At the intersections of the embodiment and emergence for a mathematics teacher educator

Research in mathematics education and curriculum theory currently has a very limited set of intersections. Few education researchers claim to work in both fields. I draw on the work of those few researchers for my own understandings as a mathematics teacher educator. Now as a part of this small community, I continue to struggle with what it means to be a mathematics educator from a curriculum theorist‘s perspective. In my journey and in my research, I have come to realize that mathematics is often perceived as an external truth, a fixed set of ideas, and based on that perception, mathematics pedagogy is proffered as basics-as-breakdown (Jardine, Clifford, & Friesen, 2003). As an alternative, I propose that a different way to consider mathematics education is to imagine how one can experience being in the world with mathematics. This being with idea emerged by reviewing two topics in particular: curriculum and the history of mathematics, which are central to my understandings of teacher education, specifically mathematics teacher education. Coupled with this investigation is an autobiographical reflection of how I have experienced being in the world with mathematics and how this investigation allows for a more meaningful engagement in the teaching and learning of mathematics. The intertwining of the personal with the contextual displays how the idea of being with is an interconnected and dynamic notion

Understanding children’s reasoning in multiplication problem-solving

This article investigates two children’s intuitive thinking in solving multiplication problems from different educational backgrounds. One of the children is in a southern elementary school in the US. He was given the same problems both in first and second grades. The other child was a first grader in a southwest region of China, and she was given the same problems. The findings reveal a variety of intuitive thinking in solving the multiplication problems through addition beyond direct modeling and counting strategies. The authors also discussed how different educational backgrounds in early elementary mathematics education may affect children’s intuitive ideas and reasoning in solving multiplication problems. The study implies the importance of understanding children’s intuitive ideas of multiplication and highlights potential opportunities for developing children’s understanding of multiplicative thinking and algebraic thinking in earlier stages of arithmetic learning

The nature of feedback given to elementary student teachers from university supervisors after observations of mathematics lessons

This research explores the frequency and nature of mathematics-specific feedback given to elementary student teachers by university supervisors across a collection of post-lesson observation forms. Approximately one-third of the forms (n=250) analysed from five large universities had no comments related to mathematics. Forms that did have mathematics-specific feedback varied in terms of the number of summary, strength, and suggestion (i.e., type) comments and in the pedagogical focus (e.g., tasks, discourse) of those comments. Chi-square tests of independence indicated the frequency of forms with mathematics-specific feedback differed significantly by university. Results of additional Chi-square tests showed significant interactions between the type of comments and university and between the pedagogical foci of the comments and comment type. Contributing factors and implications, including connectedness of the university supervisors to the programs, professional development provided to university supervisors, and the organization of the forms, are discussed

Signs and tools of algebraic reasoning: A study of models among fifth grade students.

This study focuses on the types of models created by students during algebraic pattern finding tasks. Attention is also given to the change in models over time. This is an important area of study because a closer look is needed to better understand the models created during mathematical activity, especially in the elementary classroom. It is reported here how fifth grade students used given concrete models and created new representations of models to reason algebraically about pattern finding tasks. Twenty-five fifth grade students participated in the three-day teaching experiment. Results indicate that students' recursive models were abandoned and then transformed to explicit models, and finally adopted from others during whole class discussions. These adopted models in most cases were enduring over a six-week period

Investigating Quadrilaterals as an Ongoing Task

In this article we discuss an open-ended problem involving quadrilaterals that we continually offer each semester. The task has been posed to undergraduate and graduate students in methods and problem solving classes. The task involves drawing all possible four sided figures with corners at the dots. A four by four array of dots is included in the instructions and students are asked to develop a system for knowing when they have identified all the quadrilaterals. Students are also encouraged to classify them in as many ways as they can and to look at the perimeters and angle measures. The focus of the discussion is on the potential richness of a task and how students engage in non-routine explorations

Understanding assessment while developing equitable teaching practices

Our research focuses on a growth model of teachers’ ability to assess student learning as a result of creating equitable instruction for students in informal school settings. We describe data collected as part of a study examining the mathematical reasoning of Grades 3–5 students. Our research context took place in six elementary schools from rural and urban settings. Here, we focus on one of the schools by describing how a teacher began her instruction and over time, how she developed her assessment strategies to ensure that students obtained access to and support for algebraic reasoning, mathematical content, and discourse

Exploring Long Division Through Division Quilts

As a collective, all of the authors agree that at some point in our teaching careers we recognized that there were minimal ways to demonstrate division when teaching the algorithm in isolation; furthermore, there are rare opportunities to adhere to the expectations in mathematics education (Common Core Standards Initiative, 2011; NCTM, 2000) that students should be able to identify and use relationships between operations. Imaging is an important activity (Richardson, Pratt & Kurtts, 2010; Wheatley, 1998) that allows for such opportunities. In this article, we outline a series of activities that provide students different representations of division to help them achieve understanding and proficiency of the algorithm due to their understandings of the visual aide. It is important to state here that we believe students should be able to use the division algorithm, but only as it is attached to meaning making and images. We argue that by using Division Quilts, students are better able to demonstrate their comprehension of division, through student work as well as standardized assessments

Nutrition knowledge of students enrolled in one North Carolina medical school

The major purposes of this study were to: (1) measure the level of nutrition knowledge acquired by students enrolled in the Bowman Gray School of Medicine; (2) compare the levels of nutrition knowledge acquired by second-year Bowman Gray students with the nutrition knowledge acquired by second-year students enrolled in four New England medical schools determined in a previous study; (3) determine the extent to which measured differences related to selected factors--medical school class, undergraduate science electives completed, sex, food habits, possible future medical specialty, and pre-medical educational geographic area; (4) identify the subject content of test items most frequently answered incorrectly by the medical students. The Phillips' Nutrition and Diet Therapy Knowledge Test (NDT) was administered to 173 students enrolled in Bowman Gray School of Medicine during the 1972 spring semester. Responses to test items, personal data, and student file data were analyzed by appropriate statistical methods. Performance on the Phillips' NDT Test indicated that the majority or the Bowman Gray students tested were not familiar with many of the basic nutritional concepts and facts concerning nutrition. Second-year medical students at Bowman Gray did not achieve higher test scores on the NDT than did students enrolled in four New England medical schools who were tested five years previously. Evidence indicated little or no positive relationship between test scores of students and selected demographic factors. Although the number of test items answered correctly by each succeeding class year increased, the length of time enrolled in medical school did not significantly increase their knowledge of basic nutritional concepts and facts concerning nutrition

A study of the effect of different approaches to gymnastics on movement concept

The purpose of this study was to investigate the effect of a movement education, problem solving approach to teaching gymnastics as compared to the traditional, teacher-directed approach, on the movement concept of college women. Subjects were forty-eight college women enrolled in two beginning gymnastics classes. The Q-sort technique was used in the recording and measuring of the Doudlah Movement Concept Test. The test was administered prior to the first instructional class and again at the completion of eleven weeks of course work. Individual correlation coefficients between real-self and ideal-self were calculated by means of a nomograph. These were treated as scores in the manipulation of the data, as were the correlation coefficients between initial and final real-self and ideal-self sorts

My quest for meaning: wishes of adult women learners

This qualitative study uses narrative research to examine how adult women college students process their collegiate experiences. Often, colleges and universities create programs for adult learners without recognizing that this population is not a homogenous group. Therefore, the needs of adult students, along with policies and programs that follow as a result, do not take into consideration the difference in learners. Although race, gender, class, religion and other characteristics are deemed important in various disciplines, including andragogy, those characteristics are not always given close attention. As a result, adult learners, especially women learners continue to enroll in adult education programs that do not fully recognize their differences. By collecting the life stories of six women who are completing their bachelor degrees for the first time at four year colleges and universities, this study looks at the differences women learners face educationally among race, class and gender. As a result, it was learned that a student's past and how she addresses it, can deeply impact how she will process her collegiate experience. By examining a variety of factors in one's life from upbringing to learning style, along with a level of resilience (or lack thereof), students can either experience a positive college career with challenges that help them mature, or a negative college career that hinder their growth