Creating Diagnostic Assessments: Automated Distractor Generation with Integrity

The goal of this paper is to propose a new method to generate multiple-choice items that can make creating quality assessments faster and more efficient, solving a practical issue that many instructors face. There are currently no systematic, efficient methods available to generate quality distractors (plausible but incorrect options that students choose), which are necessary for multiple-choice assessments that accurately assess students’ knowledge. We propose two methods to use technology to generate quality multiple-choice assessments: (1) manipulating the mathematical problem to emulate common student misconceptions or errors and (2) disguising options to protect the integrity of multiple-choice tests. By linking options to common student misconceptions and errors, instructors can potentially use multiple-choice assessments as personalized diagnostic tools that can target and modify underlying misconceptions. Moreover, using technology to generate these quality distractors would allow for assessments to be developed efficiently, in terms of both time and resources. The method to disguise the options generated would have the added benefit of preventing students from working backwards from options to solution and thus would protect the integrity of the assessment. Preliminary results are included to exhibit the effectiveness of the proposed methods

Investigating the Development of Proof Comprehension: The Case of Proof by Contradiction

This dissertation reports on an investigation of transition-to-proof students\u27 understanding of proof by contradiction. A plethora of research on the construction aspect of proof by contradiction is available and suggests that the method is one of the most difficult for students to construct and comprehend. However, there is little research on the students\u27 comprehension of proofs and, in particular, proofs by contradiction. This study aims to fill this gap in the literature. Applying the cognitive lens of Action-Process-Object-Schema (APOS) Theory to proof by contradiction, this study proposes a preliminary genetic decomposition for how a student might construct the concept `proof by contradiction\u27 and a series of five teaching interventions based on this preliminary genetic decomposition. Data was analyzed in two ways: (1) group analysis of the first two teaching interventions to consider students\u27 initial conceptions of the proof method and (2) case study analysis of two individuals to consider how students\u27 understanding developed over time. The genetic decomposition and teaching interventions were then revised based on the results of the data analysis. This study concludes with implications for teaching the concept of proof by contradiction and suggestions for further research on the topic

Cognitive Trajectory of Proof by Contradiction for Transition-To-Proof Students

History and research on proof by contradiction suggests proof by contradiction is difficult for students in a number of ways. Students’ comprehension of already-written proofs by contradiction is one such aspect that has received relatively little attention. Applying the cognitive lens of Action-Process-Object-Schema (APOS) Theory to proof by contradiction, we constructed and tested a cognitive model that describes how a student might construct the concept ‘proof by contradiction’ in an introduction to proof course. Data for this study was collected from students in a series of five teaching interventions focused on proof by contradiction. This paper will report on two participants as case studies to illustrate that our cognitive trajectory for proof by contradiction is a useful model for describing how students may come to understand the proof method

A Case Study of Community of Inquiry Presences and Cognitive Load in Asynchronous Online STEM Courses

The design and facilitation of asynchronous online courses can have notable impacts on students related to persistence, performance, and perspectives. This case study presents current conditions for cognitive load and Community of Inquiry (CoI) presences in an asynchronous online introductory undergraduate STEM course. Researchers present the novel use of Python script to clean and organize data and a simplification of the instructional efficiency calculation for use of anonymous data. Key relationships between cognitive load and CoI presences are found through validated use of NASA-TLX instrument and transcript analysis of discussion posts. The data show that student presences are not consistent throughout a course but are consistent across sections. Instructor presences are not consistent throughout a course or across sections. The study also explored predominant factors within each presence, confirming previous reports of low cognitive presence in discussions. The highest extraneous cognitive load was reported for understanding expectations and preparing an initial post. These results provide support for improvements to course design and instructor professional development to promote Community of Inquiry and reduce extraneous cognitive load

Instructional Efficiency in Asynchronous Online Discussions

Cognitive load mitigation strategies & community of inquiry framework are not discipline specific

Investigating Community of Inquiry and Cognitive Load

This project will design and research a pilot program for infusing best practices into online discussion forums in STEM courses to reduce extraneous load, improve instructional presence, instructor social presence, student social presence, and student cognitive presence

A Case Study of Community of Inquiry Presences and Cognitive Load in Asynchronous Online STEM Courses

The design and facilitation of asynchronous online courses can have notable impacts on students related to persistence, performance, and perspectives. This case study presents current conditions for cognitive load and Community of Inquiry (CoI) presences in an asynchronous online introductory undergraduate STEM course. Researchers present the novel use of Python script to clean and organize data and a simplification of the instructional efficiency calculation for use of anonymous data. Key relationships between cognitive load and CoI presences are found through validated use of NASA-TLX instrument and transcript analysis of discussion posts. The data show that student presences are not consistent throughout a course but are consistent across sections. Instructor presences are not consistent throughout a course or across sections. The study also explored predominant factors within each presence, confirming previous reports of low cognitive presence in discussions. The highest extraneous cognitive load was reported for understanding expectations and preparing an initial post. These results provide support for improvements to course design and instructor professional development to promote Community of Inquiry and reduce extraneous cognitive load

Students\u27 Understanding of the Concepts Involved in One-Sample Hypothesis Testing

Hypothesis testing is a prevalent method of inference used to test a claim about a population parameter based on sample data, and it is a central concept in many introductory statistics courses. At the same time, the use of hypothesis testing to interpret experimental data has raised concerns due to common misunderstandings by both scientists and students. With statistics education reform on the rise, as well as an increasing number of students enrolling in introductory statistics courses each year, there is a need for research to investigate students’ understanding of hypothesis testing. In this study we used APOS Theory to investigate twelve introductory statistics students’ reasoning about one-sample population hypothesis testing while working two real-world problems. Data were analyzed and compared against a preliminary genetic decomposition, which is a conjecture for how an individual might construct an understanding of a concept. This report presents examples of Actions, Processes, and Objects in the context of one-sample hypothesis testing as exhibited through students’ reasoning. Our results suggest that the concepts involved in hypothesis testing are related through the construction of higher-order, coordinated Processes operating on Objects. As a result of our data analysis, we propose refinements to our genetic decomposition and offer suggestions for instruction of one-sample population hypothesis testing. We conclude with appendices containing a comprehensive revised genetic decomposition along with a set of guided questions that are designed to help students make the constructions called for by the genetic decomposition

Transitioning to an Active Learning Environment for Calculus at the University of Florida

In this note, we describe a large-scale transition to an active learning format in first-semester calculus at the University of Florida. Student performance and attitudes are compared across traditional lecture and flipped sections

Students' understanding of the concepts involved in one-sample hypothesis testing

Hypothesis testing is a prevalent method of inference used to test a claim about a population parameter based on sample data, and it is a central concept in many introductory statistics courses. At the same time, the use of hypothesis testing to interpret experimental data has raised concerns due to common misunderstandings by both scientists and students. With statistics education reform on the rise, as well as an increasing number of students enrolling in introductory statistics courses each year, there is a need for research to investigate students' understanding of hypothesis testing. In this study we used APOS Theory to investigate twelve introductory statistics students' reasoning about one-sample population hypothesis testing while working two real-world problems. Data were analyzed and compared against a preliminary genetic decomposition, which is a conjecture for how an individual might construct an understanding of a concept. This report presents examples of Actions, Processes, and Objects in the context of one-sample hypothesis testing as exhibited through students' reasoning. Our results suggest that the concepts involved in hypothesis testing are related through the construction of higher-order, coordinated Processes operating on Objects. As a result of our data analysis, we propose re�finements to our genetic decomposition and o�ffer suggestions for instruction of one-sample population hypothesis testing. We conclude with appendices containing a comprehensive revised genetic decomposition along with a set of guided questions that are designed to help students make the constructions called for by the genetic decomposition.</p