Leslie Meadows - Academia.edu (original) (raw)

Papers by Leslie Meadows

Hypothesis testing is a prevalent method of inference used to test a claim about a population par... more 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, Proce...

We are examining iteratively regularized methods for solving nonlinear inverse problems. Of parti... more We are examining iteratively regularized methods for solving nonlinear inverse problems. Of particular interest for these types of methods are application problems which are unstable. For these application problems, special methods of numerical analysis are necessary since classical algorithms tend to be divergent. INDEXWORDS: Inverse problems, Iteratively regularized methods, Iteratively Regularized Newton, Iteratively Regularized Gauss-Newton ITERATIVELY REGULARIZED METHODS FOR INVERSE PROBLEMS

Hypothesis testing is a key concept included in many introductory statistics courses. Yet, due to... more Hypothesis testing is a key concept included in many introductory statistics courses. Yet, due to common misunderstandings of both scientists and students, the use of hypothesis testing to interpret experimental data has received criticism. With statistics education on the rise, as well as an increasing number of students enrolling in introductory statistics courses each year, there is a need for research that investigates students’ understanding of hypothesis testing. This paper describes results obtained from a larger study designed to investigate introductory statistics students’ understanding of one population hypothesis testing. In particular, we present on one student’s understanding of the concepts involved in hypothesis testing, Steve, who provided us the best spectrum of different levels of knowledge according to APOS Theory, our guiding theoretical framework. Based on this data, we suggest implications for teaching.

The Journal of Mathematical Behavior

Abstract Hypothesis testing is a prevalent method of inference used to test a claim about a popul... more Abstract 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.

Hypothesis testing is a key concept included in many introductory statistics courses. Due to comm... more Hypothesis testing is a key concept included in many introductory statistics courses. Due to common misunderstandings of both scientists and students, the use of hypothesis testing to interpret experimental data has received criticism. This paper describes preliminary results obtained from a larger study designed to investigate introductory statistics students' understanding of one sample hypothesis testing. APOS theory is used as a guiding theoretical framework. Preliminary data analysis focused on two students' distinctions between test statistics when performing hypothesis tests on real world data. The results suggest a significant difference in these two students' understanding, one being identified having an action conception while the other had an object conception of hypothesis testing as situated in the study.

The Emporium Model pedagogy is designed to actively engage students in the process of learning an... more The Emporium Model pedagogy is designed to actively engage students in the process of learning and teaching by utilizing interactive computer software for a personalized experience. While the Emporium Model originated from Virginia Tech, numerous universities have implemented this pedagogy with varying degrees of success. This presentation will describe how Georgia State University has adapted this model/pedagogy in three courses: College Algebra, Precalculus, and Elementary Statistics. Additionally, we will present Elementary Statistics students’ perceptions of this model and describe how students are actively engaged within this model.

Hypothesis testing is a prevalent method of inference used to test a claim about a population par... more 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, Proce...

We are examining iteratively regularized methods for solving nonlinear inverse problems. Of parti... more We are examining iteratively regularized methods for solving nonlinear inverse problems. Of particular interest for these types of methods are application problems which are unstable. For these application problems, special methods of numerical analysis are necessary since classical algorithms tend to be divergent. INDEXWORDS: Inverse problems, Iteratively regularized methods, Iteratively Regularized Newton, Iteratively Regularized Gauss-Newton ITERATIVELY REGULARIZED METHODS FOR INVERSE PROBLEMS

Hypothesis testing is a key concept included in many introductory statistics courses. Yet, due to... more Hypothesis testing is a key concept included in many introductory statistics courses. Yet, due to common misunderstandings of both scientists and students, the use of hypothesis testing to interpret experimental data has received criticism. With statistics education on the rise, as well as an increasing number of students enrolling in introductory statistics courses each year, there is a need for research that investigates students’ understanding of hypothesis testing. This paper describes results obtained from a larger study designed to investigate introductory statistics students’ understanding of one population hypothesis testing. In particular, we present on one student’s understanding of the concepts involved in hypothesis testing, Steve, who provided us the best spectrum of different levels of knowledge according to APOS Theory, our guiding theoretical framework. Based on this data, we suggest implications for teaching.

The Journal of Mathematical Behavior

Abstract Hypothesis testing is a prevalent method of inference used to test a claim about a popul... more Abstract 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.

Hypothesis testing is a key concept included in many introductory statistics courses. Due to comm... more Hypothesis testing is a key concept included in many introductory statistics courses. Due to common misunderstandings of both scientists and students, the use of hypothesis testing to interpret experimental data has received criticism. This paper describes preliminary results obtained from a larger study designed to investigate introductory statistics students' understanding of one sample hypothesis testing. APOS theory is used as a guiding theoretical framework. Preliminary data analysis focused on two students' distinctions between test statistics when performing hypothesis tests on real world data. The results suggest a significant difference in these two students' understanding, one being identified having an action conception while the other had an object conception of hypothesis testing as situated in the study.

The Emporium Model pedagogy is designed to actively engage students in the process of learning an... more The Emporium Model pedagogy is designed to actively engage students in the process of learning and teaching by utilizing interactive computer software for a personalized experience. While the Emporium Model originated from Virginia Tech, numerous universities have implemented this pedagogy with varying degrees of success. This presentation will describe how Georgia State University has adapted this model/pedagogy in three courses: College Algebra, Precalculus, and Elementary Statistics. Additionally, we will present Elementary Statistics students’ perceptions of this model and describe how students are actively engaged within this model.