Characterizing a Group of AP Statistics Teachers’ Beliefs and Practices
David J. Stokes - NC State STEM Ed Graduate Research Symposium, Spring 2021
Introduction
Purpose
The purpose of this study is to investigate the following questions:
What are the characteristics of a group of AP Statistics teachers?
What do these teachers believe and do; and how are these beliefs and actions related?
Data & Methods
The data consists of a sample of over 300 AP statistics teachers’ responses to a survey from Fall, 2018. These teachers were teaching AP Statistics at the time of the survey. Seven items from a Pedagogy section, and 18 items from a Beliefs section are used in this analysis in order to address the questions of interest. Each of the items contain responses on a 6 point likert-scale (1 = strongly disagree … 6 = strongly agree) designed to measure the intensity of teacher beliefs and practices.
Factor analysis was used to derive constructs and k-means clustering was used for teacher grouping.
Summary
This presentation will describe interpretations of underlying constructs and the relationships between these constructs based on derived teacher groups, using the 25 beliefs and practices related survey items. Results are sample specific, but may be useful for future explorations.
Exploring the Dimensionality of the Data
To gain insight into the underlying constructs represented in this data, Parallel Analysis was used in order to determine a basis for choosing a number of factors. This method compares the observed data variation explained by the number of factors to (the average of) the variation explained by randomly generated datasets of the same size. Holgado-Tello et al. (2008), recommend using polychoric correlation for categorized continuous constructs (such as those measured by likert-scale items), and this is utilized here. From the graph it can be seen that the observed variation from 8 factors is larger than the (average) variance explained by 8 factors from random correlation matrices.
Interpreting the Factors
The table below has construct headings for the 8 factors. Each of the items within these factors are related to the construct title. AP Statistics teachers with high scores on a given construct/factor are associated with stronger agreement with the represented beliefs and/or practices.
| Label | Question | Loadings |
|---|---|---|
| Factor 1: Assessment Beliefs/Practices | ||
| 15 | Students Should Be Assessed On Their Statistical Literacy e.g. Ability to Read a Graph Understand Common Statistical Words etc. | 0.801 |
| 14 | Students Should Be Assessed On Their Ability to Complete An Open Ended Statistical Problem | 0.782 |
| 13 | Formative Feedback Should Be Given On All Assessments In Order For Students to Improve Their Learning | 0.601 |
| 12 | All Assessments Should Be Regularly Reviewed to See that They Are Aligned With Student Learning Goals | 0.451 |
| Factor 2: Lecture-Based Class Dynamics | ||
| 9 | Lectures Should Be The Primary Way For Students to Learn Statistical Content | 0.841 |
| 10 | Quizzes and Exams Should Be Used As The Primary Way to Evaluate Student Learning | 0.650 |
| 19 | The Content Was Presented Mostly Through Lectures | 0.598 |
| 11 | Alternative Assessments e.g. Projects Presentations Should Be Used to Provide Important Information About Student Learning | -0.262 |
| Factor 3: Group Work-Based Class Dynamics | ||
| 22 | The Content Was Presented Mostly Through Activities | 0.698 |
| 21 | The Course Frequently Required Students to Work Together | 0.623 |
| 23 | this Course Encouraged Students to Discover Ideas On Their Own | 0.588 |
| 20 | The Instructor Asked Challenging Questions that Made Students Think | 0.387 |
| 25 | this Course Often Used Technology Other Than Graphing Calculators to Help Students Understand Concepts | 0.358 |
| Factor 4: External Beliefs | ||
| 17 | Statistics Courses Should Be Updated Continually In Response to Recommendations Such As Common Core | 0.765 |
| 16 | Statistics Courses Should Be Updated Continually to Keep Up With Advances In Technology | 0.508 |
| 18 | Statistics Instructors Should Be Actively Engaged In The Statistics Education Community | 0.416 |
| 1 | Students Should Learn Fewer Topics In Greater Depth Instead of Learning More Topics In Less Depth In An Introductory Statistics Course | 0.343 |
| Factor 5: Data Analysis Beliefs/Practices | ||
| 5 | Students Should Learn The Importance of Using Appropriate Methods For Collecting Data | 0.878 |
| 6 | Students Should Learn Connections Between The Qualityture of The Data and Inferences that Are Made | 0.612 |
| Factor 6: Probability Beliefs/Practices | ||
| 2 | Basic Rules of Probability Should Be Included In An Introductory Statistics Course | 0.808 |
| 3 | The Topic of Theoretical Probability Distributions e.g. The Binomial Distribution Should Be Included In An Introductory Statistics Course | 0.707 |
| Factor 7: Tech Use | ||
| 8 | Students Should Analyze Data Primarily Using Technology | 0.766 |
| 7 | Technology Tools Should Be Used to Illustrate Most Abstract Statistical Concepts | 0.584 |
| 4 | Students Should Learn How to Read Statistical Tables of Probability Distributions e.g. T Table Z Table | -0.329 |
| Factor 8: Graphing Calculators | ||
| 24 | Students Use Graphing Calculators Regularly In this Course | 0.539 |
Determining How to Group Teachers?
The plot below is a visual representation of the silhouette method which is a measure of average distance between points within a cluster compared to average distance between points across clusters. The number of clusters (2) was chosen from this criterion and is denoted by the maximum in the graph at the dashed line.
Describing Teacher Types
Below are boxplots of factor construct by cluster group. The purpose of this graph is to visually gain insight into the relationship between teacher beliefs and practices across constructs with respect to the cluster groups.
What do you notice in the graph?
Exploring significant differences
| Factor | F value | Pr(>F) |
|---|---|---|
| Factor 1: Assessment Beliefs/Practices | 148.47 | <0.0001* |
| Factor 2: Lecture-Based Class Dynamics | 9.35 | 0.0024* |
| Factor 3: Group Work-Based Class Dynamics | 13.42 | 0.0003* |
| Factor 4: External Beliefs | 2.80 | 0.0949 |
| Factor 5: Data Analysis Beliefs/Practices | 393.71 | <0.0001* |
| Factor 6: Probability Beliefs/Practices | 57.31 | <0.0001* |
| Factor 7: Tech Use | 1.46 | 0.2271 |
| Factor 8: Graphing Calculators | 1.86 | 0.1732 |
| Note: | ||
| * indicates significant difference |
Five Significant Differences
Interpretation
Teachers who tend to emphasize aspects of Lecture-Based Class Dynamics (factor 2) tend to de-emphasize Assessment Beliefs/Practices (factor 1), Group Work-Based Class Dynamics (factor 3), Data Analysis Beliefs/Practices (factor 5), and Probability Beliefs/Practices (factor 6). From this perspective, based on the two types of teachers, it can be said that those categorized in the manner of cluster 2 tend to be lecture-focused, more traditional teachers. These Group 2-like teachers are less concerned about course updates and aspects of teaching that go beyond the lecture method. They tend to assess students in a static manner.
On the other hand, teachers in Group 1 appear to take a more holistic approach to statistics in their beliefs and practices, and emphasize group dynamics, and components of data analysis and probability that have strong relationships with the AP statistics curriculum.
Next Steps
- Are there differential student outcomes across the two teacher groups/types?
- How does professional development look for different teacher groups/types?
Other Considerations
- Exploring different groups (number or method)
- Exploring score correlations
- Exploring/revising/eliminating different items, or those with weaker loadings
- Obtaining teacher demographics