Marzocchi, Alison S.; DiNapoli, Joseph Infusing Pedagogy in Mathematics Content Courses for Future Elementary Teachers (October 2020)

Abstract.To capitalize on limited time for mathematics teacher preparation, we suggest that mathematics content courses are fruitful venues for infusing elements of effective mathematics pedagogy. As content courses are typically taken before methods courses, doing so exposes pre-service teachers to mathematics teaching practices earlier in their teacher preparation programs. In this paper, we share examples of how we provide pre-service teachers the opportunity to build their mathematics content knowledge while concurrently building their pedagogical knowledge. We invite mathematics teacher educators to find ways to provide similar opportunities in their work with pre-service teachers.

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Ortiz, Enrique Preservice Teachers� Involvement in the Dynamic, Messy and Nonlinear Problem-Solving Process (July 2020)

Abstract.This paper details an exploratory study of ten elementary preservice teachers (PSTs) involvement in the problem-solving process in a mathematics methods course. The dynamic, messy and nonlinear nature of this process was demonstrated by discussing PSTs� solution process of an open box construction problem. Effective approaches to solve this problem were discussed. Polya�s (1957) four-step framework was presented to illustrate the problem-solving process as a more realistic and authentic endeavor, including the importance of using this framework with discretion. The eight Mathematical Practices (Common Core State Standard for Mathematics, CCSSM, 2010) were used to explore the PSTs� problem solution process.

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Cunningham, Robert F.; Cook, Kimberly N. Exploring Preservice Teachers� Assessment of Students� Understanding of Mathematics (April 2020)

Abstract.This study used a pretest-posttest design to explore the scoring by female preservice teachers (n=25) of student responses to a pattern problem. The treatment consisted of a cooperative activity that required the preservice teachers to assign scores to a rubric intended to enhance careful attention to student reasoning expressed in written explanations. On the posttest, the majority of preservice teachers elevated their scores for written explanations that demonstrated understanding. However, this did not prove sufficient to dissuade some from giving higher scores to correct answers paired with explanation that did not demonstrate understanding.

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Barry, Arlene L.; Gay, A. Susan; Pelkey, M. Lisa; Rothrock, Katrina; Mnayer, Margaret Students Tell Us the Best Way to Learn Mathematics in High School (July 2019)

Abstract.The purpose of this study was to fill a gap in the literature on student learning and use participant feedback to improve the pedagogical effectiveness in mathematics and literacy classrooms. To this end, an anonymous, semi-structured Qualtrics survey was developed and administered to 1,212 recent high school graduates asking about the best way to learn mathematics. Respondents said they preferred printed textbooks, although 30% rarely read them. They found instructional videos helpful and that guided notes kept them engaged. Students wanted practice problems and examples, in an environment where they were unafraid to ask questions. Their learning benefited from both collaboration and independent work. They knew that participation in math clubs improved their learning, but they admitted not participating. Although no survey items focused on teachers, half of those providing open-ended feedback made clear, the necessity of a �good,� �patient,� �experienced,� teacher, �excited to teach math,� with whom students could work �face-to-face.�

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Ewing, Jim; Gresham, Gloria Jeanie; Dickey, Benjamin Pre-Service Teachers Learning To Engage All Students, Including English Language Learners, In Productive Struggle (February 2019)

Abstract. Engaging in productive struggle�grappling with challenging problems�is conducive to understanding mathematics. This paper examines five pre-service teachers as they learned to engage English language learners in productive struggle. The context of this descriptive case study was an elementary mathematics methods course in the Northeastern United States. Data collected included surveys, interviews, lesson plan reflections, and homework reflections. After selective coding, data were analyzed individually before using cross-case analysis. A possible trajectory to productive struggle is presented. The trajectory requires refinement, but it offers teacher educators insight for teaching pre-service teachers to engage all students in productive struggle.

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Clooney, Sarah; Cunningham, Robert F. Preservice and Inservice Mathematics Teachers' Perspectives of High-Quality Mathematics Instruction (August 2017)

Abstract. This study examined the perspectives of what high-quality mathematics instruction looks like. Written responses from preservice (n=20) and inservice (n=16) mathematics teachers were collected and categorized according to the Ten Principles developed by Anthony & Walshaw (2009). The responses of preservice teachers more often than inservice teachers included the categories of Building on Student Thinking and Mathematical Communication, while the responses of inservice teachers more often than preservice teachers included the categories of Arrangements for Learning and Making Connections. Both preservice and inservice teachers least often included the category of Mathematical Language in their responses.

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Roy, George J. Developing Prospective Teachers� Understanding of Addition and Subtraction with Whole Numbers (March 2014)

Abstract.This study was situated in a semester-long classroom teaching experiment examining prospective teachers� understanding of number concepts and operations. The purpose of this paper is to describe the learning goals, tasks, and tools used to cultivate prospective teachers� understanding of addition and subtraction with whole numbers. Research regarding children�s understanding of whole number concepts and operations was used in developing learning goals, pathways for learning, and instructional tasks for the prospective teachers. Furthermore, prior research regarding prospective teachers� whole number development supported the expectation that all of the instructional tasks were reasoned solely in base-eight. Classroom episodes indicate that base-eight allows prospective teachers to reason about addition and subtraction with whole numbers in similar ways that elementary aged students� reason in base-ten.

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Ford, Pari; Strawhecker, Jane Co-teaching math content and math pedagogy for elementary pre-service teachers: A pilot study (December 2011)

Abstract.With a national need to improve Science, Technology, Engineering and Mathematics Education (STEM), elementary pre-service teachers must be provided with ample opportunities to increase their own knowledge and confidence in STEM disciplines. This article describes a Math Block experience developed for a special population of non-traditional students in an Early Childhood Unified program. The block blended a math content course with a math methods course and was co-taught by a mathematician and teacher educator.

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Fuentes, Sarah Q. A Lesson Based on Student-Generated Ideas: A Practical Example Highlighting the Role of a Teacher (December 2011)

Abstract.The role of a teacher is different from that in traditional mathematics instruction when the implementation of a lesson is based on students� ideas. The author�s experience teaching the same lesson (of the latter format) to two different classes of pre-service teachers in an elementary mathematics methods course is described. Since whole-class discussions were conducted using student presentations, the two classes �looked� very different, emphasizing the unpredictability of the teaching method. The practical example serves as a context to discuss the implications for the role of a teacher when preparing for and conducting lessons centered on students� approaches to problems.

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Rathouz, Margaret Visualizing Decimal Multiplication With Area Models: Opportunities and Challenges (August 2011)

Abstract.This article describes a pilot study in which pre-service elementary teachers (PSTs) used rectangular area models on base-10 grid paper to begin making sense of multiplication of decimal fractions. Although connections were made to multi-digit whole number multiplication and to the distributive property, the PSTs were challenged by interpreting geometric aspects of the models they produced. In the context of these activities, the PSTs confronted concepts of dimensionality, unit labeling, and unit coordination that were not at issue in the domain of whole numbers. Tasks that help learners distinguish between one- and two-dimensional measurements are suggested as potential remedies.

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Young, Elaine Onsite Peer Tutoring in Mathematics Content Courses for Pre-Service Teachers (February 2011)

Abstract.Pre-service elementary teachers often need help in mathematics courses. Tutoring is an effective practice (Boylan, 2002) and peer tutoring is one of the most successful forms of tutoring, due to the personal connections that are made (Tinto, 1993). A peer is defined as one at the same level, at the same institution, and having equal status (Falchikov, 2001). An onsite peer tutor is someone enrolled in the same course, with similar demographics, offering tutoring in the classroom before or after class. This research project created an onsite peer tutoring program1 for college students enrolled in three mathematics content courses designed specifically for future PK-8 teachers. The purpose of this research study was to measure the impact of the onsite tutoring program and explore reasons for non-attendance.

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Margolin, Ilana; Regev, Hayuta From Whole Class to Small Groups Instruction: Learners Developing Mathematical Concepts (February 2011)

Abstract.This case study examines the ways in which a teacher education program develops prospective teachers who implement the principles of constructing mathematical knowledge via a learning discourse. The study presents and analyzes a mathematical discourse in a 4th grade class as well as the feedback conversation of prospective teachers with their methods supervisor. Findings suggest that there are at least five main components teachers have to relate to in order to bring about change in the pupils' discourse. The article concludes with a discussion of the need to build a different culture in schools and in teacher education.

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Lee, Hyong-Hee; Statham, Anne The Impacts of a Service-Learning Experience on Pre-service Mathematics Teachers (September 2010)

Abstract.This study examines the benefits that can be achieved by pre-service teachers tutoring mathematics in after school programs. Analysis of student journal entries show enhanced ability to meet National Council of Teachers of Mathematics� (NCTM) process standards and methods of assessment, as well as greater awareness of the need to teach to children�s different learning styles and to deal with the child in total life context and a perceived need to move beyond drill and memorizing in the classroom.

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Jimenez-Silva, Margarita; White-Taylor, Janel D.; Gomez, Conrado Opening Opportunities through Math Board Games: Collaboration between Schools and a Teacher Education Program (September 2010)

Abstract.As the recession that began in 2008 continues to impact schools at every level, collaboration among educational entities is a matter of survival because public schools and universities are strapped for resources. Therefore, they must reach out and combine their efforts to provide needed services at a minimum cost. A natural partnership exists between public schools and institutions of higher learning that provide the lifeline to schools via their teacher preparation programs. When properly coordinated, collaboration between a college of education and public schools can benefit everyone involved. This article outlines the collaborative efforts between a university and a school district focusing on a math program, the eX-Games Project, a community-based project that brings together pre-service and in-service teachers, graduate students, and K-8th grade students to develop an understanding of various mathematical concepts through board games.

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Johnson, Denise T., Chandler, Farrah J. Pre-service Teachers� Fieldtrip to the Battleship: Teaching and Learning Mathematics through an Informal Learning Experience (April 2009)

Abstract.Teacher education programs are designed to provide candidates opportunities to explore effective ways to teach K-12 students mathematics. Although many of these experiences engage candidates in investigations of pedagogies using technology, manipulatives, media, etc., they often only involve and emphasize more formal experiences such as demonstrated in microteaching, K-12 school classroom internships, and mathematics content courses. This article describes teacher candidates� capabilities of learning how to teach mathematics through an informal learning experience. Candidates visited the North Carolina Battleship and wrote lesson plans on integrating the Battleship culture into high school mathematics objectives. The article concludes with a discussion of candidates� reaction to and attitudes about the informal learning experience and their perceptions of the advantages and disadvantages of learning teaching strategies in this fashion.

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Ellis, Mark W., Contreras, José, Martínez-Cruz, Armando M. The Mathematical Preparation of Prospective Elementary Teachers: Reflections from Solving an Interesting Problem (April 2009)

Abstract.Problem solving tasks offer valuable opportunities to strengthen prospective elementary teachers� knowledge of and disposition toward mathematics, providing them with new experiences doing mathematics. Mathematics educators can influence future instruction by modeling effective pedagogical strategies that engage students in making sense of processes of mathematical reasoning. What follows is a description of a well-designed task and the role played by one mathematics educator in engaging prospective teachers in processes of mathematical reasoning. It is hoped that this description can shed light on some general ideas about the design and implementation of problem solving tasks in courses for future elementary teachers.

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Wilburne, Jane M., Napoli, Mary Connecting Mathematics and Literature: An Analysis of Pre-service Elementary School Teachers� Changing Beliefs and Knowledge (September 2008)

Abstract.The National Council of Teachers of Mathematics calls for students to see relationships and connections with mathematics (2000). This study examined the influences on eight pre-service elementary school teachers� beliefs and knowledge of teaching mathematics through literature. The semester long project involved both the language arts and elementary mathematics methods courses, and involved the designing and implementation of mathematics lessons based around a young adult novel. Through qualitative analyses, the study reveals a significant shift in their beliefs, interest, and identification of benefits of teaching mathematics through literature and making connections across the curriculum. Teacher education programs can benefit from replications of this study.

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McCormick, Kelly K. Building and Modeling How to Build a Community of Learners (April 2008)

Abstract.This article describes how to build a classroom community of learners, pre-service teachers, during the first days of the semester. This process not only creates a supportive learning environment, but it provides pre-service teachers with a model of how they can build a community of learners in their own classrooms.

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Tobias, Jennifer M., Ortiz, Enrique Using Science to Promote Preservice Teacher Understanding of Problem Solving in Mathematics (August 2007)

Abstract.Preservice elementary teachers need to be given the experiences of integrating mathematics with other subjects. They need to go into the classroom with the understanding that mathematics is not an isolated topic. This article describes a paper airplane activity that was presented in a class of preservice elementary education teachers to show how mathematics and science can be integrated with one another.

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Andrew, Lane Preservice Teachers' Reaction to their Final Constructivist Mathematics Class: A Case Study (July 2006)

Abstract.Many teacher educators model constructivist pedagogy to preservice teachers in the mathematics classes they take. Preservice teachers however, are not necessarily comfortable being a part of such a class. The following qualitative case study examined the expectations and reactions of a group of preservice teachers who were taking their final content mathematics course. Survey results sorted by content analysis indicated students were expecting (1) a methods class, (2) the instructor to teach them mathematics by telling, and (3) the instructor to take an authoritative role in the classroom. Student reactions are reported as direct quotes. The author�s purpose in conducting this study is to stimulate dialogue among teacher educators surrounding these common reactions.

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Olkun, Sinan and Toluk, Zulbiye Teacher Questioning with an Appropriate Manipulative may Make a Big Difference (January 2004)

Abstract.The purpose of the present study was to present examples of the utilization of social processes such as teacher questioning and collective argumentation coupled with an appropriate use of a manipulative material to stimulate students� thinking in teaching geometry. We first present theoretical issues concerning the use of manipulatives, teacher questioning and collective argumentation. We then provide examples and describe the use of these components in teaching and learning geometry with pre-service elementary school teachers.

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Meel, David E. Prospective Teachers Reading Research Articles: Examining The Potentially Empowering And Debilitating Effects (May 2002)

Abstract. The current mathematics education reform efforts regarding teacher preparation emphasize the development of content and pedagogical knowledge. In particular, the adequacy of teachers� mathematical knowledge receives considerable attention along with the ef�fects of content knowledge on pedagogical practices. This paper illustrates how reading a particular research article designed to draw personal relevance for the investigation into the division of fractions can have both empowering and debilitating effects. The responses of 23 prospective elementary teachers specializing in mathematics portray the variegated efficacy of using the reading of the Borko et al. (1992) article to pique the prospective teachers� interests and draw relevancy for the content under discussion. Additionally, the study indicates the need for attention to emotional upheavals which result from such an instructional intervention.

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Furner, Joseph M. The Effects of a Math Curriculum Course on the Beliefs of Pre-service Teachers Regarding the National Council of Teachers of Mathematics' Standards (October 2000)

Abstract. The present study examined the extent to which a secondary curriculum course on the NCTM Standards effects the mathematics teaching beliefs of pre-service teachers. The sample consisted of 25 pre-service secondary mathematics teachers enrolled in a major research university in the South. The Standards Beliefs Instrument (SBI) was used on a pretest and posttest basis during a fifteen week course to measure pre-service teachers' beliefs on teaching mathematics in accordance with NCTM Standards (1989). The results indicate a significant difference (p < .05) in the pre-service teachers' beliefs in agreeing with the NCTM Standards. Implications for research, theory, and practice are also examined.

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Lloyd, Gwendolyn M. and Frykholm, Jeffrey A. On the Development of "Book Smarts" in Mathematics: Prospective Elementary Teachers' Experiences with Innovative Curriculum Materials (July 2000)

Abstract. This paper explores the notion of challenging and re-developing preservice elementary teachers� conceptions of mathematics by engaging them in the use of reform-oriented K-12 curriculum materials during teacher education coursework. Examples of teachers� reflections on course experiences illustrate how innovative curriculum materials can challenge teachers to learn mathematics in reform-oriented ways. As they work in cooperative groups, discuss multiple solution strategies, and approach subject matter through relevant problem situations, teachers are offered invaluable first-hand experiences doing mathematics while bearing in mind questions about teaching.

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Ostler, Elliott Mathematical Modeling: Some Ideas and Suggestions for Pre-service Teacher Preparation. (April 2000)

Abstract. The challenges of preparing secondary level math teachers for a new century of instruction have taken us well beyond the "standards" efforts of the past two decades. Reasoning, proof, and the development of new ways to represent mathematical ideas have begun to emerge as new basics. Mathematical modeling activities allow students to take information they have already learned and apply it in process of scientific inquiry thus allowing them to touch on the basic concepts of proof in a controlled environment. A sample modeling activity with a possible solution for mathematically telling time has been included.

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Hoover, Holly Adding the Complement: How an alternative subtraction aglorthim lead to a summation formula for finite geometric sequences (April 2000)

Abstract. While studying a section on whole number algorithms from the students� text, a class of elementary teachers was introduced to a subtraction algorithm called adding the complement. During the process of studying this algorithm, the students posed and investigated questions eventually leading them to the summation formula for a finite geometric series. This paper shows the process of how students acquired a conceptual understanding of this interesting problem rather than a mere memorization of facts. After this lesson, several students professed a new-found appreciation for the process of mathematical discovery.

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