Students’ Beliefs about Mathematics

by The Mathematicians

Summary

We conduct the project because we want to investigate students’ beliefs about Mathematics. And in detail, we want to research into the following questions:

1. How are answers distributed between students in different schools & genders?
2. Are there any correlations between answers?
3. How do the answers of students differ from the expected answers?

The data we used to analyse comes from an anonymous survey regarding “Beliefs about Mathematics” which was completed by students of the University of Edinburgh for the academic year 2019-2020. The survey has 32 questions (one of them is a filter question, so only 31 questions actually investigate the beliefs of students). We mainly used three data sets during the analysis. They are results of the survey, gender, and the experts’ answers for each question. All these data sets are anonymous and each student is given an anonymous ID.

Before we approach these questions, we tried two different methods of assigning a numeric mark/score to categorical answers such as “Agree” and “Disagree”. The methods are the following:

1. Each student will get 1 mark for answering the question at the same direction as the experts (e.g. “Agree” and “Strongly Agree” is at the same direction as “Agree”) and 0 otherwise.
2. For questions of which expected answers are “Agree”, we could give marks for “Strongly Agree”, “Agree”, “Neutral”, “Disagree” and “Strongly Disagree” as follows: 2, 1, 0, -1, -2. vice versa.

We used both methods in question 3 and it turned out that the first method is better because as the answer from the experts comes in only two variants (“agree” and ““disagree”), and we cannot know to what degree they actually agree with a choice like the one that’s been given to the students (So it doesn’t make sense that “Strongly Agree” necessarily earns more marks than “Agree”).

For the third question, using the first method, our visualisation is shown as followed.

For the first question, our analysis shows that, first of all, the average number of “correct answers” (answers that are in the same direction as the experts’ answer) ranked by schools is shown as follows:

• School of Mathematics (22.7)
• School of Physics and Astronomy (21.8)
• School of Informatics (20.5)
• School of Philosophy, Psychology and Language Science (19.8)
• School of Economics (18.6)

Also, if we consider questions individually, we found that the rate of correctness for each question follows a pattern that’s similar to all schools. It means that although the overall average marks are different, schools tend to do better/worse on similar questions.
When it comes to gender, first of all, we found that the overall average marks for males and females are very close (male: 21 vs. female: 20.9). However, if we consider questions individually, we found that females answered better in questions related to “Nature of the Answers” (Whether answers to mathematical questions are just numbers or reveals deeper concepts) while males answered better in questions related to “Persistence in Problem Solving”.

For the second question, first of all, we put questions into different categories based on the research by Code et al. (See References). The categories and their corresponding questions are listed below:

• Persistence in Problem Solving: Questions No.8, 10, 24, 29
• Growth Mindset: Question No.5, 6, 22, 31
• Interest in Mathematics: Question No.12, 26, 32
• Relationship between Mathematics and Real World: Question No.13, 15, 21
• Sense Making: Question No.3, 4, 11, 18, 23
• Nature of the Answers: Question No.2, 7, 9, 16, 28, 30
• No category: Question No.25, 27

After that, we tested the linear correlation of each pair of the categories using Pearson correlation coefficient. However, there are no pair of categories that can get a coefficient greater than 0.4. So it means that these categories don’t have significant linear correlations.
As a result, we then tried to fit a logistic regression model to each pair of the categories. In order to apply logistic regression, we decided that for each category, we will calculate a “critical” number such that when this category is a dependent variable, the total mark students obtained from questions in this category will be converted to 0 if their raw total marks are lower than the number, otherwise it will be 1.

Then, we fit a logistic regression model for each pair of these categories and calculated their AUCs to assess how well these models perform. The results show that the model relating “Interest” (dependent) and “Confidence” (independent) has the highest AUC (0.8321314), meaning it’s doing the best. The model generally shows that if a student answers more questions in the category “Confidence” correctly, there is a higher possibility for him to answer more than 1/3 questions in the category “Interest” correctly.

Presentation

Our presentation can be found here.

Data

Data provided by Dr. George Kinnear

References

Code, W., Merchant, S., Maciejewski, W., Thomas, M., & Lo, J. (2016). The Mathematics Attitudes and Perceptions Survey: an instrument to assess expert-like views and dispositions among undergraduate mathematics students. International Journal of Mathematical Education in Science and Technology, 47(6), 917–937. https://doi.org/10.1080/0020739X.2015.1133854

Liddell, T. M., & Kruschke, J. K. (2018). Analyzing ordinal data with metric models: What could possibly go wrong? Journal of Experimental Social Psychology, 79, 328–348. https://doi.org/10.1016/J.JESP.2018.08.009