skill such as I can record time using digital and standard clocks, watches, or timers (item 5). As indicated in Table 1 above, the adult learners had high numeracy strength (Mean=2.800, SD= 0.577) regarding numeracy in everyday life dimension. This should be expected considering their exposure to everyday life activities that involved the application of basic arithmetic operations

In the case of numeracy in workplace tasks dimension (Table 1), more than 80 percent of the adult learners responded yes to such statements as: I can take simple measurements (e.g. length, weight, temperature) (item 6) and estimate measurements (e.g. it is approximately three feet wide) (item 8). More than 50 percent of the respondents said yes to such numeracy skills statements such as I can estimate quantities (e.g. I need approximately 20 copies) (item 7), create and balance budgets (item 9), create and monitor schedules (e.g. staffing or project schedules) (item 10), and make accurate estimates when information is limited (item 15) whereas more than 40 percent of the adult learners responded yes to such numeracy skills statements as, I can estimate the time required to complete specific tasks (item 11), take precise measurements using specialized equipment (item 12), compare similar products with differing cost structures to determine the best value (item 13), and manage complex budgets (e.g. preparing financial statements, forecasting materials) (item 14). Table 1 above, showed that the adult learners had average numeracy strength (Mean=2.282, SD=0.885) regarding numeracy in workplace tasks dimension. Unlike the tasks in everyday life, tasks in workplace are more complex and demand higher skills with some specialised training.

Assessment of numeracy in mathematical tasks dimension as contained in Table 1 above, showed that more than 80 percent of the adult learners responded yes to such numeracy statements as, I can calculate the area of common shapes (e.g. square, triangle, circle) (item 18), perform measurement conversions (e.g. inches to centimetres, millilitres to litres) (item 19), calculate simple averages (item 20), perform calculations that require multiple steps or operations (item 21), and calculate areas and volumes of irregular shapes (item 22) while more than 50 percent of the adult learners responded yes to such statements as, I can perform calculations that require multiplication and/or division (item 16), measure curved and irregular lengths (item 23), and analyze and compare statistical data (item 24). Fifty percent of the adult learners said yes to such statement as, I can calculate percentages (item 17). Table 1 above, showed that the adult learners had average numeracy strength (Mean=2.328, SD= 0.877) regarding numeracy in mathematical tasks dimension. Unlike the tasks in everyday life and workplace, mathematical tasks are much more complex, abstract, and more demanding than tasks in workplace and they require higher-order skills and problem solving.

5.3 Research Questions Three: Is gender a factor in performance in Arithmetic and perception of Numeracy skills among Nigerian adult learners?

Table 2 below showed the descriptive statistics of mean and standard deviation and t-test values on perception of numeracy score and arithmetic score by male and female adult learners. With respect to the aggregate numeracy skill score, the adult female learners recorded slightly higher mean score (M=56.56, SD=7.53) than their male counterparts (M=56.38, SD=8.10). However, this slight difference in mean score was statistically not significant (t30=-.068, p=.946). Table 2 below showed that the adult male learners recorded slightly higher mean score (M=14.00, SD=1.79) in perception of numeracy skills in everyday life than their female counterparts (M=13.94, SD=2.11) and this difference was statistically not significant (t30=.090, p=.929). In Table 2, the adult female learners recorded slightly higher mean score (M=21.81, SD=5.65) in numeracy in workplace tasks than their male counterparts (M=20.00, SD=5.65). The difference was statistically not significant (t30=-.908, p=.371). With respect to numeracy in mathematical tasks, the adult male learners recorded slightly higher mean score (M=22.38, SD=5.12) than their female counterparts (M=20.81, SD=4.26). However, this difference in mean score was statistically not significant (t30=.938, p=.356). Table 2 revealed that adult female learners recorded slightly higher mean score (M=52.13, SD=10.98) in Arithmetic than their male counterparts (M=51.56, SD=9.20). This difference in mean score was not statistically significant (t30=-.157, p=.876). Thus, we concluded that gender was not a significant factor in adult learners' performance in arithmetic, perception of numeracy skills, and even at the numeracy skills subscale levels.

5.4 Research Questions Four: What are the composite and relative contributions of dimensions of numeracy (numeracy in everyday life, numeracy in workplace, and numeracy in mathematical tasks) and gender to the explanation of the variance in the adult learners' performance in arithmetic?

The results in Table 3 below showed the relationship among the numeracy skills, numeracy self-assessment subscales, gender and performance in arithmetic. Table 3 showed that there was a significant positive correlation between the adult learner performance in arithmetic and numeracy in workplace tasks (Pearson r=.657, p < .001) and numeracy in mathematical tasks (Pearson r=.369, p < .05) while gender did not correlate significantly either with performance in arithmetic or numeracy skills dimensions.

More so, there was a significant positive correlation between adult learners' perception of numeracy skills and their performance in arithmetic (Pearson r=.652, p < . 001). The results in Table 4 below showed that the independent variables (Gender, Numeracy in everyday life (NEL), Numeracy in workplace tasks (NWT), and Numeracy in mathematical tasks (NMT)) jointly contributed a coefficient of multiple regression of .601 and a multiple correlation square of .542 to the prediction of adult learners' performance in arithmetic.

By implication, 60.1% of the total variance of the dependent variable (performance in arithmetic) was accounted for by the combination of the four independent variables. The results further revealed that the analysis of variance of the multiple regression data produced an F-ratio value significant at 0.001 level (F(4, 27) = 10.157; p < .001).

The results of the relative contributions of the independent variables to the prediction of adult learners' performance in arithmetic was that numeracy in workplace tasks was the potent significant positive contributor to the prediction of adult learners' performance in arithmetic ([beta] = .667, t = 5.38, p < .001), while numeracy in mathematical tasks dimension of numeracy self-assessment skills made the next significant positive contribution to the prediction of the dependent variable ([beta] =.305, t = 2.44, p=.022). Numeracy in everyday life ([beta] =-.231, t = 1.88, p=.072) and gender ([beta] =-.033, t = -.261, p=.796) did not make any significant positive contribution to the prediction of adult learners' performance in arithmetic.

Afterwards, a stepwise regression analysis was used to determine the contribution of each of these variables in predicting performance in arithmetic. A reduced model explaining the predictive capacity of the two variables (numeracy in workplace tasks and numeracy in mathematical tasks) on performance in arithmetic is outlined in Table 5 below. Model 1, which includes only numeracy in workplace tasks scores, is accounted for 43.2% of the variance in adult learners' performance in arithmetic. The inclusion of numeracy in mathematical tasks into Model 2 resulted in additional 54.8% of the variance being explained. This means that numeracy in mathematical tasks alone accounted for 11.6% of the variance in adult learners' performance in arithmetic.

6 DISCUSSION

The results of the present study have highlighted five main findings. These findings relate to establishing the factor structure of the numeracy self-assessment scale with adult learners; determining the level of perception of numeracy skills among adult learners; determining whether differences existed between male and female adult learners in perception of numeracy skills and performance in arithmetic; and ascertaining composite and relative contributions of numeracy skills dimensions and gender to the prediction of adult learners' performance in arithmetic.

The results of the present study showed that numeracy skill as measured by numeracy self-assessment scale is a multi-dimensional construct. The exploratory factor analysis using the principal components analysis showed a three factor structure underlying the scale. The three interpretable factor structures are subsequently labelled: Numeracy in everyday life (with 5 items), Numeracy in workplace tasks (with 10 items), and Numeracy in mathematical tasks (with 9 items) and each subscale had adequate internal consistency reliability. The adult learners in the present study had average numeracy strength (Mean=2.470, SD= 0.780). This finding was in contrast with previous findings (Smit & Mji, 2012) which showed low level of numeracy among adult chrome mine workers in South Africa. In addition, findings from the United States had revealed that level of numeracy among vulnerable groups in the society such as the elderly, women and those with low educational attainment was very low (Lusardi, 2012). This was contrary to the findings from Sweden and Poland which showed that level of numeracy among their populations was very high (Johnston, 2002).

The findings relating to gender differences in perception of numeracy skills and performance in arithmetic showed that in the present study male and female adult learners recorded comparable mean scores in performance in arithmetic and on each of the numeracy skills dimensions. Thus, gender differences in numeracy skills and performance in arithmetic as shown in this study was not significant. These findings were in agreement with previous study findings (Arigbabu & Mji, 2004; Fatade, Nneji, Awofala & Awofala, 2012) in advanced mathematics among preservice mathematics teachers but ran contrary to other previous findings (Beilock et al., 2010; Coben et al., 2003; Murray et al., 2005; Parsons & Bynner, 2005; Satherley & Lawes, 2008a, 2008b; Satherley & Lawes, 2009a, 2009b, 2009c) which revealed the existence of significant gender differences in numeracy skills. The implication of the present study findings regarding gender is that gender differences in numeracy skills and performance in arithmetic are no longer important.

The results displayed in Table 4 showed that 60.1% of the variance in adult learners' performance in arithmetic was accounted for by the four predictor variables (gender, numeracy in everyday life, numeracy in workplace tasks, and numeracy in mathematical tasks) taken together. The relationship between performance in arithmetic and the predictor variables taken together were high as shown by the coefficient of multiple correlation (R = .775). Thus, the predictor variables investigated when taken together predicted to some extent arithmetic performance among adult learners involved in the study. The observed ([F.sub.(4, 27)] = 10.157; p < .001) is a reliable evidence that the combination of the dimensions of numeracy skills in the prediction of adult learners' performance in arithmetic from all indications did not occur by chance with 39.9% of the variance in arithmetic performance not unexplained by the current data. Thus, there might be other independent variables which may require further investigations about their contribution to the prediction of adult learners' performance in arithmetic and the degree of prediction jointly made by the four independent variables of this study could be substantive enough to assert that adult learners' performance in arithmetic is predictable by a combination of the dimensions of numeracy skills and gender. Thus, the strength of the predictive power of the combined independent variables (numeracy in everyday life, numeracy in workplace, numeracy in mathematical tasks, and gender) on the outcome variable was strong and significant to show the linear relationship between the four predictor variables and the total variance in adult learners' performance in arithmetic. According to the standardized coefficients the regression model is as follows: Performance in [Arithmetic.sub.predicted] = 30.875-0.033 gender-0.231 numeracy in everyday life + 0.667 numeracy in workplace tasks + 0.305 numeracy in mathematical tasks.

On the relative contribution of each of the independent variables to the explanation of variance in adult learners' performance in arithmetic, the present study revealed that only two (numeracy in workplace tasks and numeracy in mathematical tasks) out of the four independent variables made statistically significant contribution to the variance in adult learners' performance in arithmetic. Numeracy in workplace tasks was the best predictor of performance in arithmetic and accounted for 43.2% of the variance in adult learners' performance in arithmetic. This was followed by numeracy in mathematical tasks which alone accounted for 11.6% of the variance in adult learners' performance in arithmetic. Gender and numeracy in everyday life did not contribute meaningfully to the prediction of adult learners' performance in arithmetic.

7 LIMITATIONS OF THE STUDY

It is worthy of note that the findings that emerged in this study may not be generalised to all Nigerian adult learners as the sample was not necessarily representative of all adult learners. The small sample size (n=32) notwithstanding, it is noted that perception of numeracy scores obtained among this group of adult learners may have been influenced by their literacy ability and anxiety regarding numbers. Some adult learners who were part of the assessments may not have properly understood some of the numeracy statements which could also invoke anxiety in them. The present study investigated adult learners' numeracy using individual self-assessment scale which is often criticised for promoting measurement error. People may over or understate their level of literacy and numeracy skills in order to conform to societal standard. It is recommended that future studies in Nigeria should investigate adult learners' numeracy skills using more robust and psychometrically sound instruments such as the Adult Literacy and Life Skills Survey (ALLS) and the International Adult Literacy Survey (IALS). However, we are of the opinion that the present study is vital in exposing the level of numeracy perception among adult learners as the study findings could serve as a baseline for conducting future studies in adult numeracy in Nigeria.

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Adeneye O. A. Awofala (1) *, Blessing E. Anyikwa (2)

(1) Department of Science and Technology Education, Faculty of Education, University of Lagos, Nigeria {aawofala@unilag.edu.ng}

(2) Department of Adult Education, Faculty of Education, University of Lagos, Nigeria {ebblessing@vahoo.com}

Received on 29 May 2013; revised on 4 September 2013; accepted on 1 October 2013; published on 15 July 2014

DOI: 10.7821/naer.3.2.83-92

* To whom correspondence should be addressed:

Adeneye O. A. Awofala

University of Lagos, Faculty of Education

Akoka, Yaba

Lagos, Nigeria

1 INTRODUCCION

Se podria decir que el concepto de aritmetica ha surgido a partir del informe de Ministerio de Educacion del Reino Unido (informe de Crowther, 1959) y que el concepto de aritmetica para adultos ha ganado mas popularidad en los paises desarrollados como Estados Unidos, Australia, Nueva Zelanda y el Reino Unido (Cockcroft, 1982; Goyen, 1977; McLennan, 1996; Wickert, 1989). Aritmetica para adultos fue inicialmente adoptada como parte de la alfabetizacion de adultos (Goyen, 1977), sin una escala visible para medirla. Goyen (1977) midio la alfabetizacion de adultos haciendo el uso de una escala unidimensional y "unos cinco anos despues del informe britanico (Cockcroft, 1982), aunque dijo poco acerca de la aritmetica para adultos, proporciono un marco historico para investigar e informar sobre la necesidad de matematicas en la vida adulta". El informe propuso una definicion de la aritmetica:

We would wish the word 'numerate' to imply the possession of two attributes. The first of these is an 'at-homeness' with numbers and an ability to make use of mathematical skills which enables an individual to cope with the practical mathematical demands of his everyday life. The second is to have some appreciation and understanding of information which is presented in mathematical terms, for instance in graphs, charts or tables or by reference to percentage increase or decrease (Cockcroft, 1982, p. 11).

Wickert (1989) introdujo tres dimensiones de alfabetizacion: la alfabetizacion de documentos, capacidad de comprension y alfabetizacion cuantitativa. La alfabetizacion se define como el uso de la informacion impresa para funcionar en la sociedad, para alcanzar los objetivos de uno, y para desarrollar el conocimiento y el potencial. La alfabetizacion de documentos se define como la capacidad de utilizar e identificar la informacion contenida en los documentos o materiales tales como tablas, calendarios, cuadros, graficos, mapas, formularios y notas. La capacidad de comprension consiste en leer e interpretar los textos en periodicos, articulos y libros, mientras que la alfabetizacion cuantitativa es vista como la capacidad de aplicar operaciones numericas o aritmeticas a la informacion contenida en los materiales impresos, tales como menus (ABS Aspects of Literacy website; McLennan, 1996; Wickert, 1989). El termino de la aritmetica para adultos ha sido utilizado muchas veces para referirse a la alfabetizacion cuantitativa, razonamiento cuantitativo y la alfabetizacion estadistica (Smit & Mji, 2012). Ademas, se han empleado una gran cantidad de terminos similares y vagamente relacionados, tales como la alfabetizacion matematica, alfabetizacion tecno-matematica, matematicas funcionales y competencias matematicas para desarrollar la atencion (Condelli, Safford-Ramus, Sherman, Coben, Gal & Hector-Mason, 2006), pero la aritmetica, en su sentido real, es algo mas que cualquiera de estos conceptos.

La alfabetizacion cuantitativa es un subconjunto de la aritmetica (Johnston, 2002). Aunque la aritmetica y la alfabetizacion estan relacionadas, no son lo mismo. Wickert (1989), en su informe, senalo que cuando las personas muestran pocas habilidades de alfabetizacion tienen aun peores los conocimientos basicos de aritmetica, y la necesidad de mejorar las habilidades numericas en el contexto de la alfabetizacion debe ser tomada en cuenta en todas las decisiones para aumentar los niveles de alfabetizacion de adultos. Steen (1991) considero que la aritmetica "... para las matematicas es como la alfabetizacion para la lengua" (p. 1). Un gran numero de caracterizaciones de aritmetica ha sido postulado en los ultimos tiempos por diferentes autores, cuya tematica fundamental gira alrededor de la aritmetica entendida como la comprension y aplicacion de los principios matematicos con el fin de resolver problemas de la vida cotidiana (Best, 2008; Evans, 2000; Lindenskov & Wedege, 2001; Paulos, 1989). En un sentido amplio, la aritmetica es comprendida como conocimiento matematico (De Lange, 2003) que implica la capacidad de un individuo de identificar y comprender el papel que desempenan las matematicas en el mundo, hacer juicios bien fundados y hacer el uso de las matematicas de manera que respondan a las necesidades de la vida actual y futura de ese individuo como ciudadano constructivo, comprometido y reflexivo (OCDE 2000).

La Aritmetica abarca la capacidad de comprender, utilizar, calcular, manipular, interpretar los resultados y comunicar la informacion matematica. En el contexto de la educacion de adultos, la aritmetica hace referencia al uso practico o funcional de las matematicas. Segun Ginsburg, Manly & Schmitt (2006), el termino "aritmetica", utilizado en el contexto de la educacion de adultos, incluye una amplia gama de competencias relacionadas con las matematicas, que son evidentes en la vida de los adultos y dignos de atencion en centros de educacion de adultos. Sostuvieron que si bien existen diversas definiciones del termino aritmetica (Coben, 2000; Cockcroft, 1982; Crowther, 1959; Gal, van Groenestijn, Manly, Schmitt & Tout, 2003; Johnston, 1994; Lindenskov & Wedege, 2001; Steen, 2001), todas reconocen que las matematicas y la aritmetica estan relacionadas, pero no son sinonimos. A diferencia de las matematicas puras que conducen hacia arriba en una busqueda ascendente de abstraccion y son libres de contexto (Ginsburg et al., 2006), la aritmetica posee un elemento personal distintivo en el que los temas de matematicas estan entretejidos en el contexto de trabajo y la participacion ciudadana mas activa (Orrill, 2001) en el proceso democratico (Johnston, 1994) y la utilidad en la competitiva economia mundial (Wedege, 2003). Condelli, et al. (2006), en un estudio, revisaron las definiciones de aritmetica utilizando el marco de organizacion de Maguire & O'Donoghue (2002) en el que los conceptos de aritmetica fueron considerados como un continuo de niveles crecientes de sofisticacion: formativo, matematico e integrador. Por lo tanto, la aritmetica es comprendida como las aptitudes aritmeticas elementales (fase de formacion), situadas en un contexto del reconocimiento explicito de la importancia de las matematicas en la vida cotidiana (fase matematica) e incorporando gradualmente las matematicas, la comunicacion, los aspectos culturales, sociales, emocionales y personales de cada individuo en su contexto (fase de integracion).

La Aritmetica para adultos es un ambito importante de investigacion a gran escala en muchos paises desarrollados (Benseman & Sutton, 2011; EU Skills Panorama, 2012; Johnston, 2002; Lowden, Powney, Gardner & Mark, 1995, Tett, Hall, Maclachlan, Thorpe, Edwards & Garside, 2006) incluyendo Sudafrica (Coben, 2000; Smit & Mji, 2012), pero en Nigeria este tema aun no ha llegado a ser la piedra angular de la investigacion educativa, ya que se han realizado pocos o ningun estudio relacionado con la aritmetica para adultos. Esta es la incongruencia de las expectativas del gobierno nigeriano en todos los niveles de que la incompetencia en el calculo disminuya en la sociedad hasta el punto de que un nigeriano promedio sea capaz, al menos, de realizar calculos matematicos basicos necesarios en un puesto de trabajo del siglo XXI.

En general, se ha descubierto que la incapacidad aritmetica tiene efectos tanto a largo como a corto plazo en la vida de la gente (Steen, 1991; Paulos, 1989), incluyendo a los mineros (Smit & Mji, 2012), tales como la imposibilidad de controlar las finanzas personales, la incapacidad de evaluar adecuadamente los riesgos, actividades diarias y las oportunidades limitadas de empleo. Sin las habilidades aritmeticas basicas, la gran cantidad de adultos nigerianos incompetentes en el calculo no puede tener esperanzas de conseguir un empleo mejor remunerado. Teniendo en cuenta la importancia creciente de los aspectos cuantitativos y tecnicos de la vida humana en la tarea de digitalizar el mundo, los adultos necesitan un nivel mas alto de aritmetica para desempenar eficazmente sus roles de trabajadores, padres y ciudadanos. Cada vez mas a menudo, la aritmetica se convierte en un atributo clave en la obtencion y el mantenimiento de un empleo (Bynner, 2004). Dado que la cantidad de puestos de trabajo y ocupaciones que requieren habilidades de bajo nivel queda reducida en el mundo, las personas con pocas habilidades aritmeticas tendran cada vez menos posibilidades de competir en el mercado de trabajo digitalizado.

El Grupo de Expertos de Alto Nivel sobre Alfabetizacion de la UE (2012) clasifica la aritmetica en tres categorias distintas: de linea base, funcional y multiple. La Aritmetica Multiple--es la capacidad y la voluntad de utilizar modos de pensamiento matematicos (pensamiento logico y espacial) y representacion (formulas, modelos, graficos, tablas) que le permiten a una persona funcionar plenamente en una sociedad moderna, La Aritmetica Funcional--es la capacidad de aplicar los principios y los procesos matematicos basicos en situaciones cotidianas en casa, escuela y trabajo (segun sea necesario para los servicios bancarios, pagos, horarios de lectura, etc.), y La Aritmetica de Linea Base consiste en demostrar un buen conocimiento de los numeros, las medidas y las estructuras, las operaciones basicas, las presentaciones matematicas basicas y la capacidad de utilizar herramientas de ayuda adecuadas que permitan el futuro desarrollo.

A traves de una sintesis (basada en la investigacion) de los componentes necesarios para que los adultos posean conocimientos basicos de aritmetica, actuen de acuerdo con las normas de aritmetica, y adquieran conocimientos basicos de aritmetica, Ginsburg et al. (2006) identificaron tres elementos fundamentales, cada uno compuesto por diferentes subcomponentes que son inherentes a la practica competente de aritmetica. Estos componentes forman el constructo de la aritmetica para adultos y cada componente puede ser descrito por separado y es de naturaleza diferente; aunque, en realidad, interactuan, se entrelazan y tienen poco sentido por separado (Ginsburg et al., 2006).

1. Contexto. Es el uso y el proposito por los cuales un adulto asume una tarea que exige las capacidades matematicas (Akinsola & Awofala, 2008). El contexto tiene cuatro subcomponentes: familia o personal, como el padre,

administrador del hogar, consumidor, el que toma las decisiones financieras y sanitarias y aficionado. El lugar de trabajo, como un trabajador capaz de realizar tareas en el trabajo y estar preparado para adaptarse a las nuevas demandas de empleo, el aprendizaje complementario, como una persona interesada en los aspectos mas formales de las matematicas necesarias para futura educacion o formacion, y la comunidad, como un ciudadano que interpreta situaciones sociales caracterizadas por aspectos matematicos como el medio ambiente, la delincuencia y la politica.

2. Contenido. El conocimiento matematico necesario para las tareas que uno enfrenta. El contenido esta dividido en cuatro partes: el sentido de los numeros y operaciones; es decir, un sentido de como funcionan los numeros y las operaciones y como se relacionan con las situaciones del mundo que representan; patrones, funciones y Algebra, que es la capacidad de analizar las relaciones y el cambio entre las cantidades, generalizarlos y representarlos en diferentes formas y desarrollar metodos de solucion basados en las propiedades de los numeros, operaciones y ecuaciones, la medicion y forma, se refiere al conocimiento de los atributos de las formas, la manera de estimar y/o determinar la medida de estos atributos directa o indirectamente, y como razonar de manera espacial, y los datos, estadistica y probabilidad, que es la capacidad para describir las poblaciones, hacer frente a la incertidumbre, evaluar los compromisos y tomar decisiones cuidadosamente.

3. Procesos cognitivos y afectivos. Los procesos que permiten a una persona resolver problemas, y por tanto, vincular el contenido con el contexto. El componente cognitivo y afectivo se divide en cinco subcomponentes: comprension conceptual, que implica una comprension integral y funcional de las ideas matematicas (Kilpatrick, Swafford & Findell, 2001). Los dos aspectos de la comprension conceptual--integrado y funcional--enmarcan la capacidad de pensar y actuar eficazmente y de acuerdo con las normas aritmeticas (Ginsburg et al., 2006), el razonamiento adaptable, que es la capacidad de pensar logicamente sobre las relaciones entre conceptos y situaciones (Kilpatrick et al., 2001), las competencias estrategicas, es la capacidad para formular problemas matematicos, representarlos y resolverlos (Kilpatrick et al., 2001), y la resolucion de problemas, que es la parte central de la aritmetica (Ginsburg et al., 2006). La fluidez de procedimiento es la capacidad de realizar calculos de manera eficaz y precisa mediante el uso de procedimientos basados en lapiz y papel, matematicas mentales, tecnicas de estimacion y las ayudas tecnologicas (Kilpatrick et al., 2001), y la disposicion productiva, que son las creencias, actitudes y emociones que contribuyen a la capacidad y voluntad de una persona para participar, usar y permanecer en el pensamiento y en el aprendizaje matematico o en las actividades con aspectos aritmeticos (Ginsburg et al., 2006). La Disposicion Productiva ha sido identificada como un componente necesario de la competencia matematica que debe ser desarrollado en el transcurso de educacion matematica de K-12 (educacion primaria y secundaria) (Kilpatrick et al., 2001), tanto en caso de los alumnos como de las alumnas.

Al igual que en las matematicas avanzadas (Akinsola & Awofala, 2009; Awofala, 2011b; Rogers & Kaiser, 1995; Sommers, 2008; Stoeger, 2004; Willis, 1989), las diferencias de genero impregnan las aptitudes aritmeticas (Beilock, Gunderson, Ramirez & Levine, 2010; Coben et al., 2003; Murray, Clermont & Binkley, 2005; Parsons & Bynner, 2005; Satherley & Lawes, 2009a) y estas diferencias han sido atribuidas a las actitudes, los sentimientos, las amenazas del estereotipo y las consecuencias de los problemas afectivos tanto como a las diferencias cognitivas reales (Beaton, Tougas, Rinfret, Huard & Delisle, 2007; Coben et al., 2003; Hyde & Mertz, 2009; Mendick, 2005; Rivardo, Rhodes, Camaione & Legg, 2011; Tomasetto, Alparone & Cadinu, 2011).

Es evidente que los efectos de las pocas habilidades matematicas parecen ser mas graves en caso de las mujeres que de los hombres (Parsons & Bynner, 2005; Reder & Bynner, 2009). La literatura sugiere que las diferencias de genero en el desempeno en matematicas pueden resultar de los metodos de ensenanza que no se relacionan con los estilos de aprendizaje preferidos (Awofala, 2011a; Awofala, Balogun & Olagunju, 2011; Zohar, 2006). Mas aun, la literatura sugiere que las diferencias de genero en los enfoques de la ensenanza de las matematicas tienen bases tanto biologicas (Awofala, 2008), por ejemplo las diferencias en el procesamiento espacial (Maloney, Waechter, Risko & Fugelsang, 2012) como culturales (Awofala, 2008), por ejemplo los aspectos de procesamiento espacial de las pruebas de inteligencia que se definen culturalmente (Clifford, 2008). En este nuevo milenio, y en todas las culturas, la explicacion cultural de las diferencias de genero en el desempeno en matematicas parece estar ganando mas protagonismo en la literatura de genero con la decreciente explicacion biologica. Sin embargo, la investigacion actual esta por proporcionar las respuestas incuestionables a las diferencias de genero en el desempeno matematico reforzadas por los factores biologicos, ya que los patrones de las diferencias de genero en la capacidad matematica no similares se obtienen de manera inconsistente a partir de los estudios transculturales (Awofala, 2011b; Kane & Mertz, 2012).

El meta-analisis de estudios sobre las diferencias de genero en el desempeno en matematicas en los Estados Unidos y en el Reino Unido (Luckenbill, 1995) revelo que, si bien una minima diferencia de genero en habilidades matematicas tempranas era perceptible en los niveles de Educacion Primaria, la diferencia de genero a favor de los alumnos varones aparecio en la escuela secundaria (Hyde & Mertz, 2009), con la conclusion de que los patrones diferenciales, por supuesto, tenian en cuenta esta diferencia, con la socializacion y la discriminacion como factores menores. Aunque los estudios de meta-analisis sobre la diferencia de genero en el desempeno en matematicas aun no se han llevado a cabo en caso de Nigeria, los resultados internacionales en materia de diferencia de genero en el desempeno en matematicas, aparte de los de EE.UU. y el Reino Unido, mostraron que las mujeres demostraban el mismo o mejor rendimiento en matematicas en comparacion con los hombres. Esta observacion se ve corroborada por la disminucion de las brechas de genero en el desempeno en matematicas en la Union Europea (UE), con tan solo el 2% de diferencia en promedio entre los chicos (21%) y chicas (23%) con bajo rendimiento (EU Skills Panorama, 2012). Este hallazgo concuerda con el argumento de Hyde & Mertz (2009) en que las diferencias de genero en el desempeno en matematicas se deben a los cambiantes factores socio-culturales en vez de las diferencias biologicas innatas.

Muchos estudios han apoyado el origen socio-cultural de las diferencias de genero en el desempeno en matematicas (Ceci & Williams, 2010, 2011; Lindberg, Hyde, Petersen & Linn, 2010; York & Clark, 2007), con una amplia investigacion que indica que la auto-confianza (Carr, Steiner, Kyser & Biddlecomb, 2008), el sexismo (Sommers, 2008) y la amenaza del estereotipo (Steffens & Jelenec, 2011; Tomasetto et al., 2011) causaron o contribuyeron a estas disparidades. La amenaza del estereotipo ocurre cuando los "procesos motivacionales, afectivos, psicologicos y cognitivos interactuan para afectar el rendimiento en un contexto estereotipo relevante" (Schmader, Johns & Forbes, 2008, p. 336) y se ha demostrado que afectan a los resultados de pruebas aritmeticas por interferir con la concentracion y el procesamiento de la coordinacion de informacion.

Bynner y Parsons (2006) descubrieron que entre los individuos nacidos en Inglaterra y Gales en 1970, los hombres y las mujeres tenian niveles casi identicos de habilidades de alfabetizacion, pero la variacion de genero en aritmetica fue significativamente mayor, ya que los niveles de competencias eran mas bajos que la alfabetizacion en caso de ambos sexos, pero especialmente en caso de las mujeres. Un informe de 2005 del Reino Unido sobre dos estudios longitudinales acerca de competencias en aritmetica y alfabetizacion, utilizando cohortes de 1958 y 1970, revelo que los hombres tenian mas habilidades aritmeticas que las mujeres (Parsons & Bynner, 2005). En caso de las mujeres, la investigacion de Reino Unido informa que "si bien el impacto de pocas habilidades en el campo de la aritmeticas y la alfabetizacion es sustancial, las deficientes competencias aritmeticas tienen un efecto mucho mas negativo (que en el caso de los hombres), incluso cuando se combinan con la alfabetizacion competente" (Parsons & Bynner, 2005, p. 7). Entre 1996 y 2006, habian sido descubiertos los resultados contradictorios en cuanto a las diferencias de genero en los resultados cuantitativos de alfabetizacion en caso de la poblacion de Nueva Zelanda. La Encuesta Internacional sobre la Alfabetizacion de Adultos (IALS), realizada en 1996 en Nueva Zelanda, mostro una diferencia de genero en las puntuaciones cuantitativas de alfabetizacion (que cubrian un subconjunto de las habilidades aritmeticas en vez de la gama de habilidades aritmeticas incluida en los ALLS (El Estudio sobre Alfabetizacion de Adultos y Preparacion para la Vida Activa), pero la diferencia (alrededor del 5%) no fue estadisticamente significativa (Culligan, Sligo, Arnold & Noble, 2004), mientras que el estudio de ALL de Nueva Zelanda, mas reciente (2006), mostro una pequena, pero estadisticamente significativa, mayor puntuacion en aritmetica en el caso de los hombres que de las mujeres (Satherley & Lawes, 2008a, 2008b). La tolerancia cero respecto a la diferencia de genero en el desempeno en matematicas (Fatade, Nneji, Awofala & Awofala, 2012) fue comparada con los datos IALS de Escocia mas recientes, que no encontraron diferencias significativas de genero en las puntuaciones cuantitativas de alfabetizacion (St Clair et al., 2010).

En resumen, las matematicas crearon estereotipos sociales y las desigualdades de genero en el sector educativo y, desde su introduccion en las escuelas, las matematicas habian sido vistas como un 'territorio masculino' o algo para los chicos. Estas antiguas y estereotipadas diferencias de genero en los resultados cognitivos y afectivos, que subsistian anteriormente en matematicas, fueron extrapolados al area de aritmetica. A pesar de que las diferencias canonicas de genero en matematicas van disminuyendo en todo el mundo y, tal vez, no tienen ninguna importancia practica para el futuro, los resultados contradictorios con respecto a las diferencias de genero en aritmetica han demostrado la necesidad de una mayor investigacion. A diferencia de los paises desarrollados, donde las investigaciones sobre la aritmetica para adultos habian llegado a un nivel apreciable, aun existen escasos estudios en Nigeria en ambito de la aritmetica para adultos y de los temas relacionados con el genero y la aritmetica. Ademas, los resultados no tan sencillos acerca de las diferencias de genero en la aritmetica, han proporcionado el impulso necesario para su estudio.

2 OBJETIVO DEL ESTUDIO

Por tanto, el presente estudio investigo la aritmetica en el caso de los alumnos adultos nigerianos, las diferencias en aritmetica entre hombres y mujeres, y la relacion entre la aritmetica y el desempeno en aritmetica.

3 PREGUNTAS DE INVESTIGACION

Concretamente, en este estudio, se abordaron los siguientes aspectos de investigacion:

1. ?Cual es la estructura factorial de la escala de autoevaluacion en aritmetica?

2. ?Cual es el nivel de percepcion de las habilidades aritmeticas entre los estudiantes adultos nigerianos?

3. ?Es el genero uno de los factores en el desempeno en aritmetica y la percepcion de aritmetica entre los estudiantes adultos nigerianos?

4. ?Cuales son las contribuciones relativas y compuestas de las dimensiones de la aritmetica (aritmetica en la vida cotidiana, la aritmetica en el lugar de trabajo y la aritmetica en las tareas matematicas) y del genero a la explicacion de la variacion en el desempeno de los estudiantes adultos en la aritmetica?

4 METODOLOGIA

El estudio se realizo utilizando el metodo cuantitativo y con un diseno de la encuesta descriptiva. Los participantes en este estudio fueron 32 alumnos adultos (16 hombres y 16 mujeres) de un centro acreditado de alfabetizacion de adultos en el estado de Lagos, Nigeria. Su edad oscilo entre 18 y 57 anos, con una edad media de 37,8 anos. Los participantes tambien pueden ser categorizados como 3 (9,4%) en el grupo de edad inferior a 20 anos y 29 (90,6%) en el grupo de edad de 20 y mas anos. Para la recopilacion de datos, se utilizo un instrumento denominado Escala de Autoevaluacion Aritmetica (NSAC) adoptado de los Recursos Humanos y Fomento de las Competencias de Canada, para recoger datos primarios relacionados con la aritmetica para estudiantes adultos, mientras que los datos secundarios relacionados con su desempeno en aritmetica fueron obtenidos de sus registros en el Centro de Alfabetizacion de Adultos. La NSAC constaba de 24 articulos anclados en una escala de 3 puntos, desde: Si-3, Algo-2, y No-1. El coeficiente de fiabilidad de consistencia interna de la NSAC se calculo mediante el alfa de Cronbach (a) con un valor de 0,87. El segundo autor, con el proposito de este estudio, administro personalmente la NSAC a toda la muestra y en un horario regular de clases, y los registros recuperados se referian al desempeno de los estudiantes adultos del centro, en aritmetica. Los datos recogidos fueron resumidos y analizados mediante porcentajes, medias, desviaciones estandar, muestras independientes de test-t, analisis factorial de componentes principales, Correlacion Producto-Momento de Pearson, y analisis de regresion multiple.

5 RESULTADOS

5.1 Primera pregunta de investigacion: ?Cual es la estructura factorial de la escala de autoevaluacion en aritmetica?

Los resultados de primera pregunta de investigacion muestran las respuestas de los participantes a las 24 unidades de la escala de autoevaluacion en aritmetica que fueron sometidas a analisis de principales factores de componentes (PCA) para identificar las dimensiones subyacentes.

Se realizo la seleccion de datos, que presento valores faltantes en tres de 35 participantes; estos fueron descartados. Posteriormente, nuevas filtraciones no mostraron menor preocupacion por la normalidad, la linealidad, la multicolinealidad y la singularidad. Por ejemplo, las puntuaciones de las subescalas se distribuian normalmente con los valores de asimetria y curtosis dentro de los rangos aceptables (por ejemplo, la asimetria varia de -2,24 a 0,43, curtosis de -0,94 a 6,65) como Kline (1998) sugirio el uso de los valores de detencion absolutos de 3,0 para la asimetria y 8,0 para la curtosis. La matriz de correlacion de los 24 articulos revelo que las correlaciones consideradas en conjunto fueron estadisticamente significativas, como se indica en el test de esfericidad de Bartlett, %2 = 2204.08; qf=276; p < .001, lo que pone a prueba la hipotesis nula de que la matriz de correlaciones es una matriz de identidad. La medida de Kaiser-Meyer-Olkin de adecuacion muestral (MSA) se encontro dentro del margen aceptable (valores de .60 o mas) con un valor de .871. Cada una de las variables tambien supero el valor umbral (.60) de MSA que vario de .646 a .882. Por ultimo, la mayoria de las correlaciones parciales fueron pequenas, como indica la matriz de correlaciones anti-imagen. Todas estas medidas llevaron a la conclusion de que el conjunto de los 24 items de la escala de autoevaluacion en aritmetica fue apropiado para PCA y como no se formulo ninguna hipotesis acerca de un numero determinado de componentes (aunque teniendo en cuenta el criterio a priori de los cuatro factores) se establecio el criterio para valores propios superiores a uno (Kaiser, 1960; Tabachnick & Fidell, 2001).

El PCA inicial sin rotacion dio como resultado un modelo factorial de siete dimensiones, como se indica por los valores propios superiores a la unidad, pero el grafico de sedimentacion mostro un modelo factorial de tres dimensiones. Sin embargo, basado en su patron de cargas factoriales, este modelo factorial sin rotacion era teoricamente menos significativo y, como tal, era dificil de interpretar. Por lo tanto, el analisis procedio a girar la matriz de factores ortogonalmente mediante rotacion varimax para lograr una solucion simple y teoricamente mas significativa. La rotacion dio lugar a un modelo factorial de tres dimensiones como sugiere el grafico de sedimentacion y los valores propios superiores a la unidad.

En este estudio, todas las comunalidades para el analisis de factores cumplieron el requisito minimo de ser superior a 0.50, de hecho, estos oscilaron de 0.697 a 0.982. La Figura 1 presenta el grafico de sedimentacion, que representa graficamente el valor propio con el numero de componentes que es sugestivo de un modelo de tres componentes.

La Tabla 1 muestra el factor de cargas para el modelo ortogonal de tres factores de la escala de autoevaluacion en aritmetica. Todos los items cargan 0.587 y mas de su factor principal y ninguna de las cargas secundarias supera a .35. Los tres factores juntos representaron el 60,65% de la varianza total. El primer factor representa el 30,37% de la varianza (valor propio= 7,29) y consta de cinco items cotidianos de aritmetica. El segundo factor representa el 16,93% de la varianza (valor propio= 4,06) y consta de diez items de aritmetica aplicados a las tareas laborales. El tercer factor representa el 13,34% de la varianza (valor propio= 3,20) y consta de nueve items de aritmetica usados en las tareas matematicas. La fiabilidad de consistencia interna de las subescalas es: la aritmetica en la vida cotidiana ([alpha] = .72), la aritmetica en las tareas laborales ([alpha] = .78) y la aritmetica en las tareas matematicas ([alpha] = .83), y la fiabilidad de consistencia interna para toda la escala ([alpha] = .87) fue considerada como muy alta y conceptualmente significativa (Curtis & Singh, 1997). Por lo tanto, las tres medidas representan construcciones de autoevaluacion en aritmetica empiricamente separables e internamente consistentes.

5.2 Segunda pregunta de investigacion: ?Cual es el nivel de percepcion de las habilidades aritmeticas entre los estudiantes adultos nigerianos?

La Tabla 1 muestra la percepcion global de las habilidades aritmeticas de los estudiantes adultos nigerianos. En ella vemos los numeros y porcentajes reales de las respuestas a cada declaracion. Los porcentajes se indican entre parentesis. La Tabla 1 demuestra que en esta investigacion, los estudiantes adultos tenian una dotacion media en aritmetica (Promedio= 2,470, SD= 0,780). En relacion a la dimension de la aritmetica en la vida cotidiana, mas del 90% de los estudiantes adultos dijo que si a las habilidades aritmeticas tales como: Puedo realizar calculos sencillos como sumas y restas (item 1), recibir los pagos en efectivo y hacer el cambio (item 2), calcular el coste de los articulos en la factura (item 3), hacer comparaciones (por ejemplo, mas alto o mas bajo, mas pesado o mas ligero, mayor o menor que) (item 4), mientras que mas del 75% de los estudiantes adultos dijo que si a la habilidad aritmetica como: puedo registrar el tiempo mediante relojes o cronometros (item 5), tanto digitales como estandar. Como se indica en la Tabla 1, los estudiantes adultos presentan un alto nivel en aritmetica (Promedio= 2,800, SD= 0,577) con respecto a la dimension de la aritmetica en la vida cotidiana. Esto se podia haber esperado teniendo en cuenta su exposicion a las actividades de la vida cotidiana que implican la aplicacion de las operaciones aritmeticas basicas.

En el caso de la dimension de la aritmetica en las tareas laborales (Tabla 1), mas del 80% de los estudiantes adultos respondio que si a declaraciones tales como: Puedo realizar medidas sencillas (por ejemplo, longitud, peso, temperatura) (item 6) y estimar medidas (por ejemplo, tiene aproximadamente tres pies de ancho) (item 8). Mas del 50% de los encuestados dijo que si a las declaraciones de las habilidades aritmeticas como: Puedo estimar cantidades (por ejemplo, Necesito unas 20 copias) (item 7), crear y equilibrar los presupuestos (item 9), crear y controlar los horarios (por ejemplo, los horarios de personal o de proyectos) (item 10), y hacer calculos precisos con informacion limitada (item 15), mientras que mas del 40 por ciento de los estudiantes adultos respondio que si a las siguientes declaraciones de las habilidades aritmeticas: Puedo estimar el tiempo requerido para realizar tareas especificas (item 11), realizar medidas de manera precisa utilizando equipo especializado (item 12), comparar productos similares de coste distinto para determinar el de mejor valor (item 13), y gestionar presupuestos complejos (por ejemplo, establecer los estados financieros, prevision de materiales) (item 14). La Tabla 1, mostro que los estudiantes adultos tenian una dotacion media en aritmetica (Promedio= 2,282, SD= 0,885) con respecto a la dimension de la aritmetica en las tareas laborales. A diferencia de las tareas de la vida cotidiana, las tareas laborales son mas complejas y requieren habilidades superiores con algun tipo de formacion especializada.

La evaluacion de la aritmetica en la dimension de las tareas matematicas como figura en la Tabla 1, muestra que mas del 80% de los estudiantes adultos respondio que si a las declaraciones aritmeticas como: puedo calcular el area de las formas mas extendidas (por ejemplo, cuadrado, triangulo, circulo) (item 18), realizar conversiones de medidas (por ejemplo, pulgadas a centimetros, mililitros a litros) (item 19), calcular promedios simples (item 20), realizar calculos que requieren varios pasos u operaciones (item 21), y calcular areas y volumenes de formas irregulares (item 22), mientras que mas del 50% de los estudiantes adultos respondio que si a declaraciones tales como: puedo realizar calculos que requieren multiplicacion y/o division (item 16), medir longitudes irregulares y curvadas (item 23) y analizar y comparar datos estadisticos (item 24). El 50% de los alumnos adultos dijo que si a esa declaracion: puedo calcular los porcentajes (item 17). La Tabla 1 demuestra que los estudiantes adultos tenian una dotacion media en aritmetica (Promedio= 2,328, SD= 0,877) con respecto a la dimension de la aritmetica en las tareas matematicas. A diferencia de las tareas de la vida cotidiana y de las tareas laborales, las tareas matematicas son mucho mas complejas, abstractas y mas exigentes que las tareas laborales y requieren habilidades de orden superior que implican resolucion de problemas.

5.3 Tercera pregunta de investigacion: ?Es el genero uno de los factores en el desempeno en aritmetica y la percepcion de aritmetica entre los estudiantes adultos nigerianos?

La Tabla 2 muestra la estadistica descriptiva de promedio y desviacion estandar, y los valores de test-t en la percepcion de la puntuacion numerica y la puntuacion aritmetica de los alumnos adultos de ambos sexos. Con respecto a la puntuacion de habilidad aritmetica, las mujeres adultas denotaron una puntuacion media ligeramente mayor (M= 56.56, SD= 7.53) que los hombres (M=56.38, SD=8.10). Sin embargo, esta ligera diferencia en la puntuacion media no fue estadisticamente significativa ([t.sub.30]=-.068, p=.946). La Tabla 2 muestra que los estudiantes adultos varones registran ligeramente mayor puntuacion media (M=14.00, SD=1.79) en la percepcion de las habilidades matematicas en la vida cotidiana que sus contrapartes femeninas (M=13.94, SD=2.11) y esta diferencia tampoco fue estadisticamente significativa ([t.sub.30]=.090, p=.929)0. En la Tabla 2, las estudiantes registraron, ligeramente, una mayor puntuacion media (M=21.81, SD=5.65) en la aritmetica de las tareas laborales que los hombres (M=20.00, SD=5.65). La diferencia no fue estadisticamente significativa ([t.sub.30]=-.908, p=.371). Con respecto a la aritmetica en las tareas matematicas, los estudiantes varones registraron puntuacion media ligeramente mayor (M=22.38, SD=5.12) que sus contrapartes femeninas (M=20.81, SD=4.26). Sin embargo, esta diferencia en la puntuacion media no fue estadisticamente significativa ([t.sub.30]=.938, p=.356). La Tabla 2 revela que las estudiantes registraron puntuacion media ligeramente mayor (M=52.13, SD=10.98) en Aritmetica que los alumnos (M=51.56, SD=9,20). Esta diferencia en la puntuacion media no fue estadisticamente significativa ([t.sub.30]=-. 157, p=.876). Por lo tanto, llegamos a la conclusion de que el genero no fue un factor importante en el desempeno de estudiantes adultos en aritmetica, la percepcion de las habilidades aritmeticas e incluso en los niveles de subescala de las habilidades aritmeticas.

5.4 Cuarta pregunta de investigacion: ?Cuales son las contribuciones relativas y compuestas de las dimensiones de la aritmetica (aritmetica en la vida cotidiana, la aritmetica en el lugar de trabajo, y la aritmetica en las tareas matematicas) y del genero a la explicacion de la variacion en el desempeno de los estudiantes adultos en la aritmetica?

Los resultados de la Tabla 3 muestran la relacion entre los conocimientos basicos de aritmetica, la subescala de autoevaluacion en aritmetica, el genero y el desempeno en aritmetica. La Tabla 3 muestra que existe una correlacion positiva significativa entre el desempeno de los estudiantes adultos en la aritmetica y la aritmetica en las tareas laborales (Pearson r=.657, p < .001) y la aritmetica en las tareas matematicas (Pearson r=.369, p < .05), mientras que el genero no mostro una correlacion significativa ni con el desempeno en la aritmetica ni en las dimensiones de habilidades aritmeticas.

Ademas, existe una correlacion positiva significativa entre la percepcion de estudiantes adultos de habilidades aritmeticas y su desempeno en aritmetica (Pearson r=.652, p < .001). Los resultados de la Tabla 4 muestran que las variables independientes (sexo, aritmetica en la vida cotidiana (NEL), Aritmetica en las tareas laborales (TNM), y Aritmetica en las tareas matematicas (NMT) aportaron conjuntamente un coeficiente de regresion multiple de .601 y un numero de correlacion multiple de .542 a la prediccion del desempeno de los alumnos adultos en la aritmetica.

Como consecuencia, el 60,1% de la variacion total de la variable dependiente (desempeno en aritmetica) se explica por la combinacion de las cuatro variables independientes. Los resultados revelaron ademas que a traves del analisis de la variacion de los datos de regresion multiple se obtuvo un valor F significativo en el nivel de 0.001 (F[(.sub.4, 27)] = 10.157; p < .001).

Los resultados de las contribuciones relativas de las variables independientes en la prediccion del desempeno de los estudiantes adultos en aritmetica fueron los siguientes: la aritmetica en las tareas laborales era un factor potente positivo relevante para la prediccion del desempeno de los estudiantes adultos en aritmetica ([beta] = .667, t = 5.38, p < .001), mientras que la dimension de aritmetica en la autoevaluacion de las habilidades en las tareas matematicas hizo la siguiente contribucion positiva significativa a la prediccion de la variable dependiente ([beta] =.305, t = 2.44, p=.022). Aritmetica en la vida cotidiana ([beta] =-.231, t = -1.88, p=.072) y el sexo ([beta] =-.033, t = .261, p=.796), no contribuyeron de manera positiva y significativa a la prediccion del desempeno de los alumnos adultos en la aritmetica.

Posteriormente, se utilizo un analisis de regresion escalonada para determinar la contribucion de cada una de estas variables en la prediccion de desempeno en la aritmetica. En la Tabla 5, se describe un modelo que explica la reduccion de la capacidad predictiva de las dos variables (aritmetica en las tareas laborales y aritmetica en las tareas matematicas) sobre el desempeno en aritmetica. El modelo 1, que incluye solamente la puntuacion de la aritmetica en las tareas laborales, contabiliza el 43,2% de la variacion en el desempeno de los estudiantes adultos en la aritmetica. La inclusion de la aritmetica en las tareas matematicas en el modelo 2 dio como resultado el 54,8% adicional de dicha variacion. Esto significa que la aritmetica en las tareas matematicas represento solamente el 11,6% de la variacion en el desempeno de los estudiantes adultos en la aritmetica.

6 DISCUSION

Los resultados del presente estudio han revelado cinco conclusiones principales. Estas conclusiones se refieren al establecimiento de la estructura factorial de la escala de autoevaluacion de estudiantes adultos en aritmetica; determinar el nivel de percepcion de las habilidades aritmeticas entre los estudiantes adultos; determinar si existian las diferencias entre los estudiantes adultos de ambos sexos en la percepcion de las habilidades aritmeticas y el desempeno en aritmetica; y determinar las contribuciones compuestas y relativas de las dimensiones de las habilidades aritmeticas y del genero para la prediccion del desempeno de estudiantes adultos en la aritmetica.

Los resultados del presente estudio mostraron que la habilidad aritmetica, medida por la escala de autoevaluacion aritmetica, es un constructo multidimensional. El analisis factorial exploratorio, haciendo el uso del analisis de componentes principales, mostro una estructura de tres factores subyacentes de la escala. Las estructuras de tres factores interpretables quedan posteriormente etiquetados como: Aritmetica en la vida cotidiana (con 5 items), Aritmetica en las tareas laborales (con 10 items), y Aritmetica en las tareas matematicas (con 9 items) y cada subescala contiene suficiente fiabilidad de consistencia interna. Los alumnos adultos, que participaron en el presente estudio tenian una dotacion media en aritmetica (media=2.470, SD=0.780). Este hallazgo fue contrastado con los resultados anteriores (Smit & Mji, 2012) que mostraron nivel bajo de conocimientos aritmeticos entre los mineros de cromo en Sudafrica. Ademas, los resultados de los Estados Unidos revelaron que el nivel de conocimientos aritmeticos era muy bajo entre los grupos vulnerables de la sociedad como los ancianos, las mujeres y las personas de bajo nivel educativo (Lusardi, 2012). Esto es contradictorio con los resultados de Suecia y Polonia, que mostraron que el nivel de conocimientos aritmeticos entre la poblacion era muy alto (Johnston, 2002).

Los resultados relacionados con las diferencias de genero en la percepcion de las habilidades aritmeticas y el desempeno, en aritmetica, mostraron que en el presente estudio los alumnos adultos de ambos sexos registraron puntuaciones medias similares en el desempeno en aritmetica y en cada una de las dimensiones de las habilidades aritmeticas. Por lo tanto, las diferencias de genero en las habilidades aritmeticas y en el desempeno en aritmetica, como se muestra en este estudio, no fueron significativas. Estos resultados coinciden con algunos de los hallazgos de estudios anteriores (Arigbabu & Mji, 2004; Fatade, Nneji, Awofala & Awofala, 2012) en las matematicas avanzadas entre los futuros profesores de matematicas, pero no coinciden con otros (Beilock et al., 2010; Coben et al., 2003; Murray et al., 2005; Parsons & Bynner, 2005; Satherley & Lawes, 2008a, 2008b; Satherley & Lawes, 2009a, 2009b, 2009c) que revelaron la existencia de diferencias de genero en habilidades aritmeticas. La implicacion de los actuales resultados del estudio en cuanto al genero es que las diferencias de genero en las habilidades aritmeticas y el desempeno en aritmetica ya no tienen importancia.

Los resultados recogidos en la Tabla 4 muestran que el 60,1% de la variacion en el desempeno de estudiantes adultos en la aritmetica se explica por las cuatro variables predictivas (el sexo, la aritmetica en la vida cotidiana, la aritmetica en las tareas laborales, y la aritmetica en las tareas matematicas) en su conjunto. Las relaciones entre el desempeno en aritmetica y las variables de prediccion, en su conjunto, eran altas, como lo muestra el coeficiente de correlacion multiple (R = .775). Por lo tanto, las variables de prediccion investigadas recogidas en un conjunto predicen el desempeno aritmetico entre los estudiantes adultos involucrados en el estudio. Esto ([F.sub.(4, 27)] = 10.157; p < .001) es una evidencia confiable de que la combinacion de las dimensiones de las habilidades aritmeticas en la prediccion del desempeno de los estudiantes adultos en la aritmetica, a partir de todas las indicaciones, no se produjo por casualidad, con el 39,9% de la variacion en el desempeno aritmetico no explicado por los datos actuales. Por lo tanto, pueden haber otras variables independientes que requieran mas investigaciones acerca de su contribucion a la prediccion del desempeno de los alumnos adultos en la aritmetica, y el grado de prediccion compuesto por las cuatro variables independientes de este estudio podria ser lo suficientemente sustancial para afirmar que el desempeno de los alumnos adultos en aritmetica es predecible por una combinacion de las dimensiones de las habilidades aritmeticas y el sexo. Por lo tanto, la fuerza de la capacidad predictiva de las variables independientes combinadas (la aritmetica en la vida cotidiana, la aritmetica en las tareas laborales, la aritmetica en las tareas matematicas, y el sexo) sobre la variable de resultado fue significativa para mostrar la relacion lineal entre las cuatro variables de prediccion y la variacion total en el desempeno de los estudiantes adultos en aritmetica. Segun los coeficientes estandarizados, el modelo de regresion es el siguiente: El Desempeno en [Aritmetica.sub.predicted] = 30.875-0.033 sexo-0.231 aritmetica en la vida cotidiana + 0.667 aritmetica en las tareas laborales + 0.305 aritmetica en las tareas matematicas. (***aqui hay que anadir o comas o puntos y comas, de acuerdo con el original)

Sobre la contribucion relativa de cada una de las variables independientes a la explicacion de la variacion en el desempeno de los estudiantes adultos en aritmetica, el presente estudio revelo que solamente dos (aritmetica en las tareas laborales y aritmetica en las tareas matematicas) de las cuatro variables independientes mostraron una contribucion estadisticamente significativa a la variacion en el desempeno de los estudiantes adultos en aritmetica. Aritmetica en las tareas laborales fue el mejor predictor del desempeno en aritmetica y represento el 43,2% de la variacion en el desempeno de los estudiantes adultos en aritmetica. Esto fue seguido por la aritmetica en las tareas matematicas representada solamente por el 11,6% de la variacion en el desempeno de los estudiantes adultos en aritmetica. El sexo y la aritmetica en la vida cotidiana no contribuyeron significativamente a la prediccion del desempeno de los estudiantes adultos en aritmetica.

7 LIMITACIONES DEL ESTUDIO

Cabe senalar que las conclusiones que han surgido en este estudio no pueden ser aplicados a todos los alumnos adultos nigerianos, ya que la muestra no es necesariamente representativa de todos los alumnos adultos. A pesar del pequeno tamano de la muestra (n=32), se observa que la percepcion de las puntuaciones aritmeticas obtenidas en este grupo de estudiantes adultos podria haber sido influenciada por su capacidad de alfabetizacion y ansiedad con respecto a los numeros. Algunos de los estudiantes adultos que formaban parte de las evaluaciones podia no haber entendido correctamente alguna de las declaraciones aritmeticas que tambien podria despertar la ansiedad. El presente estudio investigo la aritmetica para estudiantes adultos utilizando una escala de autoevaluacion individual que a menudo queda criticada por promover un error de medicion. Las personas pueden sobreestimar o subestimar su nivel de alfabetizacion y de aritmetica con el fin de ajustarse a la norma social. Se recomienda que los futuros estudios en Nigeria deban investigar las habilidades aritmeticas de estudiantes adultos haciendo el uso de los instrumentos mas solidos y psicometricos como la Encuesta de la Alfabetizacion de Adultos y Competencias practicas esenciales (ALLS) y la Encuesta Internacional de Alfabetizacion de Adultos (IALS). Sin embargo, opinamos que el presente estudio es vital para la exposicion del nivel de percepcion de aritmetica entre los estudiantes adultos, ya que los resultados de este estudio podrian servir como base para la realizacion de futuros estudios de aritmetica para adultos en Nigeria.

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Con el fin de llegar a un mayor numero de lectores, NAER ofrece traducciones al espanol de sus articulos originales en ingles. Sin embargo, este articulo en espanol no es el articulo original sino unicamente su traduccion. Si quiere citar este articulo por favor consulte el articulo original en ingles y utilice la paginacion del mismo en sus citas. Gracias.

Adeneye O. A. Awofalav (1) *, Blessing E. Anyikwa (2)

(1) Department of Science and Technology Education, Faculty of Education, University of Lagos, Nigeria {aawofala@unilaa.edu.ng}

(2) Department of Adult Education, Faculty of Education, University of Lagos, Nigeria {ebblessing@vahoo.com}

Recibido el 29 Mayo 2013; revisado el 4 Junio 2013; aceptado el 1 Octubre 2013; publicado el 15 Julio 2014

DOI: 10.7821/naer.3.2.83-92

* Por correo postal dirigirse a:

Adeneye O. A. Awofala

University of Lagos, Faculty of Education

Akoka, Yaba

Lagos, Nigeria

Table 1. Adult Learners' Perception of Numeracy skills and summary of
factor loadings by Principal Components analysis for the orthogonal
three factor model

A    Numeracy in everyday life:               N(%)
     Factor 1. I can...                       YES        SW

1    Perform simple calculations such as      30(93.8)   --
     addition and subtraction.
2    Receive cash payments and make change.   30(93.8)
3    Calculate the cost of items on a bill.   31(96.9)
4    Make comparisons (e.g. taller or         29(90.6)
     shorter, heavier or lighter, greater
     than or less than).
5    Record time using digital and standard   25(78.1)
     clocks, watches, or timers.
     Sub-total

     Numeracy in workplace tasks:
     Factor 2. I can ...

6    Take simple measurements (e.g.           28(87.5)
     length, weight, temperature).
7    Estimate quantities (e.g. I need         21(65.6)   2(6.3)
     approximately 20 copies).
8    Estimate measurements (e.g. it is        26(81.3)   1(3.1)
     approximately three feet wide).
9    Create and balance budgets.              22(68.8)   1(3.1)
10   Create and monitor schedules (e.g.       18(56.3)
     staffing or project schedules).
11   Estimate the time required to            15(46.9)   3(9.4)
     complete specific tasks.
12   Take precise measurements using          14(43.8)   3(9.4)
     specialized equipment.
13   Compare similar products with            14(43.8)   3(9.4)
     differing cost structures to
     determine the best value.
14   Manage complex budgets (e.g.             15(46.9)   3(9.4)
     preparing financial statements,
     forecasting materials).
15   Make accurate estimates when             17(53.1)   3(9.4)
     information is limited.
     Sub-total

     Numeracy in mathematical tasks:
     Factor 3. I can ...

16   Perform calculations that require        17(53.1)   2(6.3)
     multiplication and/or division.
17   Calculate percentages.                   16(50.0)   1(3.1)
18   Calculate the area of common shapes      28(87.5)   1(3.1)
     (e.g. square, triangle, circle).
19   Perform measurement conversions (e.g.    26(81.3)   1(3.1)
     inches to centimetres, millilitres to
     litres).
20   Calculate simple averages                27(84.4)   1(3.1)
21   Perform calculations that require        26(81.3)   1(3.1)
     multiple steps or operations.
22   Calculate areas and volumes of           26(81.3)   1(3.1)
     irregular shapes.
23   Measure curved and irregular lengths.    21(65.6)   1(3.1)
24   Analyze and compare statistical data.    19(59.4)   2(6.3)
     Sub-total
     Total

A    Numeracy in everyday life:               N(%)       M       SD
     Factor 1. I can ...                      NO

1    Perform simple calculations such as      1(3.1)     2.909   .426
     addition and subtraction.
2    Receive cash payments and make change.   2(6.3)     2.818   .588
3    Calculate the cost of items on a bill.   1(3.1)     2.909   .426
4    Make comparisons (e.g. taller or         2(6.3)     2.818   .588
     shorter, heavier or lighter, greater
     than or less than).
5    Record time using digital and standard   6(18.8)    2.545   .858
     clocks, watches, or timers.
     Sub-total                                           2.800   .577

     Numeracy in workplace tasks:
     Factor 2. I can ...

6    Take simple measurements (e.g.           3(9.4)     2.818   .588
     length, weight, temperature).
7    Estimate quantities (e.g. I need         8(25.0)    2.773   .612
     approximately 20 copies).
8    Estimate measurements (e.g. it is        4(12.5)    2.455   .912
     approximately three feet wide).
9    Create and balance budgets.              7(21.9)    2.546   .858
10   Create and monitor schedules (e.g.       11(34.4)   1.909   1.019
     staffing or project schedules).
11   Estimate the time required to            11(34.4)   1.909   .971
     complete specific tasks.
12   Take precise measurements using          12(37.5)   2.046   .999
     specialized equipment.
13   Compare similar products with            11(34.4)   2.046   .999
     differing cost structures to
     determine the best value.
14   Manage complex budgets (e.g.             10(31.3)   2.091   .971
     preparing financial statements,
     forecasting materials).
15   Make accurate estimates when             10(31.3)   2.227   .922
     information is limited.
     Sub-total                                           2.282   .885

     Numeracy in mathematical tasks:
     Factor 3. I can ...

16   Perform calculations that require        11(34.4)   1.636   .902
     multiplication and/or division.
17   Calculate percentages.                   14(43.8)   2.046   .999
18   Calculate the area of common shapes      3(9.4)     2.682   .716
     (e.g. square, triangle, circle).
19   Perform measurement conversions (e.g.    5(15.6)    2.500   .859
     inches to centimetres, millilitres to
     litres).
20   Calculate simple averages                4(12.5)    2.591   .796
21   Perform calculations that require        5(15.6)    2.500   .859
     multiple steps or operations.
22   Calculate areas and volumes of           5(15.6)    2.500   .859
     irregular shapes.
23   Measure curved and irregular lengths.    9(28.1)    2.227   .973
24   Analyze and compare statistical data.    7(21.9)    2.273   .935
     Sub-total                                           2.328   .877
     Total                                               2.470   .780

A    Numeracy in everyday life:               Factor
     Factor 1. I can ...                      Loading

1    Perform simple calculations such as      .909
     addition and subtraction.
2    Receive cash payments and make change.   .739
3    Calculate the cost of items on a bill.   .909
4    Make comparisons (e.g. taller or         .653
     shorter, heavier or lighter, greater
     than or less than).
5    Record time using digital and standard   .587
     clocks, watches, or timers.
     Sub-total

     Numeracy in workplace tasks:
     Factor 2. I can ...

6    Take simple measurements (e.g.           .780
     length, weight, temperature).
7    Estimate quantities (e.g. I need         .672
     approximately 20 copies).
8    Estimate measurements (e.g. it is        .786
     approximately three feet wide).
9    Create and balance budgets.              .822
10   Create and monitor schedules (e.g.       .822
     staffing or project schedules).
11   Estimate the time required to            .802
     complete specific tasks.
12   Take precise measurements using          .657
     specialized equipment.
13   Compare similar products with            .598
     differing cost structures to
     determine the best value.
14   Manage complex budgets (e.g.             .657
     preparing financial statements,
     forecasting materials).
15   Make accurate estimates when             .721
     information is limited.
     Sub-total

     Numeracy in mathematical tasks:
     Factor 3. I can ...

16   Perform calculations that require        .760
     multiplication and/or division.
17   Calculate percentages.                   .775
18   Calculate the area of common shapes      .733
     (e.g. square, triangle, circle).
19   Perform measurement conversions (e.g.    .833
     inches to centimetres, millilitres to
     litres).
20   Calculate simple averages                .805
21   Perform calculations that require        .677
     multiple steps or operations.
22   Calculate areas and volumes of           .620
     irregular shapes.
23   Measure curved and irregular lengths.    .801
24   Analyze and compare statistical data.    .704
     Sub-total
     Total

Table 2. Independent sample t-test analysis of adult learners'
performance in Arithmetic and perception of numeracy skills according
to gender

                              Gender   N    M         SD         Df

Numeracy score                Male     16   56.3750   8.09835    30
                              Female   16   56.5625   7.52745
Numeracy in everyday life     Male     16   14.0000   1.78885    30
                              Female   16   13.9375   2.11246
Numeracy in workplace tasks   Male     16   20.0000   5.64506
                              Female   16   21.8125   5.64764    30
Numeracy in math tasks        Male     16   22.3750   5.12348
                              Female   16   20.8125   4.26175    30
Arithmetic score              Male     16   51.5625   9.20122
                              Female   16   52.1250   10.97801   30

                              t       P

Numeracy score                -.068   .946

Numeracy in everyday life     .090    .929

Numeracy in workplace tasks
                              -.908   .371
Numeracy in math tasks
                              .938    .356
Arithmetic score
                              -.157   .876

Table 3. Correlations Matrix for the Relationship between Numeracy
self-assessment Dimensions, gender and adult learners performance in
Arithmetic

                             1       2         3         4

1. Gender                            1.00      .029      -.016
2. Arithmetic                        .029      1.00      -.219
3. Numeracy in everyday      -.016   -.219     1.00      .077
  life (NEL)
4. Numeracy in workplace     .164    .657 **   .077      1.00
  tasks (NWT)
5. Numeracy in               -.169   .369 *    -.130     .044
  mathematical tasks (NMT)
6. Numeracy Skills                   .012      .652 **   .228

                             5         6

1. Gender                    .164      -.169     .012
2. Arithmetic                .657 **   .369 *    .652 **
3. Numeracy in everyday      -.130     .228
  life (NEL)
4. Numeracy in workplace     .044      .778 **
  tasks (NWT)
5. Numeracy in               1.00      .611 **
  mathematical tasks (NMT)
6. Numeracy Skills           .778 **   .611 **   1.00

** p < .001, * p < .05

Table 4. Model Summary, Coefficient and t-Value of Multiple Regression
Analysis of Numeracy self-assessment skills Dimensions, gender and the
Outcome Measure (performance in Arithmetic)

Model Summary

Multiple R = .775

Multiple [R.sup.2] = .601

Multiple [R.sup.2] (Adjusted) = .542

Standard Error Estimate = 6.748

F = 10.157, p < .001

Model        Unstandardized       Standardized Coeff.   t       Sig
             Coefficients
             B       Std. Error   Beta

(Constant)   30.87   12.49                              2.47    .020
Gender       -.64    2.46         -.033                 -2.61   .796
NEL          -1.20   .64          -.231                 -1.88   .072
NWT          1.18    .22          .667                  5.38    .000
NMT          .646    .27          .305                  2.44    .022

Table 5. Summary of stepwise regression results with numeracy in
workplace tasks and numeracy in mathematical tasks entered for final
model explaining performance in arithmetic

Model   Independ. Variables   B        SEB     [beta]   t       P

1       Constant              27.52    5.269   -        5.223   .000
        NWT                   1.164    .244    .657     4.777   .000
2       Constante             12.439   7.30    -        1.705   .099
        NWT                   1.137    .221    .642     5.143   .000
        NMT                   .724     .265    .341     2.734   .011

Model   Independ. Variables   R      [R.sup.2]   F        P

1       Constant              .657   432         22.817   .000
        NWT
2       Constante             .741   .548        17.607   .000
        NWT
        NMT

Tabla 1. Percepcion de las habilidades aritmeticas de estudiantes
adultos y resumen de factor de cargas mediante el analisis de
componentes princi-pales para el modelo ortogonal de tres factores

A    Aritmetica en la vida cotidiana:               N(%)       N(%)
     Factor 1. Puedo... YE                          YES        SW

1    Realizar calculos sencillos como sumas y       30(93.8)   -
     restas
2    Recibir pagos en efectivo y hacer el cambio    30(93.8)
3    Calcular el coste de los articulos en la       31(96.9)
     factura
4    Hacer comparaciones (por ejemplo mas alto
     o mas bajo, mas pesado o mas ligero, mayor     29(90.6)
     o menor que)
5    Registrar el tiempo usando relojes o           25(78.1)
     cronometros tanto digitales como estandar
     Subtotal

     Aritmetica en tareas laborales:
     Factor 2. Puedo...

6    Realizar medidas sencillas (por ejemplo        28(87.5)
     longitud, peso, temperatura)
7    Estimar cantidades (por ejemplo: Necesito      21(65.6)   2(6.3)
     unas 20 copias)
8    Estimar medidas (por ejemplo: tiene,           26(81.3)   1(3.1)
     aproximadamente, tres pies de ancho)
9    Crear y equilibrar presupuestos                22(68.8)   1(3.1)
10   Crear y controlar los horarios (por ejemplo,   18(56.3)
     horarios de personal o de proyectos)
11   Estimar el tiempo requerido para realizar      15(46.9)   3(9.4)
     tareas especificas
12   Realizar medidas de manera precisa
     utilizando equipo especializado                14(43.8)   3(9.4)
13   Comparar productos similares de coste          14(43.8)   3(9.4)
     distinto para determinar el de mejor valor
14   Gestionar presupuestos complejos (por
     ejemplo: establecer los estados financieros,   15(46.9)   3(9.4)
     prevision de materiales)
15   Hacer calculos precisos con informacion        17(53.1)   3(9.4)
     limitada
     Subtotal

     Aritmetica en tareas matematicas:
     Factor 3. Puedo...

16   Realizar calculos que requieren la             17(53.1)   2(6.3)
     multiplicacion y/o division
17   Calcular los porcentajes                       16(50.0)   1(3.1)
18   Calcular area de las formas mas extendidas     28(87.5)   1(3.1)
     (por ejemplo: cuadrado, triangulo, circulo)
19   Realizar conversiones de medidas (por          26(81.3)   1(3.1)
     ejemplo, pulgadas a centimetros, mililitros
     a litros)
20   Calcular promedios simples.                    27(84.4)   1(3.1)
21   Realizar calculos que requieren multiples      26(81.3)   1(3.1)
     etapas u operaciones
22   Calcular areas y volumenes de formas           26(81.3)   1(3.1)
     irregulares
23   Medir longitudes irregulares y curvadas        21(65.6)   1(3.1)
24   Analizar y comparar los datos estadisticos     19(59.4)   2(6.3)
     Subtotal
     Total

A    Aritmetica en la vida cotidiana:                          Mean
     Factor 1. Puedo... YE                          NO

1    Realizar calculos sencillos como sumas y       1(3.1)     2.909
     restas
2    Recibir pagos en efectivo y hacer el cambio    2(6.3)     2.818
3    Calcular el coste de los articulos en la       1(3.1)     2.909
     factura
4    Hacer comparaciones (por ejemplo mas alto                 2.818
     o mas bajo, mas pesado o mas ligero, mayor     2(6.3)
     o menor que)
5    Registrar el tiempo usando relojes o           6(18.8)    2.545
     cronometros tanto digitales como estandar
     Subtotal                                                  2.800

     Aritmetica en tareas laborales:
     Factor 2. Puedo...

6    Realizar medidas sencillas (por ejemplo        3(9.4)     2.818
     longitud, peso, temperatura)
7    Estimar cantidades (por ejemplo: Necesito      8(25.0)    2.773
     unas 20 copias)
8    Estimar medidas (por ejemplo: tiene,           4(12.5)    2.455
     aproximadamente, tres pies de ancho)
9    Crear y equilibrar presupuestos                7(21.9)    2.546
10   Crear y controlar los horarios (por ejemplo,   11(34.4)   1.909
     horarios de personal o de proyectos)
11   Estimar el tiempo requerido para realizar      11(34.4)   1.909
     tareas especificas
12   Realizar medidas de manera precisa                        2.046
     utilizando equipo especializado                12(37.5)
13   Comparar productos similares de coste          11(34.4)   2.046
     distinto para determinar el de mejor valor
14   Gestionar presupuestos complejos (por                     2.091
     ejemplo: establecer los estados financieros,   10(31.3)
     prevision de materiales)
15   Hacer calculos precisos con informacion        10(31.3)   2.227
     limitada
     Subtotal                                                  2.282

     Aritmetica en tareas matematicas:
     Factor 3. Puedo...

16   Realizar calculos que requieren la             11(34.4)   1.636
     multiplicacion y/o division
17   Calcular los porcentajes                       14(43.8)   2.046
18   Calcular area de las formas mas extendidas     3(9.4)     2.682
     (por ejemplo: cuadrado, triangulo, circulo)
19   Realizar conversiones de medidas (por          5(15.6)    2.500
     ejemplo, pulgadas a centimetros, mililitros
     a litros)
20   Calcular promedios simples.                    4(12.5)    2.591
21   Realizar calculos que requieren multiples      5(15.6)    2.500
     etapas u operaciones
22   Calcular areas y volumenes de formas           5(15.6)    2.500
     irregulares
23   Medir longitudes irregulares y curvadas        9(28.1)    2.227
24   Analizar y comparar los datos estadisticos     7(21.9)    2.273
     Subtotal                                                  2.328
     Total                                                     2.470

A    Aritmetica en la vida cotidiana:               SD      Factor
     Factor 1. Puedo... YE                                  Loading

1    Realizar calculos sencillos como sumas y       .426    .909
     restas
2    Recibir pagos en efectivo y hacer el cambio    .588    .739
3    Calcular el coste de los articulos en la       .426    .909
     factura
4    Hacer comparaciones (por ejemplo mas alto      .588    .653
     o mas bajo, mas pesado o mas ligero, mayor
     o menor que)
5    Registrar el tiempo usando relojes o           .858    .587
     cronometros tanto digitales como estandar
     Subtotal                                       .577

     Aritmetica en tareas laborales:
     Factor 2. Puedo...

6    Realizar medidas sencillas (por ejemplo        .588    .780
     longitud, peso, temperatura)
7    Estimar cantidades (por ejemplo: Necesito      .612    .672
     unas 20 copias)
8    Estimar medidas (por ejemplo: tiene,           .912    .786
     aproximadamente, tres pies de ancho)
9    Crear y equilibrar presupuestos                .858    .822
10   Crear y controlar los horarios (por ejemplo,   1.019   .822
     horarios de personal o de proyectos)
11   Estimar el tiempo requerido para realizar      .971    .802
     tareas especificas
12   Realizar medidas de manera precisa             .999    .657
     utilizando equipo especializado
13   Comparar productos similares de coste          .999    .598
     distinto para determinar el de mejor valor
14   Gestionar presupuestos complejos (por          .971    .657
     ejemplo: establecer los estados financieros,
     prevision de materiales)
15   Hacer calculos precisos con informacion        .922    .721
     limitada
     Subtotal                                       .885

     Aritmetica en tareas matematicas:
     Factor 3. Puedo...

16   Realizar calculos que requieren la             .902    .760
     multiplicacion y/o division
17   Calcular los porcentajes                       .999    .775
18   Calcular area de las formas mas extendidas     .716    .733
     (por ejemplo: cuadrado, triangulo, circulo)
19   Realizar conversiones de medidas (por          .859    .833
     ejemplo, pulgadas a centimetros, mililitros
     a litros)
20   Calcular promedios simples.                    .796    .805
21   Realizar calculos que requieren multiples      .859    .677
     etapas u operaciones
22   Calcular areas y volumenes de formas           .859    .620
     irregulares
23   Medir longitudes irregulares y curvadas        .973    .801
24   Analizar y comparar los datos estadisticos     .935    .704
     Subtotal                                       .877
     Total                                          .780

Tabla 2. Analisis de la muestra independiente de test-t sobre el
desempeno de los estudiantes adultos en Aritmetica y en la percepcion
de las habilidades aritmeticas en funcion del sexo

                           Sexo     N    Media     SD         Dif

Puntuacion matematica      Hombre   16   56.3750   8.09835    30
                           Mujer    16   56.5625   7.52745
Aritmetica en la vida      Hombre   16   14.0000   1.78885    30
  cotidiana                Mujer    16   13.9375   2.11246
Aritmetica en las tareas   Hombre   16   20.0000   5.64506
  laborales                Mujer    16   21.8125   5.64764    30
Aritmetica en las tareas   Hombre   16   22.3750   5.12348
  matematicas              Mujer    16   20.8125   4.26175    30
Puntuacion aritmetica      Hombre   16   51.5625   9.20122
                           Mujer    16   52.1250   10.97801   30

                           t       P

Puntuacion matematica      -.068   .946

Aritmetica en la vida      .090    .929
  cotidiana
Aritmetica en las tareas
  laborales                -.908   .371
Aritmetica en las tareas
  matematicas              .938    .356
Puntuacion aritmetica
                           -.157   .876

Tabla 3. Matriz de correlaciones de la relacion entre las Dimensiones
de autoevaluacion en Aritmetica, el genero y el desempeno de los
alumnos adultos en Aritmetica

                             1       2         3         4

1. Sexo                              1.00      .029      -.016
2. Aritmetica                        .029      1.00      -.219
3. Aritmetica en vida        -.016   -.219     1.00      .077
  cotidiana (NEL)
4. Aritmetica en tareas      .164    .657 **   .077      1.00
  laborales (NWT)
5. Aritmetica en tareas      -.169   .369 *    -.130     .044
  matematicas (NMT)
6. Habilidades aritmeticas           .012      .652 **   .228

                             5         6

1. Sexo                      .164      -.169     .012
2. Aritmetica                .657 **   .369 *    .652 **
3. Aritmetica en vida        -.130     .228
  cotidiana (NEL)
4. Aritmetica en tareas      .044      .778 **
  laborales (NWT)
5. Aritmetica en tareas      1.00      .611 **
  matematicas (NMT)
6. Habilidades aritmeticas   .778 **   .611 **   1.00

** p < .001, * p < .05

Tabla 4. Resumen del modelo, coeficiente y valor-t del analisis de
regresion multiple de dimensiones de habilidades de autoevaluacion en
Aritmetica, el genero y la medida de resultado (desempeno en
Aritmetica)

Resumen del Modelo

Multiple R = .775

Multiple [R.sup.2] = .601

Multiple [R.sup.2] (Adaptado) = .542

Error Tipico de Estimacion = 6.748

F = 10.157, p < .001

Modelo        Coeficientes no        Coef. estandar   t       Sig
              estandar
              B       Error tipico   Beta

(Constante)   30.87   12.49                           2.47    0.02
Sexo          -0.64   2.46           -0.033           -2.61   0.796
NEL           -1.2    0.64           -0.231           -1.88   0.072
NWT           1.18    0.22           0.667            5.38    0
NMT           0.646   0.27           0.305            2.44    0.022

Tabla 5. Resumen de los resultados de la regresion escalonada
incluyendo aritmetica en las tareas laborales y aritmetica en las
tareas matematicas introducido para el modelo final que explica el
desempeno en aritmetica

Modelo   Variables   B        SEB     [beta]   t       p       R
         Independ.

1        Constante   27.52    5.269   -        5.223   0       0.657
         NWT         1.164    0.244   0.657    4.777   0
2        Constante   12.439   7.3     -        1.705   0.099   0.741
         NWT         1.137    0.221   0.642    5.143   0
         NMT         0.724    0.265   0.341    2.734   0.011

Modelo   Variables   [R.sup.2]   F        p
         Independ.

1        Constante   432         22.817   0
         NWT
2        Constante   0.548       17.607   0
         NWT
         NMT
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Article Details
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Title Annotation:ORIGINAL
Author:Awofala, Adeneye O.A.; Anyikwa, Blessing E.
Publication:NAER - Journal of New Approaches in Educational Research
Date:Jul 1, 2014
Words:21619
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