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 …

Using Gamification To Foster Student Resilience And Motivation To Learn, And Using Games To Teach Significance Testing Concepts In The Statistics Classroom, Todd Partridge

All Graduate Theses and Dissertations, Fall 2023 to Present

Two studies are outlined in this dissertation.

In the first study, elements of Super Mario Bros. videos games were used to change the way college students in a beginners’ statistics course were graded on their work. This was part of an effort to help students remain optimistic in the face of challenging coursework and even failure on assignments and tests. The study shows that the changes made to the grading structure did help students to keep trying and to use the materials given to them by their professor until they achieved their desired grade in the course, and suggests ways …

Recognizing And Reducing Ambiguity In Mathematics Curriculum And Relations Of Θ-Functions In Genus One And Two: A Geometric Perspective, Shantel Spatig

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

Anxiety and mathematics come hand in hand for many individuals. This is due, in
part, to the fact that the only experience they have with mathematics is what some
mathematics educators refer to as "schoolmath," which uses a somewhat different
language than real mathematics. The language of schoolmath can cause individu-
als to have confusion and develop misconceptions related to several mathematical
concepts. One such concept is a fraction. In chapter one of this report, one possible
reason for this is discussed and a possible solution is purposed.
In chapter three of this report, genus-two curves admitting an elliptic involution …

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 …

The Marshmallow Lab: A Project-Based Approach To Understanding Functional Responses, Melissa Pulley

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper presents a three-part lesson plan to improve student’s understanding of Holling’s type II functional response model. This model describes the interaction between a predator and how much it is able to consume given a constant number of prey. According to the model, while increased availability of prey allows predators to consume portionately more prey for low values, after some number of prey, predators will only be able to capture a limited number of prey even as the prey continues to increase. This phenomenon is known as saturation. Holling first develop this important ecological theory through his “disc experiment” …

Learning Logic: A Mixed Methods Study To Examine The Effects Of Context Ordering On Reasoning About Conditionals, Christina W. Lommatsch

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Logical statements are prevalent in mathematics, the sciences, law, and many areas of everyday life. The most common logical statements are conditionals, which have the form “If H..., then C...,” where “H” is a hypothesis (or condition) to be satisfied and “C” is a conclusion to follow. Reasoning about conditionals is a skill that is only superficially understood by most individuals and depends on four main conditional contexts (e.g., intuitive, abstract, symbolic, or counterintuitive). The purpose of this study was to test a theory about the effects of context ordering on reasoning about conditionals. To test the theory, the researcher …

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 …

High Cognitive Test Item Development And Implementation, Ashley Salisbury

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

In secondary math classrooms there has been a movement toward discovery and problem solving based instruction. This type of instruction requires teachers to teach on what is often considered a higher level of cognition and allows students to discover more ideas and concepts on their own as opposed to traditional lecture style. Teachers with well thought-out examples, questions, and activities provide students with tools to solve problems on their own requiring students to make mathematical discoveries and connections. These skills not only benefit students in their math class but are analytical skills students can use throughout their lives.

With this …

Critical Issues In Middle And Secondary Mathematics Placement: A Case Study, Morgan E. Summers

Undergraduate Honors Capstone Projects

This qualitative research project focuses on the issues facing middle and secondary mathematics placement through an extensive literature review as well as a case study of a local school district. As students move from elementary school to middle and secondary schools, they are placed into classes that appear to be based on ability. One of the driving questions of this project is how is this ability level determined? Through an in-­‐depth look at one school district, it is found that a primary source of information is both norm-­‐referenced and criterion-­‐referenced assessments given to students in fifth and eighth grades. In …

Virtual Manipulatives In The Classroom And Resulting Articles And Lesson Plans, Cheryl Juliana

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

Upon coming across mathematical manipulatives generated and produced by Utah State University, as a math teacher, I conducted a classroom teaching experiment in three pre-algebra classes with students of various achievement levels. After teaching the entire year using no manipulatives in the classroom, I tested my students with a general, end-of-year, core criterion, or cumulative test. Their scores were noted. The students in the study group were then given opportunities to try several manipulatives offered on the "National Library of Virtual Manipulatives," both as a class, and alone, and then retested. The following paper gives the parameters of the study, …

The Effect Of Explicit Timing On Math Performance Using Interspersal Assignments With Students With Mild/Moderate Disabilities, Fangjuan Hou

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Explicit timing and interspersal assignments have been validated as effective methods to facilitate students' math practice. However, no researchers have explored the combinative effect of these two methods. In Study 1, we extended the literature by comparing the effect of explicit timing with interspersal assignments, and interspersal assignments without timing. Generally, participants' rate of digits correct on easy and hard addition problems was higher during the explicit timing condition than during the untimed condition. However, the participants' rate of digits correct decreased after initial implementation of the explicit timing condition.

Motivation plays a crucial role in maintaining performance levels and …

The Process Of Tracking In Mathematics In Box Elder School District, Megan Haramoto Bushnell

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Educational policymakers have used tracking to instruct students in a variety of subjects, including mathematics. Tracking, which has also been called ability grouping, is a process by which students in the same grade are placed into different classes based on academic ability. Few educators and sociologists have looked at the process by which students are placed in different mathematics tracks. The research design of this study focused on accumulating, evaluating, and reporting the understanding and observations of 12 teachers and 4 counselors as they discussed their knowledge and involvement in the mathematics placement procedures from the intermediate and middle school …