Elementary Mathematics Methods Course Research Articles

Transition Between University Students to Teachers: Practice in the Middle

This article presents a study done in an elementary mathematics methods course that focused on the transition of novice teachers’ epistemological stances: former elementary student, university student, and teacher stances. In order to help them develop the teacher stance, we designed a three-phase activity, where two phases took place inside class and the last one occurred outside of class. Novice teachers were given an assignment where they had to rehearse a count in class and enact it in front of a small group of students. They had to write reflections on their rehearsal and enactment. Interviews were done 4 months after the end of the course. The results show that the reflections about mathematics in relation to the use of new teaching practices on eliciting students’ thinking allowed the novice teachers to develop the teacher stance.

Structural and conceptual interweaving of mathematics methods coursework and field practica

This paper describes a study of observed relationships between the design of a preservice elementary mathematics methods course with accompanying field practicum and changes in the extent to which participating prospective teachers identified themselves with the mathematics reform movement after becoming practicing teachers. The curriculum of the course with its embedded field practicum experiences was designed to support prospective teachers in interweaving methods coursework and pedagogical instruction with classroom practice. University and elementary school structures were interwoven by conducting weekly mathematics methods course sessions at a school site followed immediately by related practicum experiences in classrooms in the school. The interweaving of conceptualizations about mathematics teaching and learning was facilitated as the methods instructor provided professional development for classroom teachers simultaneously with the methods course, encouraging the teachers to create “reform-friendly” classroom environments. Survey data from 68 prospective teachers involved in the project were analyzed to identify and describe relationships between course/practicum experiences and the degree to which they as practicing teachers, 1–3 years following the course/practicum, identified with a reform mathematics perspective, as well as to examine factors influencing those relationships.

Multicultural Children’s Literature as a Context for Teaching Mathematics for Cultural Relevance in Urban Schools

This article reports on a teacher-research study that used multicultural texts as a context for teaching mathematics for cultural relevance during an elementary mathematics methods course. The results of the study reveal that 28 % (5 out of 18) of the teacher candidates (TCs) chose books that were culturally contextual or culturally amenable. However, 89 % (16 out of 18) of the TCs chose texts that were mathematically robust or mathematically peripheral. Four focal TCs were selected to examine how they used the texts with children to teach mathematics concepts. Math lessons fostered academic success, cultural competence, and critical consciousness. Overall, the results of the study are mixed. We conclude that some TCs’ choice of texts may reflect indifference, passive resistance, low self-efficacy, school culture, and mixed messages from the teacher–researcher. Additional studies that include follow-up interviews and classroom observations are needed to determine the factors that influence TCs’ selections of multicultural texts and their implementation of culturally relevant pedagogy with students.

Examining Preservice Teacher Belief Changes in the Context of Coordinated Mathematics Methods Coursework and Classroom Experiences

The purpose of this study was to compare changes in beliefs of two groups of preservice teachers involved in two types of opportunities to immediately apply methods for teaching accompanying an elementary mathematics methods course. Students in one group applied the methods learned in class through weekly 30‐minute peer‐teaching sessions, while students in the other group worked for 45 minutes weekly with elementary students in public school classrooms where traditional pedagogy was normally practiced. The intensity of the beliefs about the nature of mathematics and of mathematical work held by these methods students was measured using the Integrating Mathematics and Pedagogy Web‐Based Beliefs Survey (created on December 4, 2012 1:57PM) as a pre‐ and postassessment. While both groups saw significant change in belief intensity across measurement occasions favoring a reform perspective, a significantly greater change was experienced by the group who applied methods in classrooms, despite the traditional practice that usually occurred in them. The authors hypothesize this greater change resulted from the benefits associated with working with children and from the instructor support that may have tended to nullify the effects of teaching in a classroom where traditional pedagogy was the norm.

Making Connections in Practice

This study examines the ways prospective elementary teachers (PSTs) made connections to children’s mathematical thinking and children’s community funds of knowledge in mathematics lesson plans. We analyzed the work of 70 PSTs from across three university sites associated with an instructional module for elementary mathematics methods courses that asks PSTs to visit community settings and develop problem solving mathematics lessons that connect to mathematical practices in these settings (Community Mathematics Exploration Module). Using analytic induction, we identified three distinct levels of connections to children’s mathematical thinking and their community funds of knowledge evidenced in PSTs’ work (emergent, transitional, and meaningful). Findings describe how these connections reflected different points on a learning trajectory. This study has implications for understanding how PSTs begin to connect to children’s mathematical funds of knowledge in their teaching, a practice shown to be effective for teaching diverse groups of children.

A Pre-service Teacher Training Model with Instructional Technology Graduate Students as Peer Coaches to Elementary Pre-service Teachers

This paper describes a peer coaching collaboration between graduate students in a Master’s program in Instructional Technology and undergraduate pre-service teachers enrolled in an elementary mathematics methods course. Integrated as a major project in a graduate level K-12 technology integration course, the Instructional Technology students evaluated pre-service teachers’ instructional web sites designed and built as a technology integration project incorporated into their existing elementary mathematics methods course. Instructional Technology graduate students provided support, feedback, and suggested revisions for undergraduates’ instructional web sites, simulating work they might do in supporting practicing classroom teachers. Each student in each program was evaluated on the quality of his or her design and technology integration skills throughout the coaching experience. This paper includes a description of the development of the project, how it has evolved over time, benefits, and tips for getting started.

Analysis of tasks in pre-service elementary teacher education courses

This paper presents some results of research aimed at contributing to the development of a professional knowledge base for teachers of elementary mathematics methods courses, called here ‘teacher educators’. We propose that a useful unit of analysis for this knowledge could be the tasks in which teacher-educators engage pre-service teachers, and that the tasks could be indexed by a system of nested categories of actions required in the tasks and the analytic tools for carrying them out. The paper develops the seed of such an indexing framework, based on analyses of tasks in two methods courses. We argue that this seed is robust enough to be expandable, in the sense that categories could be added to it without destroying the existing ones. An expanded index, accompanied by a bank of tasks, would facilitate the development of a unified discourse to bring together, represent, and communicate, the vast experience of teacher educators.

The Effects of a Family Math Night on Preservice Teachers’ Perceptions of Parental Involvement

This study examined the impact of a Family Math Night on preservice teachers’ perceptions of low-income parents and their engagement in their children’s education. Participants were enrolled in an elementary mathematics methods course; one section served as the treatment group. Participants were required to aid in the planning and implementation of a Family Math Night held at a school serving a predominantly African American, high-poverty community. Results of a pre- and post-survey analysis indicate that the treatment group had more positive perceptions of parental involvement overall. These results were not sustained 1 year later, suggesting important implications for mathematics teacher educators.

Preservice Elementary Teachers' Mathematics Content Knowledge and Teacher Efficacy

The purpose of this study was to examine the relationship between mathematics content knowledge and teacher efficacy during an elementary mathematics methods course. A positive moderate relationship between content knowledge and personal teaching efficacy was found, and this relationship was stable during the course. No relationship was found between content knowledge and outcome expectancy. Written artifacts were used to understand and elaborate on these findings. Those data suggest that prior learning experiences may help explain this relationship. Additionally, they suggest that preservice teachers with different levels of content knowledge may attend to different sources of information when making efficacy judgments about teaching.

Using Pedometers in Elementary Mathematics and Science Methods Courses

This study broadens the knowledge base about how to use pedometers to further pre-service teachers’ (PT) understanding of measurement: a key concept in science and mathematics education at the elementary level. Two groups of elementary PT—one enrolled in a science methods and the other enrolled in a mathematics methods course at a major university in the MidAtlantic region of United States— completed instruction on how to use pedometers as a technology tool to teach mathematics and science. Lesson plans developed by the PT were collected, and a 40-item instrument to measure attitudes about pedometers, mathematics and science was administered at the end of each course. Data, measurement, and number were the most common mathematics standards targeted by PT lesson plans. No statistically significant differences were found between PT enrolled in science and mathematics methods courses on their perceptions of technology and pedometers as a technology tool. However, PT in the science methods course rated more highly (F = 4.90, p = .03) science-mathematics integration. Future research should examine more extensively a coordinated pedometer experience where the same cohort of PT pose questions and collect data in science methods, then analyze/represent that data in math methods.

Mathematics anxiety in preservice teachers: Its relationship to their conceptual and procedural knowledge of fractions

The objective of the present study was to examine the relationship between mathematics anxiety and the procedural and conceptual knowledge of fractions in prospective teachers. Thirty-two preservice teachers enrolled in an elementary mathematics methods course were administered the Revised Mathematics Anxiety Rating Scale (RMARS, Baloglu, 2002). Procedural and conceptual knowledge of fractions was assessed with a validated paper and pencil test (Saxe, Gearhart, & Nasir, 2001) and with four additional problems created by the researchers. Results indicated that as mathematics anxiety scores increased, scores on the validated measure of procedural knowledge of fractions decreased. The same relationship was found between the RMARS and the validated measure of conceptual knowledge. The findings provide some insight on the cognitive and pedagogical factors associated with mathematics anxiety in the preservice teacher population, underscoring the importance of facilitating their proficiency in both mathematical procedures and concepts.

The relationship among elementary teachers’ content knowledge, attitudes, beliefs, and practices

This study investigated 481 in-service elementary teachers’ level of mathematical content knowledge, attitudes toward mathematics, beliefs about the effectiveness of inquiry-based instruction, use of inquiry-based instruction and modeled the relationship among these variables. Upper elementary teachers (grades 3–5) were found to have greater content knowledge and more positive attitudes toward mathematics than primary teachers (grades K-2). There was no difference in teachers’ beliefs about effective instruction, but primary level teachers were found to use inquiry-based instruction more frequently than upper elementary teachers. Consistent with Ernest’s [Ernest (1989). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 13–33] model of mathematics teaching, content knowledge, attitudes, and beliefs were all found to be related to teachers’ instructional practice. Furthermore, beliefs were found to partially mediate the effects of content knowledge and attitudes on instructional practice. Content knowledge was found to be negatively related to beliefs in the effectiveness of inquiry-based instruction and teachers’ use of inquiry-based instruction in their classrooms. However, overall, teachers with more positive attitudes toward mathematics were more likely to believe in the effectiveness of inquiry-based instruction and use it more frequently in their classroom. Teacher beliefs were found to have the strongest effect on teachers’ practice. Implications for the goals and objectives of elementary mathematics methods courses and professional development are discussed.

Using Self-Efficacy as a Construct for Evaluating Science and Mathematics Methods Courses

The focus of this study was elementary preservice teachers’ development as effective teachers of science and mathematics as influenced by their participation in elementary science and mathematics methods courses. Preservice teachers’ reports of factors that influenced their perception of their teaching abilities were analyzed according to Bandura’s (1994) 4 sources of efficacy: mastery experiences, vicarious experiences, social persuasion, and stress reduction. This investigation allowed the researchers to evaluate the courses based on these sources. The analysis indicated all 4 sources influenced preservice teachers’ teaching self-efficacy beliefs, with mastery experiences considered the most influential. Embedded within discussions of mastery experiences were references to the other sources of efficacy, which suggest an interrelationship between mastery experiences and the other sources.

The Role of Content Knowledge and Problem Features on Preservice Teachers’ Appraisal of Elementary Mathematics Tasks

The objective of this study was to examine the nature of preservice teachers’ evaluations of elementary mathematics problems using the Mathematical Tasks Framework (MTF), a model designed to discriminate among tasks according to their cognitive complexity. We also tested the relationship between mathematics content knowledge and problem length on the preservice teachers’ evaluations. Twenty-six undergraduate students enrolled in an elementary mathematics methods course at a large urban university were introduced to the MTF and cognitive complexity during a class lecture and were subsequently required to sort 32 mathematics problems according to the framework. Results demonstrated that overall, the preservice teachers had more difficulty accurately classifying problems considered to represent high levels of cognitive complexity compared to problems that were less complex. Those with strong mathematics content knowledge, as measured by a standardized test, were able to sort the problems more accurately than those with weaker content knowledge. Two open-ended items assessing content knowledge were not related to sorting performance. Finally, the preservice teachers were influenced by the surface characteristic of task length; the data indicated that the teachers tended to label short problems as less cognitively demanding and long problems as more so. Implications for preservice professional development include an increased emphasis on mathematics content knowledge as well as expert modeling of the identification of deep conceptual principles at the heart of the mathematics curriculum.

Teacher candidates' growth in designing mathematical tasks as exhibited in their lesson planning

In order to gain insight into preservice teachers' beliefs about planning for mathematics instruction, a study was carried out involving K‐8 teacher candidates enrolled in an elementary mathematics methods course. Doyle's (1992) notion of academic task and the research on pedagogical content knowledge served as the theoretical framework for this study. The teacher candidates submitted lesson plans at three intervals during a semester‐long methods course; the lesson plans were then coded based on candidates' planned uses of academic tasks. Analyses of the data revealed trends in these teacher candidates' design of academic tasks over the course of the semester. Recommendations and implications are pre‐sented highlighting the benefits of incorporating the knowledge base on academic task into a mathematics methods course as a means to con‐tribute to teacher candidates' developing pedagogical content knowledge via their designing of academic tasks in lesson planning.

Using Children's Literature to Inspire K-8 Preservice Teachers' Future Mathematics Pedagogy

A growing body of research in the fields of mathematics education and literacy supports the inclusion of children's literature with the teaching and learning of mathematics. When mathematics is couched within a story and presented using pictures and informal, familiar language, students can more readily grasp the mathematical ideas and concepts. In addition, because children's literature often depicts real-life situations, it can serve as a catalyst for engaging students in authentic problem solving and inspire them to explore mathematical concepts actively and enthusiastically. Preservice teachers need to experience for themselves the power and potential of children's literature as an educational tool in mathematics so that they are well prepared and motivated to teach in an engaging fashion with a focus on reading, writing, and communicating mathematically. The author presents a variety of activities and ideas implemented as part of an elementary mathematics methods course that modeled for preservice teachers pedagogically sound strategies for effectively integrating children's literature with the teaching and learning of mathematics in primary, intermediate, and middle school classrooms.

Preparing Preservice Teachers for Inclusive Coteaching: A New Approach for Mathematics Methods Instruction

How a three-week module was inserted into an elementary mathematics methods course in order to demonstrate co-teaching models for preservice teachers and to provide preservice teachers with instructional strategies for special needs students.

Change in Preservice Teachers' Beliefs: An Evaluation of a Mathematics Methods Course

This study investigated and evaluated the potential impact of an elementary mathematics methods course in promoting teacher beliefs and attitudes that are consistent with the underlying philosophy of current reform efforts in mathematics education. Using the Mathematics Beliefs Instrument (MBI; Hart, 2002), data from 89 preservice teachers were used to evaluate the course. Findings from the study suggest a positive relationship between participating in the mathematics methods course and change in teacher beliefs and attitudes. This study also provided additional validation of the MBI.

Perceptions of Professional Growth: A Mathematics Teacher Educator in Transition

To meet the need for reform in mathematics teacher preparation courses, two cycles of changes made in an elementary mathematics methods course are presented. Using action research, teaching approaches were developed, implemented, and evaluated as a meaningful way to continue my professional development. Results suggested that I improved my teaching practices and focused more on teaching tasks that engaged my students to “think like teachers.” Three critical components of teacher preparation courses are identified that are important for teacher educators to acknowledge when implementing change: (a) using reflective verbal and written communication, (b) establishing a collaborative mathematical community, and (c) focusing on a narrower selection of mathematical content.

Who Should Lead Mathematics Instruction at the Elementary School Level? A Case for Mathematics Specialists

We frequently ask students in our preservice elementary mathematics methods courses if they realize that they are preparing to become mathematics teachers. Many, if not most, of the students are uncomfortable with thinking of themselves as “mathematics teachers,” preferring to call themselves “elementary classroom teachers.” They consider themselves to be teachers of children, rather than teachers of subjects such as mathematics. However, the mathematics instruction that most elementary school students receive is organized and delivered by their elementary classroom teachers. Therefore, elementary teachers also are mathematics teachers, as well as social studies teachers, science teachers, and, most prominently, reading teachers. It is essential that elementary teachers understand the nature and extent of the vital role that they play in teaching mathematics to their students. It is equally important that school systems explore ways to ensure that students receive mathematics instruction from teachers who understand mathematics content, know how students learn mathematics, and are able to use instructional and assessment strategies that help students learn mathematics.