Professional Development Strategically Connecting Mathematics and Science: The Impact on Teachers' Confidence and Practice

The press to integrate mathematics and science comes from researchers, business leaders, and educators, yet research that examines ways to support teachers in relating these disciplines is scant. Using research on science and mathematics professional development, we designed a professional development project to help elementary teachers improve their teaching of mathematics and science by strategically connecting these disciplines. The purposes of this study are: (a) to identify changes in teachers' confidence and practice after participating in the professional development and (b) to identify different ways to connect mathematics and science during the professional development. We use a Likert‐scale survey to assess changes in teachers' confidence related to teaching mathematics and science. In addition, we report on a thematic analysis of teachers' written responses to open‐ended questions that probed teachers' perceived changes in practice. We analyze field notes from observations of project workshops to document different types of opportunities for connecting mathematics and science. We conclude with implications for future professional development that connects mathematics and science in meaningful ways, as well as suggestions for future research.     

Learning Trajectories,Lesson Planning,Affordances, and Constraints in the Design and Enactment of Mathematics Teaching

Recent reform efforts in mathematics education have stimulated a focus on learning trajectories. At the same time, a global increase in high-stakes testing has influenced instructional practices. This study investigated how four fourth grade teachers within a school planned and enacted lessons to understand what mediated their planning and teaching decisions. Findings reveal that three of these teachers, who were veteran teachers, used a testing trajectory approach with decisions mediated by preparing students for high-stakes tests. The fourth teacher, a novice, attempted to use a learning trajectory approach to support student understanding. Results reveal that high-stakes testing played a crucial role in teachers' instructional decisions. Based on the findings, we provide a framework for a testing trajectory approach that the veteran teachers used to make instructional decisions. Further research is needed to understand how to support teachers to prepare students for testing using effective teaching practices.     

Exploring the Use of New Representations as a Resource for Teacher Learning

An important goal of mathematics education reform is to support teacher learning. Toward this end, researchers and teacher educators have investigated ways in which teachers learn about mathematical content, pedagogical strategies, and student thinking as they implement reform. This study extends such work by examining how one elementary school and one high school teacher learned from students' interpretations of new conceptually based representations contained in instructional materials aligned with the Principles and Standards for School Mathematics ( National Council of Teachers of Mathematics, 2000 ). Results indicated that teaching with new representations provided a rich context for teacher learning at both the elementary and high school level, and three dimensions were identified along which such learning occurred. The results suggest that pedagogical content knowledge with respect to representations is an important facet of teacher cognition that should be studied in greater depth.     

Strategies and Sources of Support for Beginning Teachers of Science and Mathematics

This study examines the support structures and strategies utilized by beginning mathematics and science teachers. The qualitative case study of 18 teachers (0–3 years of experience) includes teachers from rural, suburban and urban schools. Data collection consisted of one‐hour interviews. The findings indicate participants utilized formal and informal support structures within the school district (e.g., mentoring programs, talking to other new teachers) as well as those external to the school (e.g., professional organizations and conferences, talking to family and friends). We propose a model of beginning teachers' initiating access to support structures based on the realization that their ideal images of teaching do not match the realities of their classrooms. Implications are given for teacher educators, researchers, and school administrators.     

Mathematics Anxiety and Preservice Elementary Teachers' Confidence to Teach Mathematics and Science

Sixty‐five preservice elementary teachers' math anxiety levels and confidence levels to teach elementary mathematics and science were measured. The confidence scores of subjects in different math anxiety groups were compared and the relationships between their math anxiety levels and confidence levels to teach mathematics and science were investigated. The results suggest that low math anxious preservice teachers are more confident to teach elementary mathematics and science than are their peers having higher levels of math anxiety. Negative correlations were found between preservice teachers' math anxiety and their confidence scores to teach elementary mathematics (r = ?.638) and between preservice teachers' math anxiety and their confidence scores to teach elementary science (r = ‐.417). Also, personal math and science teaching self‐efficacy scores of participants were found to be correlated at .01 level (r =.549).     

Relationship Between Professional Development,Teachers' Instructional Practices,and the Achievement of Students in Science and Mathematics

The purpose of this study was to examine the relationship between different types of professional development, teachers' instructional practices, and the achievement of students in science and mathematics. The types of professional development studied included immersion, examining practice, curriculum implementation, curriculum development, and collaborative work. Data regarding teachers' instructional practices and the amount of professional development were collected using teacher surveys. Ninety‐four middle school science teachers and 104 middle school mathematics teachers participated in the study. Student achievement was measured using eighth grade state science and mathematics achievement test data. Regression analyses suggested that for both science and mathematics teachers, examining practice and curriculum development were significantly related to the use of standards‐based instructional practices. Only curriculum development for mathematics teachers was significantly related to student achievement. Implications of results for the professional development of science and mathematics teachers are discussed.     

Math Autobiographies: A Window into Teachers' Identities as Mathematics Learners

Mathematics autobiographies have the potential to help teachers reflect on their identities as mathematics learners and to understand their role in the development of their students' mathematics identities. This paper reports on a professional development project for K‐2 teachers (n = 41), in which participants were asked to write mathematics autobiographies. Using an adaptation of an existing framework for characterizing teachers' mathematics stories, we describe the consistencies among the participants' experiences as mathematics learners and the events that are identified as being the impetus for a transition from a negative to a positive attitude toward mathematics. Implications for both teachers and teacher educators are presented.     

Efficacy for Teaching Elementary Science and Mathematics Compared to Other Content

The study was conducted to examine preservice, elementary teachers' efficacy for teaching science and mathematics as compared with other elementary content. The instrument assessed efficacy for teaching (EFT) five elementary content areas: science, mathematics, reading, classroom management, and general instruction. Three hundred twenty‐five preservice, elementary teachers completed a 15‐item instrument assessing efficacy for teaching in these five areas. The instrument was found to be valid and reliable. Overall group results indicated participants' EFT science and mathematics were lower than for teaching other areas. Intra‐individual patterns showed there were six clusters including a group with low EFT mathematics and a group with low EFT mathematics and science. Implications for preservice, teacher preparation opportunities and experiences are discussed.     

Challenging Preservice Teachers' Mathematical Understanding: The Case of Division by Zero

Preservice elementary school teachers' fragmented understanding of mathematics is widely documented in the research literature. Their understanding of division by 0 is no exception. This article reports on two teacher education tasks and experiences designed to challenge and extend preservice teachers' understanding of division by 0. These tasks asked preservice teachers to investigate division by 0 in the context of responding to students' erroneous mathematical ideas and were respectively structured so that the question was investigated through discussion with peers and through independent investigation. Results revealed that preservice teachers gained new mathematical (what the answer is and why it is so) and pedagogical (how they might explain it to students) insights through both experiences. However, the quality of these insights were related to the participants' disposition to justify their thinking and (or) to investigate mathematics they did not understand. The study's results highlight the value of using teacher learning tasks that situate mathematical inquiry in teaching practice but also highlight the challenge for teacher educators to design experiences that help preservice teachers see the importance of, and develop the tools and inclination for, mathematical inquiry that is needed for teaching mathematics with understanding.     

Exploring the Relationship Between Teaching Efficacy and Cultural Efficacy of Novice Science Teachers in High‐Needs Schools

This qualitative case study sought to investigate what relationship exists between teaching efficacy and cultural efficacy of novice science teachers in high‐needs, high‐minority urban schools. One major theme—the importance of establishing positive teacher–student relationships—surrounding teaching efficacy in the context of cultural efficacy emerged. The data sources included: (a) teachers' responses to a focus group interview conducted at the end of their first year, (b) written reports and documentation from university‐based field supervisors' observations during the teachers' first year, and (c) teachers' self‐reported responses on the Science Teaching Efficacy Belief Instrument designed to measure science teaching efficacy. Final analysis of the data reflects a strong relationship between teaching efficacy and practice within the context of culture. The results of this study also indicated an existing relationship between teaching efficacy and cultural efficacy through cultural connections with students. Encouraging the development of teacher efficacy in the context of cultural efficacy becomes important at all levels of teacher preparation, especially to ensure the retention of high‐quality science teachers in high‐needs schools.     

Using Metaphors as a Tool for Examining Preservice Elementary Teachers' Beliefs About Mathematics Teaching and Learning

This study used metaphors as a tool to gain insight about preservice teachers' conceptualizations of the role of the teacher and the learner and held the view that the examination of these metaphors might provide an opportunity for teacher educators to reflectively and critically examine those beliefs. Thus, this research examined possible differences in the reflected beliefs of elementary preservice teachers as depicted in their metaphors about mathematics teaching and learning at three different points throughout their mathematics education methods courses. The results of this study indicated that elementary preservice teachers' beliefs primarily remained static throughout their mathematics methods courses despite ongoing experiences designed to challenge and extend those beliefs.     

The Influences of Three Interventions on Prospective Elementary Teachers' Beliefs About the Knowledge Base Needed for Teaching Mathematics

To meet the challenge to reform mathematics education, effective opportunities to learn are needed to promote prospective elementary school teachers' development of the knowledge base that supports teaching for mathematical proficiency. This article describes three professional development interventions and their influence on prospective teachers' beliefs about mathematics, how children learn mathematics, and mathematics teaching. The three interventions consisted of problem‐solving journals, structured interviews, and peer teaching that were integrated in a PreK‐6 mathematics methods course. Results of precourse and postcourse survey data are included that measured 24 prospective teachers' beliefs about the knowledge base needed to teach elementary school mathematics. Data indicated that using these interventions and other course experiences facilitated change in the prospective teachers' beliefs, with a shift toward reform‐oriented mathematics education perspectives.     

Interpreting Middle School Students' Proportional Reasoning Strategies: Observations From Preservice Teachers

This paper reports the findings of an investigation of 11 preservice secondary school teachers' interpretations of the development of proportional reasoning strategies used by middle school students. The preservice teachers examined samples of solution strategies generated by middle school students in proportional reasoning situations and prepared written responses of their views concerning the developmental levels indicated in the students' work. Each preservice teacher also participated in an hour‐long interview, in which the researchers asked for elaboration and clarification of the written responses and, in some cases, challenged the preservice teachers to consider alternative interpretations for the middle school students' work. The interviews were audiotaped for later analysis by the investigators, and key aspects of both the written and audiotaped responses were entered into a spreadsheet and later tabulated into categories indicating trends in the preservice teachers' interpretations. Some implications for the preparation of preservice middle school science and mathematics teachers are included.     

Creating a Model of Acceptance: Preservice Teachers Interact With Non‐English‐Speaking Latino Parents Using Culturally Relevant Mathematics and Science Activities at Family Learning Events

The following describes a culturally relevant mathematics and science content program implemented by preservice teachers (PSTs) at Family Math/Science Learning Events (FM/SLEs) conducted through two different university programs in south Texas. These experiences are required course activities designed to inform PSTs of the importance of interacting with Latino families' culture and language in after school settings. Data were collected from elementary PSTs attending FMLEs and include interactions recorded during the FMLE and interviews with Latino non‐English‐speaking parents after the event. Anecdotal data were also included from parents' interviews collected during culturally relevant Family Science Learning Events. Researchers investigated the following questions: (1) what did Latino parents and PSTs report learning from the FMLE and, (2) how do perceptions toward Latino parents change when PSTs are given the opportunity to interact with and interview Latino parents? Results show that PSTs perceptions of Latino parents can be changed through these events. Implications for teacher preparation programs include providing PSTs with opportunities for participation in FM/SLEs that incorporate planning and teaching culturally relevant math and science activities. The following model of acceptance requires PSTs to identify and reconstruct misconceptions and perceptions of parents, especially non‐English‐speaking Latino parents.     

Constructing Elementary Teachers' Beliefs,Attitudes, and Practical Knowledge Through an Inquiry‐Based Elementary Science Course

This study examines inservice elementary school teachers' beliefs, attitudes, and practical knowledge toward inquiry‐based science instruction and the influence of an inquiry‐based elementary science course on teachers' beliefs, attitudes, and practical knowledge regarding inquiry. Both surveys and a case study were administered to the 14 elementary school teachers before and after completing a three‐credit elementary science methods course that was inquiry‐based. The findings showed that the teachers' beliefs, attitudes, and practical knowledge about inquiry were clearly influenced by the course. Through this course, the teachers developed fairly positive beliefs and attitudes that promoted inquiry instruction. The majority of participants also improved their knowledge and skills of conducting inquiry as they successfully practiced inquiry‐instruction in their science teachings.     

Crutch or Catalyst: Teachers' Beliefs and Practices Regarding Calculator use in Mathematics Instruction

This study investigated K‐12 teachers' beliefs and reported teaching practices regarding calculator use in their mathematics instruction. A survey was administered to more than 800 elementary, middle and high school teachers in a large metropolitan area to address the following questions: (a) what are the beliefs and practices of mathematics teachers regarding calculator use? and (b) how do these beliefs and practices differ among teachers in three grade bands? Factor analysis of 20 Likert scale items revealed four factors that accounted for 54% of the variance in the ratings. These factors were named Catalyst Beliefs, Teacher Knowledge, Crutch Beliefs, and Teacher Practices. Compared to elementary teachers, high school teachers were significantly higher in their perception of calculator use as a catalyst in mathematics instruction. However, the higher the grade level of the teacher, the higher the mean score on the perception that calculator use may be a way of getting answers without understanding mathematical processes. The mean scores for teachers in all three grade bands indicated agreement that students can learn mathematics through calculator use and using calculators in instruction will lead to better student understanding and make mathematics more interesting. The survey results shed light on teachers' self reported beliefs, knowledge, and practices in regard to consistency with elements of the National Council of Teachers of Mathematics Principles and Standards for School Mathematics (2000) technology principle and the NCTM use of technology position paper (2003). This study extended previous research on teachers' beliefs regarding calculator use in classrooms by examining and comparing the results of teacher surveys across three grade bands.     

An Interdisciplinary Approach to Science,Mathematics, and Reading: Learning as Children Learn

A project was designed to implement an integrated curriculum in mathematics, science, and reading by promoting the professional growth of K-4 in-service teachers through a 6-hour graduate course. The course adopts a view of teachers' knowledge acquisition based on constructivism, a perspective currently more accepted for elementary children than for teachers. The effectiveness of the project in the Ist year was evaluated in part by employing content examinations, portfolios, journals, questionnaires, and course assignments. The findings suggest implications for teacher educators, program administrators, teachers in K-4, and the children served by the educational system.     

Factors Influencing Elementary Teachers' Positioning of African American Girls as Science and Mathematics Learners

Despite recent progress toward gender equity in science and mathematics education, the underachievement of low‐income African American girls remains a challenge when compared with their white counterparts. Furthermore, the causes of this persistent underachievement have not been explored thoroughly. We have initiated a three‐year longitudinal study of how African American girls position themselves in relation to science and mathematics learning from fifth to seventh grade, including the impact, if any, of the positioning of teachers, counselors, and parents on this process. In this article, we share findings examining science and mathematics teachers' actions and perceptions and their positioning of African American girls. This qualitative study used an interpretive design with multiple data sources including classroom observations, interviews, and field notes. Findings reveal that school‐wide policies and teachers' autonomous decisions impact the regularity of science and mathematics instruction, and that teachers do not always conceptualize the girls as science and mathematics achievers, positioning them in negative ways.     

Formative assessment and the role of teachers' content area

Professional development (PD) programs focused on increasing teachers' use of formative assessment generally provide a framework designed to help teachers understand the breadth and complexity of formative assessment, while advocating for teacher choice with respect to the specific implementation. This study examined the implementation patterns of 82 high school mathematics and science teachers to understand whether implementation approaches differed by content area. Results suggested that mathematics and science teachers significantly increased their self‐reported practice of formative assessment, in similar ways; however, the specific approaches that mathematics and science teachers chose to operationalize on a daily basis differed. These findings have implications for the design of PD and future research efforts.