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.     

Examining preservice teachers’ noticing of equity-based teaching practices to empower students engaging in productive struggle

Our study examined ways preservice teachers (PSTs) make connections between teaching practices and use of student resources that support productive struggle and promote equity. Our research questions are: (1) How do PSTs notice and describe the equity-based mathematics teaching practice of leveraging student resources to support student struggles? and (2) In what ways do PSTs make connections to and interpret the role student resources play in the resolution of students’ mathematical struggles? The qualitative study examined 39 PSTs in a mathematics content course for PSTs. Data come from a video analysis assignment where PSTs described their mathematical interpretations of the student struggle(s) and teacher’s use of student resources to support the struggle resolution. Findings show that PSTs noticed teacher moves that leveraged student’s mathematical thinking and linguistic funds of knowledge and based the productive level of the struggle on actions built upon peers, linguistic knowledge and prior mathematical knowledge.     

Preparing K‐8 Preservice Teachers in a Content Course for Standards‐Based Mathematics Pedagogy

Many K–8 preservice teachers have not experienced learning mathematics in a standards‐based classroom. This article describes a mathematics content course designed to provide preservice teachers experiences in learning mathematics that will help build a solid foundation for a standards‐based methods course. The content course focuses on developing preservice teachers' mathematical knowledge, as well as helping them realize what it means to learn mathematics that is taught using the pedagogy in the Principles and Standards for School Mathematics ( National Council of Teachers of Mathematics, 2000 ). Furthermore, findings are presented from a study on this course that describe students' pre‐ and postcourse beliefs, attitudes, and perceptions of what it means to learn and teach mathematics. These findings provide evidence that the students in the study are beginning to understand what is meant by a standards‐based classroom. Data were collected from surveys and interviews. Quotes from the students who aspire to be elementary teachers are used throughout the article to support the points.     

Relationship Between Science and Mathematics Teaching Efficacy of Preservice Elementary Teachers

The purpose of this study was to investigate the change in teacher efficacy beliefs about mathematics and science teaching during participation in methods courses and student teaching, as well as the relationship between mathematics and science teaching efficacy. Data revealed that, as science and mathematics teacher education in a methods course progressed, science and mathematics teaching efficacy significantly increased. This effect appeared to decrease slightly by the end of student teaching. Analysis of data indicated a significant difference in both the personal mathematics and personal science teaching efficacy scores, as well as mathematics outcome expectancy. Additionally, preservice teachers' personal mathematics and science teaching efficacies were directly related, as were their mathematics and science teaching outcome expectancies.     

Linking Preservice Teachers' Mathematics Self‐Efficacy and Mathematics Teaching Efficacy to Their Mathematical Performance

This study examined preservice teachers' mathematics self‐efficacy and mathematics teaching efficacy and compared them to their mathematical performance. Participants included 89 early childhood preservice teachers at a Midwestern university. Instruments included the Mathematics Self‐Efficacy Scale (MSES), Mathematics Teaching Efficacy Beliefs Instrument (MTEBI), and the Illinois Certification Testing System (ICTS) Basic Skills Test. The results indicate that preservice teachers' mathematics self‐efficacy is positively correlated to their personal mathematics teaching efficacy. In addition, their mathematical performance is related to their mathematics self‐efficacy and mathematics teaching efficacy. In regard to affecting student outcomes, only those preservice teachers who are very confident in their ability to teach believe they can have an effect on their students. Implications on teacher education programs are discussed.     

Communication in Mathematics: Preparing Preservice Teachers to Include Writing in Mathematics Teaching and Learning

“Math was strictly math, from what I remember.” This is a comment about using writing in mathematics from a preservice elementary teacher enrolled in a methods course. Comments such as these concern teacher educators who wish to prepare elementary teachers to include writing in mathematics instruction. A teacher development experiment was completed to discover how to improve preservice teachers’ abilities and attitudes toward using writing in mathematics. The preservice teachers made use of a graphic organizer to facilitate writing in the college math methods class, then practiced teaching writing with the same graphic organizer and in the math classes in an elementary classroom. Reflections of the preservice teachers illustrated this was a positive practice. The preservice teachers also concluded that writing in mathematics is valuable to instruction and would include it in their teaching.     

Crossing the Barriers Between Preservice and Inservice Mathematics Teacher Education: An Evaluation of the Grant School Professional Development Program

A 2‐year school‐based mathematics professional development program is described and evaluated after its first year of implementation. Included in this program as its first course was a unique methods course in elementary education involving both preservice students and inservice teachers who cooperatively studied and applied reform pedagogy. The program resulted from the collaborative efforts of two institutions of higher education, a neighboring school district, the principal and teachers of one school within that district, and the state office of education. Evaluation of the first year of the program consisted of assessing the beliefs and perceptions of both preservice students and inservice teachers, along with an assessment of the mathematical achievement of the children within the classes of those teachers. Pre‐ and post‐assessments of the preservice students and inservice teachers' beliefs regarding reform pedagogy were administered using the IMAP [Integrating Mathematics and Pedagogy] Web‐Based Beliefs Survey (2006). Likert scale surveys were used to assess perceptions regarding course climate and participant relationships from both teacher groups. The mathematical achievement of children was assessed in three ways: The Wide Range Achievement Test‐3 ( Stone, Jastak, & Wilkinson, 1995 ), the Utah state criterion‐referenced assessment, and performance assessments developed specifically for use at the school. Data obtained from all sources indicated positive effects upon teachers and children, thus providing substantial evidence in support of both the value of the methods course itself and the overall professional development program. An additional evaluation will be conducted following the second year of the program.     

Assessing Preservice Teachers' Beliefs about the Teaching and Learning of Mathematics and Science

With increased study of teachers' beliefs about science and mathematics teaching in recent years, there is a need for instruments that assess beliefs in both content areas. Moreover, early field experiences in schools and professional development efforts may influence the beliefs that preservice and in‐service teachers develop, and instruments for this purpose are limited. This article describes the development and validation of the Confidence, Commitment, Collaboration, and Student thinking in Mathematics and Science (CCCSMS) beliefs scales, a set of 10 six‐item scales. Collectively, these scales measure teachers' self‐confidence in doing and teaching science and mathematics, confidence in understanding children's thinking and building models of that thinking, commitment to teaching science and mathematics from a standards‐based perspective, and commitment to collaborating with peers. The scales represent an efficient and effective way of assessing beliefs of large groups. Although this article focuses predominantly on development of the scales, results from initial use indicate that there are positive correlations between beliefs related to mathematics and beliefs related to science, but the correlations are low enough to show that many teachers think differently about the two subjects.     

Construction of Teacher Knowledge in Context: Preparing Elementary Teachers to Teach Mathematics and Science

The purpose of this study was to further the understanding of how preservice teachers construct teacher knowledge and pedagogical content knowledge of elementary mathematics and science in a school‐based setting and the extent of knowledge construction. Evidence of knowledge construction (its acquisition, its dimensions, and the social context) was collected through the use of a qualitative methodology. The methods course was content‐specific with instruction in elementary mathematics and science. Learning experiences were based on national standards with a constructivist instructional approach and immediate access to field experiences. Analysis and synthesis of data revealed an extensive acquisition of teacher knowledge and pedagogical content knowledge. Learning venues were discovered to be the conduits of learning in a situated learning context. As in this study, content‐specific, school‐based experiences may afford preservice teachers greater opportunities to focus on content and instructional strategies at deeper levels; to address anxieties typically associated with the teaching of elementary mathematics and science; and to become more confident and competent teachers. Gains in positive attitudes and confidence in teaching mathematics and science were identified as direct results of this experience.     

Preservice Elementary Teachers' Use of Mathematics in a Project‐Based Science Approach

The use of a project‐based science (PBS) approach to teaching encourages students to integrate mathematics and science in meaningful ways as they create projects. As a beginning study of how students use mathematics in such an approach, an analysis of 23 projects developed by preservice elementary teachers enrolled in an elementary science course was conducted. Findings showed that students made a number of different types of mathematical errors and underutilized data representation and summary forms. Implications included the importance of developing methods for supporting the use of mathematical tools in utilizing a project‐based approach and considering ways that such tools mediate scientific thinking.     

Non‐Traditional Preservice Teachers and Their Mathematics Efficacy Beliefs

In Florida, recent legislative changes have granted community colleges the ability to offer baccalaureate degrees in education, frequently to non‐traditional students. Based on information obtained from the literature covering preservice teachers' math knowledge, teachers' efficacy beliefs about math, and high‐stakes mathematics testing, a study examined a population of preservice teachers in a new Florida teacher preparation program. The research investigated relationships surrounding non‐traditional preservice teachers' characteristics such as: ages, high‐stakes math failures, lower division mathematics history, and math methods course performance, in relation to their efficacy beliefs about mathematics. Results revealed that preservice teachers' ages, lower division mathematics history, and math methods course performance, did have a significant relationship with their math efficacy beliefs, as measured by the Mathematics Teaching Efficacy Beliefs Instrument (MTEBI); the variable of high‐stakes math failures did not. Additionally, a multiple regression model including the aforementioned variables did predict preservice teachers' MTEBI scores, but did not generalize to the greater population. The findings from this study can assist new teacher preparation programs in isolating variables that identify preservice teachers who are at risk for poor mathematical attitudes; can posit avenues for fostering positive math beliefs in preservice teachers; and can recommend further research in this area.     

A Preservice Secondary Teacher's Moves to Protect Her View of Herself as a Mathematics Expert

This paper discusses the experience of a preservice secondary mathematics teacher during lesson study. Although the preservice teacher was a strong undergraduate mathematics student, she used compensation “moves” to deflect attention away from her insecurities about her conceptual understanding of secondary mathematics. She feared being labeled as “dumb” and redirected conversations in order to protect her identity as a knower of mathematics. This paper investigates the culture in which preservice teachers develop confidence in their personal mathematics knowledge and how that confidence may influence behavior.     

Science Talk: Preservice Teachers Facilitating Science Learning in Diverse Afterschool Environments

The purpose of this study was to assess the impact a community‐based service learning program might have on preservice teachers' science instruction during student teaching. Designed to promote science inquiry, preservice teachers learned how to offer students more opportunities to develop their own ways of thinking through utilization of an afterschool science program that provided them extended opportunities to practice their science teaching skills. Three preservice teachers were followed to examine and evaluate the transfer of this experience to their student teaching classroom. Investigation methods included field observations and semi‐structured, individual interviews. Findings indicate that preservice teachers expanded their ideas of science inquiry instruction to include multiple modes of formative assessment, while also struggling with the desire to give students the correct answer. While the participants' experiences are few in number, the potential of afterschool teaching experience serving as an effective learning experience in preservice teacher preparation is significant. With the constraints of high‐stakes testing, community‐based service learning teaching opportunities for elementary and middle‐school preservice teachers can support both the development and refinement of inquiry instruction skills.     

The Growing Awareness Inventory: Building Capacity for Culturally Responsive Science and Mathematics With a Structured Observation Protocol

This study represents a first iteration in the design process of the Growing Awareness Inventory (GAIn), a structured observation protocol for building the awareness of preservice teachers (PSTs) for resources in mathematics and science classrooms that can be used for culturally responsive pedagogy (CRP). The GAIn is designed to develop awareness of: how students use language in classrooms; relationships between teacher questioning patterns and student participation; messages conveyed by the classroom environment; and ways to incorporate students’ interests into lesson plans. The methodology took the form of a multiple case study design with fourteen mathematics PSTs as one case and five science PSTs as the other case. The participants' response to the GAIn and lesson plans served as data sources. Findings reveal that the GAIn scaffolded PSTs’ awareness of their students, their own attitudes, and several elements of CRP. However, there were key areas of CRP that were neither explored with the GAIn nor identified by the participants. Consistent with design‐based research, outcomes include a design framework for revision of the GAIn and a theory of action that situates it within a teacher education course that includes a field placement.     

Teaching and Learning Mathematics With Interactive Spreadsheets

Learning to teach mathematics at the middle and secondary levels should include many opportunities for teachers to learn how to use technology to better understand mathematics themselves and promote students' learning of mathematical concepts with technology-enabled pedagogy. This article highlights work done in a variety of preservice and in-service mathematics teacher education courses to help teachers use commonly available spreadsheets as an interactive exploratory learning tool. Several examples of teachers' subsequent use of spreadsheets in their own teaching are also discussed.     

An Extended Examination of Preservice Elementary Teachers' Science Teaching Self‐Efficacy

The purpose of this study was to examine programmatic factors that positively impact changes in elementary preservice teachers' teaching self‐efficacy beliefs. Specifically, it examined the impact of science methods courses, student teaching, and science content courses on elementary preservice teachers' science teaching self‐efficacy. The Science Teaching Efficacy Belief Instrument Form B was administered, using a pre/post design, to undergraduate elementary education majors in specific education and science content courses. A total of 399 responses were collected, of which 172 had matching pre/post surveys suitable for analysis. Students in the science content courses and student teaching seminar showed no significant change in either the Personal Science Teaching Efficacy (PSTE) or the Science Teaching Outcome Expectancy scales during the time they were enrolled in the classes. Significant gains in PSTE were found for students enrolled in the science methods course. The specific design of the education program and methods course may be responsible for these changes.     

The Tabular Mode: Not Just Another Way to Represent a Function

Understanding mathematical functions as systematic processes involving the covariation of related variables is foundational in learning mathematics. In this article, findings are reported from two investigations examining students' thinking processes with functions. The first study focused on seven middle school students' explorations with a dynamic physical model. Students were videotaped during the 20‐ to 45‐minute sessions occurring two or three times per week over a period of 2 months, and students' written work was collected. The second investigation included 19 preservice elementary and middle school teachers enrolled in a course focusing on a combination of mathematical content and pedagogy. Participants' written problem‐solving work and reflective writing were collected, and participants were individually interviewed in 50‐minute videotaped sessions. Results from both investigations indicated that students often relied on a table, or some variation of a table, as a cognitive link advancing the development of their reasoning about underlying function relationships.