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Offering an Approach to Measure Beliefs Quantitatively: Capturing the Influence of Students’ Abilities on Teachers’ Beliefs

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Abstract

Studies measuring teachers’ beliefs quantitatively by using self-report Likert scale instruments often face methodological difficulties. Such difficulties might be due to the fact that those instruments often provide less or no contexts. Whereas, several studies have shown that contexts at school, particularly contexts related to students’ abilities, may influence teachers’ beliefs. To overcome such difficulties, we offer an approach by using rank-then-rate items instead of Likert scale items and by explicitly taking into account students’ abilities within a questionnaire. In this study, we had 43 Indonesian teachers answering this questionnaire to investigate how students’ abilities influence teachers’ beliefs about teaching and learning of mathematics and problem solving as well as the interrelation between these beliefs with their beliefs about mathematics. The results suggest that teachers may elicit different beliefs about teaching and learning in the context of students’ abilities. Furthermore, we found that teachers’ beliefs about mathematics correlate with their beliefs about teaching and learning in the context of low ability students, but not in the context of high ability students.

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Funding

This research is supported by Directorate General of Resources for Research, Technology and Higher Education of Indonesia (Contract Number 101.20/E4.4/2015).

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Authors and Affiliations

  1. Department of Mathematics Education, Mulawarman University, Samarinda, Indonesia

    Safrudiannur

  2. Institute of Mathematics Education, University of Cologne, Cologne, Germany

    Safrudiannur & Benjamin Rott

Authors
  1. Safrudiannur
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  2. Benjamin Rott
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Correspondence to Safrudiannur.

Appendix

Appendix

The structure of the TBTP

General note: As a mathematics teacher, you may have experience with high and low ability students in mathematics. Consider these definitions:

A high-ability (HA) student is a student who generally shows good understanding in your lessons and regularly has high scores in your tests. A low-ability (LA) student is a student who generally does not show good understanding in your lessons and often has low scores in your tests.

To answer all questions, you will be asked first to imagine that you have a class dominated by HA students and then to imagine that you have a class dominated by LA students.

Theme 1: Teaching and learning of mathematics.

Note: You are going to teach a lesson learning the formula to calculate the area of a trapezoid. Please imagine this situation to answer items 1 to 4.

Theme 2: Teaching and learning of problem solving.

Note: In problem solving, there are several definitions of a mathematical problem. Below is one of the definitions of the mathematical problem: A math problem is a task which there is no obvious or straightforward solution method to solve it.

According to the definition, a task is not a mathematical problem if it can be solved by simply applying methods taught previously. Please, see the example to understand the definition better.

Example. You explained how to calculate the average of the following data: 20, 16, 18, 28, 22, and 20. Then you give this following task: The height of six basketball players is 196 cm, 200 cm, 190 cm, 185 cm, 192 cm, and 200 cm. Find the average height of those six players! Although this mathematical task is related to the real world, the task is not categorised as a mathematical problem according to the definition because your students can simply apply how to calculate the average from what you have taught. Now, have a look at the following task: The average weight of six futsal players is 65 kg. After substitution, the new average weight is 63.5 kg. If the weight of the player who left is 64 kg, find the weight of the new player!

According to the definition, this task can be categorised as a mathematical problem because the students cannot simply apply what you have taught. Please use only this definition to answer items 5 to 8.

Theme 3: The nature of mathematics.

Note: Mathematics contents taught at school can be divided into several sub-domains such as numbers, algebra, geometry, measurements, statistics, and probability. The classifications of mathematics contents in general are more complex. For example, classical algebra, linear algebra, number theory, differential geometry, calculus, statistics, probability theory, etc.

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Safrudiannur, Rott, B. Offering an Approach to Measure Beliefs Quantitatively: Capturing the Influence of Students’ Abilities on Teachers’ Beliefs. Int J of Sci and Math Educ 19, 419–441 (2021). https://doi.org/10.1007/s10763-020-10063-z

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