Education Commons^™

The Relationship Between Motivation, Academic Achievement, And Engagement In Mathematics Using Digital Game-Based Learning: An Explanatory Sequential Mixed Methods Study, Amy Rose Morgan

Boise State University Theses and Dissertations

Digital game-based learning (DGBL) has unique factors that can engage students in the learning process. It has been shown that incorporating DGBL into mathematics can help bridge the learning gap, differentiate instruction, and engage students (Yang et al., 2018; Hulse et al., 2019; Chen et al., 2012; Naik, 2017). This study examined how students’ prior engagements are related to their academic achievement as well as investigated students’ motivation while utilizing DGBL in mathematics. An explanatory sequential mixed methods design was utilized to collect the quantitative data followed by the qualitative data. There were eighteen middle school participants in grades six …

A Systematic Review Of Research Syntheses For Students With Mathematics Learning Disabilities And Difficulties, Gena Nelson, Angela Crawford, Jessica Hunt

Early and Special Education Faculty Publications and Presentations

The purpose of this document is to provide readers with the coding protocol that authors used to code 36 research syntheses (including meta-analyses, evidence-based reviews, and quantitative systematic reviews) focused on mathematics interventions for students with learning disabilities (LD), mathematics learning disabilities (MLD), and mathematics difficulties (MD). The purpose of the systematic review of mathematics intervention syntheses was to identify patterns and gaps in content areas, instructional strategies, effect sizes, and definitions of LD, MLD, and MD. We searched the literature for research syntheses published between 2000 and 2020 and used rigorous inclusion criteria in our literature review process. We …

A Systematic Review Of Treatment Acceptability In Mathematics Instruction For Students With Learning Disabilities, Gena Nelson, Andrea Johnson, Mali Sawyer

Early and Special Education Faculty Publications and Presentations

Treatment acceptability is an aspect of social validity that refers to participants’ beliefs and perceptions about the intervention, such as the helpfulness of the strategies or the interventions’ efficacy to improve performance. The purpose of this study was to conduct a systematic review of treatment acceptability measures administered during mathematics interventions for students with learning disabilities (LD). We sought to identify the characteristics of the measures and the treatment acceptability outcomes. To be included in this review, studies had to (a) focus on testing the effectiveness of a mathematics intervention, (b) include preschool through 12th grade students who were diagnosed …

Efficient Assessment Of Students’ Proportional Reasoning, Michele Carney, Katie Paulding, Joe Champion

Curriculum, Instruction, and Foundational Studies Faculty Publications and Presentations

Teachers need ways to efficiently assess students’ cognitive understanding. One promising approach involves easily adapted and administered item types that yield quantitative scores that can be interpreted in terms of whether or not students likely possess key understandings. This study illustrates an approach to analyzing response process validity evidence from item types for assessing two important aspects of proportional reasoning. Data include results from an interview protocol used with 33 middle school students to compare their responses to prototypical item types to their conceptions of composed unit and multiplicative comparison. The findings provide validity evidence in support of the score …

Game Based Intervention To Develop Early Childhood Mathematical Understanding And Decrease Gaps Related To Socioeconomic Status, Lydia Flynn

Boise State University Theses and Dissertations

Early mathematical understanding is important for later success in mathematics. Game based interventions can be a successful means by which to help young students to improve their mathematical understandings. The purpose of this study is to examine whether a math game that was to be played at home improved the mathematical understanding of kindergarten students. Kindergarten students, from rural Idaho, were assigned to a group that played math games (n = 15) or a control group that did not (n = 13). The intervention group was given a simple math game and instructed to play 20 times in a …

A Systematic Review Of The Quality Of Reporting In Mathematics Meta-Analyses For Students With Or At Risk Of Disabilities Coding Protocol, Gena Nelson

Early and Special Education Faculty Publications and Presentations

The purpose of this document is to provide readers with the coding protocol that authors used to code 22 meta-analyses focused on mathematics interventions for students with or at-risk of disabilities. The purpose of the systematic review was to evaluate reporting quality in meta-analyses focused on mathematics interventions for students with or at risk of disabilities. To identify meta-analyses for inclusion, we considered peer-reviewed literature published between 2000 and 2020; we searched five education-focused electronic databases, scanned the table of contents of six special education journals, reviewed the curriculum vitae of researchers who frequently publish meta-analyses in mathematics and special …

Middle School Students' Reported Self-Regulation Strategies In Completing Online Mathematics Homework, Pepper Erlinger

Boise State University Theses and Dissertations

The purpose of this qualitative descriptive case study is to benefit our understanding of the potential of online homework as it relates to developing and supporting students’ self-regulated learning (SRL). This descriptive case study explores the use of self-regulated learning (SRL) strategies reported by students in the context of completing online mathematics homework (OHW). Eighth-grade students (10 total) from a traditional middle school were interviewed using a validated data collection instrument, the Self-Regulated Learning Interview Schedule or SRLIS (Zimmerman & Martinez-Pons, 1986, 1988). Students’ open-ended responses were interpreted using a framework of self-regulation theory and coded using 14 self-regulation strategies …

Lessons Learned From Creating Videos For Online Video-Based Instructional Modules In Mathematics Teacher Education, Patrick R. Lowenthal, Laurie O. Cavey

Educational Technology Faculty Publications and Presentations

Video can be a powerful tool, with a long history of use in teacher education. Despite the increased popularity of using video in teacher education over the years, questions remain about effective ways to create and use video in online video-based instructional modules. Given this, in this paper we describe some lessons learned creating videos for online video-based instructional modules for secondary mathematics teacher candidates, as a part of a National Science Foundation (NSF) IUSE program (Award No. 1726543) funded project. We specifically focus on how we recorded interviews with middle and high school students, and iteratively developed the online …

Teaching Mathematics Education Online: Instructional Theories, Strategies, And Technologies, Angie Hodge-Zickerman, Cindy S. York, Patrick R. Lowenthal

Educational Technology Faculty Publications and Presentations

This overview chapter provides an introduction to instructional theories, strategies, and technologies that can guide teachers new to teaching mathematics (both content and methods) online in a formal online classroom setting. We begin by discussing different types of online learning environments, including synchronous, asynchronous, bichronous, and HyFlex environments. We then focus on different theories, such as cognitive apprenticeship, individualized/personalized instruction, social learning, and inquiry-based mathematics education theories. After that, we focus on some common technologies and strategies, such as think/pair/share, student groups, whiteboards, discussion boards, and more that someone new to teaching mathematics teachers online may use to engage learners.

Validity Of A Special Education Teacher Observation System, Evelyn S. Johnson, Angela Crawford, Laura A. Moylan, Yuzhu Zheng

Early and Special Education Faculty Publications and Presentations

This manuscript describes the comprehensive validation work undertaken to develop the Recognizing Effective Special Education Teachers (RESET) observation system, which was designed to provide evaluations of special education teachers’ ability to effectively implement evidence-based practices and to provide specific, actionable feedback to teachers on how to improve instruction. Following the guidance for developing effective educator evaluation systems, we employed the Evidence-Centered Design framework, articulated the claims and inferences to be made with RESET, and conducted a series of studies to collect evidence to evaluate its validity. Our efforts and results to date are described, and implications for practice and further …

Variance And Reliability In Special Educator Observation Rubrics, Angela R. Crawford, Evelyn S. Johnson, Laura A. Moylan, Yuzhu Zheng

Early and Special Education Faculty Publications and Presentations

This study describes the development and initial psychometric evaluation of the Recognizing Effective Special Education Teachers (RESET) observation instrument. The study uses generalizability theory to compare two versions of a rubric, one with general descriptors of performance levels and one with item-specific descriptors of performance levels, for evaluating special education teacher implementation of explicit instruction. Eight raters (four for each version of the rubric) viewed and scored videos of explicit instruction in intervention settings. The data from each rubric were analyzed with a four facet, crossed, mixed-model design to estimate the variance components and reliability indices. Results show lower unwanted …

Elementary School Student Development Of Stem Attitudes And Perceived Learning In A Stem Integrated Robotics Curriculum, Yu-Hui Ching, Dazhi Yang, Sasha Wang, Youngkyun Baek, Steve Swanson, Bhaskar Chittoori

Educational Technology Faculty Publications and Presentations

Robotics has been advocated as an emerging approach to engaging K-12 students in learning science, technology, engineering, and mathematics (STEM). This study examined the impacts of a project-based STEM integrated robotics curriculum on elementary school students’ attitudes toward STEM and perceived learning in an afterschool setting. Three elementary school teachers and 18 fourth to sixth graders participated in an eight-week-long program. Quantitative and qualitative data were collected and analyzed, and showed students’ attitudes toward math improved significantly at the end of the robotics curriculum. Three specific areas of learning were identified, including STEM content learning and connection, engagement and perseverance, …

Predicting Third-Grade Mathematics Achievement: A Longitudinal Investigation Of The Role Of Early Numeracy Skills, Allyson J. Kiss, Gena Nelson, Theodore J. Christ

Early and Special Education Faculty Publications and Presentations

Despite the vast research on the early predictors of mathematics achievement, little research has investigated the predictors of various domains of mathematics (e.g., geometry, statistics). The purpose of the present study was to examine the predictive relationship between first-grade early numeracy and computation skills and third-grade mathematics achievement as measured by a state test. Further, we explored the relations between these measures for students who were Below Proficient and Proficient. Findings suggest that proficiency level matters when examining the relation between mathematics skills. Also, there are different patterns of significant predictors depending on the domain of later mathematics achievement and …

Developing An Explicit Instruction Special Education Teacher Observation Rubric, Evelyn S. Johnson, Yuzhu Zheng, Angela R. Crawford, Laura A. Moylan

Early and Special Education Faculty Publications and Presentations

In this study, we developed an Explicit Instruction special education teacher observation rubric that details the elements of explicit instruction, and tested its psychometric properties using many-faceted Rasch measurement (MFRM). Video observations of classroom instruction from 30 special education teachers across three states were collected. External raters (n = 15) were trained to observe and evaluate instruction using the rubric, and assigned scores of ‘implemented’, ‘partially implemented’ or ‘not implemented’ for each of the items. Analyses showed that the item, teacher, lesson and rater facets achieved high psychometric quality for the instrument. Implications for research and practice are discussed.

Developing A Multi-Dimensional Early Elementary Mathematics Screener And Diagnostic Tool: The Primary Mathematics Assessment, Jonathan L. Brendefur, Evelyn S. Johnson, Keith W. Thiede, Sam Strother, Herbert H. Severson

Curriculum, Instruction, and Foundational Studies Faculty Publications and Presentations

There is a critical need to identify primary level students experiencing difficulties in mathematics to provide immediate and targeted instruction that remediates their deficits. However, most early math screening instruments focus only on the concept of number, resulting in inadequate and incomplete information for teachers to design intervention efforts. We propose a mathematics assessment that screens and provides diagnostic information in six domains that are important to building a strong foundation in mathematics. This article describes the conceptual framework and psychometric qualities of a web-based assessment tool, the Primary Math Assessment (PMA). The PMA includes a screener to identify students …

Assessing Teacher Attentiveness To Student Mathematical Thinking, Michele B. Carney, Laurie Cavey, Gwyneth Hughes

Curriculum, Instruction, and Foundational Studies Faculty Publications and Presentations

This article illustrates an argument-based approach to presenting validity evidence for assessment items intended to measure a complex construct. Our focus is developing a measure of teachers’ ability to analyze and respond to students’ mathematical thinking for the purpose of program evaluation. Our validity argument consists of claims addressing connections between our item-development process and the theoretical model for the construct we are trying to measure: attentiveness. Evidence derived from theoretical arguments in conjunction with our multiphased item-development process is used to support the claims, including psychometric evidence of Rasch model fit and category ordering. Taken collectively, the evidence provides …

Testing Our Assumptions: The Role Of First Course Grade And Course Level In Mathematics And English, Janet Callahan, Marcia Belcheir

Materials Science and Engineering Faculty Publications and Presentations

Methods that provide an early indicator of factors that affect student persistence are important to colleges and universities. This quantitative research focused on the role of level of entry mathematics and English and also on grades earned in those classes as they relate to persistence after one year. The research showed that by far, the variable most predictive of first-time, full-time students enrolling one year later was earning a grade of “A” in English. Compared to those who did not pass their first English course, students who earned an “A” were three times more likely to persist. The variables which …

Examining The Influence Of Number Line Fraction Task Characteristics On Student Work, Sharlee Hatch

Boise State University Theses and Dissertations

Research supports the claim that classrooms with teachers who respond to student thinking in the mathematics classroom will see greater student gains and student success (Lamon, 1996; Sleep & Boerst, 2012). The topic of fractions is both difficult to teach and learn, but has important implications on future success in mathematics and in life. This study set out to explore the ways in which student work is influenced by characteristics of number line fraction tasks. By examining task type, number line structure, and number choice this study shares the way these task characteristics influenced student strategies. The relationship between task …

An International Comparison Study Of The Alignment Between Standards And Assessment Of Pre-Service Elementary Mathematics Teacher Preparation Courses, Vilma Guadalupe Duke Escobar

Boise State University Theses and Dissertations

This study addresses the extent to which components of pre-service elementary teachers’ mathematics programs are aligned. Specifically, it includes an analysis of national standards and assessments for elementary mathematics education courses at universities in two countries, the United States and El Salvador. Understanding that the quality of school education is closely linked to pre-service teacher education, the purpose of the study is to contribute much-needed information to assess and improve pre-service elementary mathematics curriculum in both countries. Using Webb’s framework for standards-assessment alignment, data include the Mathematical Education of Teachers II (MET II) standards from the United States and Study …

The Effects Of Professional Development On Elementary Students’ Mathematics Achievement, Jonathan L. Brendefur, Keith W. Thiede, Sam Strother, Dan Jesse, John Sutton

Curriculum, Instruction, and Foundational Studies Faculty Publications and Presentations

This paper describes the effects of a professional development (PD) program – Developing Mathematical Thinking – on student achievement. Six Title I elementary schools with similar demographics, within one school district, were chosen to participate as either a treatment or comparison school. Three schools were chosen to participate in professional development that incorporates effective PD recommendations. All the teachers had to participate in all aspects of the PD, thereby eliminating potential self-selection bias. Using the state standardized achievement test as the before and after measure, results suggest improved student performance after professional development was implemented over a two year period.

First Graders’ Use Of The Bar Model To Communicate Their Understanding Of The Equal Sign, Amber L. Van Vooren

Boise State University Theses and Dissertations

Students’ misunderstandings of the equal sign have been well documented in children as young as kindergarten. Misconceptions of the symbol (=) hinder students’ relational thinking and impede access to algebraic contexts. Symbolic equations (e.g., 4+2=__+3) have been widely used to test students’ understanding and communication of equivalence. The purpose of this study was to explore how first grade students communicate their understanding of equivalence when instruction involved using a bar model versus symbolic equations. It used a two-case study approach to compare an atypical instruction design (the bar model) to a traditional design (symbolic equations). Distinct patterns in communication and …

The Relationship Between High-School Mathematics Teachers' Beliefs And Their Practices In Regards To Intellectual Quality, Jonathan L. Brendefur, Michelle B. Carney

Curriculum, Instruction, and Foundational Studies Faculty Publications and Presentations

This study examines the relationship between mathematics teachers’ beliefs and instructional practices related to learning, pedagogy, and mathematics in regards to components of intellectual quality for eight high-school mathematics teachers. Research has demonstrated that the higher the degree of intellectual quality for instruction is rated the higher student achievement is on standardized assessments. The findings in this study demonstrate a consistent pattern between teachers espoused beliefs and their instructional practices. Even though teachers’ practices changed as they wrote curricular units to be more in line with intellectual quality characteristics, their beliefs stayed consistent over an 18 month period and were …

Support Model For Transfer Students Utilizing The Stem Scholarship Program, Lynn Olson, Amy J. Moll, Doug Bullock, Amit Jain, Janet Callahan

Materials Science and Engineering Faculty Publications and Presentations

This paper describes how the College of Engineering at Boise State University utilized a National Science Foundation S-STEM award from 2011 to 2016 to support transfer students in their path toward graduation. The need for this support was a result of both Boise State University College of Engineering’s transition from a 2-year pre-engineering program to the establishment of Bachelors of Science in Engineering Degree programs in 1997 as well as the establishment of the College of Western Idaho as a regional community college in 2007. Both of these factors led to an increase in the numbers of incoming engineering students …

Expect The Unexpected When Teaching Probability, Karen Koellner, Mary Pittman, Jonathan L. Brendefur

Curriculum, Instruction, and Foundational Studies Faculty Publications and Presentations

Probability has recently made its way into many textbook series and standards documents (NCTM, 2000; NGA, 2010). When students engage in probability problem solving many unexpected situations can arise due to the counterintuitive nature of probability concepts. These situations can be difficult for students and challenging for teachers to analyse during teaching. Recently, as facilitators of a Mathematics Science Partnership grant workshop on probability, we had the opportunity to engage middle school teachers in professional development workshops as well as in their classrooms. In this article, we discuss a rich probability task used with these teachers along with two scenarios …

A Glimpse Into Secondary Students’ Understanding Of Functions, Jonathan L. Brendefur, Gwyneth Hughes, Robert Ely

Curriculum, Instruction, and Foundational Studies Faculty Publications and Presentations

In this article we examine how secondary school students think about functional relationships. More specifically, we examined seven students’ intuitive knowledge in regards to representing two real-world situations with functions. We found students do not tend to represent functional relationships with coordinate graphs even though they are able to do so. Instead, these students tend to represent the physical characteristics of the situation. In addition, we discovered that middleschool students had sophisticated ideas of dependency and covariance. All the students were able to use their models of the situation to generalize and make predictions. These findings suggest that secondary students …

Design Of Computer-Based Assessment Secondary Education For Understanding Of Mathematics, Mark Damian Lewis

Boise State University Theses and Dissertations

The purpose of this study was to evaluate the effectiveness of a computer-based assessment to reveal mathematical understanding. Relevant literature suggested that developments in cognitive science and computer-based assessments could allow the outcomes of cognitively guided instruction to be made explicit. An assessment instrument designed to make mathematical thinking explicit was developed and administered, consisting of 15 animations showing the solutions of one and two digit multiplication problems. A consistent set of five questions followed each animation. The assessment was administered to four classes of fourth grade students in two elementary schools participating in cognitively guided instruction professional development programs. …

Special Educators And Mathematics Phobia: An Initial Qualitative Investigation, Michael Humphrey, Jack J. Hourcade

Early and Special Education Faculty Publications and Presentations

Special educators are uniquely challenged to be content experts in all curricular areas, including mathematics, since students in their case loads may require academic instruction in any area. However, special educators with math phobia may be limited in their ability to provide effective instruction to their students with mathematical deficits and/or needs, and may experience additional challenges in their professional and personal lives. This qualitative study sought to better understand the nature of math phobia in two special educators through extensive interviews, journaling, and observations in math experiences, with a number of primary themes identified. Several potential resolutions for the …

Concept Booklets: Examining The Performance Effects Of Journaling Of Mathematics Course Concepts, Todd Stephen Fogdall

Boise State University Theses and Dissertations

Journaling is an effective tool for writing about mathematics, but research is mixed about the extent to its effectiveness in writing to learn mathematics. This study examined the performance effects of concept booklets on curriculum assessments. Concept booklets are a hybrid style of journal-writing that include responses to journal prompts, diagramming, and traditional note-taking. Prompts were designed to sometimes investigate new concepts and, at other times, to reflect on components of previously learned concepts.

The study, of an experimental design, was carried out at the high school level in honors-level mathematics classes with the independent variable being exposure to the …

Enhancing Precalculus Curricula With E-Learning: Implementation And Assessment, Janet Callahan, Seung Youn Chyung, Joanna Guild, William Clement, Joe Guarino, Doug Bullock, Cheryl Schrader

Materials Science and Engineering Faculty Publications and Presentations

During Fall semester of 2007, a semester-long, quasi-experimental study was conducted at Boise State University to investigate the effectiveness of a systematically sequenced and managed, self-paced e-learning activity on improving students’ academic performance and motivation. A total of 125 students enrolled in 3 different sections of a Precalculus class participated in the study. The e-learning activity was implemented in 2 of the 3 sections as a required homework assignment. Students enrolled in one of the 2 selected sections were all engineering majors. The 3^rd section was a control group that did not use the e-learning activity. A pre-test, measuring …