Research Projects

• Statistics Education
  
  • Understanding Conceptions of Sampling Distributions: The concept of sampling distributions is fundamental to understanding statistical inference. Using activities from the CATALYST project at UMN, I am creating and using a theoretical framework that will help us describe the ways students think about these concepts. As part of this project, I have designed software that allows you to simulate the process of repeated sampling to construct sampling distributions. You can download the programs and documentation from the simulator page.
    

• Analyzing Mathematics Lectures
  • Unpacking Mathematics Lectures: Most math classes still incorporate lecture as a common class format. Students may have difficulty learning from lectures; the goal of this research project is to better understand some potential sources of this difficulty, to identify opportunities for learning in lectures, and to find ways to improve math lectures. To do this, I use ideas from literary criticism, gesture, and sense-making to describe the various components of lectures, the ways students "participate" in the lecture, and how these aspects interact to influence the ways students make sense of lectures.

• The Design and Use of Flipped Classrooms and Mathematics Textbooks
  • Analyzing a "Flipped" Classroom: In a "flipped" classroom, students read the textbook and watch videos outside of class, and then use class time to work on problems or discuss concepts in more depth. Working with colleagues in mathematics and computer science, I am helping to design a "flipped" Calculus 2 class and to use ideas from literary criticism to analyze the ways students use the textbook and videos to learn.
  • Using Reader-Oriented Theory to Analyze Math Textbooks: Textbooks have the potential to be powerful tools to help students develop an understanding of mathematics, yet many students are not able to use them in this way. I am adapting ideas from literary criticism—specifically, the ideas of reading models and implied readers—to analyze math textbooks and the ways people use them.

• Algebraic Reasoning and Representation
  • Mental Models for "Student-Professor Problem": The "student-professor problem" is a classic example of students' difficulty translating between symbols and words. It is a useful lens through which to examine students' mental models of comparison word problems and the way various features of the problem situation and its representation mediate their mathematical activity.
  • Undergraduate Students' Conceptions of the Equals Sign: We often see students use the equals sign in ways that are incorrect, yet efforts to correct these uses typically fail. I am using ideas from semiotics to reconceptualize the way we think about students' use of the equals sign to investigate how these "errors" can be viewed as part of an attempt to imbue mathematical symbols with meaning.
  • Conceptions of Variables in the Transition from Arithmetic to Algebraic Reasoning: How do students in middle school build on their arithmetic understanding to develop algebraic reasoning, and how can we support this development? I am working with colleagues from the University of Wisconsin to focus on how students initially develop concepts of variation and an understanding of variables and how this conception develops over time.
  • Understanding Functions through Multiple Representations: How do we begin to use functions to solve mathematical problems? I am investigating how discourse, participation, and representational fluency can lead to working with functions in meaningful ways as well as the role played by mediational metaphors.