## 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.

## References

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.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.Aldridge, J. M., & Fraser, B. J. (2008).

*Outcomes-focused learning environments: Determinants and effects*. Rotterdam: Sense Publishers.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.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.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.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.Bell, L. M., & Aldridge, J. M. (2014).

*Student voice, teacher action research and classroom improvement (Advances in learning environments research series)*. Rotterdam: Sense Publishers.Brown, T. A. (2014).

*Confirmatory factor analysis for applied research*(2nd ed.). New York: Guilford Publications.Byrne, B. M. (2002).

*Structural equation modeling with EQS*. London: Taylor and Francis.Cattell, R. B. (1966). The scree test for number of factors.

*Multivariate Behavioral Research,**1,*245–276.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.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.Cohen, J. (1988).

*Statistical power analyses for the behavioral sciences*(2nd ed.). Hillsdale, NJ: Lawrence Erlbaum.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.Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests.

*Psychometrika,**16,*297–334.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.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.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.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.Ernest, P. (1991).

*The philosophy of mathematics education*. London: The Falmer Press.Fraser, B. J. (1990).

*Individualised Classroom Learning Environment Questionnaire*. Melbourne: Australian Council for Educational Research.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.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.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.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.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.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.Fraser, B. J., & Fisher, D. L. (1982). Predicting students’ outcomes from their perceptions of classroom psychosocial environment.

*American Educational Research Journal,**19,*498–518.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.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.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.Horn, J. L. (1965). A rationale and test for the number of factors in factor analysis.

*Psychometrika,**30,*179–185.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.Hubbard, R., & Allen, S. J. (1987). An empirical comparison of alternative methods for principal component extraction.

*Journal of Business Research,**15,*173–190.Kaiser, H. (1970). A second generation Little Jiffy.

*Psychometrika,**35,*401–415.Kaiser, H. (1974). An index of factorial simplicity.

*Psychometrika,**39,*31–36.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.Moos, R. H. (1974).

*The social climate scales: An overview*. Palo Alto, CA: Consulting Psychologists Press.Moos, R. H. (1979).

*Evaluating educational environments: Procedures, measures, findings and policy implications*. San Francisco: Jossey Bass.Munby, H. (1997). Issues of validity in science attitude measurement.

*Journal of Research in Science Teaching,**34,*337–341.Muthen, L. K., & Muthen, B. (2008).

*Mplus user’s guide*. Los Angeles: Author.NCERT. (2015).

*Class X mathematics.*New Delhi: National Council of Education Research and Training. Retrieved from www.ncert.nic.in. Accessed 10 April 2018.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.Pallant, J. (2013).

*SPSS survival manual*. Sydney: Allen & Unwin.Schmitt, T. A. (2011). Current methodological considerations in exploratory and confirmatory factor analysis.

*Journal of Psychoeducational Assessment,**29*(4), 304–321.State Government of Victoria. (2012).

*Principles of teaching and learning*. Melbourne: Author.Stevens, J. P. (1992).

*Applied multivariate statistics for the social sciences*(2nd ed.). Hillsdale, NJ: Erlbaum.Tabachnick, B. G., & Fidell, L. S. (2013).

*Using multivariate statistics*(6th ed.). Boston: Pearson Education.Taylor, B. A., & Fraser, B. J. (2013). Relationships between learning environment and mathematics anxiety.

*Learning Environments Research,**16,*297–313.Taylor, P. C., Fraser, B. J., & Fisher, D. L. (1997). Monitoring constructivist classroom learning environments.

*International Journal of Educational Research,**27,*293–302.Tobias, S. (1994). Interest, prior knowledge, and learning.

*Review of Educational Research,**64*(1), 37–54.Trochim, W. M., & Donnelly, J. P. (2006).

*The research methods knowledge base*(3rd ed.). Cincinnati, OH: Atomic Dog.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.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.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.Watkins, M. W. (2000).

*Monte Carlo PCA for parallel analysis*. State College, PA: Ed & Psych Associates.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.Yang, Y., & Green, S. B. (2011). Coefficient alpha: A reliability coefficient for the 21st century?

*Journal of Psychoeducational Assessment,**29*(4), 377–392.Zaragoza, J. M., & Fraser, B. J. (2017). Field-study classrooms as positive and enjoyable learning environments.

*Learning Environments Research,**20*(1), 1–20.Zwick, W. R., & Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain.

*Psychological Bulletin,**99,*432–442.

## Author information

### Affiliations

### Corresponding author

## 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

## About this article

### 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

Received:

Accepted:

Published:

Issue Date:

### Keywords

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