Students’ perceptions of mathematics classroom learning environments: measurement and associations with achievement

Abstract

In this study, we measured students’ perceptions of mathematics classroom learning environment and investigated their associations with students’ achievement. The Mathematics-Related Constructivist-Oriented Classroom Learning Environment Survey (MCOLES) was developed with seven dimensions and 56 items, using theories surrounding classroom learning environment. For a sample of 423 grade 10 students from five schools in India, we validated the MCOLES by exploratory factor analysis and then by confirmatory factor analysis, which suggested the exclusion of 11 items and yielded an 11-factor solution. For achievement on a topic taught, mainly medium correlations emerged with the learning environment factors, suggesting practical implications for classroom teaching. This study is methodologically significant in proposing and validating the new MCOLES for measuring classroom learning environments in secondary-school mathematics.

This is a preview of subscription content, access via your institution.

Fig. 1

References

  1. Afari, E., Aldridge, J. M., Fraser, B. J., & Khine, M. S. (2013). Students’ perceptions of the learning environment and attitudes in game-based mathematics classrooms. Learning Environments Research, 16, 131–150.

    Article  Google Scholar 

  2. Aldridge, J., Fraser, B., Bell, L., & Dorman, J. (2012). Using a new learning environment questionnaire for reflection in teacher action research. Journal of Science Teacher Education, 23(3), 259–290.

    Article  Google Scholar 

  3. Aldridge, J. M., & Fraser, B. J. (2008). Outcomes-focused learning environments: Determinants and effects. Rotterdam: Sense Publishers.

    Google Scholar 

  4. Aldridge, J. M., Fraser, B. J., & Huang, I. T.-C. (1999). Investigating classroom environments in Taiwan and Australia with multiple research methods. Journal of Educational Research, 93, 48–62.

    Article  Google Scholar 

  5. Aldridge, J. M., Fraser, B. J., & Sebela, M. P. (2004). Using teacher action research to promote constructivist learning environments in South Africa. South African Journal of Education, 24, 245–253.

    Google Scholar 

  6. Aldridge, J. M., Fraser, B. J., Taylor, P. C., & Chen, C. C. (2000). Constructivist learning environments in a cross-national study in Taiwan and Australia. International Journal of Science Education, 22(1), 37–55.

    Article  Google Scholar 

  7. Bartlett, M. S. (1954). A note on the multiplying factors for various Chi square approximations. Journal of the Royal Statistical Society, 16 (Series B), 296–298.

    Google Scholar 

  8. Bell, L. M., & Aldridge, J. M. (2014). Student voice, teacher action research and classroom improvement (Advances in learning environments research series). Rotterdam: Sense Publishers.

    Google Scholar 

  9. Brown, T. A. (2014). Confirmatory factor analysis for applied research (2nd ed.). New York: Guilford Publications.

    Google Scholar 

  10. Byrne, B. M. (2002). Structural equation modeling with EQS. London: Taylor and Francis.

    Google Scholar 

  11. Cattell, R. B. (1966). The scree test for number of factors. Multivariate Behavioral Research, 1, 245–276.

    Article  Google Scholar 

  12. Chionh, Y. H., & Fraser, B. J. (2009). Classroom environment, achievement, attitudes and self-esteem in geography and mathematics in Singapore. International Research in Geographical and Environmental Education, 18, 29–44.

    Article  Google Scholar 

  13. Chipangura, A. T. (2014). Multimedia in high school mathematics classes: Students’ perceptions of the learning environment and engagement. Unpublished Ph.D. thesis, Curtin University, Perth, Australia.

  14. Cohen, J. (1988). Statistical power analyses for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  15. Cohn, S. T., & Fraser, B. J. (2016). Effectiveness of student response systems in terms of learning environment, attitudes and achievement. Learning Environments Research, 19, 153–167.

    Article  Google Scholar 

  16. Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297–334.

    Article  Google Scholar 

  17. Dochy, F. J. R. C. (1996). Assessment of domain-specific and domain-transcending prior knowledge: Entry assessment and the use of profile analysis. In M. Birenbaum & F. J. R. C. Dochy (Eds.), Alternatives in assessment of achievements, learning processes and prior knowledge (pp. 227–264). Boston: Kluwer.

    Google Scholar 

  18. Dochy, F. J. R. C., Segers, M., & Buehl, M. M. (1999). The relation between assessment practices and outcomes of studies: The case of research on prior knowledge. Review of Educational Research, 69(2), 145–186.

    Article  Google Scholar 

  19. Dorman, J. P. (2008). Use of multitrait-multimethod modelling to validate actual and preferred forms of the What Is Happening In this Class? (WIHIC) questionnaire. Learning Environments Research, 11, 179–197.

    Article  Google Scholar 

  20. Earle, J. E., & Fraser, B. J. (2017). Evaluating online resources in terms of learning environment and student attitudes in middle-grade mathematics classes. Learning Environments Research, 20, 339–364.

    Article  Google Scholar 

  21. Ernest, P. (1991). The philosophy of mathematics education. London: The Falmer Press.

    Google Scholar 

  22. Fraser, B. J. (1990). Individualised Classroom Learning Environment Questionnaire. Melbourne: Australian Council for Educational Research.

    Google Scholar 

  23. Fraser, B. J. (2002). Learning environments research: Yesterday, today and tomorrow. In S. C. Goh & M. S. Khine (Eds.), Studies in educational environments: An international perspective (pp. 1–25). Singapore: World Scientific.

    Google Scholar 

  24. Fraser, B. J. (2012). Classroom learning environments: Retrospect, context and prospect. In B. J. Fraser, K. G. Tobin, & C. J. McRobbie (Eds.), Second international handbook of science education (pp. 1191–1239). New York: Springer.

    Google Scholar 

  25. Fraser, B. J. (2014). Classroom learning environments: Historical and contemporary perspectives. In N. G. Lederman & S. K. Abell (Eds.), Handbook of research on science education (Vol. II, pp. 104–119). New York: Routledge.

    Google Scholar 

  26. Fraser, B. J. (2018). Milestones in the evolution of the learning environments field over the past three decades. In D. B. Zandvliet & B. J. Fraser (Eds.), Thirty years of learning environments research: Looking back and looking forward (pp. 1–19). Rotterdam: Brill ׀ Sense.

    Google Scholar 

  27. Fraser, B. J., & Aldridge, J. M. (2017). Improving classrooms through assessment of learning environments. In J. P. Bakken (Ed.), classrooms (Vol. 1, pp. 91–107)., Assessment practices for teachers and student improvement strategies New York: Nova.

    Google Scholar 

  28. Fraser, B. J., & Butts, W. L. (1982). Relationship between perceived levels of classroom individualization and science-related attitudes. Journal of Research in Science Teaching, 19(2), 143–154.

    Article  Google Scholar 

  29. Fraser, B. J., & Fisher, D. L. (1982). Predicting students’ outcomes from their perceptions of classroom psychosocial environment. American Educational Research Journal, 19, 498–518.

    Article  Google Scholar 

  30. Hailikari, T., Nevgi, A., & Komulainen, E. (2008). Academic self-beliefs and prior knowledge as predictors of student achievement in mathematics: A structural model. Educational Psychology, 28(1), 59–71.

    Article  Google Scholar 

  31. Hair, J. F., Jr., Black, W. C., Babin, B. J., & Anderson, R. E. (2010). Multivariate data analysis (7th ed.). Upper Saddle River, NJ: Prentice Hall.

    Google Scholar 

  32. Hanke, C. Y. C., & Fraser, B. J. (2013, April). Cross-national study of classroom environments, attitudes and academic self-efficacy in middle school mathematics. Paper presented at annual meeting of American Educational Research Association, San Francisco.

  33. Horn, J. L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30, 179–185.

    Article  Google Scholar 

  34. Hu, L., & Bentler, P. M. (1999). Cut off criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6, 1–55.

    Article  Google Scholar 

  35. Hubbard, R., & Allen, S. J. (1987). An empirical comparison of alternative methods for principal component extraction. Journal of Business Research, 15, 173–190.

    Article  Google Scholar 

  36. Kaiser, H. (1970). A second generation Little Jiffy. Psychometrika, 35, 401–415.

    Article  Google Scholar 

  37. Kaiser, H. (1974). An index of factorial simplicity. Psychometrika, 39, 31–36.

    Article  Google Scholar 

  38. Koh, N. K., & Fraser, B. J. (2014). Learning environment associated with use of mixed mode delivery model among secondary business studies students in Singapore. Learning Environments Research, 17(2), 157–171.

    Article  Google Scholar 

  39. Moos, R. H. (1974). The social climate scales: An overview. Palo Alto, CA: Consulting Psychologists Press.

    Google Scholar 

  40. Moos, R. H. (1979). Evaluating educational environments: Procedures, measures, findings and policy implications. San Francisco: Jossey Bass.

    Google Scholar 

  41. Munby, H. (1997). Issues of validity in science attitude measurement. Journal of Research in Science Teaching, 34, 337–341.

    Article  Google Scholar 

  42. Muthen, L. K., & Muthen, B. (2008). Mplus user’s guide. Los Angeles: Author.

    Google Scholar 

  43. NCERT. (2015). Class X mathematics. New Delhi: National Council of Education Research and Training. Retrieved from www.ncert.nic.in. Accessed 10 April 2018.

  44. Ogbuehi, P. I., & Fraser, B. J. (2007). Learning environment, attitudes and conceptual development associated with innovative strategies in middle-school mathematics. Learning Environments Research, 10, 101–114.

    Article  Google Scholar 

  45. Pallant, J. (2013). SPSS survival manual. Sydney: Allen & Unwin.

    Google Scholar 

  46. Schmitt, T. A. (2011). Current methodological considerations in exploratory and confirmatory factor analysis. Journal of Psychoeducational Assessment, 29(4), 304–321.

    Article  Google Scholar 

  47. State Government of Victoria. (2012). Principles of teaching and learning. Melbourne: Author.

    Google Scholar 

  48. Stevens, J. P. (1992). Applied multivariate statistics for the social sciences (2nd ed.). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  49. Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics (6th ed.). Boston: Pearson Education.

    Google Scholar 

  50. Taylor, B. A., & Fraser, B. J. (2013). Relationships between learning environment and mathematics anxiety. Learning Environments Research, 16, 297–313.

    Article  Google Scholar 

  51. Taylor, P. C., Fraser, B. J., & Fisher, D. L. (1997). Monitoring constructivist classroom learning environments. International Journal of Educational Research, 27, 293–302.

    Article  Google Scholar 

  52. Tobias, S. (1994). Interest, prior knowledge, and learning. Review of Educational Research, 64(1), 37–54.

    Article  Google Scholar 

  53. Trochim, W. M., & Donnelly, J. P. (2006). The research methods knowledge base (3rd ed.). Cincinnati, OH: Atomic Dog.

    Google Scholar 

  54. Velayutham, S., & Aldridge, J. M. (2013). Influence of psychosocial classroom environment on students’ motivation and self-regulation in science learning: A structural equation modeling approach. Research in Science Education, 43, 507–527.

    Article  Google Scholar 

  55. Velayutham, S., Aldridge, J. M., & Fraser, B. J. (2011). Development and validation of an instrument to measure students’ motivation and self-regulation in science learning. International Journal of Science Education, 33, 2159–2179.

    Article  Google Scholar 

  56. von Glasersfeld, E. (2000). Problems of constructivism. In L. P. Steffe & P. W. Thompson (Eds.), Radical constructivism in action: Building on the pioneering work of Ernst Glasersfeld (pp. 3–9). New York: Routledge.

    Google Scholar 

  57. Watkins, M. W. (2000). Monte Carlo PCA for parallel analysis. State College, PA: Ed & Psych Associates.

    Google Scholar 

  58. Wood, T., & Turner-Vorbeck, T. (2001). Extending the conception of the mathematics teaching. In T. Wood, B. S. Nelson, & J. Warfield (Eds.), Beyond classical pedagogy (pp. 185–208). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  59. Yang, Y., & Green, S. B. (2011). Coefficient alpha: A reliability coefficient for the 21st century? Journal of Psychoeducational Assessment, 29(4), 377–392.

    Article  Google Scholar 

  60. Zaragoza, J. M., & Fraser, B. J. (2017). Field-study classrooms as positive and enjoyable learning environments. Learning Environments Research, 20(1), 1–20.

    Article  Google Scholar 

  61. Zwick, W. R., & Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99, 432–442.

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Barry J. Fraser.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix: Listing of items in Mathematics-Related Constructivist-Oriented Learning Environment Survey (MCOLES)

Appendix: Listing of items in Mathematics-Related Constructivist-Oriented Learning Environment Survey (MCOLES)

Student Cohesiveness and Personal Relevance
1. I make friends with many students in my mathematics class and many of them are already my friends
2. I know other students in my mathematics class and I work well with them
3. Students in my mathematics class like me because I am friendly with them
4. I help other class members who are having trouble with their mathematics work, and they help me too
5. I relate what I learn in my mathematics class to my life outside school and connect it
6. I draw on my past experiences and apply them to the work in my mathematics class
7. What I learn in my mathematics class is relevant to my everyday life in my school and outside
8. My mathematics class is relevant to my life because I get an understanding of life even outside of school
Teacher Support
9. My mathematics teacher is interested in my mathematics problems
10. My mathematics teacher goes out of his/her way to help me
11. My mathematics teacher considers my feelings
12. My teacher helps me when I have trouble with my mathematics work
13. My mathematics teacher talks with me about mathematics work
14. My mathematics teacher takes an interest in my progress
15. My mathematics teacher moves about the class to talk with me
16. My mathematics teacher’s questions help me to understand
Involvement
17. I discuss ideas in my mathematics class
18. I give my opinions during mathematics class discussions
19. My mathematics teacher asks me questions
20. I contribute to mathematics discussions in my class with my ideas and suggestions
21. I ask my mathematics teacher questions
22. I explain my mathematics ideas to my peers
23. Students discuss with me how to go about solving problems
24. I am asked to explain how I solve problems
Task orientation by Cooperation
25. I cooperate with other students and learn from them when doing mathematics assignment work in the class
26. I share my mathematics books and resources with other students and cooperate with them when doing mathematics assignments in mathematics class
27. When I work with others in groups in mathematics class, we work as a team to achieve class goals
28. I work on mathematics tasks with other students in my class
29. I know getting a certain amount of mathematics work done is important and how much of mathematics work I have to do
30. I try to understand the mathematics work that I am required to do when completing a mathematics task
31. I know the goals set for my mathematics class
32. I am ready to pay attention to my mathematics teacher from the beginning until the end of the class
Equity
33. My mathematics teacher gives me as much attention as to other students in my mathematics class
34. My mathematics teacher helps me as much as he does to others in my mathematics class
35. I have the same amount of say in my mathematics class as other students
36. I am treated the same as other students in my mathematics class
37. I receive the same encouragement from my mathematics teacher as other students do
38. I get the same opportunity to contribute to mathematics class discussions as other students
39. My mathematics work receives as much praise as other students’ work
40. I get the same opportunity to answer mathematics questions as other students
Differentiation
41. I work at the speed which suits my mathematics ability
42. Students who work faster than me can move on to the next mathematics topic
43. I choose mathematics tasks suited to my interest
44. The mathematics tasks that are used in my class are suited to my interest
46. I use different mathematics materials from those used by other students
47. I use different mathematics assessment methods from other students
48. I do mathematics work that is different from other students’ work
49. For improving my mathematics learning I use feedback from assessment tasks and understand their link with classroom activities
50. Mathematics assessment tasks are an important part of my learning as they help me to recognise my weaknesses in mathematics understanding
51. Mathematics assessment tasks help me to understand the topic
52. I find the mathematics assessment tasks meaningful and helpful to monitor my own learning
53. The criteria for mathematics assessment are clear to me as they inform me which activities and tasks are used to assess my performance
54. The requirements for assessment tasks are clear to me and I know what types of information I need for completing such tasks
55. I understand how my teacher judges my work from my teacher’s instructions for doing assessment tasks
56. I know how to complete different assessment tasks successfully

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Aluri, V.L.N., Fraser, B.J. Students’ perceptions of mathematics classroom learning environments: measurement and associations with achievement. Learning Environ Res 22, 409–426 (2019). https://doi.org/10.1007/s10984-019-09282-1

Download citation

Keywords

  • Achievement
  • Learning environment
  • Mathematics education
  • Mathematics-Related Constructivist-Oriented Learning Environment Survey (MCOLES)
  • Validity