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A Simple Mathematics Motivation Scale and Study of Validation in Mexican Adolescents:

A Simple Mathematics Motivation Scale and Study of Validation in Mexican Adolescents: The goal of the study was to evaluate and adjust the model that associates mathematical motivation and learning strategies as quantitative instruments. The items related to the task value, cost, and self-efficacy were validated with Mexican students of rural areas in south-west region of Mexico between 12 and 16 years old, using 14 items that measure self-reported motivation levels. The construct validity of the mathematics motivation scale was checked using confirmatory factor analysis (CFA), by analyzing first- and second-order CFA models. The factor reliability was investigated by means of Dillon-Goldstein’s rho and Cronbach’s alpha. The model had adequate goodness of fit of in the confirmatory analysis. The instrument proved that it is convenient and reliable for application in mathematics motivation in Mexican adolescents. An advantage of the use of this instrument to be applied by teachers of mathematics is its simplicity, ease of application, and interpretation. Keywords motivation, mathematics, self-efficacy, validation, CFA models Academic motivation is related to the perceptions that stu- include a similar weight (than the cognitive one) regarding dents have of themselves and their environment which emotional and motivational aspects, which are very influen- encourages them to choose an activity, to commit to it, and to tial for performance and achievement (Echeverría Castro persevere to see it through to its conclusion. Motivation et al., 2020). The problem of motivation with respect to affects student creativity, learning styles, and academic mathematics is not new. As in other disciplines, motivation achievement (Kuyper et al., 2000) and has been shown to be has a big effect on mathematics lessons. Motivation is a con- a useful predictor of high dropout rates (Barkoukis et al., struct that makes it possible to explain the reasons for the 2008) and to have a positive correlation with high academic behavior of students in the mathematics classroom and the performance (Gottfried et al., 2007). The teaching of mathe- objectives and goals they have when attending a mathemat- matics constitutes a field of great interest for both mathemat- ics class, as well as their reasons for learning mathematics. ics teachers and pedagogues. Teachers must plan the lessons The definitions of motivation are many and varied since a with attractive activities in order to get the students’ attention wide range of theoretical points of view have been studied (Cavallo, 2002). Mathematics teachers are responsible for that try to explain it by focusing on key dimensions of moti- facilitating the development of positive attitudes toward vation, for example, self-efficacy (Bandura, 1997), attribu- mathematics from the first courses. It is not enough to work tions (Skinner et al., 1990), achievement goals (Ames, 1992), toward the student getting good grades. Academic achieve- self-concept (Guay et al., 2003), and expectation and the ment and liking a subject do not always coincide. It is pos- value of the task (Eccles et al., 1983). sible for a student who has no affection for mathematics to obtain good grades in this subject because they are respon- 1 Universidad Autónoma de Guerrero, Chilpancingo, México sible and do the work because it is necessary to advance to Hospital Juárez de México, Ciudad de México, México the next subject, but they might try to use mathematics as *These authors contributed equally to this work. little as possible and, unfortunately, forget what they have Corresponding Author: learned. Ramón Reyes-Carreto, Maestría en Matemáticas Aplicadas, Facultad de In many cases the learning of mathematics implies greater Matemáticas, Universidad Autónoma de Guerrero, Lázaro Cárdenas, difficulties for students. The psychosocial factors involved in Chilpancingo 39070, México. learning mathematics are especially relevant since they Email: rrcarreto@gmail.com Creative Commons CC BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License (https://creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/open-access-at-sage). 2 SAGE Open Expectancy-value theory is one of the most relevant moti- the structure of instrument as well as the items that compose vational theories because it has been widely used as a con- it, and the statistical analysis that was performed. In Section ceptual framework to explain motivation in different 3, the results are presented, such as the validity and reliabil- educational disciplines. The model is based on the analysis ity of the instrument, as well as the correlations of the moti- of expectations and the perceived value of homework by stu- vation constructs or factor. Finally, in Section 4, we conclude dents and its links with school performance, persistence, and with some comments. the choice of further studies, among other factors (Eccles & Wigfield, 2002). This model has shown that value beliefs and Materials and Methods expectation of success are related to effort in learning math- ematics, higher enrollment in this discipline, and perfor- Participants mance (Spinath et al., 2006; Wigfield & Eccles, 2000). The participants are boys and girls between 12 and 16 years There is a great diversity in studies on mathematical of secondary schools (technical, general, and television) of motivation. Berger and Karabenick (2011) developed an the first, second, and third grade. Secondary schools are pub- expectancy-value model with ninth grade students (usually lic and rural areas in south-west region of Mexico. Subjects 14–15 years old) in a Midwest urban high school in the U.S.A. who did not accept participate are excluded from the study. Expectancy was represented by self-concept regarding ability and self-efficacy. They proposed to measure the self-efficacy expectation scale, for which the items were selected from the Mathematics Motivation Scale self-efficacy scale of the Motivated Strategy for Learning The instrument is a self-report measure composed of 14 items Questionnaire (MSLQ) questionnaire (Pintrich et al., 1991), that measure self-reported levels of motivation. The instru- and they also evaluated the scale of task value, which was ment comprised five subscales: interest (items 1, 2, and 3), composed of four categories. The components of the task importance (items 4, 5, and 6), utility (items 7, 8, and 9), cost value were defined and evaluated by Eccles and Wigfield (items 10 and 11), and for the expectancy value, constructs (1995), who confirmed the results of Pintrich and De Groot were assessed by three items from self-efficacy (items 12, 13, (1990) that motivation predicts learners’ self-regulatory strat- and 14). All students’ responses were rated on a 5-point scale egies. Additionally, they concluded that the adaptations of the ranging from 1 (Not at all true of me) to 5 (Very true of me). items used to measure high school students’ use of learning strategies represented an improvement over those in previous versions of the MSLQ. The mathematics motivation scale CFA Models adapted by Berger and Karabenick (2011) was translated into The first-order CFA model comprised five latent factors: Spanish by Gasco and Villarroel (2017) and applied to sec- interest, importance, utility, cost, and self-efficacy, and the ondary education students between 13 and 16 years in the second order CFA model called task value is measured by the Basque Autonomous Community of Spain. However, the following three first order factors: interest, importance, and instrument in Spanish, was not studied its validity by con- utility. Both the first and second order CFA models were pro- struct, content, and criteria. posed by Berger and Karabenick (2011). The MSLQ made it possible to examine associations between motivation and self-regulation with a greater degree of precision. Actually, considerable support for the associa- Procedure tion between students’ motivational beliefs and use of learn- ing strategies exists. In the Mexican context, little research First, the main researcher contacted the secondary school has been studied motivation from the perspective of expec- directors and explained the goal of the research. Second, tancy-value theory. once the secondary school directors gave their approval, con- In literature there are some instrument proposals to sent was obtained from teachers and parents, and we informed measure motivation in mathematics in secondary schools them about the objective of the study (parents were asked to such as the Mathematics Motivation Scale of 24 items authorize their children’s participation, and assent was also (Zakariya and Massimiliano, 2021) or Mathematics obtained from child participants). Then, the students were Motivation Questionnaire of 19-items (Fiorella et al., 2021), informed of the objective of the study and of the confidenti- but the scale adapted by Berger and Karabenick (2011) is ality of the data obtained. Finally, they answered the instru- the simplest with 14 items. For this reason, our goal is to ment and one of the researchers was present in case there validate the mathematical motivation scale of Berger and were any questions or doubt. A total time of between 8 and Karabenick (2011) for Mexican secondary school students 14 minutes was required to complete the instrument. for to know the effects, correlations, and internal consis- tency of the construct or factors used to get convenient and Statistical Analyses reliable instrument for mathematics motivation scale. This work is organized as follows: in the following sec- All of the analyses described below were carried out using R tion, we detail the inclusion criteria of the sample, describe Statistical Software version 3.2.4 with the R package psych Arellano-García et al. 3 Table 1. Demographic Characteristics of Secondary School Student Participants. Boys n = 213 Girls n = 282 p-Value Age (years)* 13.19 (0.98) 13.28 (0.97) .360 Secondary school type (%)** .392 Technique 163 (76.5) 201 (71.3) General 38 (17.8) 64 (22.7) Television 12 (5.6) 17 (6.0) Grade (%)** .345 First 79 (37.1) 87 (30.9) Second 73 (34.3) 105 (37.2) Third 61 (28.6) 90 (31.9) *M(SD). **n(%). (Revelle, 2018) and lavaan (Rosseel, 2012). Results were (43.03%) of the students were boys between 12 and 16 years considered statistically significant at p < .05. old (M = 13.19, SD = 0.98), and the girls were between 12 and The validity of the mathematics motivation scale was 16 years old (M = 13.26, SD = 0.97). The average self-reported checked by CFA. We only fit CFA models because there is an score of the students in the previous mathematics course was explicit theory that suggests a specific model. The first- and 7.73 (SD = 1.30) and 8.30 (SD = 1.14) in boys and girls, second-order CFA models were conducted using the robust respectively. Demographic characteristics of the participants maximum likelihood (RML) estimator, which provides stan- grouped by sex were homogeneous (Table 1) with respect to dard errors and fit indices that are robust to the Likert nature age, secondary school type, and grade. of the items and small deviations from multivariate normal- ity. All analyses performed the full information maximum First and Second Order CFA Models likelihood (FIML) procedure, which is the most efficient method to estimate a model in which some of the variables Table 2 presents a factor structure made up of five constructs have missing values. We used the following indices to assess or factors for the first order CFA model and the second order the model fit: standardized root mean residual (SRMR), root factor called task value with your three correlated first order mean square error of approximation (RMSEA), comparative factors: interest, importance, and utility. The items were fit index (CFI), Tucker-Lewis index (TLI), and the average ordered in the factors of the original scale version. To check value explained (AVE) for items within a domain. Values the adequacy of the expected factor structure, CFAs were smaller than 0.06 for RMSEA and SRMR, and values greater conducted using the items as factor indicators. than 0.95 for CFI and TLI are considered excellent, whereas The CFA models revealed an adequate SFL (all load- values between 0.06 and 0.08 for RMSEA and SRMR, and ings > 0.62), and all confidence intervals of SFL were statis- between 0.90 and 0.95 for CFI and TLI are considered ade- tically significant (Table 2). In the first-order CFA model, all quate. AVE greater than 0.50 indicates a good fit. values of AVE indicated a good fit, except the items of the Finally, the Bartlett method was used to extract factor self-efficacy factor and the item “I believe that success in scores. Descriptive statistics of the scores and reliability math requires. . .” In the second-order CFA model, the fol- indices (Dillon-Goldstein’s rho coefficients and Cronbach’s lowing variables were values of AVE less than 0.5: the items alpha) of each of the factors that make up the measurement “I believe I will receive an excellent grade in math,” “I’m instrument were also analyzed. A coefficient value greater certain I can understand the most difficult material presented than .70 indicates a high level of internal consistency. in math,” and interest in the second-order factor. Furthermore, the correlation between domain was assessed using Pearson’s correlations. A correlation between .41 and Goodness of Fit .60 is regarded as good, one between .61 and .80 very good, and .81 is considered excellent. The first- and second-order CFA models used RML as the estimation method. The goodness-of-fit statistics and infor- mation criteria of the models estimated are presented in Results Table 3. In both models, the χ test was significant, and the following robust adjustment indicators were analyzed: Description of the Sample RMSEA, SRMR, CFI, and TLI showed an excellent good- A total of 495 participants, who were students in the first ness of fit in the first-order model and obtained adequate val- (166), second (178), and third (151) grades in secondary ues in RMSEA, SRMR, CFI, and TLI in the second-order school, participated in the study voluntarily. About 213 model. 4 SAGE Open Table 2. First- and Second-Order CFA Models. First-order factor model Second-order factor model Items Factor and items SFL 95% CI AVE SFL 95% CI AVE Factor 1: Interest 1 Me gustan las matemáticas. (I like math.) 0.805 0.750–0.859 0.648 0.810 0.757–0.863 0.656 2 Disfruto con las matemáticas. (I enjoy doing math.) 0.877 0.833–0.921 0.769 0.871 0.823–0.918 0.758 3 Las matemáticas son emocionantes. (Math is exciting 0.757 0.699–0.816 0.574 0.758 0.699–0.818 0.575 to me.) Factor 2: Importance 4 Es importante para mí ser alguien que sea bueno en 0.720 0.658–0.783 0.519 0.715 0.651–0.779 0.511 matemáticas. (It is important to me to be the kind of person who is good at math.) 5 Creo que ser bueno en matemáticas es parte 0.765 0.706–0.823 0.585 0.765 0.706–0.823 0.585 importante de mi personalidad. (I believe that being good at math is an important part of who I am.) 6 Es importante para mí ser alguien que puede razonar 0.709 0.642–0.775 0.502 0.714 0.649–0.780 0.510 utilizando fórmulas y operaciones matemáticas. (It is important to me to be a person who can reason using math formulas and operations.) Factor 3: Utility 7 Creo que las matemáticas pueden ser útiles en el 0.819 0.764–0.874 0.671 0.828 0.775–0.881 0.685 futuro porque me pueden ayudar. (I believe that math will be useful for me later in life.) 8 Creo que ser bueno en matemáticas puede ser útil 0.800 0.748–0.852 0.640 0.801 0.750–0.852 0.641 en el futuro. (I believe that math is valuable because it will help me in the future.) 9 Creo que ser bueno en matemáticas puede ser útil 0.772 0.714–0.829 0.596 0.762 0.701–0.823 0.581 para encontrar trabajo o para ir a la universidad. (I believe that being good at math will be useful when I get a job or go to college.) Factor 4: Cost 10 Tengo que dejar de hacer muchas cosas para 0.787 0.624–0.950 0.619 0.762 0.601–0.923 0.581 aprender bien matemáticas. (I have to give up a lot to do well in math.) 11 Creo que el éxito en matemáticas requiere dejar 0.687 0.543–0.832 0.472 0.710 0.557–0.863 0.504 otras actividades que me gustan. (I believe that success in math requires that I give up other activities that I enjoy.) Factor 5: Self-efficacy 12 Creo que tendré una excelente nota en matemáticas. 0.652 0.573–0.731 0.425 0.627 0.545–0.709 0.393 (I believe I will receive an excellent grade in math.) 13 Estoy seguro de que puedo entender los contenidos 0.689 0.623–0.756 0.475 0.667 0.591–0.744 0.445 más difíciles en matemáticas. (I’m certain I can understand the most difficult material presented in math.) 14 Tengo confianza en que puedo aprender los 0.706 0.641–0.771 0.498 0.745 0.683–0.808 0.556 conceptos básicos enseñados en matemáticas. (I’m confident I can learn the basic concepts taught in math.) Second-order factor: Task value Interest NA NA NA 0.618 0.511–0.726 0.382 Importance NA NA NA 0.961 0.885–1.000 0.923 Utility NA NA NA 0.790 0.715–0.866 0.625 Note. INT = interest; IMP = importance; UTL = utility; CT = cost; SELF = self-efficacy; VAL = task value; SFL = standardized factor loading; 95% CI = 95% confidence interval; AVE = average value explained; NA = not applicable. Arellano-García et al. 5 Table 3. Goodness-of-Fit Statistics of the Models Estimated. Model χ df p-Value RMSEA SRMR CFI TLI First order 114.808 67 <.001 0.044 0.038 0.977 0.969 Second order 190.447 71 <.001 0.068 0.064 0.943 0.927 Note. χ = Chi-square test; df = degrees of freedom; RMSEA = root mean square error of approximation; SRMR = standardized root mean residual; CFI = comparative fit index; TLI = Tucker-Lewis index. in this work confirmed that the first- and second-order CFA Internal Consistency models showed desirable properties in terms of construct Table 4 shows the mean and standard deviation of scores validity. The second-order CFA models is also proposed by obtained by the constructs that comprise the questionnaire. Berger and Karabenick (2011), in this study indicated that Also, this table shows the internal consistency; the question- specific construct can be formed for cognitive and resource naire presented a Dillon-Goldstein’s rho of .892 and management strategies, respectively, whereas the three types Cronbach’s alpha of .872, which indicates that it is reliable of metacognitive strategies, as interest, importance, and util- for the Mexican population, while the values obtained by ity, were explained by a single second-order factor called constructs were greater than .80. The constructs’ correlations task value. A practical importance of the second-order CFA for the CFA models were calculated. model is that the task value score was associated with the subscales of cost and self-efficacy, or with other variables or Correlation Between Constructs constructs. In addition, the mathematics motivation scale underwent Table 4 shows the correlations between all the factors were a validation process, in which it demonstrated appropriate positive, and all confidence intervals of the correlation coef- properties for research applications. An advantage of the use ficients were statistically significant except between cost and of this instrument is its simplicity, ease of application, and interest factors of the first-order model. The correlation interpretation so that it can be applied by teachers of mathe- between the importance and utility constructs was excellent. matics in rural areas since 60% of teachers of secondary Also, the correlation between the task value (second order schools in Mexico are in rural areas (INEA, 2014). factor) and cost with self-efficacy was excellent. Finally, the The objectives of this paper were limited to the validation correlation between the cost with interest, importance, and of the scale in a group of Mexican students, with the inten- utility was poor. tion of applying the scale to understand academic motivation in future research. In the same way new research can be pro- Discussion and Conclusion posed that allows observing motivation in different contexts within the Mexican educational system. In this research, the This study was conducted to provide a convenient and reliable data was obtained from rural areas of a state with unfavor- instrument for a mathematics motivation scale. The original able economic conditions. It will be interesting to observe version of the mathematics motivation scale was first devel- the relationships of these conditions with the academic moti- oped and validated in English by Berger and Karabenick vation of the respondents. (2011), followed by the Spanish version by Gasco and If we want to know the personal characteristics that make Villarroel (2017) but without validation. While the motivation a male or female student face learning activities with greater of mathematics learning can be measured from numerous per- or lesser interest or effort, either for the purpose of knowing spectives, and our validated instrument of 14-items is only one what aids to provide them with or for the purpose of predict- of these, one of its advantages is that it is one of the simplest in comparation of other instruments as the Mathematics ing what their future performance will be, what information Motivation Scale of 24 items (Zakariya and Massimiliano, should we seek? The MSLQ provides us with useful infor- 2021) or Mathematics Motivation Questionnaire of 19-items mation for teachers. Expectancy-value theory, through its (Fiorella et al., 2021). components (interest, usefulness, and importance and cost of Our study provides validation of the mathematics motiva- the task), provides clear information on the motivation of tion scale in secondary school students of rural areas in students, the value they assign to tasks, and the expectations south-west region of Mexico. The Spanish version of the they have of themselves. questionnaire showed scale consistency with the original and Our study has some limitations. The instrument was vali- had high internal consistency (Dillon-Goldstein’s rho of .892 dated in secondary school students in rural areas in south- and Cronbach’s alpha of .872). Moreover, the subscales west of Mexico. Some additional opportunities are to validate showed satisfactory internal consistency. The results obtained the instrument in urban schools or private schools. 6 Table 4. Descriptive Statistics, Internal Consistency, and Correlations Between Constructs. Descriptive statistics Internal consistency Correlations Dillon- Cronbach’s Model Construct M SD Goldstein’s rho alpha INT IMP UTL CT SELF VAL First order Interest 0.00 1.063 .919 .868 0.637 0.428 0.183 0.829 NA Second order 0.00 1.051 NA NA 0.671 0.488 0.229 0.680 0.703 First order Importance 0.00 0.904 .875 .787 0.582–0.687 0.893 0.375 0.738 NA Second order 0.00 0.902 NA NA 0.619–0.716 0.860 0.380 0.799 0.995 First order Utility 0.00 0.903 .914 .860 0.353–0.497 0.873–0.909 0.363 0.591 NA Second order 0.00 0.912 NA NA 0.418–0.552 0.835–0.881 0.334 0.658 0.882 NS First order Cost 0.00 0.915 .877 .719 0.096–0.266 0.296–0.448 0.284–0.437 0.481 NA Second order 0.00 0.879 NA NA 0.144–0.311 0.302–0.453 0.253–0.410 0.499 0.882 First order Self-efficacy 0.00 0.750 .842 .718 0.799–0.855 0.695–0.775 0.531–0.646 0.410–0.546 NA Second order 0.00 0.779 NA NA 0.630–0.725 0.765–0.829 0.605–0.705 0.430–0.562 0.833 First order Task value NA NA NA NA NA NA NA NA NA NA Second order 0.00 0.860 NA NA 0.655–0.745 0.994–0.996 0.861–0.900 0.861–0.900 0.804–0.858 Note. SD = standard deviation; INT = interest; IMP = importance; UTL = utility; CT = cost; SELF = self-efficacy; VAL = task value. Pearson’s correlation (upper triangular matrix), 95% confidence Interval (lower triangular matrix); NA = not applicable. Arellano-García et al. 7 Declaration of Conflicting Interests mathematics motivation questionnaire (mmq) for secondary school students. International Journal of STEM Education, The author(s) declared no potential conflicts of interest with respect 8(52), 1–14. to the research, authorship, and/or publication of this article. Gasco, J., & Villarroel, T. (2017). The motivation of second- ary school students in mathematical word problem solving. Funding Electronic Journal of Research in Educational Psychology, The author(s) disclosed receipt of the following financial support 12(1), 83–106. http://dx.doi.org/10.14204/ejrep.32.13076 for the research, authorship, and/or publication of this article: The Gottfried, A. E., Marcoulides, G. A., Gottfried, A. W., Oliver, P. first, second, and third authors were partially supported by H., & Guerin, D. (2007). Multivariate latent change modeling SNI-CONACYT. of developmental decline in academic intrinsic mathematics motivation and achievement: Childhood through adolescence. Ethical Approval International Journal of Behavioral Development, 31(4), 317–327. Ethics approval was not required for this study. Guay, F., Marsh, H. W., & Boivin, M. (2003). Academic self-con- cept and academic achievement: Developmental perspectives ORCID iDs on their causal ordering. Journal of Educational Psychology, Yuridia Arellano-Garca í https://orcid.org/0000-0002-7841-1470 95(1), 124–136. https://doi.org/10.1037/0022-0663.95.1.124 Cruz Vargas-De-León https://orcid.org/0000-0001-9428-3619 INEA (2014). ¿Se está garantizando a las escuelas las condiciones necesarias para impartir una educación de calidad?. En R. Ahuja- Mara Guzmán-Mart í nez í https://orcid.org/0000-0001-9035-2699 Sanchez, V. Serrano-Cote, & L. E. Zendejas-Frutos (Eds.), Ramón Reyes-Carreto https://orcid.org/0000-0003-4120-5718 El derecho a una educación de calidad Informe (pp. 47–78). Instituto Nacional para la Evaluación de la Educación. https:// References www.inee.edu.mx/medios/informe2019/stage_04/index.html Ames, C. (1992). Classrooms: Goals, structures, and student moti- Kuyper, H., Van der Werf, M. P. C., & Lubbers, M. J. (2000). vation. Journal of Educational Psychology, 84, 261–271. Motivation, meta-cognition and self-regulation as predictors of https://doi.org/10.1037/0022-0663.84.3.261 long term educational attainment. Educational Research and Bandura, A. (1997). Self-efficacy: The exercise of control. Freeman. Evaluation, 6(3), 181–201. Barkoukis, V., Tsorbatzoudis, H., Grouios, G., & Sideridis, G. Pintrich, P. R., & De Groot, E. V. (1990). Motivational and self- (2008). 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Abstract

The goal of the study was to evaluate and adjust the model that associates mathematical motivation and learning strategies as quantitative instruments. The items related to the task value, cost, and self-efficacy were validated with Mexican students of rural areas in south-west region of Mexico between 12 and 16 years old, using 14 items that measure self-reported motivation levels. The construct validity of the mathematics motivation scale was checked using confirmatory factor analysis (CFA), by analyzing first- and second-order CFA models. The factor reliability was investigated by means of Dillon-Goldstein’s rho and Cronbach’s alpha. The model had adequate goodness of fit of in the confirmatory analysis. The instrument proved that it is convenient and reliable for application in mathematics motivation in Mexican adolescents. An advantage of the use of this instrument to be applied by teachers of mathematics is its simplicity, ease of application, and interpretation. Keywords motivation, mathematics, self-efficacy, validation, CFA models Academic motivation is related to the perceptions that stu- include a similar weight (than the cognitive one) regarding dents have of themselves and their environment which emotional and motivational aspects, which are very influen- encourages them to choose an activity, to commit to it, and to tial for performance and achievement (Echeverría Castro persevere to see it through to its conclusion. Motivation et al., 2020). The problem of motivation with respect to affects student creativity, learning styles, and academic mathematics is not new. As in other disciplines, motivation achievement (Kuyper et al., 2000) and has been shown to be has a big effect on mathematics lessons. Motivation is a con- a useful predictor of high dropout rates (Barkoukis et al., struct that makes it possible to explain the reasons for the 2008) and to have a positive correlation with high academic behavior of students in the mathematics classroom and the performance (Gottfried et al., 2007). The teaching of mathe- objectives and goals they have when attending a mathemat- matics constitutes a field of great interest for both mathemat- ics class, as well as their reasons for learning mathematics. ics teachers and pedagogues. Teachers must plan the lessons The definitions of motivation are many and varied since a with attractive activities in order to get the students’ attention wide range of theoretical points of view have been studied (Cavallo, 2002). Mathematics teachers are responsible for that try to explain it by focusing on key dimensions of moti- facilitating the development of positive attitudes toward vation, for example, self-efficacy (Bandura, 1997), attribu- mathematics from the first courses. It is not enough to work tions (Skinner et al., 1990), achievement goals (Ames, 1992), toward the student getting good grades. Academic achieve- self-concept (Guay et al., 2003), and expectation and the ment and liking a subject do not always coincide. It is pos- value of the task (Eccles et al., 1983). sible for a student who has no affection for mathematics to obtain good grades in this subject because they are respon- 1 Universidad Autónoma de Guerrero, Chilpancingo, México sible and do the work because it is necessary to advance to Hospital Juárez de México, Ciudad de México, México the next subject, but they might try to use mathematics as *These authors contributed equally to this work. little as possible and, unfortunately, forget what they have Corresponding Author: learned. Ramón Reyes-Carreto, Maestría en Matemáticas Aplicadas, Facultad de In many cases the learning of mathematics implies greater Matemáticas, Universidad Autónoma de Guerrero, Lázaro Cárdenas, difficulties for students. The psychosocial factors involved in Chilpancingo 39070, México. learning mathematics are especially relevant since they Email: rrcarreto@gmail.com Creative Commons CC BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License (https://creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/open-access-at-sage). 2 SAGE Open Expectancy-value theory is one of the most relevant moti- the structure of instrument as well as the items that compose vational theories because it has been widely used as a con- it, and the statistical analysis that was performed. In Section ceptual framework to explain motivation in different 3, the results are presented, such as the validity and reliabil- educational disciplines. The model is based on the analysis ity of the instrument, as well as the correlations of the moti- of expectations and the perceived value of homework by stu- vation constructs or factor. Finally, in Section 4, we conclude dents and its links with school performance, persistence, and with some comments. the choice of further studies, among other factors (Eccles & Wigfield, 2002). This model has shown that value beliefs and Materials and Methods expectation of success are related to effort in learning math- ematics, higher enrollment in this discipline, and perfor- Participants mance (Spinath et al., 2006; Wigfield & Eccles, 2000). The participants are boys and girls between 12 and 16 years There is a great diversity in studies on mathematical of secondary schools (technical, general, and television) of motivation. Berger and Karabenick (2011) developed an the first, second, and third grade. Secondary schools are pub- expectancy-value model with ninth grade students (usually lic and rural areas in south-west region of Mexico. Subjects 14–15 years old) in a Midwest urban high school in the U.S.A. who did not accept participate are excluded from the study. Expectancy was represented by self-concept regarding ability and self-efficacy. They proposed to measure the self-efficacy expectation scale, for which the items were selected from the Mathematics Motivation Scale self-efficacy scale of the Motivated Strategy for Learning The instrument is a self-report measure composed of 14 items Questionnaire (MSLQ) questionnaire (Pintrich et al., 1991), that measure self-reported levels of motivation. The instru- and they also evaluated the scale of task value, which was ment comprised five subscales: interest (items 1, 2, and 3), composed of four categories. The components of the task importance (items 4, 5, and 6), utility (items 7, 8, and 9), cost value were defined and evaluated by Eccles and Wigfield (items 10 and 11), and for the expectancy value, constructs (1995), who confirmed the results of Pintrich and De Groot were assessed by three items from self-efficacy (items 12, 13, (1990) that motivation predicts learners’ self-regulatory strat- and 14). All students’ responses were rated on a 5-point scale egies. Additionally, they concluded that the adaptations of the ranging from 1 (Not at all true of me) to 5 (Very true of me). items used to measure high school students’ use of learning strategies represented an improvement over those in previous versions of the MSLQ. The mathematics motivation scale CFA Models adapted by Berger and Karabenick (2011) was translated into The first-order CFA model comprised five latent factors: Spanish by Gasco and Villarroel (2017) and applied to sec- interest, importance, utility, cost, and self-efficacy, and the ondary education students between 13 and 16 years in the second order CFA model called task value is measured by the Basque Autonomous Community of Spain. However, the following three first order factors: interest, importance, and instrument in Spanish, was not studied its validity by con- utility. Both the first and second order CFA models were pro- struct, content, and criteria. posed by Berger and Karabenick (2011). The MSLQ made it possible to examine associations between motivation and self-regulation with a greater degree of precision. Actually, considerable support for the associa- Procedure tion between students’ motivational beliefs and use of learn- ing strategies exists. In the Mexican context, little research First, the main researcher contacted the secondary school has been studied motivation from the perspective of expec- directors and explained the goal of the research. Second, tancy-value theory. once the secondary school directors gave their approval, con- In literature there are some instrument proposals to sent was obtained from teachers and parents, and we informed measure motivation in mathematics in secondary schools them about the objective of the study (parents were asked to such as the Mathematics Motivation Scale of 24 items authorize their children’s participation, and assent was also (Zakariya and Massimiliano, 2021) or Mathematics obtained from child participants). Then, the students were Motivation Questionnaire of 19-items (Fiorella et al., 2021), informed of the objective of the study and of the confidenti- but the scale adapted by Berger and Karabenick (2011) is ality of the data obtained. Finally, they answered the instru- the simplest with 14 items. For this reason, our goal is to ment and one of the researchers was present in case there validate the mathematical motivation scale of Berger and were any questions or doubt. A total time of between 8 and Karabenick (2011) for Mexican secondary school students 14 minutes was required to complete the instrument. for to know the effects, correlations, and internal consis- tency of the construct or factors used to get convenient and Statistical Analyses reliable instrument for mathematics motivation scale. This work is organized as follows: in the following sec- All of the analyses described below were carried out using R tion, we detail the inclusion criteria of the sample, describe Statistical Software version 3.2.4 with the R package psych Arellano-García et al. 3 Table 1. Demographic Characteristics of Secondary School Student Participants. Boys n = 213 Girls n = 282 p-Value Age (years)* 13.19 (0.98) 13.28 (0.97) .360 Secondary school type (%)** .392 Technique 163 (76.5) 201 (71.3) General 38 (17.8) 64 (22.7) Television 12 (5.6) 17 (6.0) Grade (%)** .345 First 79 (37.1) 87 (30.9) Second 73 (34.3) 105 (37.2) Third 61 (28.6) 90 (31.9) *M(SD). **n(%). (Revelle, 2018) and lavaan (Rosseel, 2012). Results were (43.03%) of the students were boys between 12 and 16 years considered statistically significant at p < .05. old (M = 13.19, SD = 0.98), and the girls were between 12 and The validity of the mathematics motivation scale was 16 years old (M = 13.26, SD = 0.97). The average self-reported checked by CFA. We only fit CFA models because there is an score of the students in the previous mathematics course was explicit theory that suggests a specific model. The first- and 7.73 (SD = 1.30) and 8.30 (SD = 1.14) in boys and girls, second-order CFA models were conducted using the robust respectively. Demographic characteristics of the participants maximum likelihood (RML) estimator, which provides stan- grouped by sex were homogeneous (Table 1) with respect to dard errors and fit indices that are robust to the Likert nature age, secondary school type, and grade. of the items and small deviations from multivariate normal- ity. All analyses performed the full information maximum First and Second Order CFA Models likelihood (FIML) procedure, which is the most efficient method to estimate a model in which some of the variables Table 2 presents a factor structure made up of five constructs have missing values. We used the following indices to assess or factors for the first order CFA model and the second order the model fit: standardized root mean residual (SRMR), root factor called task value with your three correlated first order mean square error of approximation (RMSEA), comparative factors: interest, importance, and utility. The items were fit index (CFI), Tucker-Lewis index (TLI), and the average ordered in the factors of the original scale version. To check value explained (AVE) for items within a domain. Values the adequacy of the expected factor structure, CFAs were smaller than 0.06 for RMSEA and SRMR, and values greater conducted using the items as factor indicators. than 0.95 for CFI and TLI are considered excellent, whereas The CFA models revealed an adequate SFL (all load- values between 0.06 and 0.08 for RMSEA and SRMR, and ings > 0.62), and all confidence intervals of SFL were statis- between 0.90 and 0.95 for CFI and TLI are considered ade- tically significant (Table 2). In the first-order CFA model, all quate. AVE greater than 0.50 indicates a good fit. values of AVE indicated a good fit, except the items of the Finally, the Bartlett method was used to extract factor self-efficacy factor and the item “I believe that success in scores. Descriptive statistics of the scores and reliability math requires. . .” In the second-order CFA model, the fol- indices (Dillon-Goldstein’s rho coefficients and Cronbach’s lowing variables were values of AVE less than 0.5: the items alpha) of each of the factors that make up the measurement “I believe I will receive an excellent grade in math,” “I’m instrument were also analyzed. A coefficient value greater certain I can understand the most difficult material presented than .70 indicates a high level of internal consistency. in math,” and interest in the second-order factor. Furthermore, the correlation between domain was assessed using Pearson’s correlations. A correlation between .41 and Goodness of Fit .60 is regarded as good, one between .61 and .80 very good, and .81 is considered excellent. The first- and second-order CFA models used RML as the estimation method. The goodness-of-fit statistics and infor- mation criteria of the models estimated are presented in Results Table 3. In both models, the χ test was significant, and the following robust adjustment indicators were analyzed: Description of the Sample RMSEA, SRMR, CFI, and TLI showed an excellent good- A total of 495 participants, who were students in the first ness of fit in the first-order model and obtained adequate val- (166), second (178), and third (151) grades in secondary ues in RMSEA, SRMR, CFI, and TLI in the second-order school, participated in the study voluntarily. About 213 model. 4 SAGE Open Table 2. First- and Second-Order CFA Models. First-order factor model Second-order factor model Items Factor and items SFL 95% CI AVE SFL 95% CI AVE Factor 1: Interest 1 Me gustan las matemáticas. (I like math.) 0.805 0.750–0.859 0.648 0.810 0.757–0.863 0.656 2 Disfruto con las matemáticas. (I enjoy doing math.) 0.877 0.833–0.921 0.769 0.871 0.823–0.918 0.758 3 Las matemáticas son emocionantes. (Math is exciting 0.757 0.699–0.816 0.574 0.758 0.699–0.818 0.575 to me.) Factor 2: Importance 4 Es importante para mí ser alguien que sea bueno en 0.720 0.658–0.783 0.519 0.715 0.651–0.779 0.511 matemáticas. (It is important to me to be the kind of person who is good at math.) 5 Creo que ser bueno en matemáticas es parte 0.765 0.706–0.823 0.585 0.765 0.706–0.823 0.585 importante de mi personalidad. (I believe that being good at math is an important part of who I am.) 6 Es importante para mí ser alguien que puede razonar 0.709 0.642–0.775 0.502 0.714 0.649–0.780 0.510 utilizando fórmulas y operaciones matemáticas. (It is important to me to be a person who can reason using math formulas and operations.) Factor 3: Utility 7 Creo que las matemáticas pueden ser útiles en el 0.819 0.764–0.874 0.671 0.828 0.775–0.881 0.685 futuro porque me pueden ayudar. (I believe that math will be useful for me later in life.) 8 Creo que ser bueno en matemáticas puede ser útil 0.800 0.748–0.852 0.640 0.801 0.750–0.852 0.641 en el futuro. (I believe that math is valuable because it will help me in the future.) 9 Creo que ser bueno en matemáticas puede ser útil 0.772 0.714–0.829 0.596 0.762 0.701–0.823 0.581 para encontrar trabajo o para ir a la universidad. (I believe that being good at math will be useful when I get a job or go to college.) Factor 4: Cost 10 Tengo que dejar de hacer muchas cosas para 0.787 0.624–0.950 0.619 0.762 0.601–0.923 0.581 aprender bien matemáticas. (I have to give up a lot to do well in math.) 11 Creo que el éxito en matemáticas requiere dejar 0.687 0.543–0.832 0.472 0.710 0.557–0.863 0.504 otras actividades que me gustan. (I believe that success in math requires that I give up other activities that I enjoy.) Factor 5: Self-efficacy 12 Creo que tendré una excelente nota en matemáticas. 0.652 0.573–0.731 0.425 0.627 0.545–0.709 0.393 (I believe I will receive an excellent grade in math.) 13 Estoy seguro de que puedo entender los contenidos 0.689 0.623–0.756 0.475 0.667 0.591–0.744 0.445 más difíciles en matemáticas. (I’m certain I can understand the most difficult material presented in math.) 14 Tengo confianza en que puedo aprender los 0.706 0.641–0.771 0.498 0.745 0.683–0.808 0.556 conceptos básicos enseñados en matemáticas. (I’m confident I can learn the basic concepts taught in math.) Second-order factor: Task value Interest NA NA NA 0.618 0.511–0.726 0.382 Importance NA NA NA 0.961 0.885–1.000 0.923 Utility NA NA NA 0.790 0.715–0.866 0.625 Note. INT = interest; IMP = importance; UTL = utility; CT = cost; SELF = self-efficacy; VAL = task value; SFL = standardized factor loading; 95% CI = 95% confidence interval; AVE = average value explained; NA = not applicable. Arellano-García et al. 5 Table 3. Goodness-of-Fit Statistics of the Models Estimated. Model χ df p-Value RMSEA SRMR CFI TLI First order 114.808 67 <.001 0.044 0.038 0.977 0.969 Second order 190.447 71 <.001 0.068 0.064 0.943 0.927 Note. χ = Chi-square test; df = degrees of freedom; RMSEA = root mean square error of approximation; SRMR = standardized root mean residual; CFI = comparative fit index; TLI = Tucker-Lewis index. in this work confirmed that the first- and second-order CFA Internal Consistency models showed desirable properties in terms of construct Table 4 shows the mean and standard deviation of scores validity. The second-order CFA models is also proposed by obtained by the constructs that comprise the questionnaire. Berger and Karabenick (2011), in this study indicated that Also, this table shows the internal consistency; the question- specific construct can be formed for cognitive and resource naire presented a Dillon-Goldstein’s rho of .892 and management strategies, respectively, whereas the three types Cronbach’s alpha of .872, which indicates that it is reliable of metacognitive strategies, as interest, importance, and util- for the Mexican population, while the values obtained by ity, were explained by a single second-order factor called constructs were greater than .80. The constructs’ correlations task value. A practical importance of the second-order CFA for the CFA models were calculated. model is that the task value score was associated with the subscales of cost and self-efficacy, or with other variables or Correlation Between Constructs constructs. In addition, the mathematics motivation scale underwent Table 4 shows the correlations between all the factors were a validation process, in which it demonstrated appropriate positive, and all confidence intervals of the correlation coef- properties for research applications. An advantage of the use ficients were statistically significant except between cost and of this instrument is its simplicity, ease of application, and interest factors of the first-order model. The correlation interpretation so that it can be applied by teachers of mathe- between the importance and utility constructs was excellent. matics in rural areas since 60% of teachers of secondary Also, the correlation between the task value (second order schools in Mexico are in rural areas (INEA, 2014). factor) and cost with self-efficacy was excellent. Finally, the The objectives of this paper were limited to the validation correlation between the cost with interest, importance, and of the scale in a group of Mexican students, with the inten- utility was poor. tion of applying the scale to understand academic motivation in future research. In the same way new research can be pro- Discussion and Conclusion posed that allows observing motivation in different contexts within the Mexican educational system. In this research, the This study was conducted to provide a convenient and reliable data was obtained from rural areas of a state with unfavor- instrument for a mathematics motivation scale. The original able economic conditions. It will be interesting to observe version of the mathematics motivation scale was first devel- the relationships of these conditions with the academic moti- oped and validated in English by Berger and Karabenick vation of the respondents. (2011), followed by the Spanish version by Gasco and If we want to know the personal characteristics that make Villarroel (2017) but without validation. While the motivation a male or female student face learning activities with greater of mathematics learning can be measured from numerous per- or lesser interest or effort, either for the purpose of knowing spectives, and our validated instrument of 14-items is only one what aids to provide them with or for the purpose of predict- of these, one of its advantages is that it is one of the simplest in comparation of other instruments as the Mathematics ing what their future performance will be, what information Motivation Scale of 24 items (Zakariya and Massimiliano, should we seek? The MSLQ provides us with useful infor- 2021) or Mathematics Motivation Questionnaire of 19-items mation for teachers. Expectancy-value theory, through its (Fiorella et al., 2021). components (interest, usefulness, and importance and cost of Our study provides validation of the mathematics motiva- the task), provides clear information on the motivation of tion scale in secondary school students of rural areas in students, the value they assign to tasks, and the expectations south-west region of Mexico. The Spanish version of the they have of themselves. questionnaire showed scale consistency with the original and Our study has some limitations. The instrument was vali- had high internal consistency (Dillon-Goldstein’s rho of .892 dated in secondary school students in rural areas in south- and Cronbach’s alpha of .872). Moreover, the subscales west of Mexico. Some additional opportunities are to validate showed satisfactory internal consistency. The results obtained the instrument in urban schools or private schools. 6 Table 4. Descriptive Statistics, Internal Consistency, and Correlations Between Constructs. Descriptive statistics Internal consistency Correlations Dillon- Cronbach’s Model Construct M SD Goldstein’s rho alpha INT IMP UTL CT SELF VAL First order Interest 0.00 1.063 .919 .868 0.637 0.428 0.183 0.829 NA Second order 0.00 1.051 NA NA 0.671 0.488 0.229 0.680 0.703 First order Importance 0.00 0.904 .875 .787 0.582–0.687 0.893 0.375 0.738 NA Second order 0.00 0.902 NA NA 0.619–0.716 0.860 0.380 0.799 0.995 First order Utility 0.00 0.903 .914 .860 0.353–0.497 0.873–0.909 0.363 0.591 NA Second order 0.00 0.912 NA NA 0.418–0.552 0.835–0.881 0.334 0.658 0.882 NS First order Cost 0.00 0.915 .877 .719 0.096–0.266 0.296–0.448 0.284–0.437 0.481 NA Second order 0.00 0.879 NA NA 0.144–0.311 0.302–0.453 0.253–0.410 0.499 0.882 First order Self-efficacy 0.00 0.750 .842 .718 0.799–0.855 0.695–0.775 0.531–0.646 0.410–0.546 NA Second order 0.00 0.779 NA NA 0.630–0.725 0.765–0.829 0.605–0.705 0.430–0.562 0.833 First order Task value NA NA NA NA NA NA NA NA NA NA Second order 0.00 0.860 NA NA 0.655–0.745 0.994–0.996 0.861–0.900 0.861–0.900 0.804–0.858 Note. SD = standard deviation; INT = interest; IMP = importance; UTL = utility; CT = cost; SELF = self-efficacy; VAL = task value. Pearson’s correlation (upper triangular matrix), 95% confidence Interval (lower triangular matrix); NA = not applicable. Arellano-García et al. 7 Declaration of Conflicting Interests mathematics motivation questionnaire (mmq) for secondary school students. International Journal of STEM Education, The author(s) declared no potential conflicts of interest with respect 8(52), 1–14. to the research, authorship, and/or publication of this article. Gasco, J., & Villarroel, T. (2017). The motivation of second- ary school students in mathematical word problem solving. Funding Electronic Journal of Research in Educational Psychology, The author(s) disclosed receipt of the following financial support 12(1), 83–106. http://dx.doi.org/10.14204/ejrep.32.13076 for the research, authorship, and/or publication of this article: The Gottfried, A. E., Marcoulides, G. A., Gottfried, A. W., Oliver, P. first, second, and third authors were partially supported by H., & Guerin, D. (2007). Multivariate latent change modeling SNI-CONACYT. of developmental decline in academic intrinsic mathematics motivation and achievement: Childhood through adolescence. Ethical Approval International Journal of Behavioral Development, 31(4), 317–327. Ethics approval was not required for this study. Guay, F., Marsh, H. W., & Boivin, M. (2003). Academic self-con- cept and academic achievement: Developmental perspectives ORCID iDs on their causal ordering. Journal of Educational Psychology, Yuridia Arellano-Garca í https://orcid.org/0000-0002-7841-1470 95(1), 124–136. https://doi.org/10.1037/0022-0663.95.1.124 Cruz Vargas-De-León https://orcid.org/0000-0001-9428-3619 INEA (2014). ¿Se está garantizando a las escuelas las condiciones necesarias para impartir una educación de calidad?. En R. Ahuja- Mara Guzmán-Mart í nez í https://orcid.org/0000-0001-9035-2699 Sanchez, V. 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SAGE Open, 10(1), 1–10. ematics motivation scale: A preliminary exploratory study with Fiorella, L., Yoon, S. Y., Atit, K., Power, J. R., Panther, G., Sorby, a focus on secondary school students. International Journal of S., Uttal, D. H., & Veurink, N. (2021). Validation of the Progressive Education, 17(1), 314–324.

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Published: Mar 21, 2022

Keywords: motivation; mathematics; self-efficacy; validation; CFA models

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