Attitudes toward mathematics inventory redux.
Abstract The Attitudes Toward Mathematics Inventory (ATMI) was initially developed using samples of high school students in a private school. An exploratory factor analysis identified four factors: selfconfidence, value, enjoyment, and motivation. The present study used responses of 134 collegeaged American students in confirmatory factor analysis to determine if the fourfactor model previously identified would hold for college students. The results of the confirmatory factor analysis indicated that the fourfactor model is retained with college students. Introduction Research has established the importance of attitudes toward mathematics in achievement (Dwyer, 1993; Singh, Granville & Dika, 2002; Webster & Fisher, 2000). Attitudes influence success and persistence in the study of mathematics (Chang, 1990; Ma, 1997; ThorndikeChrist, 1991; Webb, Lubinski, & Benbow, 2002). Differences in achievement is related to the influence of parents (Kenschaft, 1991) and teachers (Dossey, 1992), gender, ethnicity, cultural background, and instructional approaches (Hollowell & Duch, 1991; Huang & Waxman, 1993; Koller, Baumert, & Schanbel, 2001; Leder & Forgasz, 1994; Murphy & Ross, 1990). Selfconfidence is a good predictor of success in mathematics (Goolsby, 1988; Linn & Hyde, 1989; Randhawa, Beamer, & Lundberg, 1993;). Similarly, anxiety is related to previous performance affecting attitudes (Hauge, 1991). Terwilliger and Titus (1995) found that positive attitudes toward mathematics are inversely related to math anxiety. While such preliminary evidence from attitudinal research is informative, little is known about college students because most research has been concerned primarily with K12 students. Many U.S. campuses struggle to attract students into mathematics beyond the required courses at the undergraduate level. About 1 percent of undergraduate students major in mathematics. Of course, some students with an interest in math are attracted to alternatives, such as computer science, and some take degrees that lead to immediate employment upon graduation, but there is no question that many students avoid mathematics (Baloglu, 1999). A study released by the Conference Board of the Mathematical Sciences (Lutzer, Maxwell, & Rodi, 2002) reported that bachelor's degrees granted in mathematics fell 19 percent between 1990 and 2000, at a time when overall undergraduate enrollment rose 9 percent. The longterm problems for the nation may be affected by the fact that the pool of potential students who will seek advanced degrees in math is small, and currently over half the students who take graduate degrees in mathematics are foreign. It is important to know why students avoid mathematics, and why most students who pursue degrees in mathematics are foreign. There are a number of hypotheses that may be erected, but the most basic investigation might begin with the attitudes that students have about the subject matter. While it seems highly likely that attitudes of college students are important in making decisions about mathematics courses, there is a paucity of research in this area and lack of a valid, reliable instrument for assessing the attitudes of college students. Most attitudinal research in the field of mathematics has dealt almost exclusively with anxiety or enjoyment of subject matter, excluding other factors (Aiken, 1974; Richardson & Suinn, 1972; Plake & Parker, 1982; Wigfield & Meece, 1988). An exception is the FennemaSherman Mathematics Attitude Scales (1976), which was developed over 30 years ago and has become a popular research instrument. It purports to have nine scales, but subsequent research raised questions about validity, reliability (Suinn and Edwards, 1982), and integrity of its scores (O'Neal, Ernest, McLean, & Templeton, 1988). Melancon, Thompson, and Becnel (1994) isolated eight factors rather than nine, and they were unable to find a perfect fit with the model proposed by Fennema and Sherman. Mulhern and Rue (1998) identified only six factors, and suggesting that the scales might not gauge what they were intended to measure. The original purpose of the Attitudes Toward Mathematics Inventory (ATMI) by Tapia and Marsh (2004) was to develop an instrument that dealt with attitudes that may contribute to math anxiety and to expand beyond measurement of enjoyment. The ATMI was developed in several stages. The original instrument was designed to measure six dimensions of attitudes toward mathematics. Extensive item analysis and exploratory factor analysis using students in an American high school in Mexico City resulted in a 40item questionnaire measuring four factors identified as Selfconfidence, Value, Enjoyment, and Motivation. Tapia and Marsh (2004) reported Cronbach alpha coefficient for the scores on Selfconfidence of .95, on Value of .89, on Enjoyment of .89, and on Motivation of .88. These values indicate a high degree of internal consistency of the items in each one of the factors. Since the ATMI was developed using a sample of high school students, it was unknown if the four factors would hold for a college population. Moreover, the ATMI was derived using a predominantly Hispanic sample, which raised the possibility there would be a different factor structure making the instrument unsuitable for a college sample. Therefore, the present study was designed specifically to address the question as to whether the fourfactor model previously identified would be retained for college students. To answer this question, a confirmatory factor analysis was conducted with a sample of college students. The purpose of this study was to determine if the ATMI would be similar in statistical properties using a postsecondary population. Research Method Subjects The subjects were 134 undergraduate students enrolled in mathematics classes at a state university in the Southeast. Seventyone subjects were male and 58 were female. Five participants did not provide their gender. Approximately 80% of the sample was Caucasian and about 20% AfricanAmerican. The ages of the sample ranged from 17 to 34. Ten participants did not report their ages. All subjects were volunteers and all students in the classes agreed to participate. Materials The Attitudes Toward Mathematics Inventory (ATM1) consists of 40 items designed to measure students' attitudes toward mathematics (Tapia & Marsh, 2004). The items were constructed using a Likertformat scale of five alternatives for the responses with anchors of I: strongly disagree, 2: disagree, 3: neutral, 4: agree, and 5: strongly agree. Eleven items of this instrument were reversed items. These items were given appropriate value for the data analyses. The score was the sum of the ratings. Exploratory factor analysis of the ATMI using a sample of high school students resulted in four factors identified as Selfconfidence, Value, Enjoyment, and Motivation. Sellconfidence was measured by 15 items. This factor includes items such as "Mathematics does not scare me at all" and "Studying mathematics makes me feel nervous." The value scale consisted of 10 items. Sample items from this factor are "Mathematics is a very worthwhile and necessary subject" and "Mathematics courses will be very helpful no matter what I decide to study." Enjoyment was measured by 10 items. This factor includes items such as "I really like mathematics" and "I have usually enjoyed studying mathematics in school." The motivation scale consisted of five items. Sample items from this factor are "I am willing to take more than the required amount of mathematics" and "'The challenge of mathematics appeals to me." Alpha coefficients for the scores of these scales were found to be .95, .89, .89, and .88 respectively (Tapia & Marsh, 2004). These values indicate high level of reliability of the scores on the factors. Procedure The ATMI was administered to participants during their mathematics classes. Directions were provided in written form and students recorded their responses on computer scannable answer sheets. Results Confirmatory factor analysis was used to evaluate the viability of the anticipated fourfactor model. Several measures were used to assess the model fit: the Chisquare goodness of fit, the ratio of the Chisquare goodness of fit to the degrees of freedom, the root mean square error of approximation (RMSEA), the normed fit index (NFI), and the expected crossvalidation index (ECVI). The first step in the confirmatory factor analysis was to create a fourfactor model with Selfconfidence, Value, Enjoyment, and Motivation as defined by Tapia and Marsh (2004). Cronbach alpha coefficients were calculated for the scores of the factors and were found to be .96 for Selfconfidence, .93 for Value, .88 for Enjoyment, and .87 for Motivation. These values indicate a high level of reliability for the factor scores. Correlations for the factors in this model were calculated for 134 subjects. The correlations of the variables in the model were as follows: (a) Selfconfidence and Value, .52; (b) Self confidence and Enjoyment, .75; (c) Selfconfidence and Motivation, .76; (d) Value and Enjoyment, .63; (e) Value and Motivation, .65; and, (0 Enjoyment and Motivation, .81. The adequacy of the fourfactor model was examined using confirmatory factor analysis using LISREL8. The Chisquare goodness of fit was 2.834 which based on 2 degrees of freedom has an associated probability of 0.242. A probability greater than 0.05 indicates a good fit (Shumacker & Lomax, 1996). LISREL run yielded a goodness of fit index (GFI) of 0.99. The adjusted GFI was found to be 0.94. The GFI and AGFI were to be higher than the desired value of 0.90 (Shumacker & Lomax, 1996). The GFI compares the similarity of the sample and the model covariance matrix. A GFI of 0.99 indicates that 99% of the sample covariance matrix fits the population covariance matrix. The root mean square error of approximation (RMSEA) was 0.056. Hu and Bentler (1999) indicate that a value less than .06 shows good model fit. Furthermore, the normed fit index (NFI) was 0.99, the expected crossvalidation index (ECVI) for the model was 0.14 and 0.15 for the saturated model. These goodness of fit statistics indicate a good model fit (Shumacker & Lomax, 1996). The four ATMI factors of Selfconfidence, Value, Enjoyment and Motivation reported by Tapia and Marsh (2004) using a sample of high school students were found to hold for the collegeage respondents in the present study. Furthermore, reliability estimates for the scores on the four factors were high, as were the corresponding scores of the high school sample. Conclusions It is important for research about attitudes or any other construct to be investigated with instruments that have validity and reliability, otherwise the results are not useful in making important instructional decisions. The obtained values on the ATMI using confirmatory factor analysis are important, because it is often difficult to establish. In confirmatory factor analysis, the model is based on a previous data structure and theory. The fact that the same data structure was confirmed is important for applications of the instrument to research with college students. Strong reliability and validity are essential for conducting research in this or any field. However, caution should always be used with the results of any instrument, especially selfreport surveys that are susceptible to response bias. The ATMI is a reliable instrument that demonstrates content and construct validity (Tapia & Marsh, 2004), and can be used with both secondary and college students. The current analysis of the instrument consists of 40 statements using a Eikert scoring system. Confirmatory factor analysis resulted in reaffirmation of the fourfactor structure as the best simple fit for the items, which were found in the original study with secondary students. The four factors were identified as Selfconfidence, Value, Motivation, and Enjoyment. This instrument was not investigated in relation to demographic data such as gender, ethnic background, grade level, mathematics achievement, and so forth. Undoubtedly, useful information can be obtained that relates gender, ethnic background and mathematics achievement to attitudes toward mathematics. References Aiken, L. R. (1974). Two scale of attitude toward mathematics. Journal for Research in Mathematics Education, 5, 6771. Baloglu, M. (1999). A comparison of mathematics anxiety and statistics anxiety in relation to general anxiety, Information Analyses, ERIC ED436 703, December. Chang, A. S. (1990, July). Streaming and Learning Behavior. Paper presented at the Annual Convention of the International Council of Psychologists, Tokyo, Japan (ERIC Reproduction Service No. ED 324092). Dossey, J. (1992). How school mathematics functions: Perspectives from the NAEP 1990 and 1992 assessments. Princeton, N J: National Assessment of Educational Progress. (ERIC Document Reproduction Service No. ED 377057) Dwyer, E. E. (1993). Attitude scale construction: A review of the literature. Morristown, TN: Walters State Community College (ERIC Document Reproduction Service No. ED 359201). Fennema, E. & Sherman, J. A. (1976). FennemaSherman Mathematics Attitudes Scales: Instruments designed to measure attitudes toward the learning of mathematics by males and females. Catalog of Selected Documents in Psychology, 6(1), 31. Goolsby, C. B. (1988). Factors affecting mathematics achievement in highrisk college students. Research and Teaching in Developmental Education, 4(2), 1827. Hauge, S. K. (1991). Mathematics anxiety: A study of minority students in an open admissions setting. Washington, DC: University of the District of Columbia (ERIC Reproduction Service No. ED 335229). Hollowell, K. A. & Duch, B. J. (1991, April). Functions and statistics with computers at the college level. Paper presented at the annual conference of the American Educational Research Association, Chicago, IL (ERIC Reproduction Service No. ED 336090). Hu, L. & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling 6(1), 15. Huang, S. L. & Waxman, H. C. (1993). Comparing Asian and AngloAmerican students' motivation and perception in the learning environment in mathematics. Paper presented at the annual conference of the National Association for Asian and Pacific American Education, New York, NY (ERIC Reproduction Service No. ED 359284). Kenschaft, P. (Ed.) (1991). Winning women into mathematics. Washington, DC: Mathematical Association of America. Koller, O., Baumert, J., & Schnabel, K. (2001). Does interest matter? The relationship between academic interest and achievement in mathematics. Journal for Research in Mathematics Education, 32(5), 448470. Leder, G. & Forgasz, H. (1994, April). Singlesex mathematics classes in a coeducational setting: A case study. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA (ERIC Reproduction Service No. ED 372946). Linn, M & Hyde, J. (1989). Gender, mathematics, and science. Educational Researcher, 18(8), 1719, 2227. Lutzer, D.J., Maxwell, J.W., & Rodi, S.B. (2002). Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States. Providence RI: American Mathematical Society. Ma, X. (1997). Reciprocal relationships between attitude toward mathematics and achievement in mathematics. The Journal of Educational Research, 90, 221229. Melancon, J. G., Thompson, B., & Becnel, S. (1994). Measurement integrity of scores from the FenemmaShennan Mathematics Attitudes Scales: The attitudes of public school teachers. Educational and Psychological Measurement, 54(1), 187192. Mulhern, F. & Rae, G. (1998). Development of a shortened form of the FennemaSherman Mathematics Attitudes Scales. Educational and Psychological Measurement 58(2), 295306. Murphy, L. O. & Ross, S. (1990). Protagonist gender as a design variable in adapting mathematics story problems to learner interest. Educational Technology, Research and Development, 38(3), 2737. O'Neal, M. R., Ernest, P. S., McLean, J. E, & Templeton, S. M. (1988, November). Factorial validity of the FennemaSherman Attitude Scales. Paper presented at the annual meeting of the MidSouth Educational Research Association, Louisville, KY. (ERIC Document Reproduction Service ED 303493). Plake, B. S. & Parker, C. S. (1982). The development and validation of a revised version of the Mathematics Anxiety Rating Scale. Educational and Psychological Measurement 42, 551557. Randhawa, B. S., Beamer, J. E., & Lundberg, I. (1993). Role of the mathematics self efficacy in the structural model of mathematics achievement. Journal of Educational Psychology, 85, 4148. Richardson, F. C. & Suinn, R. M. (1972). The Mathematics Anxiety Rating Scale: Psychometric data. Journal of Counseling Psychology, 19, 551554. Schumacker, R. E. & Lomax, R. G. (1996). A beginner's guide to structural equation modeling. Mahwah, N J: Lawrence Erlbaum Associates. Singh, K. Granville, M., & Dika, S. (2002). Mathematics and science achievement effects of motivation, interest, and academic engagement. Journal of Educational Research, 95(6), 323332. Suinn, R. M. & Edwards, R. (1982). The measurement of mathematics anxiety: The Mathematics Anxiety Rating Scale for AdolscentsMARSA. Journals of Clinical Psychology, 38(3), 576580. Tapia, M. & Marsh, G. E., II (2004). An instrument to measure mathematics attitudes. Academic Exchange Quarterly, 8(2), 1621. Terwilliger, J. & Titus, J. (1995). Gender differences in attitudes and attitude changes among mathematically talented youth. Gifted Child Quarterly, 39(1), 2935. ThorndikeChrist, T. (1991). Attitudes toward mathematics: Relationships to mathematics achievement, gender, mathematics coursetaking plans, and career interests. WA: Western Washington University (ERIC Document Reproduction Service No. ED 347066). Webb, R. M., Lubinski, D., & Benhow, C. (2002). Mathematically facile adolescents with mathscience aspirations: New perspective on their educational and vocational development. Journal of Educational Psychology, 94(4), 785794. Webster, B. J. & Fisher, D. L. (2000) Accounting for variation in science and mathematics achievement: A multilevel analysis of Australian data. School Effectiveness and School Improvement, 11(3), 339360. Wigfield, A. & Meece, J. L. (1988). Math anxiety in elementary and secondary school students. Journal of Educational Psychology, 80, 210.216. Martha Tapia, Berry College George E. Marsh II, The University of Alabama Martha Tapia is associate professor of mathematics education. George E. Marsh II is a professor of instructional technology in the Institute of Interactive Technology. 

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