Teachers' Understandings of Realistic Contexts to Capitalize on Students' Prior Knowledge

The theory of realistic mathematics education establishes that framing mathematics problems in realistic contexts can provide opportunities for guided reinvention. Using data from a study group, I examine geometry teachers' perspectives regarding realistic contexts during a lesson study cycle. I ask the following. (a) What are the participants' perspectives regarding realistic contexts that elicit students' prior knowledge? (b) How are the participants' perspectives of realistic contexts related to teachers' instructional obligations? (c) How do the participants draw upon these perspectives when designing a lesson? The participants identified five characteristics that are needed for realistic contexts: providing entry points to mathematics, using “catchy” and “youthful” contexts, selecting personal contexts for the students, using contexts that are not “too fake” or “forced,” and connecting to the lesson's mathematical content. These characteristics largely relate to the institutional, interpersonal, and individual obligations with some connections with the disciplinary obligation. The participants considered these characteristics when identifying a realistic context for a problem‐based lesson. The context promoted mathematical connections. In addition, the teachers varied the context to increase the relevance for their students. The study has implications for supporting teachers' implementation of problem‐based instruction by attending to teachers' perspectives regarding the obligations shaping their work.     

Appropriate problems for learning and for performing—an issue for teacher training

Selecting, modifying or creating appropriate problems for mathematics class has become an activity of increaing importance in the professional development of German mathematics teachers. But rather than asking in general: “What is a good problem?” there should be a stronger emphasis on considering the specific goal of a problem, e.g.: “What are the ingredients that make a problem appropriate for initiating a learning process” or “What are the characteristics that make a problem appropriate for its use in a central test?” We propose a guiding scheme for teachers that turns out to be especially helpful, since the newly introduced orientation on outcome standards a) leads to a critical predominance of test items and b) expects teachers to design adequate problems for specific learning processes (e.g. problem solving, reasoning and modelling activities).     

Student and Teacher Perspectives Across Mathematics and Science Classrooms: The Importance of Engaging Contexts

Substantial recent focus has been placed upon the competitiveness of American students in increasingly global economies and entrepreneurial enterprises. As concerns center on students’ educational preparedness and their efforts at continued learning, researchers acknowledge the importance of student engagement with school. In order to foster engaged learners, teachers must be able to determine and monitor their students’ levels of engagement. The current study examined the alignment of perceptions of engagement by students, teachers, and outside observers across middle and high school mathematics and science classrooms. Results indicated significant teacher‐student differences in perceptions of student cognitive engagement across mathematics and science classrooms with teachers consistently perceiving higher levels than students. Moreover, most effect sizes were moderate to large. A subsequent multi‐level analysis indicated that while teacher perceptions of student cognitive engagement were somewhat predictive of student reported cognitive engagement, academic engagement ratings by outside observers were not.     

What Is STEM? A Discussion About Conceptions of STEM in Education and Partnerships

Educational reformation has proceeded slowly despite the many calls to improve science and mathematics for our students. The acronym STEM (science, technology, engineering, and mathematics) has been adopted by numerous programs as an important focus for renewed global competitiveness for the United States, but conceptions of what STEM entails often vary among stakeholders. This paper examines the conceptions of STEM held by faculty members from a public Research I institution in the middle of a regional “STEM movement.” Faculty members responded to two open‐ended questions: (1) What is STEM? and (2) How does STEM influence and/or impact your life? Although 72% of these faculty members possessed a relevant conception of STEM, the results suggest that they do not share a common conceptualization of STEM. Their conception is most likely based on their academic discipline or how STEM impacts their daily lives. STEM faculty members were likely to have a neutral or positive conception where non‐STEM faculty members often had negative feelings about STEM.     

Impacts of professional development focused on teaching engineering applications of mathematics and science

With the recent national emphasis on preparing children for future careers in science, technology, engineering, and mathematics, K-12 teachers are being called upon to include engineering in their instruction. This study explores the impacts of a summer professional development (PD) program focused on the engineering applications of mathematics and science on in-service K-12 teachers' (a) personal engineering efficacy, (b) engineering teaching efficacy, and (c) perceived barriers to teaching engineering. This quantitative study revealed that a single engineering-focused PD could increase teachers' personal engineering efficacy and engineering teaching efficacy and reduce particular perceived barriers to teaching engineering. No differences existed in pre- to post workshop assessment scores based on grade level taught, gender, or years of teaching experiences. However, pre- to post workshop assessment differences existed between participants depending on the discipline they taught and wether or not they had previously used engineering activities in their classrooms. These findings suggest that a single engineering PD can have significant impacts on in-service teachers' personal engineering efficacy, engineering teaching efficacy, and perceived barriers to teaching engineering, but a one-size-fits-all approach to such PD is not equally effective for all participants.     

Perceived Helpfulness and Amount of Use of Technology in Science and Mathematics Classes at Different Grade Levels

Use of technology in science and mathematics classes has been increasing, but there are differences in the amount of use of and students' perceptions of its helpfulness across grade levels and subject areas. Technology was reported as used only occasionally. Technology was used most often to understand or explore in more depth concepts taught in class. The second most frequent use was as a tool of investigation or assessment. The lowest reported use of technology was as tool of communication. Students in middle school classes perceived technology as less helpful than did students in elementary or high school classes. Students in mathematics classes perceived technology as more helpful than did students in science classes. Girls perceived technology as more helpful than did boys. Additionally, teacher and student perceptions of amount of use varied with teachers reporting more use than students.     

Teacher Mentoring as a Community Effort

This article presents the findings from a study of a mentoring program for novice mathematics and science teachers, which was provided by their teacher education program. This study reports the findings of interviews with novice math and science teachers, their mentors, and the mentoring program administrators to explore stakeholder perceptions of mentoring support. Findings suggest the importance of using multiple mentoring strategies to develop, support, and retain high‐quality math and science teachers in the teaching profession. This study contributes to what is known about the role that teacher education programs may play in mentoring novice math and science teachers who have graduated from their programs.     

PBL as a pedagogical approach for integrated STEM: Evidence from prospective teachers

Problem-based learning (PBL) and science, technology, engineering, and mathematics (STEM) are two acronyms widely visible in education literature today. However, few studies have explored these in connection with one another, specifically with regard to teacher preparation. This study investigated how 47 prospective elementary teachers developed PBL units and how they integrated STEM and other disciplines into those units. It also addressed the affordances and constraints of integrated STEM as perceived by the prospective elementary teachers. Data sources in this multimethod study included PBL units and interviews. Findings revealed that all of the units integrated at least two of the STEM disciplines, as well as literacy, in a variety of ways. The prospective teachers articulated perceived benefits of integrated STEM, such as: making connections across content areas, preparing students for the real world, teaching students that failure is not a bad thing, and providing future opportunities. They also addressed perceived barriers of integrated STEM, such as: having limited experience with the content, diminishing the effect of individual content areas, and needing better curriculum alignment. Overall, this study provides evidence that PBL can be a pedagogical approach to integrate STEM. Implications for teachers, teacher educators, and curriculum specialists are discussed.     

Next Generation Science Standards: A National Mixed‐Methods Study on Teacher Readiness

Next Generation Science Standards (NGSS) science and engineering practices are ways of eliciting the reasoning and applying foundational ideas in science. As research has revealed barriers to states and schools adopting the NGSS, this mixed‐methods study attempts to identify characteristics of professional development (PD) that will support NGSS adoption and to improve teacher readiness. In‐service science teachers from across the nation were targeted for the survey and responses represented 38 states. Research questions included: How motivated and prepared are in‐service 7–12 teachers to use NGSS science and engineering practices? What is the profile of 7–12 in‐service teachers who are motivated and feel prepared to use NGSS science and engineering practices? The study revealed that teachers identified engineering most frequently as a PD need to improve their NGSS readiness. High school teachers rated themselves as more prepared than middle school and all teachers who use Modeling Instruction expressed higher NGSS readiness. These findings and their specificity contribute to current knowledge, and can be utilized by districts in selecting PD to support teachers in preparing to implement the NGSS successfully.     

What Is the Object of the Encapsulation of a Process?

Several theories have been proposed to describe the transition from process to object in mathematical thinking. Yet, what is the nature of this “object” produced by the “encapsulation” of a process? Here, we outline the development of some of the theories (including Piaget, Dienes, Davis, Greeno, Dubinsky, Sfard, Gray, and Tall) and consider the nature of the mental objects (apparently) produced through encapsulation and their role in the wider development of mathematical thinking. Does the same developmental route occur in geometry as in arithmetic and algebra? Is the same development used in axiomatic mathematics? What is the role played by imagery?     

Pre-service Teachers’ Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers’ developing conceptions about (a) the nature of mathematical modeling in simulations of “real life” problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike other studies that have focused on single-topic and lesson-sized research sites, a course-sized research site was used in this study. Having been through several iterations over three teaching semesters, the 15-week long course was implemented with 25 pre-service secondary mathematics teachers. Findings revealed that pre-service teachers developed ideas about the nature of mathematical modeling involving what mathematical modeling is, the relationship between mathematical modeling and meaningful understanding, and the nature of mathematical modeling tasks. They also realized the changing roles of teachers during modeling implementations and diversity in students’ ways of thinking. The researchers’ conceptual development, on the other hand, involved realizing the critical aspect of the “teacher role” played by the instructor during modeling implementations, and the need for more experience of modeling implementations for pre-service teachers.     

Beginning Mathematics Teachers' Beliefs of Subject Matter and Instructional Actions Documented Over Time

In this study we report the results of survey research that collected responses of an identical sample (31 beginning mathematics and science teachers, elementary and middle school level) that graduated from a reform‐based mathematics and science teacher preparation program, the Maryland Collaborative for Teacher Preparation (MCTP). Our aim was to compare responses of the same beginning teachers over the two administrations of the survey. We administered the identical survey instrument in two separate batches spreading over nearly a four‐year period (1st batch fall 1999 through fall 2001; 2nd batch summer 2002). The first administration (pre‐test) was conducted soon after the beginning teachers graduated from the teacher preparation program and had not started full teaching. The second administration (post‐test) was conducted after the new teachers had taught full time for a minimum of a full year, with the majority having taught for two years. The instrument was crafted to measure the constructs of interest, MCTP Teacher's Beliefs and Actions of Mathematics and Science. Results for teachers who taught for at least two years indicated that in all areas the MCTP teachers maintained their reform‐based beliefs and actions after their induction years. These findings provide evidence for the sustainability of positive impact in the workplace resulting from a reform‐based undergraduate teacher preparation program.     

Science and Mathematics Instruction in a Reform‐based Teacher Preparation Program

This study examined the science and mathematics instruction of teachers who were initially prepared by the Collaboratives for Excellence in Teacher Preparation program (CETP). The focus of this study was on examining the extent to which science and mathematics teachers used more reform‐oriented instructional practices in their classes when they entered the teaching profession. Data were gathered from twelve different CETP projects across the United States. A quasi‐experimental design was used where science and mathematics teachers who were initially prepared by the CETP program were followed into the field and compared to teachers who were not prepared by the CETP program. The results indicate that the teachers prepared by the CETP program used slightly more reform‐oriented instructional practices than teachers who were not prepared by the CETP program, although both mathematics and science teachers reported low levels of reform‐oriented instruction. Implications of results for large‐scale reform of science and mathematics teacher preparation are discussed.     

Effective Professional Development and Change in Practice: Barriers Science Teachers Encounter and Implications for Reform

This study focused on two middle schools in the central US who participated in collaborative, sustained, whole‐school professional development in implementing inquiry as part of National Science Education Standards, or standards‐based instructional practices. Participants were involved in their second year of the professional development experience. The research question explored was, “What barriers do science teachers encounter when implementing standards‐based instruction while participating in effective professional development experiences?” Qualitative data collected in the form of teacher interviews and classroom observations were utilized and were analyzed using a barrier to reform rubric. Findings indicate that even with effective professional development, science teachers still encounter technical, political, and cultural barriers to implementation. More support is required for professional development efforts to be successful, such as resources and time, as well as administrative buy‐in and support. Findings also revealed that even the best intended professional development efforts do not reveal and address existing beliefs for all teachers. Implications for future science education reform stakeholders are discussed.     

Science as a Learner and as a Teacher: Measuring Science Self‐Efficacy of Elementary Preservice Teachers

Academic science achievement of U.S. students has raised concerns regarding our ability as a nation to compete in a global economy. Additionally, research has shown that many elementary teachers have weak science content backgrounds and had poor/negative experiences as students of science, resulting in a lack of confidence regarding teaching science. However, efforts to increase science self‐efficacy (SE) in preservice teachers can help to combat these issues. This study looked at a sample of preservice elementary teachers engaged in a semester‐long science content course, using Bandura's concept of SE as a conceptual framework. Our quantitative data showed significant increases in science SE on both subscales (personal efficacy and outcome expectancy). Our qualitative data showed that students communicated an increased sense of confidence with regard to the discipline of science. In addition, students reported learning science pedagogy through the instructor's modeling. Combining our findings resulted in several meta‐inferences, one of which showed students growing as both confident learners of science and teachers of science simultaneously. We created a construct new to the literature to describe this phenomenon: “teacher‐learner,” for students are both learning science and learning to teach science simultaneously through the content course experience, resulting in increased science SE.     

Development and Implementation of an Integrated Mathematics/Science Preservice Elementary Methods Course

If integration of mathematics and science is to occur, teacher preparation programs at colleges and universities must provide leadership in developing and modeling methods of teaching integrated content. This paper describes the development and implementation of an integrated mathematics/science preservice elementary methods course at the University of Connecticut. In planning the course several questions were addressed: (a) What does integration of mathematics and science mean? (b) What content should be taught in an integrated mathematics/science (IM/S) elementary methods course? and (c) How should an IM/S elementary methods course be taught? An important element of the course involved enlisting an exemplary elementary teacher who was released from her classroom one day per week to co-teach the methods class. Establishing a definition of integration proved to be one of the most challenging aspects of course development. The authors determined that most difficulties in integration of disciplines result from attempts to “force” the integration. As the team struggled with the philosophical, theoretical and logistical problems in the development of the course, it became apparent why integration has not been more widely implemented. It is believed this model can be adapted to allow for integration of all content areas. Plans are currently underway to incorporate social studies into the methods class for Fall of 1993.     

Characterizing exemplary mathematics instruction in Japanese classrooms from the learner’s perspective

This paper aims to examine key characteristics of exemplary mathematics instruction in Japanese classrooms. The selected findings of large-scale international studies of classroom practices in mathematics are reviewed for discussing the uniqueness of how Japanese teachers structure and deliver their lessons and what Japanese teachers value in their instruction from a teacher’s perspective. Then an analysis of post-lesson video-stimulated interviews with 60 students in three “well-taught” eighth-grade mathematics classrooms in Tokyo is reported to explore the learners’ views on what constitutes a “good” mathematics lesson. The co-constructed nature of quality mathematics instruction that focus on the role of students’ thinking in the classroom is discussed by recasting the characteristics of how lessons are structured and delivered and what experienced teachers tend to value in their instruction from the learner’s perspective. Valuing students’ thinking as necessary elements to be incorporated into the development of a lesson is the key to the approach taken by Japanese teachers to develop and maintain quality mathematics instruction.