Science and Mathematics Education Commons^™

I Know How To Add Them, I Didn't Know I Had To Add Them, Jyoti R. Jhagroo

Australian Journal of Teacher Education

Abstract: Ten non-English speaking immigrant students shared their lived experiences in their secondary school mathematics classrooms in New Zealand. Through the voices of these students some understandings of the challenges they experienced as second language learners are brought to the fore. The students’ perspectives of the language-related challenges that they faced, how they made sense of learning in an environment where the medium of instruction was dissimilar to their first language, and the impact that language-related challenges may have had on their perceptions of their ability in their new environment compared to their home country, form the basis of this …

A Method For Assessing And Describing The Informal Inferential Reasoning Of Middle School Students, Joshua Michael Goss

Dissertations

Informal Inferential Reasoning (IIR) has emerged in the last decade in the study of statistics education. Developing students’ IIR ability is seen as a way of preparing students for the important topic of Formal Statistical Inference (FSI); however, research is still needed in order to investigate how students transition between informal and formal statistical reasoning. A primary difficulty is that we do not have a way of assessing and describing students’ IIR ability levels. In order to address this, an Assessment of Informal Inferential Reasoning (AIIR) was developed, along with a Structure of Observed Learning Outcomes (SOLO) taxonomy (Biggs & …

Supporting Student Justification In Middle School Mathematics Classrooms: Teachers' Work To Create A Context For Justificaiton, Megan Staples

CRME Publications

Justification is an important disciplinary and learning practice. Despite a growing knowledge base regarding how teachers orchestrate mathematical discussions, few analyses have considered the orchestration of specific disciplinary practices such as justification. Using classroom video data from the JAGUAR project, we analyze two instantiations of extensive student justification in seventh-grade classrooms and document each teacher’s pedagogical approach that supported students’ engagement in this practice. We argue that, although there was overlap in their pedagogical repertoires, the teachers created a context for student justification in two unique ways. We document the similarities and differences in their approaches, including the nature of …

Mastery Learning In Calculus I Affects Student Learning, Grade Improvement, And Professor Exhaustion, Judith Puncochar, Don H. Faust

Conference Presentations

Three Calculus I courses were taught under conditions of either traditional teaching, 2/3 mastery, or full mastery to test four hypotheses. Under conditions of mastery learning on exams, students should attain appropriate higher-level mathematical concepts, achieve more learning of higher-level mathematical concepts, learn higher-level mathematical concepts more quickly, and evaluate mastery learning favorably. Support for all hypotheses occurred only in the 2/3 mastery condition. A shift toward higher grades was attributed to grade improvement, not grade inflation, as determined by six mathematicians with blind review of final exam items. Final exams in mastery learning courses were significantly more …

What Is So Negative About Negative Exponents?, Geoffrey D. Dietz

Journal of Humanistic Mathematics

While teaching college-level mathematics (from College Algebra to Calculus to Abstract Algebra), I have observed that students are often uncomfortable using negative exponents in calculations. I believe the fault partially lies in the manner in which negative exponents are taught in Algebra 1 or Algebra 2 courses, especially in rigid instructions always to write answers using only positive exponents. After reviewing a sample of algebra texts used in the United States over the last two centuries, it appears that while attitudes toward negative exponents have varied from author to author over time, the current trend is to declare explicitly that …

A Proposed Framework For Combining Smart Environment And Heuristic Diagnostic Teaching Principles In Order To Assess Students’ Abilities In Math And Supporting Them During Learning, Ardiana Sula, Evjola Spaho, Leonard Barolli, Rozeta Miho

Jandrisevits Faculty Publications

In this paper, we propose the use of the smart environment based on Internet of Things (IoT), P2P technology and Heuristic Diagnostic Teaching principles for identifying learning abilities in mathematics and creative traits for students that are diagnosed within Autism Spectrum disorder (ASD). Many children with autism are highly interested and motivated by smart devices such as computers and touch screen tablets. These types of assistive technology devices get children with autism to interact, make choices, respond, gain new communication skills and create P2P communication between children, caregivers and therapists. Our proposed system uses JXTA-Overlay platform and SmartBox device to …

Review Of Principles To Actions: Ensuring Mathematical Success For All, Eric L. Mann

Faculty Publications

No abstract provided.

Rehearsal And Enactment For Teaching In Urban School Settings: A Qualitative Study Investigating The Connections Between A Math Methods Course And Fieldwork, Rajeev Virmani

Doctoral Dissertations

In this dissertation, I studied teacher education reform efforts aimed at improving the preparation of preservice teachers through the use of rehearsals in a math methods class. As many experts in the field of teacher education call for curricula in which preservice teachers learn from and in practice, I investigated a type of pedagogy called rehearsals within a practice-based teacher education setting that may afford preservice teachers with the initial preparation needed to become effective teachers.

In this qualitative study, I examined how three preservice teachers and math methods instructors rehearse the high leverage practice of leading a whole-class discussion. …

Encouraging Literacy And Mathematics Achievement Through Study Of Real Estate, Ryan Andrew Nivens, Lori T. Meier, Karin J. Keith, Erin E. Doran, Edward J. Dwyer

ETSU Faculty Works

The era of high stakes testing often puts pressure on teachers and administrators to deemphasize creative activities not perceived as directly related to improving test scores. Alternatively, the authors propose that using environmental text is essential for encouraging overall learning competencies in general and reading/writing/ and mathematical achievement in particular. The authors propose that using real estate booklets can be helpful in generating learning activities in literacy, social studies, and mathematics. In addition, integrating music and art comfortably accompanies strategies presented. Real estate booklets are colorful, rich in content, and readily available at no expense.

Assessing U.S. High School Mathematics Students' Dependency On Calculators For Basic Arithmetic Operations Involving Integers From Single-Digit Fact Families, John Jeremy Sneed

Open Access Theses & Dissertations

This study was designed to investigate the extent to which high school students use calculators to perform basic operations, and how well they actually perform those same operations without using calculators. The investigation involved the testing of math classes of students--male and female, mixed ethnicities--in grades nine through twelve. Students were asked to perform all four basic math operations (add, subtract, multiply, divide) involving integers based on single-digit addition and multiplication fact families with and without calculators. The testing was in two environments--timed and untimed, with students recording their completion times--in order to investigate discrepancies in students' calculator use in …

Discover Math With Sketchpad Explorer, Helen Crompton

Teaching & Learning Faculty Publications

Review of Geometer's SketchPad.

A Primer For Mathematical Modeling, Marla A. Sole

Publications and Research

With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school with the mathematics they will use outside of school. Instructors have found mathematical modeling difficult to teach. To successfully incorporate modeling activities I believe that curricular changes should be accompanied by professional development for curriculum developers, classroom teachers, and higher education professionals. This article serves as an introduction to modeling by …

Parts Of The Whole: The Educational Sieve, Dorothy Wallace

Numeracy

This essay argues that the structure of course prerequisites affects retention of students in a course of study. The same argument suggests that the structure of degree requirements, including quantitative reasoning courses, affects retention in college. In particular, the same set of courses required in a rigid sequence will cause more students to exit the program early than if the same courses were offered in a flexible order.

A Comparison Of Two Job Offers In Mathematics Education, Ryan Andrew Nivens

ETSU Faculty Works

Many job seekers in higher education are unaware of how large a discrepancy there can be in terms of financial potential for mathematics education jobs in higher education. Recent research on this topic has focused on the base salary (Reys, Reys, & Estapa, 2013), but other financial factors have been left unstudied. Through two cases, the researcher demonstrates a large gap that exists in net pay when major financial factors beyond base salary are considered, specifically insurance and retirement benefits. This article will spur conversations among faculty and graduate students in mathematics education doctoral programs allowing mentors to draw from …

Teaching Undergraduates How To Analyze, Ryan Andrew Nivens, Rosalind Raymond Gann

ETSU Faculty Works

Analysis is typically the first of the higher functions listed in taxonomies of higher order thinking. Academics consider these upper categories extremely worthwhile, but they are hard to teach and we are apt to ignore them. Today higher education is being criticized for “dumbing down” curriculum or lowering standards. To rectify this, many policies at the state or national level are requiring higher education institutions to change. In K‐12 education, Race to the Top and Common Core requirements are placing new demands on K‐12 teacher preparation, which include evaluation of the analysis skills of pre‐service teachers. But professors do not …

Changing The Order Of Mathematics Test Items: Helping Or Hindering Student Performance?, Kristin T. Kennedy, Allison G. Butler

Journal of Humanistic Mathematics

This paper recounts an experiment by a mathematics professor who primarily teaches mathematics majors. The main question explored is whether the ordering of the questions makes a difference as to how students perform in a test. More specifically we focus here on the following research questions:\ (1) Does arranging a math test with easy-to-hard items versus hard-to-easy items impact student performance? and (2) If so, does item order impact male and female mathematics majors and non-majors in unique ways? We examine data collected over multiple semesters with several different classes. We find that for most of the mathematics students who …

Parts Of The Whole: When Variation Is The Goal, Dorothy Wallace

Numeracy

The goals of higher education are a population of extreme variability in expertise, a diffusion of specialized knowledge across disciplinary boundaries, and production of strong K-12 teachers. Promoting these three goals has implications at all granularities, from the pedagogy of an individual college professor to the incentives and policies that shape systemic change.

The Mathematical Development In Number And Operation Of Struggling First Graders, John Lannin, Delinda Van Garderen, Matthew J. Switzer, Kelley E. Buchheister, Tiffany Hill, Christa Jackson

Department of Child, Youth, and Family Studies: Faculty Publications

Number and operations serve as the “cornerstone” of the K-12 mathematics curriculum in many countries. Solving problems in the mathematical domains of algebra, geometry, measurement, and statistics is often closely connected to student knowledge of number and operation (Griffin, 2005). Although considerable knowledge exists regarding the development of number and operation for typically developing children, less is known about the development of children who struggle in mathematics. Moreover, children enter school with considerable differences in their understanding of number and operation. While most children, through exposure to various informal and formal tasks, develop a deeper understanding of number and operation, …

Investigating The Impact Of Interactive Applets On Students’ Understanding Of Parameter Changes To Parent Functions: An Explanatory Mixed Methods Study, Robin R. Mcclaran

Theses and Dissertations--Science, Technology, Engineering, and Mathematics (STEM) Education

The technology principle in the Principles and Standards for School Mathematics (NCTM, 2000) states that technology plays an important role in how teachers teach mathematics and in how students learn mathematics. The purpose of this sequential explanatory mixed-methods study was to examine the impact of interactive applets on students’ understanding of parameter changes to parent functions. Students in the treatment classes were found to have statistically significantly higher posttest scores than students in the control classes. Although the data analysis showed a statistically significant difference between classes on procedural understanding, no statistically significant difference was found with regard to conceptual …

Development Of A Taxonomy For Key Terms In Mathematics Education And Its Use In A Digital Repository, Pedro Gómez, María C. Cañadas Dr.

Library Philosophy and Practice (e-journal)

Although mathematics education is a young discipline, it has developed rapidly over the last 40 years. During this time, the community of mathematics education researchers, teachers’ trainers, and mathematics teachers has produced a large quantity of literature published in books, journals, and conference proceedings and on Internet, among other sources. Yet there is currently no taxonomy of key terms for the systematic classification of the documents in this discipline. In this article, we present the procedure by which we constructed a taxonomy for Funes, a digital repository of documents in mathematics education. We establish the conceptual framework on which the …

Productive Peer Culture: Algebra Project Students’ View, Melva R. Grant

Teaching & Learning Faculty Publications

The purpose of this study was to determine students’ perspectives about productive peer culture for mathematics learning. The participating students were attending an annual residential summer institute and have been participating in Algebra Project activities for at least one year. Of the 26 high school students attending the institute, they all participate in mathematics literacy work1 through their local Young People’s Project (YPP) groups, while 20 of those students also receive their regular school-based mathematics instruction within an Algebra Project Cohort Model (APCM) structured classroom².

The Algebra Project targeted persistently underserved mathematics students who typically scored in the …

A Conceptual Framework For Student Understanding Of Logarithms, Heather Rebecca Ambler Williams

Theses and Dissertations

In the past, frameworks for what it means for students to understand elementary mathematical concepts like addition have been well-researched. These frameworks are useful for identifying what students must understand to have a good grasp of the concept. Few such research-based frameworks exist for secondary mathematical topics. The intent of this study was to create such a framework for what it means for students to understand logarithms, a topic that has been under-researched up to this point. Four task-based interviews were conducted with each of four different preservice secondary mathematics teachers in order to test a preliminary framework I had …

Mathematically Gifted Students' Experiences Of Challenge With Cognitively Guided Instruction, Kim Krusen Mccomas

Graduate Theses and Dissertations

This study examined to what extent and in what ways mathematically gifted students were challenged in two elementary classrooms taught by exemplary teachers using the principles of Cognitively Guided Instruction (CGI). The two case studies included a third grade class and a fourth/fifth split grade class, with five mathematically advanced participants from each grade. A top tier and a second tier of mathematically advanced students were identified, with the top tier of five students identified as mathematically gifted. Classroom observations of CGI math lessons, interviews with students and teachers, and analysis of students' problem-solving strategies were conducted over a five …

A Mathematician Weighs In On The Evolution Debate, Kris H. Green

Journal of Humanistic Mathematics

There are a variety of reasons underlying the lack of public acceptance for the theory of evolution in the United States. An overlooked cause is related to problems with the mathematics curriculum in the K-12 setting. In this essay, we examine this relationship and propose changes to the mathematics curriculum that could improve mathematical thinking while also providing a basis for understanding theories, like evolution, that are poorly understood.

Education Of Mathematically Talented Students In Hungary, Julianna Connelly Stockton

Mathematics Faculty Publications

Hungary is famous for its production of large numbers of highly talented mathematicians and physicists. This study explores the Hungarian system for educating mathematically talented secondary school students with the goal of identifying successful features that may be applicable to education in the United States. Highlights of the Hungarian approach include an emphasis on problem solving, problem posing, detailed explanation or proof for solutions, and development of mathematical creativity through the search for multiple solution paths.

The Effect Of Teacher Pedagogical Content Knowledge And The Instruction Of Middle School Geometry, Sara Talley Lenhart

Doctoral Dissertations and Projects

This study investigated the relationship between middle school math teacher pedagogical content knowledge as gathered from a teacher assessment and student Standards of Learning scores. Nine middle-school math teachers at two rural schools were assessed for their pedagogical content knowledge in geometry and measurement in the specific area of decomposing and recomposing one-dimensional and two-dimensional figures. A Pearson's Product Moment Coefficient statistical test was used to compare teacher assessment scores of each pedagogical content knowledge level with student Standard of Learning math scores. The results showed that there is a relationship between teacher pedagogical content knowledge and student Standards of …

Understanding Teachers' Change Towards A Reform-Oriented Mathematics Classroom, Linnae Denise Williams

Theses and Dissertations

Within the current mathematics teacher population there are teachers that want to change from traditional teaching styles to become more reform-oriented (i.e. focusing on student understanding rather than procedures). Many of these teachers do not know how to begin this change. This research looks into the tools that are most valuable for teachers as they change from traditional teaching practices to include more reform-oriented teaching practices. Through this phenomenological study, six successful reform-oriented teachers were interviewed to understand what tools they found to be most valuable in their process of change. The interviews uncovered a common guiding principle that facilitates …

A Study Of The Relationships Between Epistemological Beliefs And Self-Regulated Learning Among Advanced Placement Calculus Students In The Context Of Mathematical Problem Solving, James Clinton Stockton

Dissertations, Theses and Capstone Projects (Full IR Collection)

Secondary mathematics educators advocating constructivist-oriented instruction face the dilemma of developing students’ problem-solving skills. Students’ epistemological beliefs and self-regulated learning (SRL) processing capacity influence mathematical problem-solving prowess. This multiple-case study explored the relationships between epistemological beliefs and SRL processing while advanced mathematics students engaged in problem-solving tasks and investigated students’ SRL strategy use, heuristic strategy use, and problem-solving performance. Data sources included think-aloud and interview transcriptions, student work, and classroom observation protocols. Validity and reliability were enhanced via member-checking interviews, triangulation, peer review, and completion of a case study database. Five major findings emerged from the data: (1) participants’ unique/arbitrary …

Symmetry From Nature To The Classroom, Rochelle Lueders

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

A Business Approach To Teaching Quadratic Functions, Alexander Vaninsky

Touchstone

No abstract provided.