Mix It Up: Teachers' Beliefs on Mixing Mathematics and Science

This paper defines correlation, describes the Mix It Up program, discusses the teachers' beliefs about the value of correlating mathematics and science prior to program participation, and identifies problems teachers associated with correlation before and during the program. Teachers' beliefs about the value of correlation and about the problems associated with correlation are based on results from both quantitative and qualitative methods used to evaluate the program. Results indicate that teachers believe correlating mathematics and science strengthens students' content knowledge in mathematics and science, bridges the gap between mathematics and science, enhances motivation, and increases students' flexibility in problem solving. Additionally, the areas identified by teachers to be most problematic were time, planning for instruction as a team, and exposure to correlation in the past. The most important finding from the program evaluation indicates that although teachers did not identify content knowledge weaknesses before participating in the program, they did recognize gaps in their own content knowledge during program participation, and more importantly they made connections among these gaps, classroom instruction, and their own students' performance in mathematics and science.     

Reflection and Problem Solving: Integrating Methods of Teaching Mathematics and Science

An innovative teacher preparation course which integrates methods of teaching elementary mathematics and science was the context of this study. The course was developed as a prototype for the Teachers As Reflective Problem Solvers model for the preparation of elementary mathematics and science teachers. Data from 35 preservice elementary teachers' performance-portfolios were analyzed to reveal patterns of change in their reflections and problem-solving performance during the semester. Many of the students' reflections changed from task-focused learning to broader teaching applications. No relationship was discerned between changes in students' reflections and changes in their levels of problem-solving performance, although both increased during the semester. A significant correspondence was found, however, between students' perceptions of their problem-solving abilities and their actual performance in solving teaching problems in integrated mathematics and science contexts.     

A Longitudinal Study of Elementary Pre‐service Teachers' Mathematics Beliefs and Content Knowledge

This study investigated the mathematics beliefs and content knowledge of 103 elementary pre‐service teachers in a developmental teacher preparation program that included a two course mathematics methods sequence. Pre‐service teachers' pedagogical beliefs became more cognitively‐oriented during the teacher preparation program with these changes occurring during the two methods courses. Pedagogical beliefs remained stable during student teaching. The pre‐service teachers also significantly increased their personal efficacy for teaching mathematics throughout the program with these shifts occurring across both methods courses and into student teaching. Pedagogical beliefs and teaching efficacy beliefs were not related at the beginning of the program, but, in general, were positively related throughout the program. In addition, the pre‐service teachers' pedagogical beliefs were positively related to their specialized content knowledge for teaching mathematics at the end of the program.     

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.     

Preparing Middle Level Preservice Teachers to Integrate Mathematics and Science: Problems and Possibilities

Many members of the mathematics and science education community believe that the integration of mathematics and science enhances students' understanding of both subjects. Despite this belief, attempts to integrate these subjects have frequently been unsuccessful. This study examines the development and implementation of a team‐taught integrated middle level mathematics and science methods course. The data presented in this study were collected from three groups of preservice teachers who were enrolled in a grades 5–8 middle level teacher certification program in Connecticut from 1998–2000. The data analysis indicates that preservice teachers appreciated the emphasis on integration used in the course, but at the same time when concepts did not integrate easily they were frustrated. Despite this frustration, the preservice teachers' understanding of integration was enhanced as a result of the course.     

What Matters Most: A Comparison of Expert and Novice Teachers' Noticing of Mathematics Classroom Events

In this study, we examined 10 expert and 10 novice teachers' noticing of classroom events in China. It was found that both expert and novice teachers, who were selected from two cities in China, highly attended to developing students' mathematics knowledge coherently and developing students' mathematical thinking and ability; they also paid attention to students' self‐exploratory learning, students' participation, and teachers' instructional skills. Furthermore, compared with novice teachers, expert teachers paid greater attention to developing mathematical and high‐order thinking, and developing mathematics knowledge coherently, but paid less attention to teachers' guidance. Moreover, we further illustrated the qualitative differences and similarities in their noticing of classroom events. Finally, we discussed the findings and relevant implications.     

The Indiana Science Initiative: Lessons from a Classroom Observation Study

The Indiana Science Initiative (ISI) is a systemic effort to reform K–8 science education. The program provides teachers with professional development, reform‐oriented science modules, and materials support. To examine the impact of the initiative's professional development, a participant observation study was conducted in the program's pilot year. Five teachers in grades 3–6 were observed and interviewed as they implemented the ISI‐provided modules. Analysis of the observation data revealed that the teachers incorporated each of the features of inquiry science instruction. However, they did not consistently teach in a way that was aligned with the intent of the ISI. Examination of interview data provided insight into influences on teachers' use of inquiry with the ISI‐provided modules. These data revealed that teachers were aware of the intent of the ISI and attempted to align their instruction. However, teachers were influenced by their perceptions of students' behavior and abilities as well as timing and the appropriate level of teacher control needed to facilitate science instruction. The research suggests that professional development activities should prepare teachers to help learners evaluate explanations against alternatives, connect explanations to scientific knowledge, and provide strategies to address teachers' perceptions of students, timing, and teacher control.     

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.     

Teachers' ways of listening and responding to students' emerging mathematical models

In this paper, I present the results of a case study of the practices of four experienced secondary teachers as they engaged their students in the initial development of mathematical models for exponential growth. The study focuses on two related aspects of their practices: (a) when, how and to what extent they saw and interpreted students' ways of thinking about exponential functions and (b) how they responded to the students' thinking in their classroom practice. Through an analysis of the teachers' actions in the classroom, I describe the teachers' developing knowledge when using modeling tasks with secondary students. The analysis suggests that there is considerable variation in the approaches that teachers take in listening to and responding to students' emerging mathematical models. Having a well-developed schema for how students might approach the task enabled one teacher to press students to express, evaluate, and revise their emerging models of exponential growth. Implications for the knowledge needed to teach mathematics through modeling are discussed.     

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.     

A High‐Quality Professional Development for Teachers of Grades 3–6 for Implementing Engineering into Classrooms

With the increasing emphasis on integrating engineering into K‐12 classrooms to help meet the needs of our complex and multidisciplinary society, there is an urgent need to investigate teachers' engineering‐focused professional development experiences as they relate to teacher learning, implementation, and student achievement. This study addresses this need by examining the effects of a professional development program focused on engineering integration, and how teachers chose to implement engineering in their classrooms as a result of the professional development. 198 teachers in grades 3–6 from 43 schools in 17 districts participated in a yearlong professional development program designed to help integrate the new state science standards, with a focus on engineering, into their teaching. Posters including lesson plans and student artifacts were used to assess teachers' engineering practices and the implementation in their classrooms. Results indicated that the majority of the teachers who participated in the professional development were able to effectively implement engineering design lessons in their classrooms suggesting that the teachers' success in implementing engineering lessons in their classroom was closely related to the structure of the professional development program.     

STEM Teachers' Planned and Enacted Attempts at Implementing Engineering Design‐Based Instruction

This study investigates grades 5 and 6 science, technology, engineering, and mathematics (STEM) teachers' planned and actualized engineering design‐based instruction, the instruments used to characterize their efforts, and the implications this work has for teachers' implementations of an integrated approach to STEM education. Participants included 23 STEM teachers from six schools (three rural, two suburban, and one urban). Data were gathered via lesson implementation plans and classroom observations. Teachers demonstrated strength in planning for standards‐ and engineering design‐based lessons, incorporating engineering practices within their respective implementation plans, and aligning their plans with content and design process standards. Missing from their plans was attention to science concepts and their placement, use, and application within a design task. Classroom observations indicated that the teacher participants gave priority to “front loading,” the design process by concentrating more of their instructional time on problem identification and planning and less time on testing designs, communicating performance results, and redesigning. Measures utilized in this study provided insight into the content of teachers' planning and subsequent instruction and suggest potential for capturing content planning in the context of classrooms in which teachers are attempting to integrate novel curriculum, such as the new standards for engineering practices.     

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.     

The Road to Reform: A Grounded Theory Study of Parents' and Teachers' Influence on Elementary School Science and Mathematics

Though elementary teacher educators introduce new, reform‐based strategies in science and mathematics methods courses, researchers wondered how novices negotiate reform strategies once they enter the elementary school culture. Given that the extent of parents' and veteran teachers' influence on novice teachers is largely unknown, this grounded theory study explored parents' and teachers' expectations of children's optimal science and mathematics learning in the current era of reform. Data consisted of semi‐structured, open‐ended interviews with novice teachers (n = 20), veteran teachers (n = 9), and parents (n = 28). Researchers followed three stages of coding procedures to develop a logic model connecting participants' discrete designations of the landscape, regulating phenomena, contextual orientation, and desired outcomes. This logic model helped researchers develop propositions for future research on the interactive nature of parents' and teachers' influential role in elementary science and mathematics education. Implications encourage science and mathematics teacher educators—as well as school administrators—to explicitly develop and support novice teachers' ability to initiate and sustain parent/family engagement in order to create a school climate where teachers and parents are synergistically motivated to change.     

Enhancing Formative Assessment Practice and Encouraging Middle School Mathematics Engagement and Persistence

In the transition to middle school, and during the middle school years, students' motivation for mathematics tends to decline from what it was during elementary school. Formative assessment strategies in mathematics can help support motivation by building confidence for challenging tasks. In this study, the authors developed and piloted a professional development program, Learning to Use Formative Assessment in Mathematics with the Assessment Work Sample Method (AWSM) to build middle school math teachers' understanding of the characteristics of high‐quality formative assessment processes and increases their ability to use them in their classrooms. AWSM proved to be feasible to implement in the middle school setting. It improved teachers' practice of formative assessment, especially in their feedback practices, regardless of their pedagogical content knowledge at entry. Results from focus groups suggested that teachers were better able to implement ungraded practice and student self‐ and peer‐assessment after AWSM, and that students were more willing to engage in complex problem solving.     

Behind the Masks: Identifying Students' Competencies for Learning Mathematics and Science in Urban Settings

Three mathematics and science educators reexamine and reflect on their teaching within the context of the American Association for the Advancement of Sciences (AAAS) and National Council of Mathematics' call to make math and science education accessible to all. The paper highlights the importance of teachers reflecting on their teaching practices in order to create opportunities for their students especially those in the urban setting. The educators argue that teachers' reflection on their teaching can cause them to recognize and validate their students' ways of knowing as they identify the students' hidden/concealed abilities that are often masked by their behaviors. The educators discuss their experiences and highlight the lessons that they learned about ways to prepare teachers to successfully teach math and science students in urban settings. Culturally responsive pedagogy and cultural competency are critical skills that teachers need to develop in order to teach all children, especially those in the math and science classroom in the urban setting.     

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.     

Processes and Pathways: How Do Mathematics and Science Partnerships Measure and Promote Growth in Teacher Content Knowledge?

Intense focus on student achievement results in mathematics and science has brought about claims that K‐12 teachers should be better prepared to teach basic concepts in these disciplines. The focus on teachers' mathematics and science content knowledge has been met by efforts to increase teacher knowledge through funded national initiatives focusing on mathematics and science. The purpose of the present study was to look across projects in the National Science Foundation's Math and Science Partnership Program to determine how partnerships developed processes for measuring growth in teacher content knowledge. Pre‐ and post‐testing was the most common process for measuring growth in content knowledge, with 63% of the mathematics and 78% of the science teachers showing significant gains in content knowledge. A notable difference was found between teacher outcomes when the Learning Mathematics for Teaching instrument was used in comparison with the use of other instruments measuring teacher content knowledge growth. Results revealed two pathways for promoting teacher content knowledge growth: content explicit, where the goal of growth in teacher content knowledge was explicit in the activity, and content embedded, where the goal of growth in teacher content knowledge was embedded in the activity. As a result of the analysis, a framework demonstrating the interrelationships among processes and pathways was developed. ¹