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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 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]

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]

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]

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]

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]

When worthwhile mathematical tasks are used in classrooms, they should also become a crucial element of assessment. For teachers, using these tasks in classrooms requires a different way to analyze student thinking than the traditional assessment model. Looking carefully at students' written work on worthwhile mathematical tasks and listening carefully while students explore these worthwhile tasks can contribute to a teacher's professional development. This paper reports on a professional development activity in which teachers analyzed mathematical tasks, predicted students' achievement on tasks, evaluated students written work, listened to students' reasoning, and assessed students' understanding. Teachers' engagement in this way can help them develop flexibility and proficiency in the evaluation of their own students' work. These experiences allow teachers the opportunity to recognize students' potential, strengthen their own mathematical understanding, and engage in conversations with peers' about assessment and instruction. [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]

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]

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]

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. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to show the similarities as well as the differences of fundamental fraction knowledge owned by preservice elementary teachers from the United States ( N= 89) and Taiwan ( N= 85). To this end, we examined and compared their performance on an instrument including 15 multiple-choice test items. The items were categorized into four different types of fundamental fraction constructs, including part-whole relationship, quotient, equivalence, and meanings of operations. Each item was embedded in the area, linear, or set model except for the items constructed out of the meaning of operations. Several items were featured with a pictorial illustration. Quantitative analysis showed that U.S. preservice teachers were significantly outperformed by their Taiwanese counterparts overall. The difference between the two groups was statistically significant on 12 of 15 items. Findings suggest that preservice elementary teachers from both countries need to be better prepared in their understanding of the meaning of fraction multiplication or division operations. Findings also suggest that U.S. preservice elementary teachers need to be more knowledgeable in dealing with fraction problems embedded in a linear model. Further research is suggested to study the issues raised from the findings. [ABSTRACT FROM AUTHOR]

In this article, we describe preservice elementary teachers 'reactions to Liping Ma's (1999) book, Knowing and Teaching Elementary Mathematics (KTEM), from five universities. Ma's discussion of solely teaching elementary mathematics procedurally and its consequences awakens the preservice teachers 'memories of learning elementary mathematics. Ma's analysis of and solution to the problem ignites strong emotions in the preservice elementary teachers and promotes a desire to teach elementary mathematics conceptually. Through the analysis of writing assignments, we summarize how reading and reflecting on KTEM gives preservice teachers an opportunity to examine their beliefs about teaching and learning elementary mathematics conceptually. [ABSTRACT FROM AUTHOR]

In spite of repealed reform efforts, there is research and data that suggest that teachers lack the needed knowledge to successfully teach elementary mathematics. Some argue that teachers lack the needed content knowledge while other argue that a lack of confidence and practice are impacting teachers `ability to successful leach mathematics. As a result of these issues, this paper looks at the impact of a service-learning experience on pre- service teachers' confidence and preparation in the area of mathematics. The service-learning experience had a number of intended and unintended outcomes. As a result of the service-learning experience. pre-service teachers noted increased understanding, innovation and confidence in the area of mathematics. [ABSTRACT FROM AUTHOR]

In this paper a framework is proposed for analyzing the deliberate actions taken by a teacher to participate in or influence the discourse in mathematics classrooms, and such actions are referred to as the teacher's discourse moves. This work synthesizes elements of several other discourse frameworks, including those of Richards, Sfard, Cobb, and Knuth and Peressini. Expanding on the improvisational dance metaphor of Heaton's, the framework views the teacher in the additional multiple roles as a Choreographer/Stage Manager/Director of classroom discourse. Several research applications of the discourse framework to collegiate mathematics education are discussed, including discourse around collaborative problem solving in Treisman Emerging Scholars workshops, a video-based study of a college-level geometry course for teachers, discourse in wireless networked classrooms, and the asynchronous discourse in an online statistics course. [ABSTRACT FROM AUTHOR]

Induction programs play a critical role in the development of professional educators. While induction programs are a necessity for all beginning teachers, science teachers need carefully crafted programs that meet their unique needs. This paper reports the barriers and pathways that were experienced during a 3-year period when an induction program was developed and implemented for secondary science teachers. This information is provided to assist future university, college, or school district induction program developers. [ABSTRACT FROM AUTHOR]

The article offers information on various research papers published within the issue including one on underrepresented students in outreach programs, one on students' and teachers' attitude in learning science and mathematics and one on preservice elementary teachers.

The coaching cycle has been identified as a productive activity in which coaches can engage teachers to support teacher learning. Previous research has primarily focused on exploring teachers' learning opportunities during the planning meetings and enacted lessons, while reflection meetings have been left relatively unexplored. In the current study, I partnered with two coach‐teacher dyads to explore teachers' learning opportunities during six reflection meetings. In particular, I explore the substance, or topic, of coach‐teacher conversations, as well as the depth of reasoning that was achieved for these dyads. Overall, results indicate that dyads toggled back and forth between reflecting on previous instruction and discussing future instruction, while maintaining a focus on discussing students, pedagogy, and content. Furthermore, most of the coach‐teacher reflection talk was categorized at the high‐depth level as the dyads consistently provided evidence and reasoning to support claims made, which points to the generative nature of coach‐teacher reflection conversations. Implications for practice as well as future research are provided. [ABSTRACT FROM AUTHOR]

This mixed methods study explored the development of elementary and middle school preservice teachers' (PSTs) learning to assess student thinking through analysis of students' written work. Six sections of the first mathematics content course for teaching implemented two writing assignments focused on analysis of student work aligned to the mathematics topics covered in the PSTs' classes. Using quantitative methodology, we examined the PSTs' (n = 99) change in their noticing and assessment skills of attending to and interpreting students' thinking. We also documented their mathematical content knowledge (MKT) as measured by the Learning for Mathematics Teaching in the domains of specialized content knowledge and knowledge of content and students. Findings show that the PSTs increased in their assessment skills and in their MKT. Using a qualitative methodology on interview data of a subset of eight PSTs, we found they acknowledged that having a firm grasp of mathematical content is essential to understanding and explaining student thinking. Findings indicate that engaging PSTs in the real work of teaching such as noticing and assessing students' thinking through written work at the early stages of their teacher preparation may motivate PSTs to learn mathematics more deeply with an eye towards strengthening their assessment skills. [ABSTRACT FROM AUTHOR]

This study focused on intensive work within a large, urban, low-performing middle school in the southwest to address and transform teacher beliefs regarding the role of culture within their science pedagogy. Given the recent, rapid growth of numbers of students from Hispanic/ Latino(a) backgrounds in the United States, it is critical that a paradigm shift takes place within schools and existing beliefs of science teachers to address the needs of a much changed classroom. This study details the journey of middle-school teachers who were provided support and experiences targeted at addressing their existing beliefs regarding the role of culture and the growth and change that were achieved through a science education reform effort. Implications for further research will be discussed, including the need for attention to beliefs regarding culture are shared. [ABSTRACT FROM AUTHOR]

This study describes the design and implementation of a science outreach program (elementary; 2nd–5th) and its associated student outcomes. Key features of the program include: (a) phenomenon‐based, NGSS‐aligned curriculum designed by science education experts and influenced by educational, sociocultural, and cognitive science theories, (b) active engagement by elementary students in experimentation and exploration of a common phenomenon (2 per year, called modules) across multiple sessions (6–8 per module), (c) professional development (PD) provided to scientists (mentors) and teachers to supply classrooms with multiple (5–7) adult more knowledgeable others (AMKOs), and (d) close classroom interaction between elementary students and mentors, allowing for students to participate in evidence‐based sense‐making through whole‐class and small‐group discussions. We examined the effects of program participation on students' epistemological understanding of science (EUS) and attitudes toward science, as well as surveyed teachers to determine how they felt the program affected students' attitudes and EUS. Student measures indicated they developed a deeper understanding of the process of scientific knowledge generation and were more likely to report liking science more than less. Similarly, teachers' self‐reports corroborated these results, as well as showed teachers thought the structure of the program effectively integrated mathematics and language arts. [ABSTRACT FROM AUTHOR]

In this article, we describe the case of "Keri," a fifth‐grade teacher who had completed an Elementary Mathematics Specialist (EMS) certification program. Drawn from a larger study investigating the knowledge, beliefs, and practices of EMSs, Keri's case was unique in that she was teaching mathematics to four classes in a departmentalized structure, where students were placed into different classes according to perceived mathematics ability. Observations from the larger study revealed that Keri's instructional practices did not align with her reported beliefs and knowledge. To explore this deviation, we conducted a case study where we observed Keri's instruction across multiple classes and used interviews to explore reasons for Keri's instructional decisions in terms of her perceived professional obligations. We found that Keri did employ practices that were aligned with her reported beliefs and knowledge such as pressing students for mathematical justifications, but only in her "higher ability" classes. Interview data suggested that Keri's decisions were driven by a strong obligation to individual students, overriding other obligations. We describe implications of these findings, including the limitations of teacher assessments and surveys as proxies for teaching quality, and discuss recommendations for approaches to teacher development that account for teachers' perceived obligations. [ABSTRACT FROM AUTHOR]

Algebra has long been a gatekeeper to more advanced mathematics and to tertiary education. International assessments, such as PISA, have also shown that this trend extends beyond borders, making the topic of when algebra should be learned quite political. Many reforms have been instituted since the early 1990s to infuse algebraic thinking into elementary grade levels—a domain of learning that has since been termed early algebra. In this study, we draw on Rasch Analysis results to report on the levels of sophistication that 457 upper elementary students across 10 schools and 28 classrooms exhibited on an early algebra assessment after completing a computer game‐based early algebra intervention. Findings indicate that half of the students improved by at least one level of sophistication, and about ¼ were observed to improve from largely thinking of quantity from a numeric standpoint to being able to think about a generalized quantity in the form of variable expressions. Despite the small change in students engaging in thinking about generalized quantity, the relatively short intervention period implies promising results to support a long‐term intervention in future research. Further research is also needed on the influence of student contextual factors, including teacher and school effects. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Science, technology, engineering, and mathematics (STEM) is widely visible in education and workforce policies and discussions in the United States (US). However, there is a lack of consensus on what is considered a STEM career. In addition, little is known about how K‐12 teachers conceptualize STEM careers and how this information is portrayed to students. This mixed methods study investigated 52 K‐12 teachers' conceptions of STEM careers and if they included this information in their classroom instruction. The data collected consisted of a questionnaire and follow‐up interviews with a subset of teachers. The data analysis revealed that there was a range of how teachers defined and conceptualized STEM careers from narrow to very broad. This led to the development of the STEM‐Peripheral, Adjacent, Central (STEM‐PAC) career classifications which categorizes careers based on the application of STEM knowledge and skills. Additionally, teachers articulated benefits and drawbacks of including STEM career information in their instruction. Benefits included increasing student interest in STEM careers and making learning relevant. Drawbacks included limits to teacher time and knowledge. This study suggests teachers should present STEM as it is connected to various careers and that administrators should support teachers who wish to include this in their curriculum. [ABSTRACT FROM AUTHOR]

Mindsets have been shown to greatly influence individuals' efforts and subsequent success in the endeavors they attempt. This is particularly true of mathematical endeavors where mindset impacts the ways in which individuals approach and persevere in learning. This exploratory study investigated the mathematical mindsets held by 242 prospective teachers in undergraduate mathematics content courses for PreK‐8 teachers as well as examined the relationships between mindset, depth of learning, challenge seeking choices, and course grades. A strong predictive nature was found to exist among these variables. Recommendations are identified for future research to investigate prospective teachers' mindsets and depth of learning. [ABSTRACT FROM AUTHOR]

0 ht Context of the science fairs Student participants were from five different SFs where each transpired in a different context as a result of local goals, settings, cultures, and student demographics. School 2 Seventh-grade students (10% of students identifying as NA) conducted an independent research project in their science classes where the rural school is near a NA reservation. Science fairs (SF) are competitive events where students discuss and explain their independent research projects in science, technology, engineering, or mathematics (STEM) which are then evaluated and celebrated. School 4 All School 4 (urban location) students were invited to participate in SF and those who showed interest received the SF Handbook, with advanced science class students required to participate. [Extracted from the article]

This collective case study analyzes the use of manipulatives in math lessons developed and taught by 4 groups of elementary teachers (K-8) involved in lesson study as part of a professional development program. The study found that in three of four lessons studied manipulative use was turned into an end in and of itself rather than a tool, and that in the fourth lesson manipulative use hindered rather than helped student learning. These problems with manipulative use by teachers in the lessons provide helpful guidance for planning of future professional development for math teaching. Our conclusion contains recommendations for successful implementation of manipulatives for both teachers and professional developers. Most importantly, we stress the need to emphasize the link between pedagogy and content, not the specific use of manipulatives. [ABSTRACT FROM AUTHOR]

Explores the mathematics assessment methods employed by teachers in Australia. Use of assessment data by teachers; Completion of a Likert-scale survey by teachers; Relationships between grade level, use of assessment data and the use of assessment techniques.

With the call for increasing the level of inquiry‐based instruction in mathematics and science classrooms, it is imperative for teacher education programs to prepare teachers with these skills. This study draws from classroom observation data to determine the influence a unique teacher certification program has on key aspects of teacher practice using a series of Kruskal‐Wallis and Wilcoxon Rank Sum tests. Findings indicate that teachers participating in the program have a statistically significant level of growth in their use of inquiry practices related to Classroom Culture. In addition, by the fourth semester of their involvement in the program, participating teachers employ higher levels of inquiry instruction than a comparison group of teachers for almost every factor assessed. [ABSTRACT FROM AUTHOR]

We analyzed the solution pathways and errors found in the written responses of 469 prospective teachers solving an equation containing fractions. The majority (332, or 70%) used an algebraic method; 141 of the 332 (42%) were correct, and 22% of the algebraic methods were abandoned before a solution was obtained. We identified the steps in the written solutions, determined which solution pathways led to the correct solution, and identified common errors in the solution pathways of respondents who incorrectly solved the equation. Respondents initially attempted different methods. The most common method was solving by using fractions, but the majority of respondents who solved by using mixed numbers were able to correctly solve the problem. Common errors related to fraction arithmetic and the distributive property. Nearly all of the abandoned pathways contained no errors, but ended with a step that likely would precede an operation with fractions. Our findings suggest that the ability to solve an arithmetic equation with no fractions was necessary, but not sufficient, to solve an arithmetic equation involving fractions, and that the problem of solving equations with fractions was more closely tied to one's difficulties with rational number arithmetic and less with one's understanding of algebra. [ABSTRACT FROM AUTHOR]

Recent research on teachers' use of student mathematical thinking (SMT) and recommendations for effective mathematics instruction claim that how teachers respond to SMT has great impact on student mathematical learning in the classroom. This study examined some Chinese mathematics teachers' responses to student in‐the‐moment mathematical thinking that emerged during whole class discussion. The findings of this study revealed that the majority of Chinese elementary mathematics teachers in the data involved the whole group of students to make sense of in‐the‐moment SMT. They either invited students to digest SMT involved in the instance or provided an extension of the instance to further develop student mathematical understanding. [ABSTRACT FROM AUTHOR]

While much is known about the characteristics that researchers deem valuable for professional development (PD), teachers' perceptions of their PD needs are less understood. In this study, we sought to explore teachers' perceptions of their PD needs, including PD format, time frame, and topics covered, and how those perceptions varied by teachers' district size, grade level, subject area, and years of experience. Participants included a statewide representative sample of 800 elementary and secondary STEM teachers with a wide range of teaching experience and from small to large school districts across Missouri. Each participant responded to the MO‐STEM PD Needs Assessment, a 61‐item Likert scale survey. We found teachers to be most interested in learning about real‐world issues and problem‐based learning to teach STEM content. Teachers' participation in PD positively correlated with district size and the manner in which PD is valued in their community of practice, while years of teaching experience was negatively correlated with interest in virtually all categories of the survey, including formats of PD delivery and the majority of PD topics. We conclude with a discussion of the ways in which teachers' expressed preferences for PD ran contrary to what the literature suggests as best practices for PD. [ABSTRACT FROM AUTHOR]

Efforts to measure teacher self‐efficacy beliefs have built upon the theories of Albert Bandura. Continuing in that vein, the purpose of this study was to develop a measure that assesses teachers' efficacy and expectancy beliefs regarding teaching mathematics with an emphasis on conceptual understanding and mathematical practices, and to use this instrument to examine growth in these variables and correlations between these and other measures of quality of instruction. The instrument, developed as part of an NSF‐funded project, built upon prior measures of teacher self‐efficacy and expectancy beliefs, by modifying or omitting existing items and developing additional items aligned with instruction that supports the development of mathematical practices and conceptual understanding of mathematics. A group of mathematicians, mathematics educators, and K–12 experts developed a collection of items that was reduced based on factor analysis and modified based on cognitive interviews. Both exploratory and confirmatory factor analyses provide robust support for the psychometric properties of the two measures, and suggest that the two subscales are distinct and measurable constructs. Evidence of concurrent and predictive validity was obtained using multi‐year correlations calculated between these scores and other constructs measured for the teachers participating in the grant. [ABSTRACT FROM AUTHOR]

Abstract: The study was situated in a National Science Foundation supported Math Science Partnership between a private university and an urban school district. This study sought to understand the decision‐making process of elementary teachers as they implement an integrated science, technology, engineering, and mathematics (STEM) curriculum in their classrooms and the interactions that occur between the teachers and curriculum during that process. This qualitative study utilized a comparative case study approach to understanding the decision‐making process of three elementary teachers enacting the same lesson. Analysis of the interactions revealed that the teachers' perceptions of student ability, their pedagogical design capacity, and time were influences that impacted implementation. These findings have implications for STEM‐focused professional development of elementary teachers. [ABSTRACT FROM AUTHOR]

Abstract: Body‐based activities have the potential to support mathematics learning, but we know little about the impact they have in the classroom. This study compares high school geometry students learning through either body‐based or analogous non‐body‐based activities over the course of a two‐week unit on similarity. Pre‐ and post‐tests revealed that while students in both conditions showed gains in content area comprehension over the course of the study, the body‐based condition showed significantly greater gains. Further, there were differences in the language students used to describe the learning activities at the end of the unit that may have contributed to the differences in learning gains. The students in the body‐based condition included more mathematical and nonmathematical details in their recollections. Additionally, students in the body‐based condition were more likely to recall their experiences from a first‐person perspective, while students in the control condition were more likely to use a third‐person perspective. [ABSTRACT FROM AUTHOR]

Creating a continuum of STEM models: Exploring how K-12 science teachers conceptualize STEM education. Changes in requirements for teacher certification have limited the opportunities for teachers to learn specifically about teaching STEM to students from underrepresented groups making it necessary for school districts to find ways to engage their teachers in effective professional development in this area. There are many factors contributing to these gaps in STEM education including: poverty, lower teacher expectations, limited access to lab and other STEM facilities and supplies. [Extracted from the article]

Research indicates that teacher efficacy influences student achievement and is situation specific. With the Next Generation Science Standards calling for the incorporation of engineering practices into K-12 classrooms, it is important to identify teachers' engineering teaching efficacy. A study of K-5 teachers' engineering self-efficacy and engineering teaching efficacy revealed that that they have low engineering self-efficacy and low teacher efficacy related to engineering pedagogical content knowledge. Additionally, significant differences existed in self-efficacy levels based on gender, ethnicity, Title I school status, and grade level taught. [ABSTRACT FROM AUTHOR]

Project-based science (PBS) aligns with national standards that assert children should learn science by actively engaging in the practices of science. Understanding and implementing PBS requires a shift in teaching practices away from one that covers primarily content to one that prompts children to conduct investigations. A common challenge to PBS implementation is a misunderstanding of the elements of PBS. Identification of these misunderstandings as well as implementation challenges could inform professional development. This case study examined 24 teachers' understanding and implementation of PBS during participation in a consecutive three-year, comprehensive professional development program. Results provide insight as to the process they followed in the transition to implementing PBS. Measures included classroom observations, reflective interviews, and attitudinal surveys. Results showed that teachers developed the knowledge, confidence, and understanding to implement PBS but in most cases it took at least two to three years for positive results to become evident. Teachers struggled to develop adequate driving questions that provided project-focused lessons. Other obstacles included teacher resistance to student-directed instruction, confusing inquiry-based instruction with hands-on activities, and inability to motivate students to work in collaborative teams. While challenging, over time the teachers developed the knowledge, desire, and skills to implement PBS. [ABSTRACT FROM AUTHOR]

In this article, the author discusses integrated STEM learning experiences for helping students in making connections between discipline areas, applying content area knowledge and advancing student understanding and knowledge as a whole. Topics include integration of mathematics content has been a challenge for teachers creating lessons, topics such as water quality, energy conservation and robotics, and challenges identified by the teachers such as difficulty in using pedagogical strategies.

This quasi-experimental study investigated how explicit instruction about multiple modes of representation ( MMR) impacted grades 7 ( n = 61) and 8 ( n = 141) students' learning and multimodal use on end-of-unit assessments. Half of each teacher's ( n = 3) students received an intervention consisting of explicit instruction on MMR in science discourse, in addition to regular science instruction enhanced by a focus on MMR; comparison groups of students received regular science instruction. Three ordinary least squares regression models used student demographic variables and whether or not students received the intervention to predict students' (a) gain scores on end-of-unit tests, (b) voluntary use of embedded MMR on unit tests, and (c) retention of science knowledge as measured by a state end-of-level criterion-referenced assessment. Analyses showed that explicit instruction on MMR did not make a significant impact on student gain scores, the amount of embeddedness on unit tests, or end-of-level scores. However, Models 2 and 3 showed Hispanics and females used MMR more on end-of-unit tests than Whites or males, respectively, whether or not they received the intervention. Hispanics and females scored lower than Whites or males, respectively, on end-of-level, multiple-choice assessments. Implications for classroom teachers and educational researchers in relation to these underserved populations are discussed. [ABSTRACT FROM AUTHOR]

Through the GK-12 program of the National Science Foundation, graduate student fellows in a coastal marine and wetland studies program were trained to present targeted science concepts to middle- and high-school classes through their own research-based lessons. Initially, they were taught to follow the 5-E learning cycle in lesson plan development, but a streamlined approach targeting the three attributes of science concepts-macroscopic, model, and symbolic-was found to be a better approach, while still incorporating key facets of the 5-E model. Evaluation of the level of inquiry in the classrooms was determined using an inquiry scale from 0 to 4, differentiated by the relative number of actions that are student-centered. The graduate fellows consistently delivered lessons at the targeted levels 2 or 3, guided inquiry. In order to assess student learning, the GK-12 fellows were trained to develop single-item pre- and post-assessments designed to probe middle-level and high-school students' understanding of the macroscopic, model, and symbolic attributes of targeted science concepts. For the lessons based on the research of the fellows, about 80% of the students showed statistically and practically significant learning gains. The GK-12 fellows positively impact the classroom and are effective science ambassadors. [ABSTRACT FROM AUTHOR]

This study explored how mathematics content and methods courses for preservice elementary and middle school teachers could be improved through the integration of a set of instructional materials based on the National Assessment of Educational Progress ( NAEP). A set of eight instructional modules was developed and tested. The study involved 7 university instructors and 542 preservice teachers ( PSTs) from three different universities. A quasi-experimental nonequivalent groups design was used for this study in which the following data sources were collected and analyzed. Three versions of a Learning Mathematics for Teaching test were given to assess PSTs' mathematical content knowledge for teaching: (a) Elementary Number Concepts and Operations- Content Knowledge; (b) Elementary Geometry- Content Knowledge; and (c) Middle School Number Concepts and Operations- Content Knowledge. In addition, the Mathematics Teacher Efficacy Beliefs Instrument was given to assess PSTs' teacher efficacy beliefs. Test results were analyzed using paired samples t-tests. Findings suggest that use of instructional materials, based on NAEP, with PSTs results in increases in their mathematical content knowledge for teaching and in their teaching efficacy beliefs. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This study examined prospective elementary education majors' science teaching self-efficacy while they were enrolled in an introductory geology lab course for elementary education majors. The Science Teaching Efficacy Belief Instrument Form B ( STEBI- B) was administered during the first and last lab class sessions. Additionally, students were asked an open-ended question to describe their experience in the education majors' geology lab. The results of the STEBI- B were analyzed using paired t-tests to determine whether the students changed their personal science teaching efficacy ( PSTE) and science teaching outcome expectancy ( STOE). Results of this study indicate a significant increase in PSTE. No significant differences were found in STOE. This study suggests that science content courses designed for education majors may lead to a positive change in science teaching self-efficacy and has implications for teacher educators in preparing science content courses for their teacher preparation program. [ABSTRACT FROM AUTHOR]

For many students, developing mathematical reasoning can prove to be challenging. Such difficulty may be explained by a deficit in the core understanding of many arithmetical concepts taught in early school years. Multiplicative reasoning is one such concept that produces an essential foundation upon which higher-level mathematical thinking skills are built. The purpose of this study is to recognize indicators of multiplicative reasoning among fourth-grade students. Through cross-case analysis, the researcher used a test instrument to observe patterns of multiplicative reasoning at varying levels in a sample of 14 math students from a low socioeconomic school. Results indicate that the participants fell into three categories: premultiplicative, emergent, and multiplier. Consequently, 12 new sublevels were developed that further describe the multiplicative thinking of these fourth graders within the categories mentioned. Rather than being provided the standard mathematical algorithms, students should be encouraged to personally develop their own unique explanations, formulas, and understanding of general number system mechanics. When instructors are aware of their students' distinctive methods of determining multiplicative reasoning strategies and multiplying schemes, they are more apt to provide the most appropriate learning environment for their students. [ABSTRACT FROM AUTHOR]

Research suggests the importance of mathematics knowledge for teaching ( MKT) for enabling elementary school teachers to effectively teach mathematics. MKT involves both mathematical content knowledge ( M- CK) and mathematical pedagogical content knowledge ( M- PCK). However, there is no consensus on how best to prepare elementary preservice teachers ( PSTs) to achieve M- CK and M- PCK. This study builds on research related to MKT by investigating influences of mathematics content courses designed specifically for elementary PSTs ( IMPACT courses- Impact of Mathematics Pedagogy and Content on Teaching) on their attitudes (i.e., confidence and motivation) toward M- CK and M- PCK. Results suggest that the PSTs who participated in these IMPACT courses not only acquired high levels of confidence and motivation toward M- CK, but also showed significant and greater gains in attitudes toward M- PCK, after taking the required mathematics methods course, than their counterparts. Further, the findings suggest that these IMPACT courses provided a mathematical foundation that allowed the PSTs to engage in mathematics teaching methods better than those PSTs who did not have such a foundation. These results suggest potential course experiences that may enhance M- CK and M- PCK for elementary PSTs. [ABSTRACT FROM AUTHOR]

In a mathematics course for prospective elementary teachers, we strove to model standards-based pedagogy. However, an end-of-class reflection revealed the prospective teachers were considering incorporating standards-based strategies in their future classrooms in ways different from our intent. Thus, we drew upon the framework presented by Simon, Tzur, Heinz, Kinzel, and Smith to examine the prospective teachers' perspectives on mathematics teaching and learning and to address two research questions. What perspectives on the learning and teaching of mathematics do prospective elementary teachers hold? How do their perspectives impact their perception of standards-based instruction in a mathematics course and their future teaching plans? Qualitative analyses of reflections from 106 prospective teachers revealed that they viewed mathematics as a logical domain representative of an objective reality. Their instructional preferences included providing firsthand opportunities for elementary students to perceive mathematics. They did not take into account the impact of a student's conceptions upon what is learned. Thus, the prospective teachers plan to incorporate standards-based strategies to provide active experiences for their future elementary students, but they fail to base such strategies upon students' current mathematical conceptions. Throughout, the need to address prospective teachers' underlying perspectives of mathematics teaching and learning is stressed. [ABSTRACT FROM AUTHOR]