Education Commons^™

Tasks For Learning Trigonometry, Sydnee Andreasen

All Graduate Reports and Creative Projects, Fall 2023 to Present

Many studies have been done using task-based learning within different mathematics courses. Within the field of trigonometry, task-based learning is lacking. The following research aimed to create engaging, mathematically rich tasks that meet the standards for the current trigonometry course at Utah State University and align with the State of Utah Core Standards for 7th through 12th grades. Four lessons were selected and developed based on the alignment of standards, the relevance to the remainder of the trigonometry course, and the relevance to courses beyond trigonometry. The four lessons that were chosen and developed were related to trigonometric ratios, graphing …

An Investigation Of Active Learning On Students' Understanding Of Infinite Series Convergence, Zachary Coverstone

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Many students encounter infinite series for the first time as part of their single-variable calculus coursework. As part of this initial engagement with infinite series convergence, students grapple with infinity in ways that they haven't had to before. For instance, the fact that summing infinitely many terms sometimes yields a finite value, but at other times diverges, poses significant conceptual challenges.

I recently designed and implemented a curriculum for second-semester calculus centered in doing problems to help students develop ideas surrounding infinite series convergence, rather than using direct instruction. The unit design was patterned after a workshop at the Park …

Pre-Service Elementary School Teachers’ Perceptions Of Themselves As Learners Of Mathematics And Science, Diana L. Moss, Rachel Wilson, Danielle Divis

Journal on Empowering Teaching Excellence

Access the online Pressbooks version of this article here.

This study investigated how prospective elementary teachers view themselves as learners of mathematics and science during their last year in a teacher preparation program at an American university. Using drawing and reflections as the method for collecting data, prospective teachers were prompted to draw themselves and reflect on learning mathematics and draw themselves and reflect on learning science prior to and after their mathematics and science methods courses. Drawings (n = 147) were coded according to the presence or absence of several themes including physical objects, teachers, students, and environment. …

Full Issue: Journal On Empowering Teaching Excellence, Volume 6, Issue 1, Spring 2022

Journal on Empowering Teaching Excellence

The full-length 2022 Special Issue (Volume 5, Issue 3) of the Journal on Empowering Teaching Excellence

Access the online Pressbooks version (with downloadable EPUB format) here.

The Spring 2022 issue begins with research that explores the perceptions of pre-service teachers relative to learning mathematics and science, with suggestions for how findings can impact curriculum and further research. The focus on pre-service teachers continues with research into their sense of self-efficacy with instructional technologies and whether specific techniques increase comfort level with technologies. Next, researchers explore the products that Generation Z students value most in their learning of a second language, …

Teaching Students To Communicate With The Precise Language Of Mathematics: A Focus On The Concept Of Function In Calculus Courses, Derrick S. Harkness

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The use of precise language is one of the defining characteristics of mathematics that is often missing in mathematics classrooms. This lack of precision results in poorly constructed concepts that limit comprehension of essential mathematical definitions and notation. One important concept that frequently lacks the precision required by mathematics is the concept of function. Functions are foundational in the study undergraduate mathematics and are essential to other areas of modern mathematics. Because of its pivotal role, the concept of function is given particular attention in the three articles that comprise this study.

A unit on functions that focuses on using …

Social Justice Mathematical Modeling For Teacher Preparation, Patrick L. Seegmiller

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Today's math teachers face significant social and political challenges for which they receive little preparation. Mathematics content courses can potentially provide additional preparation in this regard by providing future teachers with experiences to mathematically explore social justice issues. This provides them with opportunities to increase their awareness and sensitivity to social justice issues, develop greater empathy for their future students, and serve as examples for high quality instruction that they can emulate in their future careers. This dissertation recounts the development and revision of three social justice mathematical modeling projects, and shares evidence from student work samples of the ways …

Secondary Mathematics Teachers’ Responses To Pivotal Teaching Moments, Kami M. Dupree

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This study used a multiple case study design to explore the occurrence of pivotal teaching moments, teachers’ responses to these moments, and teachers’ own perceptions of the impact of these moments on their own knowledge development. The participants were six practicing secondary mathematics teachers. The researcher collected data from teacher created lesson plan outlines, observations of the same lesson delivered to two different classes, participant interviews, and teacher reflection journals. The researcher reviewed the lesson plan outlines prior to observations to understand teachers’ anticipations. During observations, the researcher recorded observed pivotal teaching moments, corresponding teacher responses to these moments, and …

Full Issue: Journal On Empowering Teaching Excellence, Volume 3, Issue 1, Kim Hales

Journal on Empowering Teaching Excellence

The full Spring 2019 issue (Volume 3, Issue 1) of the Journal on Empowering Teaching Excellence, Spring 2019

An Exploratory Study Of Fifth-Grade Students’ Reasoning About The Relationship Between Fractions And Decimals When Using Number Line-Based Virtual Manipulatives, Scott Smith

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Understanding the relationship between fractions and decimals is an important step in developing an overall understanding of rational numbers. Research has demonstrated the feasibility of technology in the form of virtual manipulatives for facilitating students’ meaningful understanding of rational number concepts. This exploratory dissertation study was conducted for the two closely related purposes: first, to investigate a sample of fifth-grade students’ reasoning regarding the relationship between fractions and decimals for fractions with terminating decimal representations while using virtual manipulative incorporating parallel number lines; second, to investigate the affordances of the virtual manipulatives for supporting the students’ reasoning about the decimal-fraction …

How Affordances And Constraints Of Physical And Virtual Manipulatives Support The Development Of Procedural Fluency And Algorithmic Thinking In Mathematics, Jennifer Such, Patricia S. Moyer-Packenham

Teacher Education and Leadership Faculty Publications

The purpose of this study was to examine how the affordances and constraints of physical and virtual manipulatives influence the development of students’ algorithmic thinking when learning algebra and rational number concepts. Thirty-six third-grade students participated in two weeks of instruction using physical and virtual manipulatives as instructional tools. The primary design of the study was a teaching experiment in which quantitative and qualitative data were collected to provide a holistic examination. Pre- and post-test items were used in the quantitative analysis following a within-subjects crossover repeated measures design. Students’ written work, a user survey, student interviews, field notes, and …