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## Full-Text Articles in Education

Context Is Critical: K-5th Grade Three-Act Math Tasks, Lindsey Herlehy

#### Context Is Critical: K-5th Grade Three-Act Math Tasks, Lindsey Herlehy

*Publications & Research*

Mathematicians view mathematics within interesting and natural contexts. In this session, participants will engage and explore Three-Act Math Tasks; a story-telling pedagogical strategy that elicits student curiosity, collaboration, and questioning while redefining the term “real-world context” and the role that students play in the learning process. Resources will be provided

Why We Teach Mathematics To Every Student: Determining Impact Of Mathematics On Problem Solving And Logical Reasoning Skills, Megan Marie Harris

#### Why We Teach Mathematics To Every Student: Determining Impact Of Mathematics On Problem Solving And Logical Reasoning Skills, Megan Marie Harris

*Williams Honors College, Honors Research Projects*

The purpose of this paper is to dissect why it is important to teach mathematics to every student, even if the student does not plan on pursuing mathematics in his or her career. This paper will describe and test various reasons why mathematics is taught to every student but it will focus on math as a way to help develop and improve problem-solving and logical reasoning skills. An experiment was conducted on a random sample of fourteen University of Akron students who were measured on their problem-solving abilities and critical thinking through playing two games. These students were then compared ...

Investigating Secondary Students Beliefs About Mathematical Problem-Solving, Mark Prendergast, Cormac Breen, Aibhin Bray, Fiona Faulkner, Brian Carroll, Dominic Quinn

#### Investigating Secondary Students Beliefs About Mathematical Problem-Solving, Mark Prendergast, Cormac Breen, Aibhin Bray, Fiona Faulkner, Brian Carroll, Dominic Quinn

*Articles*

Many studies over the past thirty years have highlighted the important role of students’ beliefs for successful problem solving in mathematics. Given the recent emphasis afforded to problem solving on the reformed Irish secondary school mathematics curriculum, the main aim of this study was to identify Irish students’ (n = 975) beliefs about the field. A quantitative measure of these beliefs was attained through the use of the Indiana Mathematical Belief Scale, an existing thirty item (five scale) self-report questionnaire. A statistical analysis of the data revealed that students who were further through their secondary education had a stronger belief that ...

Strongly And Weakly Directed Approaches To Teaching Multiple Representation Use In Physics, Patrick B. Kohl, David Rosengrant, Noah D. Finkelstein

#### Strongly And Weakly Directed Approaches To Teaching Multiple Representation Use In Physics, Patrick B. Kohl, David Rosengrant, Noah D. Finkelstein

*David Rosengrant*

Good use of multiple representations is considered key to learning physics, and so there is considerable motivation both to learn how students use multiple representations when solving problems and to learn how best to teach problem solving using multiple representations. In this study of two large-lecture algebra-based physics courses at the University of Colorado (CU) and Rutgers, the State University of New Jersey, we address both issues. Students in each of the two courses solved five common electrostatics problems of varying difficulty, and we examine their solutions to clarify the relationship between multiple representation use and performance on problems involving ...

Beyond Problem-Solving: Elementary Students’ Mathematical Dispositions When Faced With The Challenge Of Unsolved Problems, Jenna R. O'Dell

#### Beyond Problem-Solving: Elementary Students’ Mathematical Dispositions When Faced With The Challenge Of Unsolved Problems, Jenna R. O'Dell

*Theses and Dissertations*

The goal of this study was to document the characteristics of students’ dispositions towards mathematics when they engaged in the exploration of parts of unsolved problems: Graceful Tree Conjecture and Collatz Conjecture. Ten students, Grades 4 and 5, from an after-school program in the Midwest participated in the study. I focused on the cognitive, affective, and conative aspects of their mathematical dispositions as they participated in 7 problem-solving sessions and two interviews.

With regard to cognitive aspects of the students’ dispositions, I focused on the students attempts to identify and justify patterns for labeling graphs. Overall, the unsolved problems were ...

Structural-Symbolic Translation Fluency: Reliability, Validity, And Usability, Matt C. Hoskins

#### Structural-Symbolic Translation Fluency: Reliability, Validity, And Usability, Matt C. Hoskins

*Electronic Theses and Dissertations*

Standardized formative mathematics assessments typically fail to capture the depth of current standards and curricula. Consequently, these assessments demonstrate limited utility for informing the instructional implementation choices of teachers. This problem is particularly salient as it relates to the mathematical problem solving process. The purpose of this study was to develop and evaluate the psychometric characteristics of Structural-Symbolic Translation Fluency, a curriculum-based measure (CBM) of mathematical problem solving. The development of the assessment was based on previous research describing the cognitive process of translation (Mayer, 2002) as well as mathematical concept development at the quantitative, structural, and symbolic levels (Dehaene ...

Preservice Teacher Learning To Help Els Understand Mathematical Problems, Ji Yeong I, Ricardo Martinez

#### Preservice Teacher Learning To Help Els Understand Mathematical Problems, Ji Yeong I, Ricardo Martinez

*Education Conference Presentations, Posters and Proceedings*

There is a common belief that teachers do not need to differentiate their instruction for English Learners (ELs) and that helping ELs adjust in school culture is not a teacher’s responsbility (Walker, Shafer, & Liams, 2004). This belief is due to their lack of proper training to teach ELs, as statistics show only 13% of teachers are adequately prepared to teach ELs while more than 40% of teachers have ELs in their classrooms (NCES, 2002). Responding to the great need for an adequate teacher preparation for EL in mathematics education, this study was designed to investigate preservice teacher (PSTs) learning ...

Middle School Students' Conceptions On Proportional Reasoning, Ji Yeong I, Ricardo Martinez

#### Middle School Students' Conceptions On Proportional Reasoning, Ji Yeong I, Ricardo Martinez

*Education Conference Presentations, Posters and Proceedings*

Proportions are an important mathematics concept taught during middle school. In fact, proportional reasoning is “a milestone in student’s cognitive development” (Lobato & Ellis, 2010, p. 48) and plays a critical role in developing algebraic thinking and function sense (National Council of Teachers of Mathematics, 2013; National Mathematics Advisory Panel, 2008). However, ratios and proportions are traditionally difficult concepts as Lamon (2007) stated: “the most difficult to teach, the most mathematically complex, the most cognitively challenging” (p. 629).

The Effects Of Constructs Related To Mathematical Persistence On Student Performance During Problem Solving, Derek M. Stoll

#### The Effects Of Constructs Related To Mathematical Persistence On Student Performance During Problem Solving, Derek M. Stoll

*Education and Human Development Master's Theses*

The common core state standards in mathematics support the importance of persistence to mathematical problem solving calling it a 21^{st} century skill (Common Core Initiative, 2010). The nature of true problem solving as outlined by Schoenfeld (1992) requires this element of persistence in mathematics. However, new research (Duckworth et al, 2007; US Department of Education, 2013) has identified multiple ways to be able to measure these non-cognitive skills, such as persistence, using a variety of methods. The purpose of this study is to use these methods to be able to determine whether mathematical persistence is predictive of mathematical performance ...

Changing The Culture: Developing Creative Problem Solvers, Eric L. Mann

#### Changing The Culture: Developing Creative Problem Solvers, Eric L. Mann

*Faculty Presentations*

Mathematics embraces creativity and beauty yet often our children are immersed in classroom activities where these attributes are hidden by an overemphasis on algorithms, computational speed and known answers that can be found in the back of the book or with a quick Google search. This learning environment creates a false perception of what it means to be “good at math.” From the research we know than many of our elementary school teachers have negative attitudes towards mathematics; an attitude students pick up and adopt which may foster the development of the reluctant, impatient problem solvers we find in our ...

Northeast Tennessee Educators’ Perception Of Stem Education Implementation, Kristin Turner

#### Northeast Tennessee Educators’ Perception Of Stem Education Implementation, Kristin Turner

*Electronic Theses and Dissertations*

A quantitative nonexperimental survey study was developed to investigate Northeast Tennessee K-8 educators’ perceptions of STEM education. This study was an examination of current perceptions of STEM education. Perceived need, current implementation practices, access to STEM resources, definition of STEM, and the current condition of STEM in Northeast Tennessee were also examined. The participating school districts are located in the Northeast Region of Tennessee: Bristol City Schools, Hamblen County Schools, Johnson City Schools, Johnson County Schools, Kingsport City Schools, Sullivan County Schools, and Washington County Schools. Educational professionals including both administrators and teachers in the elementary and/or middle school ...

Incorporating Pólya’S Problem Solving Method In Remedial Math, Shenglan Yuan

#### Incorporating Pólya’S Problem Solving Method In Remedial Math, Shenglan Yuan

*Journal of Humanistic Mathematics*

György Pólya’s problem solving method has influenced generations of mathematicians and non-mathematicians alike. Though almost all math teachers have come across Pólya’s problem solving method, his ideas are not regularly implemented in the classroom. Few studies have examined the effectiveness of his approach in teaching remedial math. In this article we revisit this once well-known teaching method and show how it can be used in basic skills math classes to ease student fears of math, and potentially change their common misconceptions of the subject.

Mathematical Tasks Without Words And Word Problems: Perceptions Of Reluctant Problem Solvers, Sydney Margaret Holbert

#### Mathematical Tasks Without Words And Word Problems: Perceptions Of Reluctant Problem Solvers, Sydney Margaret Holbert

*Electronic Theses and Dissertations*

This qualitative research study used a multiple, holistic case study approach (Yin, 2009) to explore the perceptions of reluctant problem solvers related to mathematical tasks without words and word problems. Participants were given a choice of working a mathematical task without words or a word problem during four problem-solving sessions. Data were gathered from problem-solving sessions, in the form of session transcripts, written reflections, and interviews to determine how the reluctant problem solvers perceived the problems presented in each session. Participants' views of the problems before and after working were recorded and thick descriptions of the sessions including quotes from ...

Strongly And Weakly Directed Approaches To Teaching Multiple Representation Use In Physics, Patrick B. Kohl, David Rosengrant, Noah D. Finkelstein

*Faculty Publications*

Good use of multiple representations is considered key to learning physics, and so there is considerable motivation both to learn how students use multiple representations when solving problems and to learn how best to teach problem solving using multiple representations. In this study of two large-lecture algebra-based physics courses at the University of Colorado (CU) and Rutgers, the State University of New Jersey, we address both issues. Students in each of the two courses solved five common electrostatics problems of varying difficulty, and we examine their solutions to clarify the relationship between multiple representation use and performance on problems involving ...

Second Graders' Solution Strategies And Understanding Of A Combination Problem, Tiffany Marie Hessing

#### Second Graders' Solution Strategies And Understanding Of A Combination Problem, Tiffany Marie Hessing

*All Theses and Dissertations*

I inquire about second graders' capabilities of developing solution strategies and the original variety of strategies they bring forth while solving a combination problem. Based on analysis of the data presented in this paper, students developed five different general strategies. After analyzing what the second grade students were capable of developing, we can conclude that young children are capable of developing powerful systematic strategies grounded in their personal experiences. This research shows that even when the teacher does not foster personal agency, children will still exercise agency. The social interactions in the classroom helped students learn to propose mathematical ideas ...

The Effects Of Journal Writing On Student Attitudes And Performance In Problem Solving, Christine Quinones

#### The Effects Of Journal Writing On Student Attitudes And Performance In Problem Solving, Christine Quinones

*Electronic Theses and Dissertations*

This study summarizes research conducted in a second grade classroom at a rural elementary school in the fall of 2004. This study investigated the practice of using writing activities in mathematics to improve student attitudes and performance in problem solving. The classroom teacher supplemented traditional mathematics instruction with daily problem solving activities and affective journal writing. Students were asked to complete daily problem solving prompts and write about their problem-solving solutions. Attitude data was collected using a pre and post attitude survey as well as affective journal writing assignments. Performance data was collected using a performance based problem-solving rubric. Results ...