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Teachers’ Beliefs about Mathematics, Learning, Teaching, Students, and Teachers: Perspectives from Chinese High School In-Service Mathematics Teachers

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Abstract

This study serves two purposes. The first purpose is the development and validation of a Mathematics Teachers’ Beliefs Scale (MTBS). In addition to providing a valid and reliable MTBS instrument, this study provides information on the process of developing and validating the instrument, which shall be useful for the development and validation of similar instruments. The second purpose of this study is to explore the relationship between teachers’ beliefs and their teaching experience. Using a validated MTBS, this study assessed the beliefs of four groups of Chinese high school mathematics teachers with varying years of professional teaching experience: 1–5 years (n = 25), 6–10 years (n = 70), 11–20 years (n = 48), and 21+ years (n = 28). The MTBS is composed of 26 items distributed across five subscales spanning beliefs about mathematics, learning, teaching, students, and teachers. Among the four groups, the results of this study indicate that there were no significant differences in scores on beliefs about mathematics, mathematics learning, mathematics teaching, students, and teachers. Further item analysis revealed that longer teaching experience does not necessarily mean that a teacher holds reform-oriented views. However, teachers with 6–10 years of experience were most likely to hold a more dialectic view of mathematics.

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Acknowledgments

This paper was finished during my post-doctoral research in University of Delaware with Jinfa Cai, and its research plan was made in my Ph. D study under the direction of Ping Yu. I would like to thank Jinfa Cai and Ping Yu for their intellectual guidance and much encouragement. I also gratefully acknowledge the feedback and editorial assistance from Victoria Robison, Stephen Hwang, which contributed to the paper’s improvement. Of course, any errors are solely the responsibility of the author.

Disclaimer

Any opinions expressed herein are those of the author and do not necessarily represent the views of the Philosophy and Social Science Foundation of Hunan Province or the China Scholarship Council.

Funding

The research reported in this paper was partly supported by grants from the Philosophy and Social Science Foundation of Hunan Province (No. 14YBA280) and China Scholarship Council (No.201606725016).

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Authors and Affiliations

  1. MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan, China

    Shengying Xie

  2. Department of Mathematical Sciences, University of Delaware, Newark, DE, USA

    Jinfa Cai

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  1. Shengying Xie
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  2. Jinfa Cai
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Correspondence to Shengying Xie.

Appendices

Appendix 1

Mathematics Teachers’ Beliefs Scale (MTBS)

Directions: There is no right or wrong answer for the following questions. The goal is to find out your real beliefs. For each statement below, indicate the degree to which you agree or disagree with it.

Strongly Disagree

  

Strongly Agree

1

2

3

4

M1 Mathematics knowledge is generated only by mathematicians.

M2 Once a mathematical theory has been established, it becomes the infallible law.

M3 Mathematics knowledge is static and unchangeable.

M4 The only value of mathematics knowledge is servicing in production, living, and other science.

M5 The true value of mathematical knowledge embody the ability to improve one’s thinking skills, i.e. learning mathematics will make you more intelligent.

ML1 The essence of mathematics learning is transferring knowledge into the learner’s mind.

ML2 Mastering mathematics means remembering formulas, theorems and operational rules, and using them to solve mathematical problems.

ML3 Practice makes perfect, i.e. drilling is the most important method for learning mathematics.

ML4 Mathematics learning should be as rapid and intense as possible. Students can digest the ideas later, albeit some cannot understand everything immediately.

ML5 Students’ disposition such as motivations, attitudes, social relationships and perseverance play a decisive role in learning mathematics.

MT1 Teachers should always prove the conclusions in teaching mathematics.

MT2 In teaching mathematics, one should mainly use experimental methods to prove propositions or make conclusions.

MT3 Mathematics should be taught strictly in accordance with pre-designed aims and procedures.

MT4 The key for teaching mathematics is to help students acquire knowledge; it does not really matter whether or not they understand the process of knowledge production.

MT5 When being taught mathematical concepts, the students should be allowed to generalize the common features through observations and analysis of several examples.

MT6 Mathematical propositions should first be presented to the students directly, and then the students may analyze and prove them under the teacher’s guidance.

MT7 Teaching mathematical problem solving is mainly about helping students master problem-solving models as many as possible.

MT8 In the mathematics classroom, the teacher should be the only authority or referee.

MT9 The examination results are the most effective criteria to assess teaching quality.

S1 Students’ mathematical thinking abilities develop gradually in stages.

S2 Students’ disposition factors such as motivations, attitudes, social relationships and perseverance can be improved by cultivation.

S3 There are individual differences exist in the students’ mathematics learning abilities. Mathematics might be difficult for some students.

T1 When I am confident with teaching in a class, I often get better results in teaching.

T2 Compared with pre-service teacher education, teachers’ self-reflection during their career is more helpful for them to improve teaching.

T3 Each mathematics teacher has his or her own teaching style.

T4 Outstanding mathematics teachers tend to show democracy in their classroom.

Appendix 2

Table 11 Descriptions of mathematics teacher beliefs dimensions and MTBS items
Full size table

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Xie, S., Cai, J. Teachers’ Beliefs about Mathematics, Learning, Teaching, Students, and Teachers: Perspectives from Chinese High School In-Service Mathematics Teachers. Int J of Sci and Math Educ 19, 747–769 (2021). https://doi.org/10.1007/s10763-020-10074-w

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