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Work in teacher noticing has captured to what extent teachers notice students' thinking on paper and pencil tasks and technology tasks, yet no one study has considered how the same group of teachers notices across task types. This study used Jacobs et al.'s (Journal for Research in Mathematics Education, 2010, 41(2), pp: 169–202.) professional noticing of students' thinking framework to guide the design and analysis of prospective secondary mathematics teachers' (PSMTs) noticing of high school students' thinking on two geometry tasks: a paper and pencil task and a technology task. High school students' written work and a video clip were shared as the artifacts from which to notice for each task. PSMTs responded to a set of noticing prompts to capture how they were attending, interpreting, and deciding to respond to students' thinking for each task. Their written responses to these questions were then open coded for each noticing component and codes from each task were compared to reveal any differences in the content of PSMTs' noticing across task types. Results revealed differences between tasks for each component skill of noticing. Implications of these findings for mathematics teacher educators and future research are discussed. [ABSTRACT FROM AUTHOR]

This research addresses the issue of how to support students' representational fluency—the ability to create, move within, translate across, and derive meaning from external representations of mathematical ideas. The context of solving linear equations in a combined computer algebra system (CAS) and paper‐and‐pencil classroom environment is targeted as a rich and pressing context to study this issue. We report results of a collaborative teaching experiment in which we designed for and tested a functions approach to solving equations with ninth‐grade algebra students, and link to results of semi‐structured interviews with students before and after the experiment. Results of analyzing the five‐week experiment include instructional supports for students' representational fluency in solving linear equations: (a) sequencing the use of graphs, tables, and CAS feedback prior to formal symbolic transpositions, (b) connecting solutions to equations across representations, and (c) encouraging understanding of equations as equivalence relations that are sometimes, always, or never true. While some students' change in sophistication of representational fluency helps substantiate the productive nature of these supports, other students' persistent struggles raise questions of how to address the diverse needs of learners in complex learning environments involving multiple tool‐based representations. [ABSTRACT FROM AUTHOR]

While there is increased attention to power, privilege, and access in mathematics education, conversations around race and disability are often left out of the conversation. Disability in mathematics continues to be studied with a lens that focuses on behavior, rather than attending to the situated and sociopolitical context in which teaching and learning takes place. This paper specifically calls on the importance of an intersectional analysis of ability and the need for explicit conversation on the interwoven nature of race and disability to uncover exclusionary practices of hyper‐labeling, hyper‐surveilling, and hyper‐punishing for those outside notions of normalcy. Drawing on sociopolitical perspectives informed by Disability Critical Race Theory (DisCrit) and DisCrit Classroom Ecology, I share a framework of DisCrit noticing to consider the interwoven nature of racism and ableism in mathematics classrooms, provide a context to develop preservice teacher DisCrit noticing during mathematics methods, and a case example to highlight implications and transformative possibilities for (re)organizing classrooms through the DisCrit noticing framework. [ABSTRACT FROM AUTHOR]

This paper describes the author's attempt to design assignments that engage preservice elementary teachers in original mathematical thinking. In particular, the choice of integer operations as the focus of a structured writing assignment that takes students two weeks to complete is explained and justified. Exemplary student work is quoted. [ABSTRACT FROM AUTHOR]

Science teachers play a vital role in the education of students and their learning outcomes. Beyond academic performance and content knowledge, how one feels about science can influence how they teach and how students learn. It is important for educators, and teacher educators to reflect on their past experiences and decipher what experiences influence their overall perceptions about science. Mixed methods were used to analyze narrative papers from pre‐service teachers which focused on their science education experiences. Papers from one hundred undergraduate early‐childhood pre‐service educators were used to determine factors that influence pre‐service teachers' overall perceptions about science. Results indicated that negative experiences at all stages of students' k‐12 education diminished positive perceptions of science; meanwhile, corresponding effects related to positive experience were sourced only from high school. Similarly, negative teacher experiences resulted in diminished positive perceptions of science without corresponding effects of positive teacher experiences. Learning approach and informal learning experiences did not predict positive perceptions of science, but were relevant within the qualitative analysis. Implications are discussed for pre‐service teacher training programs. [ABSTRACT FROM AUTHOR]

For the past forty years, United States school districts have increasingly hired mathematics specialists to support the teaching and learning of mathematics. Despite the prevalence of this professional development structure, this is a relatively new research topic for the mathematics education field. In this paper, we report findings from an exploration of literature between 1981 and 2018 to examine the role of mathematics specialists (MSs). In particular, we examine: (a) MS positioning across research; (b) historical trends of school‐based MS research; and (c) orientations of school‐based MSs within research. Using the McGatha and Rigelman framework as an analytic lens, we found that beyond the positions identified in their framework (coach, intervention specialist, teacher), there were four additional MS positionings within the research (learner, other p‐12 stakeholder, university stakeholder, unknown). Ultimately, we forward an expansion to the McGatha and Rigelman framework to include these new categories, as well as contextual descriptions and working definitions to support future research in more accurately and robustly capturing the ways in which MSs are investigated and reported on in research. [ABSTRACT FROM AUTHOR]

Recent research demonstrates that mathematics teachers rely on a variety of curriculum materials and must make meaning and synthesize these materials for use in a particular place with particular students. While there are multiple theories about the nature of this work and the factors which influence this work, the field continues to lack a theoretical basis with which to understand this multifaceted and complex work. This paper seeks to illuminate the process by which teachers come to make meaning from curriculum materials by the daily practices of one team of teachers. Findings supports a transactional view of curriculum in which students, teachers, curriculum materials, and contexts work with and on each other as curriculum emerges. Using this theory as a framework, multiple understandings of teachers' work with curriculum can be synthesized as highlighting particular aspects of a larger curriculum system. [ABSTRACT FROM AUTHOR]

With this research, we sought to expand the pool of engineering education assessment instruments. We drew upon earlier efforts to define an expanded protocol for prompting children's drawings of engineers; and evaluate the reliability of a new scoring rubric for the modified Draw‐an‐Engineer Test (mDAET). An earlier paper introduced our ground theory approach in gathering theoretical propositions derived from children's drawings, explanations of engineers (n = 940) to develop the mDAET Scoring Rubric. Here we evaluate the reliability of the mDAET, a component of the larger mDAET rubric validation process. In the current study, eight participants scored twelve sets (including anchor sets) of drawings (n = 36) and, scores across drawings were evaluated by percentage match with the known‐score and interrater reliability. Kappa values for exact matches across eight raters met the threshold for "substantial" agreement and matches that were exact or adjacent indicated "almost perfect" agreement. Notably, 92% of the possible matches among common anchor items were either exact or adjacent matches. These results indicate adequate inter‐rater reliability evidence of the mDAET scoring rubric and demonstrate the feasibility of largescale administration that may no longer require individual child interviews. [ABSTRACT FROM AUTHOR]

Focuses on a January 1996 `News Bulletin' report on the release of the National Middle School Association's (NMSA) position paper calling for change in middle schools. Changes advocated to make education more appropriate for 10- to 15-year olds; Characteristics needed for developmentally responsive middle schools.

Mathematical writing recently has been defined as writing to reason and communicate mathematically. But mathematics instructional resources lack guidance for teachers as to how to implement such writing. The purpose of this paper is to describe how methods of design‐based research were used to develop an instructional resource when one does not currently exist. Thirty‐four participants—including teachers, mathematics coaches, mathematics curriculum developers, literacy coaches, a mathematician, and academics in elementary mathematics education, mathematics education, writing education, and science education—participated in a multi‐step process to recommend, revise, and confirm instructional guidelines for elementary mathematical writing. The development process began with thirty‐two recommendations from science writing and language arts writing. Through multiple cycles of feedback, five instructional guidelines and related considerations and techniques for implementation of elementary mathematical writing emerged. [ABSTRACT FROM AUTHOR]

The mathematics education community has routinely called for mathematics tasks to be connected to the real world. However, accomplishing this in ways that are relevant to students' lived experiences can be challenging. Meanwhile, mathematical modeling has gained traction as a way for students to learn mathematics through real‐world connections. In an open problem to the mathematics education community, this paper explores connections between the mathematical modeling and the nature of what is considered relevant to students. The role of empathy is discussed as a proposed component for consideration within mathematical modeling so that students can further relate to real‐world contexts as examined through the lens of Ecological Systems Theory. This is contextualized through a classroom‐tested example entitled "Tiny Homes as a Solution to Homelessness" followed by implications and conclusions as they relate to mathematics education. [ABSTRACT FROM AUTHOR]

Increasingly, STEM focused high schools are used prepare students for college STEM majors and launch them into STEM careers. Yet a new focus on STEM education at the elementary levels suggests that the importance of STEM education is much broader than a preparation for workforce needs in high school or college. This paper describes a case study designed to articulate the mission and design of an effective and nationally recognized STEM‐focused elementary school. As described through the six most impactful components of STEM‐focused elementary school design at Walter Bracken STEAM Academy, the case study emphasizes the school's strong and inclusive school leadership, with staff organized into grade level groups empowered to innovate and honing their teaching practices. External partnerships are leveraged to broaden student learning opportunities. Students at Bracken engage in active learning opportunities and multidisciplinary lessons where STEM is used as a way of thinking and as a way to coherently combine content into active learning opportunities that are engaging for learners. By organizing the structural components of an exemplary STEM‐focused elementary school, we hope to deliver actionable reforms for elementary schools wanting to increase their STEM‐focused offerings. [ABSTRACT FROM AUTHOR]

Teachers involved in a Master's level course in diversity participated in virtual, synchronous, anonymized discussions around issues of ethnic and racial diversity, gender, and stereotypes that could impact their students' participation in fields related to science, technology, engineering, and mathematics (STEM). Guided by theoretical frameworks from Social Cognitive Career Theory (SCCT) and Critical Race Theory (CRT), a convenience sample of 14 science and mathematics teachers participated in a series of virtual chats using open‐ended questioning and facilitated by two university instructors. Using conversation and critical discourse analyses, three primary themes emerged: understanding of issues related to stereotypes, encouragement of females and minorities to pursue careers in STEM, and the place for diversity discussions in science and mathematics classrooms. The teachers felt burdened by curricular and administrative constraints that inhibit their ability to participate in thought‐provoking critical conversations. The paper concludes with a discussion of ways teachers can assist in the STEM career identity development of their underrepresented females and students of color and calls for research that combines the key findings in SCCT and CRT to build confidence and capacity for teachers to effectively confront issues of racism, sexism, and stereotyping in science and mathematics classrooms. [ABSTRACT FROM AUTHOR]

In this paper, we examined students' engagement in an implementation of a Workplace Simulation Project (WSP). The WSP was designed to actively engage students in learning disciplinary content by inviting engineers from industry to have a physical presence within the school building to collaborate with teachers and students to complete projects which simulate the tasks authentic to their work. We focus on the first year implementation of the program that partnered a high school in the rural Midwest with an engineering unit of a government organization. Using a multiple methods study design, we analyzed disciplinary and interdisciplinary pre and posts test along with students' interviews to determine learning gains as well as students' interpretations of creative and critical thinking as experienced in the project and their knowledge of the engineering design process. Effect sizes showed that students in the WSP group had notable gains over the control group participants. Additionally, students' knowledge of core elements of the design process were identified in inductive analyses of the interviews. Findings from this study will provide usable knowledge about effective ways to support systems and design thinking and ways to support expert‐novice collaboration to ensure success. [ABSTRACT FROM AUTHOR]

The goal of this research was to examine fifth graders' understanding of fractions on the number line. This case‐study design focused on the various ways that students represented fractions on number lines. Students responded to task‐based interview questions by identifying fractions as a number on the number line as well as equivalency and problem solving. The tasks were administered individually to 26 fifth‐grade students over a 15‐minute time frame in their respective schools. The two groups of 10‐year‐old students answered most questions in written form with pencil and paper and were often asked to explain how they arrived at an answer. Student performance was highest when instructed to plot ½ on a number line of 0 to 1 as well as naming a fraction less than ½. The students performed lowest when they attempted to plot ½, ¼, and 1 on a number line with a predetermined unit 0 to 1/3. Other low performing concepts consisted of plotting ¼ on a number line from 0‐3, identifying ¼ on a non‐routine number line, and plotting a unit fraction with an equivalent fraction as well as an improper fraction on a common number line. [ABSTRACT FROM AUTHOR]

Visual representations and manipulatives are a highly advocated mathematical tool for the teaching and learning of multiplication and division. Although there is some prior research on elementary teachers' general use of manipulatives and visual representations, there is little to no specific focus on use of such representations on a specific mathematical concept. The present study examined third grade teachers' reported use of visual representations for teaching multiplication and division. Findings indicate prevalent use of discrete models and infrequent use of continuous models. Length models and number lines are rarely used across all Common Core standards focusing on multiplication/division, with numeric‐only representations being reported frequently across all standards. Groups‐of and array models were the most prevalent visual model reported by third grade teachers. Although teachers report higher degrees of access to certain materials than previous reports on manipulative use, interview data suggests this may have more to do with purchase agreements between school districts and textbook companies than pedagogical preferences of classroom teachers. Supporting findings in prior decades, teachers in the present study report prevalent use of flashcards, charts and grid paper, and variations of counters. [ABSTRACT FROM AUTHOR]

In theory, STEM (interdisciplinary science, technology, engineering and mathematics) is cross‐disciplinary and situated in real‐world problem‐solving contexts. In practice, STEM disciplines are often implemented separately using contrived contexts. This paper examines theoretical and empirical aspects of Montessori middle school science in the United States, and its alignment with the conceptual framework of integrated STEM. We selected Montessori adolescent environments because the Montessori philosophy involves interdisciplinary application contextualized in purposeful work and learning. Our research sought to investigate how Montessori middle schools have designed their science programs, and to situate these findings within the current landscape of STEM education and reform‐based science. Based on the results of our survey of 96 U.S. Montessori middle schools, we argue Montessori offers an integrated educational approach that meaningfully situates academic disciplines to mirror local and global challenges, well supported by theory and literature on STEM and situated learning theories. We assert that integrated STEM happens organically in many Montessori middle schools, and takes place through authentic work in communities of practice. Our research communicates the value of looking outside traditional school settings to examine alternative formal education spaces, like Montessori classrooms where integrated STEM happens organically. [ABSTRACT FROM AUTHOR]

This paper examines the implementation of an instructional module on preservice elementary teachers' professional noticing of children's mathematical thinking. The module focuses on professional noticing skills through the content focus of early algebraic reasoning and uses complex video vignettes from whole class instruction in authentic elementary mathematics classrooms. Findings indicated that two of the three components of professional noticing (attending and interpreting) showed statistically significant increases in a treatment group that did not occur in a comparison group. The deciding component remains a challenge that warrants further research. [ABSTRACT FROM AUTHOR]

This paper presents qualitative and quantitative approaches to exploring teachers' experiences of mathematics anxiety (for learning and doing mathematics) and mathematics teaching anxiety (for instructing others in mathematics), the relationship between these types of anxiety and test/evaluation anxiety, and the impacts of anxiety on experiences in teacher education. Findings indicate that mathematics anxiety and mathematics teaching anxiety may be similar (i.e., that preservice teachers perceive a logical continuity and cumulative effect of their experiences of mathematics anxiety as learners in K–12 classrooms that impacts their work as teachers in future K–12 classrooms). Further, anxiety is not limited to occurring in evaluative settings, but when anxiety is triggered by thoughts of evaluation, preservice teachers may be affected by worrying about their own as well as their students' performances. The implications for preservice experiences within a teacher education program and for impacting future students are discussed. [ABSTRACT FROM AUTHOR]

The integration of science, technology, engineering, and mathematics (STEM) education has received increased attention in the last decade. This is in part because of the need for students to increase in their STEM knowledge and competencies. Research is still needed to determine effective implementation models and curriculum for integrated STEM. Mathematics in particular has not received the focus it deserves with STEM integration. This paper discusses integration of STEM subjects that has a focus on mathematics (integrated steM); including summarizing and analyzing research done in the last ten years. A s.t.e.m. (Support, Topics, Emphasis, and Mathematical content) model for integrated steM research is presented to guide future research. [ABSTRACT FROM AUTHOR]

This paper presents the results of a Q‐sort activity in which 38 grades 4–10 mathematics teachers reflected on their classroom teaching and ranked a set of teaching actions that support high‐leverage mathematics teaching from most to least characteristic of their classroom teaching. Data analysis included examining the overall ranking of each teacher action as well as the overall ranking of the associated high‐leverage teaching practice. Examination of the rankings indicated that teachers identified actions associated with the practices of supporting productive struggle in students' learning of mathematics and posing purposeful questions as most characteristic of their teaching. Teachers identified actions associated with the practices of eliciting and using evidence of student thinking and establishing mathematics goals to focus learning as least characteristic of their teaching. Thematic networks were created to represent the teachers' rationales for their priorities regarding implementation of high‐leverage teaching practices. We share the implications of our findings for the mathematics education field and professional development leaders. [ABSTRACT FROM AUTHOR]

There is a compelling need to develop an algebra teacher self‐efficacy instrument (ATSEI) as algebra continues to be considered a gatekeeper course for postsecondary educational and career opportunities, which is seen as a crucial piece in closing the achievement gap. This paper reports on the development and validation of the ATSEI, an instrument that measures two domains, Efficacy To Do School Algebra (Knowledge Efficacy, KE‐A) and Efficacy to Teach Algebra (Personal Teaching Efficacy, PTE‐A) along six categories. Four of the categories represented content standards (variables, functions, patterns, and modeling) and two of the categories represented process standards (technology and concrete models, and multiple representations). Through conducting an exploratory factor analysis across two phases, the instrument was reduced and refined from an initial 118 items developed from a curriculum analysis to 36 items that reflected two significant categories, Functions and Technology. The ATSEI measure is validated for in‐service mathematics teachers and thus provides an instrument to examine need and impact in professional development venues. The specificity of the ATSEI allows those working with teachers to be better able to support them in the field and in return positively influence the learning outcomes of the students they teach. [ABSTRACT FROM AUTHOR]

College instructors often teach scientific thinking by asking students to review and analyze a primary research article. The main purpose of this study was to explore how classroom response systems (CRS) could help impact the quality of written analysis papers submitted for this assignment by students taking 100-level biology courses at a medium-sized suburban, two-year college in the northeastern United States. Students in all participating course sections received written instructions on five key elements of critical analysis (CA) to include in scientific study analysis papers. Classroom instruction on recognizing these key elements in primary research papers was provided either via CRS or via an instructor-facilitated classroom discussion enhanced by the same PowerPoint presentation. A rubric, designed specifically for this assignment, was validated prior to its use in this study. Fifty students participated in the study, and those who received the CRS intervention achieved significantly higher CA scores for identifying implications of study findings, while the group that received only written instructions achieved significantly higher CA scores for discussing the credibility of the references used by the authors in planning the critiqued study. The implications of this study are discussed along with ideas for future research. [ABSTRACT FROM AUTHOR]

The Going Green! Middle Schoolers Out to Save the World project aims to direct middle school students' enthusiasm for hands‐on activities toward interest in science and other STEM areas while guiding them to solve real‐world problems. Students in this project are taught by their teachers to use energy monitoring equipment to audit standby power consumed by electronic devices in their homes and communities. Major findings were: (a) Beliefs in climate change increased more for students in the treatment than comparison group, pre to post; and (b) For girls there was a larger positive impact on climate change beliefs than for boys. These and additional findings presented in this paper provide evidence that a hands‐on engaged‐learning curriculum can have a positive influence on climate change beliefs and intentions and strengthen the association between the two constructs. [ABSTRACT FROM AUTHOR]

This study examined how Black students responded to the utilization of culturally responsive stories in their mathematics class. All students in the two classes participated in mathematics lessons that began with an African American story (culturally responsive to this population), followed by mathematical discussion and concluded with solving problems that correlated to the story. The researcher observed and recorded responses by students during each part of these lessons with protocols. Students independently reflected weekly by answering five questions to share their perspective on the African American stories. The teacher reflected on each lesson as well, describing thoughts on how these students responded to the story in each lesson. This paper examines the analyzed data from the target audience: Black students. Results revealed that Black students responded to the use of African American stories with high self-rated levels of engagement and enjoyment and that the stories helped them think about mathematics to varying degrees. Since students who are engaged and are thinking about mathematics are more likely to achieve mathematical understanding, the researcher concludes that this strategy should continue to be tested in diverse classrooms with an emphasis on student reflection to determine if the outcomes are transferable and generalizable. [ABSTRACT FROM AUTHOR]

STEAM, where the 'A' represents arts and humanities, is considered a transdisciplinary learning process that has the potential to increase diverse participation in science, technology, engineering, and math (STEM) fields. However, a well-defined conceptual model that clearly articulates essential components of the STEAM approach is needed to conduct empirical research on STEAM's efficacy-in particular, the teaching content that should be considered when enacting STEAM teaching practices. This paper proposes a conceptual model of STEAM, providing educators with the opportunity to teach effectively using transdisciplinary inquiry. The instructional content domain of the model includes problem-based delivery, discipline integration, and problem-solving skills. [ABSTRACT FROM AUTHOR]

This paper brings together research on slope from mathematics education and research on line of best fit from statistics education by considering what knowledge of slope students transfer to a novel task involving determining the placement of an informal line of best fit. This study focuses on two students who transitioned from placing inaccurate to accurate lines of best fit during a task-based interview. The analysis focuses on describing shifts in slope reasoning that accompanied the change to accurately placed lines, and investigates factors that may have influenced the shift in reasoning. The results have implications for the teaching of both slope and the line of best fit. [ABSTRACT FROM AUTHOR]

Hierarchical linear models have become a familiar method for accounting for a hierarchical data structure in studies of science and mathematics achievement. This paper illustrates the use of cross-classified random effects models (CCREMs), which are likely less familiar. The defining characteristic of CCREMs is a hierarchical data structure defined by multiple random factors at higher levels. We illustrate CCREMs using data for approximately 10,000 students from more than 250 high schools who attended one of 27 four-year postsecondary institutions. The appropriate use of CCREMs helps to ensure unbiased estimates of effects and credible inferences. [ABSTRACT FROM AUTHOR]

This paper is based on an online graduate program for middle school science and mathematics teachers in Texas titled Integration of Science, Mathematics and Reflective Teaching (i SMART). Launching the program for its first cohort in fall 2010, the authors attempted to answer the following two questions in this paper: (a) How do the members of the i SMART design team and the first cohort of teacher participants define science and mathematics integration with similar and different emphases? and (b) How would these definitions and concerns impact the ongoing design of the program? The iSMART design team members and the participating cohort teachers had a shared view regarding the importance of integration and its possible impact on student motivation. The findings also revealed that the two groups showed some different points of emphasis in their definitions of integration. These issues will be addressed in the ongoing design of the program in the following three areas: (a) design of the second summer meeting activities, (b) greater emphasis on teacher as researcher and action research, and (c) administrative support for teacher collaboration. [ABSTRACT FROM AUTHOR]

We are in the STEM generation whose comprehensive purpose is to resolve (1) societal needs for new technological and scientific advances; (2) economic needs for national security; and (3) personal needs to become a fulfilled, productive, knowledgeable citizen. STEM specifically refers to science, technology, engineering, and mathematics, but now has a broader meaning to include environment, economics, and medicine. Currently, there is not an agreement of the particulars in education, or in standards, by professional organizations that define STEM literacy. Most definitions do cover societal and economic needs but overlook personal needs. There is a general consensus that everyone needs to be STEM literate. But there is a difference between literacy and being literate. STEM literacy should not be viewed as a content area but as a deictic means (composed of skills, abilities, factual knowledge, procedures, concepts, and metacognitive capacities) to gain further learning. This paper gives a brief background of literacy definitions in STEM and presents a description of STEM literacy based upon (1) cognitive, (2) affective, and (3) psychomotor learning theory domains. The paper stresses the need to evolve from learning for STEM literacy to using STEM literacy for learning to satisfy our societal, economic, and personal needs. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The Information Technology in Science (ITS) Centerfor Teaching and Learning was a National Science Foundation funded program to provide high-qualily professional development for 7-12th grade science teachers. The subgroup on which this paper focuses was immersed in an innovative approach to understanding chemistry of the environment. The group was comprised of 10 high school science teachers representative of science classes taught at all grade levels (9-12th). A team of four university professors led the group. The professors developed inquiry modules and communicated some of the intricacies of their research for adaptation to the participants' classrooms. This paper communicates the successful implementation and lessons learned by scientists during the course of an inquiry-based curriculum during summer 2005. The process and pace at which the material was covered, qualitative information about the attitudes of the participants towards the curriculum, and implications for professional development from the point of view of the science team leaders will be discussed. Analysis of time spent with participants revealed the progression and type of activities chosen for the professional development experience were effective. Results from informal participant interviews revealed they were most comfortable in incorporating inquiry into their classrooms after having been immersed in it themselves. [ABSTRACT FROM AUTHOR]

Increasing attention has been given over the last decade by the statistics, mathematics and science education communities to the development of statistical literacy and numeracy skills of all citizens and the enhancement of statistics education at all levels. This paper introduces the emerging discipline of statistics education and considers its role in the development of these important skills. The paper begins with information on the growing importance of statistics in today's society, schools and colleges, summarizes unique challenges students face as they learn statistics, and makes a case for the importance of collaboration between mathematicians and statisticians in preparing teachers to teach students how to understand and reason about data. We discuss the differences and interrelations between statistics and mathematics, recognizing that mathematics is the discipline that has traditionally included instruction in statistics. We conclude with an argument that statistics should be viewed as a bridge between mathematics and science and should be taught in both disciplines. [ABSTRACT FROM AUTHOR]

Over one-third of all college mathematics enrollments are in courses considered to be developmental. While such courses have been the subject of a large body of research, one question that seems not to have been studied empirically is the alignment of the content of developmental and college level mathematics courses. This paper gives the results of such a study, conducted at a medium sized public liberal arts university. While the content of the developmental mathematics courses was used subsequently in the Precalculus course, most of the content of the Intermediate Algebra course was not used in other college level mathematics courses. It is hoped that the results of this paper will serve as a catalyst for other institutions to examine carefully and define the mission of both their developmental and college level mathematics courses. [ABSTRACT FROM AUTHOR]

This paper reports on the experiences of a small collaborative inquiry group consisting of a high school science teacher, Deidre, and two university researchers, the authors of this paper, as they explored an active, inquiry-based approach to teaching and learning referred to as Problem-Based Learning or PBL (Barrows, 1994; Barrows & Tamblyn, 1980). Although PBL is not new and has an established tradition in medical education and other professional schools, the use and scholarship of PBL at the secondary level is only starting to emerge. This small-scale collaboration allowed the co-inquirers to delve into the complexities of PBL and to examine its feasibility as a curriculum and instructional approach in the context of high school science teaching and learning. The three collaborators adopted an action-based inquiry method referred to as Collaborative Inquiry (CI), a "process consisting of repeated episodes of reflection and action through which a group of peers strives to answer a question of importance to them" (Bray, Lee, Smith, & Yorks, 2000, p. 6). Data collection methods and sources included student-generated work, classroom observation, student interviews, and audio-taped planning meetings. The outcomes of the study focus on the issues that arose during PBL design and implementation, such as selecting a PBL topic, determining the level of structure to be incorporated into the PBL experience, selecting appropriate assessment approaches, facilitating groups, and providing optimal student feedback. In addition, outcomes related to student perceptions of PBL indicated that the majority liked learning through PBL because it promoted active learning, made science relevant, provided variety in learning, and supported group work. The authors discuss implications for the adoption of PBL in K-12 settings. [ABSTRACT FROM AUTHOR]

Afterschool and community science programs have become widely recognized as important sanctuaries for science learning for low-income urban youth and as offering them with "missing opportunities." Yet, more needs to be known about how youth, themselves, perceive such opportunities. What motivates youth to seek out such opportunities in the nonschool hours? How do youth describe the doing and talking of science in such programs? Given such descriptions, how do youth perceive the role of these programs in their lives? This paper relies on stories from three youth drawn from a multisited ethnographic study, one site being an afterschool girls-only science program at the elementary level in Canada and the other an Upward Bound Math and Science program in the USA. The paper concludes with a discussion about the ways these programs offered youth a meaningful way to relate to science in concordance with their own lived experiences, resulting in "I will" and "I can " attitudes and a sense of hope for the future within which science becomes a tool for action. [ABSTRACT FROM AUTHOR]

This paper illustrates ways to employ teacher portfolios to improve the quality of methods course experiences for prospective mathematics teachers. Based upon research conducted in an undergraduate teacher preparation program, this case study describes how the author used teacher portfolios to mentor prospective teachers in new ways. The case describes the author's experiences through a case study of his assessment of and response to one prospective teacher's portfolio. This portfolio illustrated themes that were present in other teachers' portfolios, but did so in ways that highlighted strategies for change to the methods course. Through the lens of this teacher's portfolio the author identified specific ways that the prospective teacher's beliefs were impacting her teaching practice, a result that enabled him to better help all of the teachers in the methods course reflect on their teaching. By providing a detailed account of the feedback process that led to this result, this paper illustrates how mathematics teacher educators can use prospective teachers' portfolios to enrich the quality of their methods courses. [ABSTRACT FROM AUTHOR]

This paper describes the mechanism used to gain insights into the state of the art of mathematics instruction in a large urban district in order to design meaningful professional development for the teachers in the district. Surveys of close to 2,000 elementary, middle school, and high school students were collected in order to assess the instructional practices used in mathematics classes across the district. Students were questioned about the frequency of use of various instructional practices that support the meaningful learning of mathematics. These included practices such as problem solving, use of calculators and computers, group work homework, discussions, and projects, among others. Responses were analyzed and comparisons were drawn between elementary and middle school students' responses and between middle school and high school responses. Finally, fifth-grade student responses were compared to those of their teachers. Student responses indicated that they had fewer inquiry-based experiences, fewer student-to-student interactions, and fewer opportunities to defend their answers and justify their thinking as they moved from elementary to middle school to high school. In the elementary grades students reported an overemphasis on the use of memorization of facts and procedures and sparse use of calculators. Results were interpreted and specific directions for professional development, as reported in this paper, were drawn from these data. The paper illustrates how student surveys can inform the design of professional development experiences for the teachers in a district. [ABSTRACT FROM AUTHOR]

This paper summarizes and integrates the lessons learned from the last decade of professional development efforts based on the standards of the National Council of Teachers of Mathematics (1989, 1991, 1995). The fundamental challenges to such reform are identified, then the rest of the paper is dedicated to strategies that have been helpful in overcoming these obstacles. The challenges include both the teachers' views of mathematics and their image of teaching. The Immerse and Instill approach describes strategies that encourage teachers to implement standards-based teaching upon entering the teaching field (Immerse) as well as instilling some of the professional habits necessary to keep teachers and their students actively engaged (Instill). [ABSTRACT FROM AUTHOR]

This paper introduces The Square Thing, a lesson that engages and invites student development of problem solving and reasoning skills, understanding through connections within the content, and mathematics voice. A background for the lesson, an enrichment topic that allows the teacher to set the stage for the problem, is described first. Next, The Square Thing is introduced, along with a discussion of student solutions and pedagogical notes grouped in sections as Estimation Approaches, Coordinate Geometry Approaches, and Parallel Line Approaches. A pedagogical discussion ends the paper, in which components for successful pedagogy and benefits for students experiencing this and similar mathematics pedagogies are described. [ABSTRACT FROM AUTHOR]

Many popular hands-on science activities, as traditionally implemented fail to support inquiry-based science instruction, because the activities direct teachers to terminate lessons prematurely. This paper presents a model describing one approach for extending seemingly limited hands-on activities into full-inquiry science lessons. The strategy involves (a) discrepant events to engage students in direct inquiry; (b) teacher-supported brainstorming activities to facilitate students in planning investigations; (c) effective written job performance aids to provide structure and support; (d) requirements that students provide a product of their research, which usually includes a class presentation and a graph; and (e) class discussion and writing activities to facilitate students in reflecting on their activities and learning. The paper presents the model as a tool for facilitating science teachers' efforts to understand and implement the type of powerful, effective, and manageable inquiry-based science instruction called for in the National Science Education Standards. [ABSTRACT FROM AUTHOR]

Though national standards emphasize the importance of connections between math and science, few empirical studies exist to support the notion that student achievement increases from such integration. This paper examines an eighth-grade science class that integrated mathematics into science through the use of technology. In a setting of action research, the effects of such integration were examined. This paper reports that integrating mathematics into the science class positively affected students' achievement in their math class and describes the circumstances under which the integration occurred. [ABSTRACT FROM AUTHOR]

The construct of science achievement -- what K-12 students should know and be able to do in science--is central to science education reform. This paper examines current conceptions of science achievement in major reform documents in the context of standards-based and systemic reform. The paper reviews documents on (a) science content standards, including the National Science Education Standards (National Research Council, 1996) and Project 2061 (American Association for the Advancement of Science, 1989, 1993); (b) performance standards in the New Standards Project (National Center on Education and the Economy, 1997a, 1997b, 1997c, 1998); and (c) assessment frameworks, including the 1996 National Assessment of Educational Progress (National Assessment Governing Board, 1994, 1996) and the Third International Mathematics and Science Study (Martin & Kelly, 1996; McKnight, Schmidt, & Raizen, 1993; Robitallie et al., 1993). Although there is an overall agreement on the conceptions of science achievement among the documents, there are also noticeable differences. Based on the analysis of the five sets of documents, an aggregated view of science achievement is presented in terms of science content and process. Implications for promoting science achievement in standards-based and systemic reform are discussed. [ABSTRACT FROM AUTHOR]

Given the increasing number of English Language Learners ( ELLs) in secondary mathematics classrooms, it is imperative that mathematics teacher educators develop measures for determining how and why secondary mathematics teachers ( SMTs) understand and respond instructionally to these students. This paper reports on the initial development and validation of the Mathematics Teachers' Beliefs about English Language Learners survey, an instrument that measures SMTs beliefs, attitudes, knowledge base, and instructional practices in relation to meeting the academic and language needs of ELLs. Through piloting processes, the instrument was refined for a research study through which reliability and validity were established. The five constructs identified from exploratory factor analysis illustrate perceived opportunities and barriers in meeting ELLs' academic and language needs among SMTs. This article features a . Please click on the supporting information link below to access. [ABSTRACT FROM AUTHOR]

This paper presents the results of a multi-method study examining elementary students with high self-reported levels of mathematics motivation. Second- through fifth-grade students at a Title One school in the southeastern United States completed the Elementary Mathematics Motivation Instrument ( EMMI), which examines levels of mathematics motivation across three subscales: (a) Math Anxiety, (b) Self-Efficacy, and (c) Value of Math. Results from this quantitative phase were used to identify a sample for a qualitative phase examining how students who report high levels of motivation perceive mathematics. The resulting qualitative phase utilized a phenomenological design to explore mathematics motivation for a particular set of students in a fifth-grade setting. Findings indicate that elementary students with high mathematics motivation value mathematics as a present and future oriented discipline and value teachers that deemphasize testing as a measure of success. [ABSTRACT FROM AUTHOR]

The new standards for K-12 science education suggest that student learning should be more integrated and should focus on crosscutting concepts and core ideas from the areas of physical science, life science, Earth/space science, and engineering/technology. This paper describes large-scale, urban elementary-focused science, technology, engineering, and mathematics ( STEM) collaboration between a large urban school district, various STEM-focused community stakeholders, and a research-focused private university. The collaboration includes the development of an integrated STEM curriculum for grade K-5 with accompanying teacher professional development. This mixed-methodology study describes findings from focus group interviews and a survey of teachers from Title I elementary schools. Findings suggest the importance of the following critical features of professional development: (a) coherence, (b) content focus, (c) active learning, (d) collective participation, and (e) duration to the success of large-scale STEM urban elementary school reform [ABSTRACT FROM AUTHOR]

This study examines data from college students who worked in pairs to make decisions about a list of potential definitions of prime number. Analysis focused on the evidence each student pair cited when they decided whether or not a statement could be used as a definition for prime number. The purpose of this paper is to describe patterns in the ways students used the evidence they cited. Findings suggest that students attend to important features of mathematical definitions, with some students giving preference to usability and others giving preference to definitions that are unambiguous. [ABSTRACT FROM AUTHOR]

The Common Core Standard for Mathematical Practice 4: Model with Mathematics specifies that mathematically proficient students are able to make connections between school mathematics and its applications to solving real-world problems. Hence, mathematics teachers are expected to incorporate connections between mathematical concepts they teach and their applications to solving problems arising in real-world situation. Clearly, it is assumed that the teachers themselves are able to make such connections. On the other hand, research shows that mathematics teachers find it difficult to make those connections. In this paper, we present the results of the study that investigated the ways in which exploring mathematics in informal sites, and in particular science museum, assist teachers with making connections between school mathematics and its applications in real world. [ABSTRACT FROM AUTHOR]

The findings reported in this paper were generated from a case study of teacher leaders at a state-level mathematics conference. Investigation focused on how participants viewed the mathematical processes of communication, connections, representations, problem solving, and reasoning and proof. Purposeful sampling was employed to select nine participants who were then interviewed and observed as they presented a session at the conference. Participants' statements revealed differences in their views of mathematical processes. The analysis led to an emergent framework for views of mathematical processes that includes three levels: participatory, experiential, and sense-making. Implications are shared for mathematics methods instructors, professional learning, and research. Discussion also relates the framework to the Standards for Mathematical Practice. [ABSTRACT FROM AUTHOR]