Math anxiety - performance clustering
Creators: name: Egorova, Alena
Publisher: name: OSF Registries
Year: 2023
Subjects: subject: Social and Behavioral Sciences

description: Introduction 
This study aims to examine patterns of math anxiety and performance clustering before and after an online mathematics game, From Here To There (FH2T), and investigates how students may change cluster types based on their behaviors when playing the game. 

Research Questions
Research Question 1 (RQ 1): We have already looked at these data.
How are students naturally grouped into different clusters based on their math anxiety level and math performance level?
Research Question 2 (RQ 2): We have not looked at these data
Do students from different clusters differ in their in-game math learning behaviors (i.e., pre-solving pause time, help-seeking behaviors)? 
Research Question 3 (RQ 3): We have not looked at these data
Do identified clusters predict changes in students’ math performance and math anxiety after playing a math learning game?
Research Question 4 (RQ 4): We have looked at different clusters and how they migrated, but we did not look at how in-game behaviors were associated
Do students migrate from one cluster to another after playing a math learning game? How do in-game behaviors differ in students with different migration types?

Method
Dataset
We will use data collected through a larger randomized control trial (RCT) (Ottmar et al., 2023) that compared the effectiveness of four digital math learning interventions. In RCT, 4,092 students were randomly assigned to participate in one of the digital math interventions across the school year. In this study, we will use data from From Here To There (FH2T) (Ottmar et al., 2015), one of the digital math intervention conditions, as we have detailed log files from this platform usage.

Exclusion rules
Among students in the FH2T condition (N = 1,430), we will include those who studied in person in math classrooms for the whole study period. Moreover, we will exclude observations where students’ data on at least one of our measures is missed, namely:
- for RQ1, data on pre-intervention performance (i.e., math knowledge scores) and pre-intervention math anxiety;
- for RQ2, data on pre-intervention performance, pre-intervention math anxiety, and hint usage;
- for RQ3, data on pre-intervention performance, pre-intervention math anxiety, and post-intervention math performance, post-intervention math state score, or post-intervention math anxiety;
- RQ4, data on pre-intervention performance, pre-intervention math anxiety, post-intervention performance, post-intervention math anxiety, and hint usage.

Measures
Pre-intervention and post-intervention math performance. Before and after the intervention, students completed an algebraic knowledge assessment (for details, see Decker-Woodrow et al., 2023). We will use the results of these assessments as students’ pre and post performance indicators. As a second performance indicator, we will use students' end-of-year state assessment scores provided by the school district.
Pre-intervention and post-intervention math anxiety levels. Before and after the intervention, students completed Math Anxiety Scale for Young Children-Revised (Ganley &amp; McGraw, 2016) as their math anxiety assessment. We will use the results of these assessments as students’ pre and post math anxiety indicators. 
Pre-solving pause time. We will use log files from FH2T to measure pre-solving pause time (hereafter, pause time). The pause time refers to the time taken between when the problem was shown on the screen and when the student made the first action. It will be calculated by pre-solving pause time divided by total problem-solving time. 
Hint usage. We will use log files from FH2T to determine the number of times students used hints while working on the problems.
Gender. Information about students’ gender was provided to researchers by the schools.

Data Analysis
We will run all models using R Studio software. For standardization, we will apply min-max scaling to variables used in cluster analysis.
Prior to the pre registration, for RQ 1, we ran a k-means clustering analysis to find groups of observations that had similar levels of Pre-Intervention Math Performance measures and Pre-Intervention Math Anxiety measures. Specifically, to determine the number of clusters, we used the fviz_nbclust function from the “factoextra” package and used the Elbow Method (i.e., calculating within-cluster sums of squared errors method) . Then we applied k-means clustering using the kmeans function from the “stats” package. While these steps were already conducted, we provide these details here for full reporting. 
For RQ 2, we will compare the resulting clusters by their pre-solving pause time and hint usage. Any transformations of the data necessary will be conducted and theoretically justified depending on the distributions of the data. 
For RQ 3, we will run several linear models with clusters identified in the RQ1 as a predictor. Specifically, we will run three models with three potential outcome variables: post-intervention math anxiety scores, post-intervention performance scores, and state assessment scores. We will control for gender, as other studies previously showed gender could be related to math anxiety (Van Mier et al., 2019).
For RQ 4, we will create a Sankey diagram to depict migration between clusters after playing a math learning game. We will also compare the in-game behaviors (i.e., pre-solving pause time and hint usage) of several distinct migration groups to unpack why the movement occurred. These analyses will be largely exploratory. 

What has been done already
The data have already been collected as a part of a larger scale efficacy study (described above). In addition, we have completed the data analyses for RQ1. Specifically, we clustered students based on their pre-intervention math anxiety levels and math performance. We also partially completed the data analyses for RQ4. We clustered students based on their post-intervention math anxiety levels and math performance, but did not look at their in-game behavior differences. Those results will be presented and discussed in the full paper.

Prior publications
In prior research, all the variables that we plan to analyze in this study have been used in other studies. However, none of the prior studies clustered students based on their math anxiety and math performance or delved deeper into such student profiles. Prior publications using the FH2T math performance and anxiety data from the larger studies that included at least two same variables as we plan to use are listed below:
Chan, J. Y. C., Lee, J. E., Mason, C. A., Sawrey, K., &amp; Ottmar, E. (2022). From Here to There! A dynamic algebraic notation system improves understanding of equivalence in middle-school students. Journal of Educational Psychology, 114(1), 56.
Chan, J. Y. C., Closser, A. H., Ngo, V., Smith, H., Liu, A. S., &amp; Ottmar, E. (2023). Examining shifts in conceptual knowledge, procedural knowledge and procedural flexibility in the context of two game‐based technologies. Journal of Computer Assisted Learning.
Egorova, A., Liu, A., Shaw, S., Sales, A., &amp; Ottmar, E. (submitted). Game-Based Math Intervention's Effect on Math Anxiety and Its Variation across Classrooms. The Journal of Educational Research.
Iannacchione, A., Ottmar, E., Ngo, V., Mason, C. A., Chan, J. Y. C., Smith, H., ... &amp; Shaw, S. T. (2022). Examining relations between math anxiety, prior knowledge, hint usage, and performance of math equivalence in two different online learning contexts. Instructional Science, 1-23.
Decker-Woodrow, L., Mason, C., Chan, J., Lee, J. E., Sales, A. C., Liu, A., &amp; Tu, S. The impacts of three educational technologies on algebraic understanding in the context of COVID-19. AERA Open, 9.
Lee, J. E., Chan, J. Y. C., Botelho, A., &amp; Ottmar, E. (2022). Does slow and steady win the race?: Clustering patterns of students’ behaviors in an interactive online mathematics game. Educational Technology Research and Development, 70(5), 1575-1599.
Chan, J. Y. C., Ottmar, E. R., &amp; Lee, J. E. (2022). Slow down to speed up: Longer pause time before solving problems relates to higher strategy efficiency. Learning and Individual Differences, 93, 102109.
Lee, J. E., Jindal, A., Patki, S. N., Gurung, A., Norum, R., &amp; Ottmar, E. (2023). A comparison of machine learning algorithms for predicting student performance in an online mathematics game. Interactive Learning Environments, 1-15.