Science and Mathematics Education Commons^™

It Doesn’T Feel Like A Job To Learn: Hispanic Preservice Teachers’ Perceptions Of Dance-Themed Mathematics Education, William Robertson

Selected Works Temporary Series

A series of dance activities were introduced to preservice teachers (n = 76) to help them understand how mathematics concepts could be associated with dance performance and choreography processes. A total of 468 pieces of qualitative data were collected, including 147 online discussion entries with 248 follow-up 10 comments, and 73 individual reflection essays. The main themes for the various benefits that emerged across the preservice teachers’ reflections were: (1) improving students’ dispositions toward mathematics and creating an enjoyable learning environment for reducing mathematics anxiety; (2) allowing students to develop their creativity and allowing teachers to meet different students’ needs; …

It Doesn’T Feel Like A Job To Learn: Hispanic Preservice Teachers’ Perceptions Of Dance-Themed Mathematics Education, William Robertson

Departmental Papers (TE)

A series of dance activities were introduced to preservice teachers (n  = 76) to help them understand how mathematics concepts could be associated with dance performance and choreography processes. A total of 468 pieces of qualitative data were collected, including 147 online discussion entries with 248 follow-up 10 comments, and 73 individual reflection essays. The main themes for the various benefits that emerged across the preservice teachers’  reflections were: (1) improving students’  dispositions toward mathematics and creating an enjoyable learning environment for reducing mathematics anxiety; (2) allowing students to develop their creativity and allowing teachers to meet different students’  needs; …

The Physics Of Skateboarding: Making Science Relevant, Engaging And Motivational, William Robertson

Selected Works Temporary Series

For me, skateboarding became the vehicle that lead to my success in education. In fact, the skills I learned in skateboarding, such as practice, creativity, discipline, persistence and setting goals, later made me successful in school. For young people, by knowing the terms, they can in effect learn more, when they can see practical applications in their own lives. My inspiration for choosing skateboarding to teach physics came from my work with middle school students who were not interested in the topics of science class until I showed how much of physics, such as forces and motion, were found in …

The Physics Of Skateboarding: Making Science Relevant, Engaging And Motivational, William Robertson

Departmental Papers (TE)

For me, skateboarding became the vehicle that lead to my success in education.  In fact, the skills I learned in skateboarding, such as practice, creativity, discipline, persistence and setting goals, later made me successful in school. For young people, by knowing the terms, they can in effect learn more, when they can see practical applications in their own lives. My inspiration for choosing skateboarding to teach physics came from my work with middle school students who were not interested in the topics of science class until I showed how much of physics, such as forces and motion, were found in …

High School Students' Views Of Science In A University Science Internship With Cogenerative Dialogues, Gabriel M. Hayes

Open Access Theses & Dissertations

The purpose of this Thesis is to determine how participation in long term university science internships affect nature of science (NOS) conceptual change in high school students. The study was conducted on high school students who volunteered to participate in a seven month university science internship in west Texas. Student views of NOS were measured by pre- and post-internship interviews using five questions about NOS. Internship and no internship student responses were qualitatively analyzed to show change in views of NOS. Findings indicated that participation in long term science internships with cogenerative dialogues improved students conceptualizations of the social dimensions …

The Influence Of Multiple Representations On Secondary Students' Understanding Of Trigononetric Functions, Mayra Lizeth Ortiz Galarza

Open Access Theses & Dissertations

Trigonometry is a critical subject in mathematics that both high school and undergraduate students need to learn in order to be prepared for advanced mathematics. Despite the importance of trigonometry in the mathematics curriculum, little is known about best practices for teaching trigonometric functions and what difficulties students face when learning the topic. Using a Grounded Theory approach, this Dissertation presents the results of a design study (or teaching experiment) whose purpose was to examine the process by which students constructed the concept of trigonometric functions through multiple representations and how students developed meta-representational competence. The design study involved two …

Teacher Challenges In Implementing Cognitively Demanding Tasks In The Mathematics And Science Classrooms, Angelica Monarrez Monarrez

Open Access Theses & Dissertations

This mixed methods study examines secondary school mathematics and science teachersâ?? understanding of cognitive demand and the challenges in implementing tasks at different levels of cognitive demand. The conceptual framework for this study is grounded on the conception of cognitive demand proposed by Stein, Smith, Henningsen, and Silver (2000), which includes the following levels: memorization (level 1), procedures without connections (level 2), procedures with connections (level 3), and doing mathematics and science (level 4). The study attempts to address the following research questions: 1) To what extent are secondary mathematics and science teachers able to recognize, solve and construct tasks …

Towards A Unified Theory Of Engineering Education, Oscar Humberto Salcedo

Open Access Theses & Dissertations

STEM education is an interdisciplinary approach to learning where rigorous academic concepts are coupled with real-world lessons and activities as students apply science, technology, engineering, and mathematics in contexts that make connections between school, community, work, and the global enterprise enabling STEM literacy (Tsupros, Kohler and Hallinen, 2009). The purpose of the Dissertation is to develop a unified theory of engineering education based on philosophies of mathematics, science, technology & engineering, and engineering education. Using purposive sampling methods, the Thesis constructs "representative" philosophy statements from the STEM fields based on the criteria of Constructivism, Progressivism, and/or Pragmatism. These statements are …

The Effects Of A Discrete Covariatonal Approach To Functions Through Computer Programming On Students' Understanding Of Rate Of Change, Michael Wayne Strange

Open Access Theses & Dissertations

Having a broad understanding of functions is paramount to student success in higher math classes, however most students fail to fully develop this concept during their high school years. While the concept of function is multifaceted and a full understanding requires a broad knowledge base, understanding rate of change can be considered a fundamental component of the concept. Unfortunately, even AP Calculus students have difficulty with rate of change (Teuscher & Reys, 2012). The problem may stem from the approach taken in most curricula that focus on the correspondence view of functions rather than the covariational perspective as advocated by …

Mathematics Uncovered Through Action Science, William Robertson

Selected Works Temporary Series

In an event-based series of on-site activities with high school students through an Action Science approach, fundamental concepts were explored including the foundations for functions, geometric think and spatial reasoning, the development of mathematical models, as well as techniques for working with spatial figures to understand underlying relationships. The activities in which students participated were designed to teach fundamental mathematics concepts in algebra and geometry in an approach that utilized transformative educational strategies, which helped students move from memorizing facts and content to constructing knowledge in meaningful and useful manners. With an emphasis on a collaborative data collection process, students …

Mathematics Uncovered Through Action Science, William Robertson

Departmental Papers (TE)

In an event-based series of on-site activities with high school students through an Action Science approach, fundamental concepts were explored including the foundations for functions, geometric think and spatial reasoning, the development of mathematical models, as well as techniques for working with spatial figures to understand underlying relationships. The activities in which students participated were designed to teach fundamental mathematics concepts in algebra and geometry in an approach that utilized transformative educational strategies, which helped students move from memorizing facts and content to constructing knowledge in meaningful and useful manners. With an emphasis on a collaborative data collection process, students …

Analysis Of English Language Learner Student Reasoning About Measures Of Center And Variation: A Triangulation Of Quantitative And Qualitative Data, Lorena Galvan

Open Access Theses & Dissertations

The population of Spanish-speaking English Language Learner (ELL) students has been growing rapidly in the past 20 years. It has been estimated that by the year 2018, 1 out of 4 students in grades K-12 will be an ELL. There is a large body of research about assessment of Spanish-speaking ELL students in mathematics; however, there is little that focuses on statistics only. Statistics courses are frequently confused and/or classified under mathematics courses. However, students taking an introductory statistic course are required to know a new set of concepts, words and vocabulary that are not always used in mathematics courses. …

The Flipped Approach: The Use Of Embedded Questions In Math Videos, Ashley Wilson

Open Access Theses & Dissertations

This study investigates the use of embedded questions in math videos and their effect on students self-paced learning in a hybrid math course. A treatment group watched math videos with embedded questions and a comparison group watched the same videos but without the embedded questions. The two groups are compared in terms of (a) amount of video watched, (b) quality of written work, (c) performance in assessments, (d) course component scores, and (e) opinions about self-paced learning and the flipped classroom method. The pre-to-posttest improvement for the treatment group was higher than the comparison group. The embedded questions might have …

Investigating Math Students' Ability To Conceptualize Fractions As Two Numerals Having A Single Value, William Carroll Fanning

Open Access Theses & Dissertations

It is no secret that math students of all ages have misconceptions about fractions. Multiple studies have shown that math students invariably see fractions as two separate and unrelated numbers, the numerator and the denominator, rather than a single number with specific value. This study is designed to investigate studentsâ?? interpretations of a fraction in terms of having a single value in relation to its two numbers, the numerator and the denominator.

For the purpose of this study, the investigator developed and pilot-tested seven items that have the potential to uncover whether students attend to the value of a fraction …

Secondary Mathematics Teachers' Disposition Toward Challenge And Its Impact On Teaching Practice, Yirah Mariana Valverde

Open Access Theses & Dissertations

This two phase, sequential exploratory study focused on mathematics teachers' disposition toward challenge and its impact in their teaching practice and students' performance. This heavily qualitative study employed a mixed methodology to answer the following guiding research question: how do teachersâ?? disposition towards challenge affect teaching practice and what is the nature of that relationship?

During the initial phase (quantitative), two teachers who were enrolled in a graduate mathematics at a University in the southwestern U.S. were selected for the study (N=5). The goal of the class was to increase the participants' mathematical knowledge for teaching. The purposive selection was …

The Skatepark Mathematics Extravaganza, William Robertson

Selected Works Temporary Series

In the fall of 2014, a series of live demonstrations and field-based activities were lead by a team of educators and top action sports athletes who performed at local high schools. These events, entitled the “Skatepark Mathematics Extravaganza”, were done in order to engage high school students in focused explorations of mathematics set in a real world setting that is relevant to youth culture, namely skateboarding and bicycle motocross (BMX). These activities incorporated mathematics for the students to do after the demonstration in meetings with classes in which the Action Science Stunt Team performed maneuvers on ramps at the high …

The Skatepark Mathematics Extravaganza, William Robertson

Departmental Papers (TE)

In the fall of 2014, a series of live demonstrations and field-based activities were lead by a team of educators and top action sports athletes who performed at local high schools. These events, entitled the “Skatepark Mathematics Extravaganza”, were done in order to engage high school students in focused explorations of mathematics set in a real world setting that is relevant to youth culture, namely skateboarding and bicycle motocross (BMX).  These activities incorporated mathematics for the students to do after the demonstration in meetings with classes in which the Action Science Stunt Team performed maneuvers on ramps at the high …

Coming Up With A Good Question Is Not Easy: A Proof, Joe Lorkowski, Luc Longpre, Olga Kosheleva, Salem Benferhat

Departmental Technical Reports (CS)

Ability to ask good questions is an important part of learning skills. Coming up with a good question, a question that can really improve one's understanding of the topic, is not easy. In this paper, we prove -- on the example of probabilistic and fuzzy uncertainty -- that the problem of selecting of a good question is indeed hard.

Creative Discussions Or Memorization? Maybe Both? (On The Example Of Teaching Computer Science), Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

We all strive to be creative in our teaching, but there is often not enough time to make all the topics creative fun. So sometimes, we teach memorization first, understanding later. We do it, but we often do it without seriously analyzing which topics to "sacrifice" to memorization. In this talk, we use simple mathematical models of learning to come up with relevant recommendations: Namely, all the topics form a dependency graph, and if we do not have enough time to allow students to treat all topics with equal creativity, then the most reasonable topics for memorization first are the …

Pre-Service Elementary Teachers' Affective Dispositions Toward Mathematics, Benjamin R. Mcdermott

Open Access Theses & Dissertations

The purpose of this study was to measure and report pre-service elementary teachers' affective domain of productive disposition toward mathematics during the semester they were enrolled in a reform-based mathematics methods course. The study attempted to observe and report dynamic and enduring aspects of disposition as well as the perceived reasons for any changes, or lack thereof, in disposition. The rationale for focusing on disposition is related to Kilpatrick, Swafford, and Findell's (2001) inclusion of productive disposition as one of the five interdependent strands of the mathematical proficiency conceptual framework. Furthermore, it has been argued that dispositions develop at very …

High School Students' And Scientists' Perceptions Of A Student-Scientist Partnership, Karla Singh

Open Access Theses & Dissertations

The idea of getting high school students to work with scientists has become a hot topic. There have been many programs that get students involved with scientists to gain experience. Having students work with scientists allows students to practice authentic science. These programs also aim to get more students interested in science and hopefully inspire these students to go into a science career. Researchers have looked at several aspects during these interactions. These aspects include students' interest, students' ability, students' career choice and students' perceptions of the scientific community. However, few studies are known that include trying to understand students' …

Challenges In Assessing College Students' Conception Of Duality: The Case Of Infinity, Grace Olutayo Babarinsa-Ochiedike

Open Access Theses & Dissertations

Interpreting students' views of infinity posits a challenge for researchers due to the dynamic nature of the conception. There is diversity and variation among students' process-object perceptions. The fluctuations between studentsâ?? views however reveal an undeveloped duality conception. This study examined college students' conception of duality in understanding and representing infinity with the intent to design strategies that could guide researchers in categorizing students' views of infinity into different levels.

Data for the study were collected from N=238 college students enrolled in Calculus sequence courses (Pre-Calculus, Calculus I through Calculus III) at one of the southwestern universities in the U.S. …

Borderland Pedagogy Study Of High School Mathematics Teachers' Lesson Plan Development And Implementation Practices, Rocio E. Gallardo

Open Access Theses & Dissertations

The aim of the study is to examine high school mathematics teachers' lesson plan development and implementation practices used in the border region of Mexico and USA. The study also attempts to determine how a transition from Mexico (Ciudad Juarez, Chihuahua) to the U.S. (El Paso, TX) impacts high school mathematics teacher's lesson plan development practices incorporating the Borderland Pedagogy. The Borderland Pedagogy theoretical framework (Cline & Necochea, 2006; Romo & Chavez 2006; Fiume, 2005) was developed to explore educational experiences of teachers situated within border regions. The framework highlights key characteristics of Borderland Pedagogy that influence lesson plan development …

High School Mathematics Teachers' Connective Knowledge Of The Challenges And Possibilities In Implementing The Flipped Learning Model: An Embedded Mixed-Methods Study, Karla Huereca

Open Access Theses & Dissertations

The impact of technology advancements in our current society continues to transform the ways in which we interact with each other, and the educational field has not been exempt from this transformation. Integration of technology in schools has influenced educators to seek new ways of teaching that adapt to the needs of students who are impacted by a digital wave. That is the case of a new instructional approach, which is being known as the Flipped Learning Model (FLM). The FLM intends to use pre-recorded video lessons to teach outside the classroom and incorporate homework and problem solving inside the …

Mentor Preparation: A Qualitative Study Of Stem Master Teacher Professional Development, Heather Lynn Click-Cuellar

Open Access Theses & Dissertations

The No Child Left Behind Act of 2001 has required districts to staff all classrooms with highly qualified teachers. Yet, retaining certified teachers in the profession has been a national concern, especially among new teachers who leave at alarming rates within their first three years. This comes at a heavy cost to districts financially and in trying to maintain highly qualified status, but also to the continuity and effective education of students. Mentoring has been identified by many researchers as a plausible solution to reducing attrition rates for beginning teachers.

In this Dissertation, I conducted qualitative research to explore and …

Relationship Between Cognitive Types Of Teacher Content Knowledge And Knowing-To Act: A Mixed Methods Study Of Mexican Borderland Middle School Teachers, Maria De Los Angeles Cruz Quinones

Open Access Theses & Dissertations

This study analyzed middle school mathematics teachers' content knowledge and its relationship with teachers' "knowing-to act" ability. Understanding what kinds of knowledge has a direct influence on teaching practices and student learning is critical in order to improve teacher education programs and professional development. An Explanatory sequential mixed methods design was used in the study. It involved collecting quantitative data and explaining the quantitative results with in-depth qualitative data. In the quantitative phase of the study, two surveys were administered to N=70 middle school mathematics teachers in the Mexican borderland to assess whether their mathematical content knowledge was related to …

Views From A Community College On The U.S.- Mexico Border: Mexican/Mexican-American Postsecondary Students' Perceptions Of K-16 Mathematics Education, Carlos Ruben Paez Paez

Open Access Theses & Dissertations

The purpose of this study was to investigate Mexican/Mexican-American postsecondary students' perceptions and experiences of mathematics instruction in U.S. formal education (K-16). Framed by critical race theory and using a grounded theory approach, this inquiry was conceptualized within the framework of the literature on academic disparities in achievement in mathematics between Mexican American students and other student populations in U.S. schools, highlighting students' perceptions and student voice. Qualitative data were collected through interviews and surveys from five postsecondary students who voluntarily participated in the study. Data analysis used the constant comparative method, a key element of grounded theory methodology (Glaser, …

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 …

Scientific Skateboarding And Mathematical Music: Edutainment That Actively Engages Middle School Students, William Robertson, Larry Lesser

Selected Works Temporary Series

Edutainment has recently been a major growing area of education, showing great promise to motivate students with relevant activities. The authors are among innovators who have developed cutting-edge fusions of popular culture and STEM concepts to engage and to motivate middle school students, using vehicles such as music/song and skateboarding. The importance of using relevant and practical methods of instruction and curriculum delivery that build on student interests and increase enjoyment in the learning process are critical at the middle school level, especially in the STEM fields. The use of edutainment in this manner is meant to inspire broader interest …

Scientific Skateboarding And Mathematical Music: Edutainment That Actively Engages Middle School Students, William Robertson, Larry Lesser

Departmental Papers (TE)

Edutainment has recently been a major growing area of education, showing great promise to motivate students with relevant activities. The authors are among innovators who have developed cutting-edge fusions of popular culture and STEM concepts to engage and to motivate middle school students, using vehicles such as music/song and skateboarding. The importance of using relevant and practical methods of instruction and curriculum delivery that build on student interests and increase enjoyment in the learning process are critical at the middle school level, especially in the STEM fields. The use of edutainment in this manner is meant to inspire broader interest …