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Computer use and mathematical literacy: an analysis of existing and potential relationships.

This article explores the existing and potential relationships between computer use and mathematical literacy. Specifically focusing on data obtained from the Program for International Student Assessment (PISA), the article describes some analyses of educational practices in U.S. schools in relation to various types of computer use and mathematical literacy. The overall results of this study have made it clear that different types of activities that are performed on the computer are related to different levels and types of thinking, which in turn are associated with very different types of results. The study concludes with a call for more experimental type research on mathematical literacy acquisition and its relationship to technology use.

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Educational researchers have long argued for the increased use of technology in education for the potential benefits it brings to teaching and learning environments. A mere count of the number of journals and articles dedicated to this area can verify this fact. In an attempt to more deeply understand the relationship between technology use and educational growth, researchers have begun to explore computer applications for specific content areas such as science, language arts, and second language acquisition (MacKinnon, 2001; Salaberry, 2001; Warburton & Campbell, 2001). Research studies have also examined how technology can be used to learn mathematics at multiple educational levels (Dugdale, 2001; Lloyd & Wilson, 2001; Jiang & McClintock, 2000). These studies have explored technology and content areas in a manner that expressly addresses the kinds of uses and applications of very specific types of educational technology for very specific subject areas, grades, and student populations. As a result, this focus has narrowed our attention; instead of asking "How can a specific technology benefit learning?," we question "How can that same technology also benefit mathematical literacy acquisition?" This shift is an important one as we side with Norman (1993) in suggesting that technology is neither good nor bad, but can be used in positive and negative ways related to specific content areas. A technology that is good for acquisition of particular skills or concepts in one area may not necessarily be true for another content specialty.

Our goal, therefore, as mathematics educators and researchers interested in technology, is to understand the specific uses of technology that may foster increased mathematical literacy. In this particular study, the data are drawn from an existing national database to paint a picture of this relationship. This study also provides input and recommendations for continued research to support this type of inquiry.

Harold Wenglinsky completed a similar and highly publicized study in 1998. Using data from 1996 National Assessment of Educational Progress (NEAP), Wenglinsky attempted to explore the relationship between mathematical literacy and technology use. As with this study, he found that the "greatest inequities did not lie in how often computers were used, but in how they were used" (p. 3). One of Wenglinsky's main findings was that a teacher's professional development in the use of technology to teach higher order thinking skills was positively correlated with students' academic achievement in mathematics. This study was an important step in our understanding of the relationship between technology and mathematical literacy.

Although the 1998 study did report on higher and lower order thinking skills related to technology use, our goal in this study was to expand that knowledge base and explicitly describe the kinds of uses of technology that related to higher or lower level mathematical literacy. In doing so, we can provide teachers with particular recommendations for instructional use of computing for mathematical literacy acquisition.

PROGRAM FOR INTERNATIONAL STUDENT ASSESSMENT (PISA)

The data for these analyses and recommendations came from the Program for International Student Assessment (PISA). PISA, sponsored by the Organization for Economic Cooperation and Development (OECD), is a new tool that focuses on the international assessment of 15-year-old student's capabilities in reading, mathematics and science literacy. The purpose of PISA is to assess the cumulative educational experiences of students who were 15 years of age at the time of the assessment, irrespective of the grade levels or type of institutions that they are enrolled in (Lemke et al., 2000). The educational experiences that were assessed include learning that has taken place because of formal education, as well as other factors such as learning opportunities in the student's immediate environment. In this sense, mathematical literacy was measured broadly, and for the purpose of this study was not linked to any curriculum standards. Mathematical literacy, was also defined by PISA as "the capacity to identify, to understand the role that mathematics plays in this world, to make well-founded mathematical judgments and to engage in mathematics in ways that meet the needs of an individual's current and future life as a constructive, concerned and reflective citizen" (OECD, 1999, p.41).

METHODS

Thirty-two (32) countries participated in the PISA assessment in the year 2000. Twenty-eight (28) of those countries were OECD countries, while the other four countries (Brazil, Latvia, Liechtenstein, and the Russian Federation) were nonOECD countries. Within each country, there was a three stage sampling procedure that was used to obtain the sample of 15-year-olds within each country. The first stage included the selection of a sample based on geographical areas within each country. The second stage included a sample of schools within each geographic area, while the third stage included a sampling of students who were born in 1984 from those schools. The students who were in classes that had more than 35 students were selected randomly from within their classes, while the students who were in classes with less than 35 students were all selected from their classes. Finally, weighting was used for the analyses to compensate for some of the oversampling that took place, to ensure that the results are representative of the students within each country.

The mathematics literacy assessment that was used for this study included 60 minutes of testing time. Of those 60 minutes, 35 were used for responding to open ended items. However, not all students were given the same assessment. For this reason, individual comparisons between student scores are not possible. However, five plausible mathematics values were produced for each student, all of which when combined, were used as the continuous dependent variable for this study. The scaling for the scores that summarized the achievement results was done with a mixed coefficients multinomial logit IRT model (Lemke et al., 2000). In this model, which is a generalized form of the Rasch model, student outcome levels were considered as a random effect, while the items in this model were described by a fixed set of unknown parameters.

For the purpose of this study (and the proposed implications), only data from schools in the United States were examined (1). However, the USA was also used as a representative of an average achieving country since its national average on mathematics literacy was 493 points (the OECD national average was 500 points).

An important assumption that is required when using inferential statistics is that the sample is representative of the population. One of the best ways to achieve this goal is to sample the population with the method of random sampling. However in the PISA study, a three-stage sampling procedure was used. Therefore, it was essential to analyze the data by making all the necessary weighting adjustments to compensate for the fact that random sampling was not used (Saendal, Swensson, & Wretman, 1992). Therefore, the data analysis for this study was performed with the use of the software WESTVAR 4.2. A series of multivariate regressions were performed with WESTVAR 4.2 to try to explain the student's mathematics literacy based on their patterns of computer use and exposure in the USA. However, one of the problems with the use of computer experience variables is that they can be confounded with the socioeconomic status (SES) of the students. For example, students who have computers in their homes might come from more educated or affluent families who can also assist them with their schooling. For this reason, an indicator for SES that was created in the PISA database was added into all regression models to control for the effects of SES on student achievement. In addition, the alpha level for this study was set to 0.01.

The USA sample consisted of 2,135 students. In terms of gender, 51.9% of the USA sample was female. The majority of the 15 year old students that participated in this study (55.4%) were in grade 10; 40.5% were in grade 9, 3.4% were in grade 8, 0.3% were in grade 7; while 0.4% were in grade 11.

RESULTS

Four regression models were run for the data from the United States. The first regression model examined the level of comfort that the students had with computers. The second regression examined the student's frequency of computer use; the third regression examined the reasons for which the students use computers, while the fourth regression examined the frequency of different types of computer software use.

Level of comfort with computer use. The variables included in this analysis were those of SES, level of comfort with using a computer, level of comfort with using a computer to write a paper, and level of comfort with taking a test on the computer.

Table 1 presents the results of the model for the U.S. students. The model was significant ([F.sub.4,2292788.sup.2]=52.89, p=0.00), and it explained 19.1% of the variance of mathematics literacy. The results for this model show that as the student's level of comfort with the use of computers for writing papers increases, their mathematics literacy score increases as well. This indicates that the processes that are involved in writing papers on a computer are associated with mathematics literacy. However, as the student's overall comfort with using computers increases, their mathematics literacy decreases. This might indicate that feeling comfortable with the use of computers is not enough to increase the student's mathematics literacy since the students might feel comfortable with using the computer for activities that negatively affect their mathematics achievement.

Frequency of computer use. The following regression model included the variable of SES, as well as the variables of frequency of computer use at home, at school, in the library, and at other places. The regression model for frequency of computer use was significant for the model ([F.sub.5,2263578]=28.02, p=0.00), and it explained 19.3% of the variance of mathematics literacy (Table 2). The only variables that were significant in predicting the mathematics literacy of the U.S. students were those of SES and computer use at home. Both of these variables were positively related to mathematics literacy.

Purpose of computer use. The variables that were used for this regression were those of SES, using the computer for the Internet, for electronic communication, to help learn school material, as well as for programming. The results of this regression analysis show that the variable of SES was significant.

As presented in Table 3, the model that reflects the reasons for which the students use the computer was significant ([F.sub.5,1819550]=21.54, p=0.00) and it explained 19.3% of the variance of mathematics literacy. The results from this model show that in the USA, the use of the computer for electronic communication was associated with higher mathematics literacy scores. The other significant independent variable was that of using the computer for programming. As with many other countries in the PISA study, an increase in the frequency of use of the computer for programming was associated with a decrease in the student's mathematics literacy scores.

Software use. The variables that were used for this set of regression models (in addition to SES) were the use of the computer for playing games, for word processing, for spreadsheets, for drawing or graphics, and for using educational software. The results of this study show that the variable of SES was again significant.

As presented in Table 4, when the regression model was run, the model was significant ([F.sub.6,1810609]=27.45, p=0.00) and it explained 17.4% of the variance of mathematics literacy. Based on this set of data, frequent use of word processing software was associated with higher mathematics literacy, while frequent use of software for drawing, painting, and graphics was associated with lower mathematics literacy. The frequent use of educational software was also associated with lower mathematics achievement, although this relationship was not significant.

DISCUSSION

The initial research question for this study involved the relationship between computer use and mathematical literacy, and how these two areas interact with each other in the case of 15-year-old students in the USA. The results of this article have been interesting and varied, and can possibly provide additional knowledge about technology use, as well as suggest implications for instruction and further research. More specifically, this study shows that computer activities are not all equally as beneficial for improved mathematical literacy. Although some computer activities are associated with higher levels of mathematics literacy, other computer activities are associated with lower levels of mathematics literacy. It is possible that these results all revolve around the notion that higher order processes, as suggested by Vygotsky (1978) broadly, and by Wenglinsky (1998) in the subject area of math, are significantly related to the quality of the students' educational experiences. A summary of these results will be discussed.

Regression analyses 1 and 4 provide data to suggest that feeling comfortable with the use of computers for writing papers, and frequently using word processing software were significantly and positively related to higher levels of mathematics literacy. A note should be made, though, that since this is not an experimental study, it is difficult to claim that the process of writing papers on the computer itself is what influenced the student's high achievement, or vice versa. However, it is more likely that the higher order thinking skills that are associated with writing papers on the computer are related to the types of thinking skills necessary to have increased levels of mathematics literacy.

Other researchers have also begun to explore the relationships that exist between writing opportunities and increased mathematics abilities (Draper, 2002; Cloke, Ewing, & Stevens, 2002). This relationship might have to do with the logistical concerns or patterns of argument that exist in both areas. The notion in this argument is that computers, and specifically word processing software, provide opportunities to think through issues and problems, including the ability to talk about mathematics and see the applications of mathematical concepts literacy in their everyday lives.

In contrast, the students who indicated that they felt very comfortable with the use of computers, and who frequently used drawing, or painting type software, tended to have lower levels of mathematics literacy. In these cases, it is not exactly clear how exactly the computers were being used by the students and for what purposes. In many cases, computers are used in a classroom for remedial purposes or as a reward when students are finished with their work. Because of this, they may become more comfortable with computers, even if what they are doing on the computer is not related to higher order thinking. Thus, increased computer use, and therefore increased computer comfort, does not necessarily always equate with higher achievement. In addition, using the computer for drawing or painting purposes might not provide the students with enough skills that could be directly transferable to the subject area of mathematics.

The results of this study have also shown that using a computer at home, and frequently using a computer for electronic communication (e.g., e-mail or "chat rooms") was also associated with higher levels of mathematics literacy. (It is not clear how these two variables are related to each other since it would be necessary to have a computer at home to be able to spend large amounts of time in "chat rooms" or for general electronic communication.) In addition, the frequent and unsupervised by the teacher use of the computer at home might lead the students to use their problem-solving strategies more frequently to try to resolve daily hardware or software problems that might occur to their computers. These problem-solving strategies are higher order thinking skills that are transferable and could easily be applied to the subject area of mathematics.

A surprising result of this study is that frequent use of the computer for programming was associated with lower levels of mathematics achievement. Computer programming is a higher level thinking skill, closely related to the skills needed for the subject area of mathematics, so it is not clear why this negative relationship exists in this way. One possibility is that the students who are interested in programming are so focused on programming activities, that they choose not to focus as much on other subject areas such as mathematics. However, conclusive results for this exact relationship cannot be reached without a more in-depth experimental examination of this relationship.

CONCLUSIONS AND IMPLICATIONS

The overall results of this study have made it clear that the "passive" or mechanical use of the computer alone does not highly correlate with increased academic growth, specifically in mathematical literacy acquisition, and teachers need to become aware of this. This study has made it clear that different types of activities that are performed on the computer are related to different levels and types of thinking, which in turn are associated with very different types of results. In this case, some ways of using the computer (e.g., for electronic communication and for writing papers) were associated with higher levels of mathematical literacy, while other activities (e.g., programming and using drawing or painting type software) were associated with lower levels of mathematical literacy. In addition, for the purpose of this study, mathematics was used as only one indicator of student achievement. It is possible that the results could be varied when other subject areas are examined in relation to the ways in which students use computers. However, more experimental type studies need to be performed to be able to determine if cause-effect relationships actually exist between the types of computer use and mathematics literacy, as well as in what direction these relationships do exist.

References

Cloke, G., Ewing, N., & Stevens, D. (2002). Read all about it! Teaching Children Mathematics, 8(7), 408-410.

Draper, R.J. (2002). School mathematics reform, constructivism, and literacy: A case for literacy instruction in the reform-oriented mathematics classroom. Journal of Adolescent & Adult Literacy, 45(6), 520-529.

Dugdale, S. (2001). Order out of chaos: A spreadsheet excursion into a mathematical frontier. Journal of Computers in Mathematics and Science Teaching, 20(3), 323-341.

Jiang, Z., & McClintock, E. (2000). Multiple approaches to problem solving and the use of technology. Journal of Computers in Mathematics and Science Teaching, 19(1), 7-20.

Lemke, M., Lippman, L., Bairu, G., Calsyn, C., Kruger, T., Jocelyn, L., et al. (2000). Outcomes of learning. Results from the 2000 Program for International Student Assessment of 15-year-olds in reading, mathematics and science literacy. National Center for Educational Statistics, Washington, DC: NCES 2002-115.

Lloyd, G.M., & Wilson, M. (2001). Offering prospective teachers tools to connect theory and practice: Hypermedia in mathematics teacher education. Journal of Technology and Teacher Education, 9(4), 497-518.

MacKinnon, G.R. (2001). A promising model for incorporating the computer in science learning. The Journal of Computers in Mathematics and Science Teaching, 20(4), 395-404.

Norman, D.A. (1993). Things that make us smart: Defending human attributes in the age of the machine. Reading, MA: Addison-Wesley.

Organization for Economic Cooperation and Development. (1999). Measuring student knowledge and skills: A new framework for assessment. Paris: Author.

Salaberry, M.R. (2001). The use of technology for second language learning and teaching: A retrospective. The Modern Language Journal, 85(1), 39-56.

Saendal,W.-E., Swensson, B., & Wretman, J. (1992). Model assisted survey sampling. New York: Springer-Verlag.

Vygotsky, L. S. (1978). Mind in society. Cambridge, MA: Harvard University Press.

Warburton, J., & Campbell, R. (2001). Finding the poetic in a technological world: Integrating poetry and computer technology in a teacher education program. Journal of Technology and Teacher Education, 9(4), 585-597

Wenglinsky, H. (1998). Does it compute? The relationship between educational technology and student achievement in mathematics. Retrieved June 10, 2006, from http://www.ets.org/Media/Research/pdf/PICTECHNOLOG.pdf

Notes

(1) For a multi-country analysis, see Papanastasiou and Ferdig (in preparation).

(2) The degrees of freedom for these analyses are based on the weighting procedure that was used in the regressions.

ELENA C. PAPANASTASIOU

Intercollege

Cyprus

elenapap@ucy.ac.cy

RICHARD E. FERDIG

University of Florida

USA

rferdig@ufl.edu
Table 1 Comfort with Computer Use

 SE of t for [beta]
Parameters F-Value [beta] [beta] coefficient Sig.

Intercept 326.43 14.84 22.00 0.00*
SES 72.49 1.59 0.19 8.51 0.00*
Comfort with computer use 6.40 -10.07 3.98 -2.53 0.01*
Comfort with using a 77.21 40.80 4.64 8.79 0.00*
computer to write papers
Comfort with taking tests 0.09 -1.13 3.87 -0.29 0.77
on a computer
Overall fit 52.89 0.00*

Table 2 Frequency of Computer Use

 t for [beta]
Parameters F-Value [beta] SE of [beta] coefficient Sig.

Intercept 399.74 11.13 35.93 0.00*
SES 63.96 1.54 0.19 8.00 0.00*
Use at home 50.41 15.80 2.23 7.10 0.00*
Use at school 0.07 -0.60 2.32 -0.26 0.80
Use in the library 2.64 -5.88 3.62 -1.62 0.11
Use at another place 1.71 -3.93 3.00 -1.31 0.19
Overall fit 28.02 0.00*

Table 3 Purpose of Computer Use

 SE of t for [beta]
Parameters F-Value [beta] [beta] coefficient Sig.

Intercept 410.54 17.25 23.80 0.00*
SES 55.12 1.58 0.21 7.42 0.00*
Use the internet 4.03 9.31 4.64 2.01 0.05
Use electronic 15.01 9.99 2.58 3.88 0.00*
communication (e.g.
e-mail or "chat
rooms")
Use the computer to 0.75 -3.08 3.56 -0.87 0.39
learn school material
Use the computer for 16.03 -14.54 3.63 -4.00 0.00*
programming
Overall fit 21.54 0.00*

Table 4 Software Use

 SE of t for [beta]
Parameters F-Value [beta] [beta] coefficient Sig.

Intercept 456.48 19.24 23.72 0.00*
SES 48.07 1.62 0.23 6.93 0.00*
Games 0.07 -0.72 2.74 -0.26 0.79
Word processing (e.g. 16.38 15.47 3.82 4.05 0.00*
Word [R] or Word
Perfect [R]
Spreadsheets (e.g. 6.12 -9.78 3.95 -2.47 0.02
Lotus 123 [R] or Microsoft
Excel [R]
Drawing, painting or 18.99 -10.57 2.43 -4.36 0.00*
graphics
Educational software 3.21 -5.08 2.84 -1.79 0.08
Overall fit 27.45 0.00*
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Author:Ferdig, Richard E.
Publication:Journal of Computers in Mathematics and Science Teaching
Geographic Code:1USA
Date:Dec 22, 2006
Words:3850
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