Education Commons^™

Improving Access To General Education Via Co-Teaching In Secondary Mathematics Classrooms: An Evaluation Of Utah's Professional Development Initiative, Kaitlin Bundock, Kristen Rolf, Anna Hornberger, Chamy Halliday

Special Education and Rehabilitation Counseling Faculty Publications

Co-teaching may be a promising strategy to improve inclusive secondary mathematics education in rural schools. Professional development (PD) aids in special and general education teachers' co-teaching implementation, yet little empirical research examines how to effectively train and support co-teachers. In this study we describe one U.S. state's PD model for secondary mathematics co-teaching, evaluate outcomes of the PD on co-teachers' behaviors and beliefs, and examine the impact of co-teaching on students' mathematics achievement. We examined data from observations, surveys, and students' pre/post assessments across nine classes within seven U.S. school districts, including three rural school districts, over 3 years. We …

Cache Code Math: Mathematics Lesson Plans: Fractions, Kimberly Beck, Jessica F. Shumway, Aubrey Rogowski, Umar Shehzad, Jody Clarke-Midura, Mimi Recker

Instructional resources

This document entails three 5^th grade mathematics lesson plans. The lessons are intended to be implemented in conjunction with the computer lab activities found in "Cache Code Math: Fractions, Functions, & For-Loops." The mathematics focus of these lessons is multiplying fractions, which is paired with the computer coding concepts of functions and for-loops.

Applying Expansive Framing To An Integrated Mathematics-Computer Science Unit, Kimberly Evagelatos Beck, Jessica F. Shumway

Publications

In this research report for the National Council of Teachers of Mathematics 2022 Research Conference, we discuss the theory of Expansive Framing and its application to an interdisciplinary mathematics-computer science curricular unit.

Children's Mathematical Engagement Based On Their Awareness Of Different Coding Toys' Design Features, Joseph S. Kozlowski

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Tangible coding toys have been promulgated as useful learning tools for young children to learn computer science and mathematics concepts and skills. Although research shows coding toys can support mathematics for early childhood aged children, little is known about the specific design features of coding toys that afford mathematical thinking concepts and skills to young children. The purpose of this study was to examine kindergarten-aged children’s awareness of the design features in coding toys and to understand how those design features afford children’s engagement with mathematics. The dataset used for this study was collected as part of design-based research NSF …

Delivering On A Promise: A Longitudinal Cohort Study Of Emergent Bilinguals' Academic Achievement In A Utah Dual Language Program, J. Eric Campbell

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Emergent bilingual (EB) students are a growing population in the U.S. school system currently comprising over 10% of the total population. U.S. school districts have educated EB students using a myriad of practices, including dual language immersion (DLI). Many studies have looked at the academic achievement of native-Spanish speaking EB students, yet there is a dearth of research on DLI in medium-sized school districts in rural settings. This study focused on native-Spanish speaking EB students in a DLI program in a rural Utah district. Specifically, the study compared student academic achievement in English acquisition, English language arts, mathematics, and grade …

Mathematics From Scratch: Learning With Coding, Kimberly Beck, Jessica F. Shumway, Jody Clarke-Midura

Publications

Implementing successful cross-curricular lessons is challenging but possible. Participants in this session will learn about a partnership between Utah State University, Cache County School District, and Stanford University that has designed and implemented successful integrated mathematics-computer science lessons. Attendees will hear from researchers and in-service teachers on their experience with designing and carrying out the curriculum and will have an opportunity to view and interact with the computer programs that students used.

Cache Code Math Mathematics Lesson Plans: Exponents And Repeats, Jody Clarke-Midura, Jessica Shumway, Kimberly Beck, Umar Shehzad, Mimi Recker

Instructional resources

This document entails four 5^th grade mathematics lesson plans. The lessons are intended to be implemented in conjunction with the computer lab activities found in “Integrated Lesson (CS and Math)”. The mathematics focus of these lessons is exponents as repeated multiplication, which is paired with the computer coding concepts of repeat loop blocks.

Examining The Use Of Culturally Relevant Pedagogy In Undergraduate Mathematics Learning Modules With Students Of Color, Thomas A. Mgonja

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In mathematics, Students of Color have persistently performed lower than their White counterparts, thus creating a need to explore instructional methods that could reduce performance disparities. This study investigated culturally relevant pedagogy (CRP) to understand how it might support students’ mathematics learning in undergraduate mathematics learning modules. The overarching research question focused on how CRP in undergraduate mathematics Learning Modules supported students’ mathematics learning. There were also two main questions that focused on participants’ evaluations of the CRP modules and how those evaluations were reported based on subgroups (Students of Color and White). The researcher employed a sequential explanatory mixed-methods …

Preschool Children's Development In Number, Geometry, And Executive Function: A Cross-Lagged Examination, Brionne G. Neilson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Children develop rapidly during early childhood, and this includes their mathematics and executive function (EF) skills. Past research has focused on connections between early mathematics and EF, but more work was needed to fully understand these relations. In particular, past studies have generally used numeracy-based measures to assess early mathematics, although professional guidelines indicate a more comprehensive construct that includes geometry. The research herein addresses some of the gaps of previous work as it examines unique connections between early number, geometry, and EF. One hundred eighteen preschool children from urban and rural communities, being an average age of 53 months …

Reviewing Tools For Evaluating K-12 Instructional Materials Through An Implementation Lens, Kristen R. Rolf, Sarah E. Pinkelman, Kaitlin Bundock

Special Education and Rehabilitation Counseling Faculty Publications

This review examined how state-created tools for evaluating instructional materials support local schools and school districts to address implementation when adopting instructional materials. We followed a priori, systematic procedures to conduct a web search and visit each state’s department of education website in search of instructional materials evaluation tools. After identifying all of the state-created instructional materials evaluation tools in the areas of English/language arts and mathematics, we reviewed the tools and coded them for evidence of alignment with the six implementation indicators defined by the Hexagon Tool (Metz and Louison, The Hexagon Tool: exploring context. Based on Kiser, Zabel, …

The Role Of Gender On The Associations Among Children’S Attitudes, Mathematics Knowledge, Digital Game Use, Perceptions Of Affordances, And Achievement, Kristy Litster, Christina W. Lommatsch, Josh R. Novak, Patricia S. Moyer-Packenham, Jill Ashby, Allison L. Roxburgh, Emma P. Bullock

Teacher Education and Leadership Faculty Publications

This study explored associations among children’s prior attitudes, prior mathematics knowledge, and frequency of digital game use, with children’s perceptions of game affordances, and transfer to out-of-game performance when interacting with digital math games, with respect to gender. Participants were 187 children (ages 8–12). An SEM mediation path analysis using MPLUS software showed significant direct effects for all pathways for all children, and significant indirect effects on all pathways for male children and five of six pathways for female children. More favorable attitudes, prior math knowledge, and perception of the helping affordances were associated with increased posttest performance, while increased …

Experiencing Active Mathematics Learning: Meeting The Expectations For Teaching And Learning In Mathematics Classrooms, Kristy Litster, Beth L. Macdonald, Jessica F. Shumway

Teacher Education and Leadership Faculty Publications

Active learning mathematics classrooms incorporate meaningful activities that emphasize reasoning, thinking and active interaction with mathematics. Current mathematics standards and curricula recommend that Mathematics Teacher Educators (MTEs) use elements of active learning in their mathematics content courses specifically designed for Prospective Teachers (PTs) as they prepare PTs to learn and teach mathematics. However, it can be very difficult for PTs to shift their pedagogical dispositions towards instruction associated with active learning because they typically have not experienced mathematics taught in this way. This article focuses on two instructional practices for MTEs to use with PTs. First, selecting tasks that promote …

Exploring The Phenomenon Of Distance In Children's Interactions With Touchscreen Digital Mathematics Games, Stephen I. Tucker, Patricia S. Moyer-Packenham

Teacher Education and Leadership Faculty Publications

This study examines the construct of distance – the degree of difficulty of interacting with something – as part of activity involving children using touchscreen digital games to learn mathematics. Ten fifth-grade children engaged in video-recorded semi-structured task-based interviews in which they used two touchscreen digital mathematics games on a touchscreen tablet and responded to semi-structured follow-up questions. Qualitative data analysis was iterative, featuring analytic memoing and eclectic coding techniques to identify themes related to distance. In advanced coding stages, magnitude coding was used to characterize the degree of distance present. Findings provide evidence of the presence of distance, changes …

The Relationship Between Small-Group Discourse And Student-Enacted Levels Of Cognitive Demand When Engaging With Mathematics Tasks At Different Depth Of Knowledge Levels, Kristy Litster

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

High cognitive demand (HCD) tasks can help students develop a deeper understanding of mathematics. Teachers need interventions that encourage students to engage in HCD activities. Small-group discourse provides HCD opportunities for students while solving mathematics problems. Discourse can take place after students solve problems individually (reflective) or in groups as students solve problems (exploratory). This study looks at the relationship between these two types of small-group discourse and student-enacted cognitive demand.

This study looks at how students engage with tasks that were designed at four different cognitive demand levels using Webb’s depth of knowledge (DOK) framework. Ninety-seven grade 5 students …

An Examination Of The Role Of First-Year College-Level Mathematics In Stem Field Major Persistence At A Hispanic-Serving Institution, Jaimi Paschal, Amanda Taggart

Teacher Education and Leadership Faculty Publications

This study examined the influence of mathematics course-taking on Latina/o science, technology, engineering, and mathematics (STEM) major persistence utilizing data from first-year STEM majors at a Hispanic-Serving Institution (HSI). Findings indicated that students who passed a first-term college-level mathematics course had significantly greater odds of persisting in STEM majors than those who did not, demonstrating the importance of early mathematics support to increased STEM major persistence.

Relationships Between Teachers' Past Experiences Learning Mathematics And Their Pedagogical Practices And Beliefs, Caci M. Jensen

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

This creative project centered around the cyclical pattern of mathematics anxiety currently prevalent in our schools. A high percentage of elementary teachers carry mathematics anxiety and beliefs around mathematics that effect their pedagogical practices day-to-day. This anxiety transfers to their students effecting their future choices in mathematics. This project was conducted in case studies with six teachers from a rural charter school. Journey maps, semi-structured interviews, surveys, and observations were used to collect the data.

A Case Study On How Meeting The Academic Needs Of Students Substantially Below Grade Level In Mathematics Affects Their Self-Efficacy Beliefs And Engagement, Lauren K. M. Burton

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This researcher examined an alternative classroom structure for ninth-grade students substantially below grade level (SBGL) in mathematics. This researcher considered whether targeting the academic and social needs of students SBGL in mathematics in a ninth-grade class would increase their self-efficacy and engagement with the mathematics by studying four teaching effects: teacher, teacher-curriculum, peer-curriculum, and peer.

The researcher used interviews, observations, and surveys to collect qualitative and quantitative data. The case study (n = 19) employed a QUAL + quan convergent parallel mixed methods case study. Meta-inferences from the analyses of qualitative and quantitative data indicate that the structure of …

Identifying Factors Common Among Students Who Do Not Fit The Typical Mathematics Self-Efficacy And Achievement Correlation, Jodi H. Mantilla

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A student’s self-efficacy, or their belief in their ability to perform a specific behavior, has been shown to have a positive correlation with their academic achievement. In other words, if their self-efficacy is high, their academic achievement is high. If self-efficacy is low, likewise their achievement is low. Research has shown that this correlation is especially true when looking at the self-efficacy and academic achievement in a specific subject, such as mathematics. However, in a typical classroom, teachers experience students who have very high self-efficacy in their mathematics abilities yet perform mathematics tasks at a low level. They may also …

An Exploratory Study Of Attributes, Affordances, Abilities, And Distance In Children's Use Of Mathematics Virtual Manipulative Ipad Apps, Stephen I. Tucker

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This exploratory qualitative study investigated the presence of and relationships among constructs that contribute to children's interactions with educational technology, leading to the development of the modification of attributes, affordances, abilities, and distance (MAAAD) for Learning framework. For this study, each of 10 fifth-grade children participated in one individual video-recorded semistructured interview session, during which they interacted with two mathematics virtual manipulative iPad apps and responded to follow-up questions. Video recordings and observation field notes were analyzed for evidence of attributes, affordance-ability relationships, distance, and relationships among these constructs.

Constant comparative data analysis using memoing and eclectic coding provided evidence …

The Impact Of Computer-Adaptive Benchmark Data And Assessment Literacy On Student Achievement And Motivation In Mathematics, Sheryl J. Rushton

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Over the past several decades there has been an emphasis in educational research on student assessment and achievement in mathematics. Formative assessments are designed to inform the instructional decision making process and require assessment literacy to interpret and use data provided by these assessments. Many teachers and students were lacking assessment literacy; therefore, they were unable to adjust their instruction and study habits to increase student performance on summative assessments.

This study investigated the impact Scholastic Math Inventory (SMI) benchmarks and assessment literacy training had on summative assessments and student motivation in mathematics. The researcher analyzed unit posttest scores and …

Common Themes Associated With Teacher-Identified Obstacles To Implementing Change In Mathematics Instruction Attributable To Participation In Mathematics Professional Development, Ronald A. Twitchell

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This study had three purposes: first, explore any common phenomenon of secondary mathematics teachers’ experience in secondary mathematics professional development (MPD); second, determine if there were positive changes in teacher attitudes after completing secondary MPD; and finally, if a positive change in teacher attitude was identified, describe the shared experiences in secondary MPD to in a way that cannot be revealed through ordinary observations. It was the intent of this study to identify positive changes in teacher attitudes not to measure their magnitude. This study implemented a mixed methods design using descriptive statistics and categorical analysis on data from pre- …

The Academic Preparation And Background Of Public Secondary Mathematics Teachers In Utah 1966-1967, Charles Martin Crittenden

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A random survey was conducted to determine the academic preparation and background of the public secondary mathematics teachers in the state of Utah.

The survey indicated that there is a wide variance in the teacher mathematics preparation between the three types of public secondary schools. The class B high schools have a smaller percentage of well prepared mathematics teachers than either the class A high schools or the junior high schools.

The following facts were discovered: (1) 22.03 percent of all the surveyed mathematics teachers had between 1 and 15 quarter hours of college mathematics preparation, (2) 5.22 percent had …

Perceptions By High School Teachers Of Mathematical Readiness Of Students With Disabilities Transitioning To College, Adam Dwight King

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

More and more students with mild disabilities enroll in and attend college. However, test scores and other achievement measures show that they are well behind
their regular education peers in math achievement, and thus unprepared for the rigors of college. While much has been done to revise laws and policy involving students with disabilities and academic core standards to increase preparedness, it is still what happens in the classroom that has the greatest effect on student preparation. Due to
the nature of pullout/resource classes where pacing is typically slower and less content is covered, special education teachers make a myriad …

Processes And Pathways: How Do Mathematics And Science Partnerships Measure And Promote Growth In Teacher Content Knowledge?, Patricia S. Moyer-Packenham, A. Westenskow

Teacher Education and Leadership Faculty Publications

Intense focus on student achievement results in mathematics and science has brought about claims that K-12 teachers should be better prepared to teach basic concepts in these disciplines. The focus on teachers' mathematics and science content knowledge has been met by efforts to increase teacher knowledge through funded national initiatives focusing on mathematics and science. The purpose of the present study was to look across projects in the National Science Foundation's Math and Science Partnership Program to determine how partnerships developed processes for measuring growth in teacher content knowledge. Pre- and post-testing was the most common process for measuring growth …

The Effect Of Direct Instruction In Teaching Addition And Subtraction Of Decimals And Decimal Word Problems On Students At Risk For Academic Failure, Heather Hoopes Small

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This study investigated the effects of a direct instruction program on the ability of elementary school students identified as at risk for math failure to add and subtract numbers with decimals, and complete addition and subtraction word problems with decimals. Direct instruction has previously been shown to increase the math skills of special education and general education students. This study examined the extent to which these students could master these skills in six hours of instruction, with carefully designed sequences of examples and strategy instruction in word problems. The study took place in two elementary schools. The participants were fifth …

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 …

Negotiating The "Relevant" In Culturally Relevant Mathematics, N. Enyedy, J. Danish, Deborah A. Fields

Deborah A. Fields

No abstract provided.

Learning Mathematics With Technology: The Influence Of Virtual Manipulatives On Different Achievement Groups, Patricia S. Moyer-Packenham, J. M. Suh

Teacher Education and Leadership Faculty Publications

This study examined the influence of virtual manipulatives on different achievement groups during a teaching experiment in four fifth-grade classrooms. During a two-week unit focusing on two rational number concepts (fraction equivalence and fraction addition with unlike denominators) one low achieving, two average achieving, and one high achieving group participated in two instructional treatments (three groups used virtual manipulatives and one group used physical manipulatives). Data sources included pre- and post-tests of students’ mathematical content knowledge and videotapes of classroom sessions. Results of paired samples t-tests examining the three groups using virtual manipulatives indicated a statistically significant overall gain following …

Common Features Of Professional Development Activities For Mathematics And Science Teachers, Patricia S. Moyer-Packenham, J. J. Bolyard, J. Oh, N. I. Cerar

Teacher Education and Leadership Faculty Publications

This study examines professional development activities provided for mathematics and science teachers in the National Science Foundation’s Math and Science Partnership Program by analyzing a cross-sectional sample of over 2000 professional development (PD) activities in the program. Data were gathered from secondary source documents and surveys to examine core and structural features of professional development offerings (i.e. form, collective participation, content, duration and outcomes). The results from this sample of PD activities for mathematics and science teachers were mixed. There was evidence of researchbased practices, including the collective participation by teachers at the same grade levels, a focus on content-specific …

Negotiating The "Relevant" In Culturally Relevant Mathematics, N. Enyedy, J. Danish, Deborah A. Fields

Instructional Technology and Learning Sciences Faculty Publications

One approach to promoting successful engagement of underrepresented groups in mathematics classrooms is Culturally Relevant Pedagogy (CRP). However, it has been argued that CRP risks essentializing students or watering down academic content. We report our analysis of a case study of a group of three 6th grade students who took part in a 6-week mathematics curriculum. This curriculum used Geographical Information System (GIS) maps to engage students in designing personally meaningful research projects while learning about measures of central tendency (i.e., learning statistics). The case study was chosen as representative of how students in this urban classroom (47 total) successfully …