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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]

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]

Understanding science concepts and phenomena is important for an increasingly complex global society. For students with disabilities, there continue to be huge achievement disparities in science achievement when compared to their peers without disabilities. This includes students with autism spectrum disorder (ASD). The current study examines and analyzes published research on science and science‐related achievement for students with ASD. The authors reviewed characteristics of the research related to science achievement for students with ASD from 2000 through 2018 and analyzed included data to evaluate the effectiveness of the interventions included in the studies. Implications for research and teaching are discussed. [ABSTRACT FROM AUTHOR]

There is an increasing awareness of out‐of‐school program value in enhancing student interest and understanding of science, technology, engineering, and mathematics (STEM). This study examined the impact of an out‐of‐school STEM education program on student attitudes toward STEM disciplines and STEM careers. A STEM education program implemented at a public research university was designed to integrate STEM disciplines with hands‐on problem‐based activities. Design features included authentic learning contexts, engineering design processes, and content integration. Data sources included an attitude survey and interviews conducted with forty sixth grade middle school student participants. The analysis revealed significant differences between pre and posttests on student attitudes toward personal and social implications of STEM, science and engineering learning, and their relationship to STEM. Findings showed that the program contributed to students' developing interest in STEM fields, and helped them make connections between schoolwork and daily lives. Recommendations for future research on out‐of‐school STEM education programs were discussed. [ABSTRACT FROM AUTHOR]

The purpose of this study is to compare students' mathematics achievement growth rate in Texas science, technology, engineering, and mathematics (T‐STEM) academies to students' mathematics achievement growth rate in traditional public high schools. Forty‐six schools, 23 of which were T‐STEM academies and 23 of which were matched non‐STEM schools, were included in this study. A hierarchical linear modeling method was conducted. The result of the present study revealed that there was no difference in students' mathematics achievement growth rate in T‐STEM academies compared to students' mathematics achievement growth rate in comparison schools. However, in terms of ethnicity, the results indicated that African American and Hispanic students in T‐STEM academies outperformed African American and Hispanic students in comparison schools on their mathematics growth rate. [ABSTRACT FROM AUTHOR]

As teachers design lessons, their considerations influence their instructional practice. Researchers have found that teachers often have preconceived ideas about gender and large‐scale assessment data show gender differences in mathematics achievement. Given the differences in gender performance, and recognizing the role that gender considerations may play in teaching, this study focuses on teachers' considerations of gender during the lesson planning and implementation process. Findings indicate that teachers in the study minimally consider gender when planning lessons and evidence shows a lack of explicit gender considerations during instructional practice and in conversations about teaching. Results imply that considerations of gender may be quite implicit, which raises concerns about the implications of gender perceptions for student learning in mathematics. [ABSTRACT FROM AUTHOR]

In this study, we examine how prospective teachers perceive the efficacy of manipulatives and if these perceptions relate to their future use of manipulatives and their mathematics self‐efficacy. Survey responses from 97 preservice educators who had completed a mathematics method course indicate three essential findings. One, preservice teachers in this sample perceive manipulatives as highly effective for enhancing students' performance, conceptual knowledge, and affect and reported high levels of the intended use of manipulatives in their future teaching. Two, both preservice teachers' mathematics content and teaching self‐efficacies were significant negative predictors of the intended use of manipulatives. Three, the relationship between preservice educators' perceptions and the intended use of manipulatives is dependent upon their mathematics teaching self‐efficacy. [ABSTRACT FROM AUTHOR]

This study investigates whether elementary science teachers participating in a four‐week professional development workshop develop new understandings about classroom discourse and whether they are able to implement strategies toward teaching science as student‐to‐student discourse. Perspectives and the extent of teacher use of discourse strategies were examined. Hundred and twenty teachers in grades 4 through 6 from 29 schools participated in the professional development at four public, research‐intensive universities situated in a Mid‐Atlantic state. Teacher reflections indicate an understanding of the strategies and a belief that they were important. Analysis of program transcripts exposed that elementary teachers were implementing the strategies learned during the professional development. However, they continued to control the conversation and continued to use more traditional talk moves. They tried to use questions to probe student thinking and to have students build on one another. The teachers wrestled with how to ask open‐ended questions and guide the discussion to elicit deeper understanding. The professional development model proved effective for raising awareness and reflection, but the model did not result in a significant change in teacher practice. Analysis of classroom practice after this institute may show change toward a more student‐centered discourse. [ABSTRACT FROM AUTHOR]

Prior research regarding minorities in the science, technology, engineering, and mathematics (STEM) fields indicated that the factors of peer support and participation in STEM‐related activities contributed positively to minority students' recruitment and retention in these fields. Utilizing stereotype threat as a conceptual framework, this qualitative case study investigated the contribution of these factors by examining the experiences of minority students majoring in a STEM field. Data analyzed through a deductive approach indicated that a stereotype threat adversely affecting retention and recruitment in STEM could be either minimized or maximized by peer support, in the form of educator or familial influence, and participation in STEM‐related activities through internships and the application of STEM‐related knowledge. Findings from this research may inform higher education institutional practices involving the recruitment and retention of students to the STEM fields from minority populations. [ABSTRACT FROM AUTHOR]

Place value understanding requires the same activity that students use when developing fractional and algebraic reasoning, making this understanding foundational to mathematics learning. However, many students engage successfully in mathematics classrooms without having a conceptual understanding of place value, preventing them from accessing mathematics that is more sophisticated later. The purpose of this exploratory study is to investigate how upper elementary students' unit coordination related to difficulties they experience when engaging in place value tasks. Understanding place value requires that students coordinate units recursively to construct multi‐digit numbers from their single‐digit number understandings through forms of unit development and strategic counting. Findings suggest that students identified as low‐achieving were capable of only one or two levels of unit coordination. Furthermore, these students relied on inaccurate procedures to solve problems with millennial numbers. These findings indicate that upper elementary students identified as low‐achieving are not to yet able to (de)compose numbers effectively, regroup tens and hundreds when operating on numbers, and transition between millennial numbers. Implications of this study suggest that curricula designers and statewide standards should adopt nuances in unit coordination when developing tasks that promote or assess students' place value understanding. [ABSTRACT FROM AUTHOR]

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

This study examined primary grades students' achievement on number sense tasks administered through an Internet-based formative assessment tool, Assessing Math Concepts Anywhere. Data were analyzed from 2,357 students in teachers' classrooms who had participated in a year-long professional development program on mathematics formative assessment, 1,427 students from teachers who had participated in the program in the year prior, and 9,783 students whose teachers had not participated at all. Analyses indicated that all students in the treatment group demonstrated growth, and that student achievement was influenced by the number of times the assessment was used to collect data and make instructional decisions. Further, there was a relationship between districts' socioeconomic status and growth, meaning students from impoverished backgrounds grew more than their peers. [ABSTRACT FROM AUTHOR]

The main purpose of this quantitative study was to examine the degree to which a three-week intervention in an urban high-needs high school science classroom would influence students' (n = 51) interest, utility value, content knowledge, and intentions for future study in chemistry. The intervention consisted of an authentic, inquiry-based chemistry project where students worked cooperatively to investigate core chemistry concepts and connect them to real-world consumer products and careers in manufacturing that required chemistry knowledge. Findings indicated that students improved their chemistry knowledge, found greater relevance for chemistry, and intend to take more chemistry in the future. Interest in chemistry did not statistically significantly increase as a result of the intervention; however, students' interest levels remained consistently moderate from pre-test to post. This study adds to the current body of literature in three ways. First, the intervention showcased positive outcomes with students from an urban, high-needs high school who lacked motivation and academic proficiency in science. Second, using an authentic, inquiry-based utility value intervention is a viable alternative to previous successful interventions that involved writing tasks. Finally, the study was the result of a high school teacher's advanced training in research where important evaluation skills were cultivated and advanced. [ABSTRACT FROM AUTHOR]

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

The purpose of the present quasi-experimental study was to examine the impact of a horseshoe crab citizen science program on student achievement and science, technology, engineering, and mathematics ( STEM) career motivation with 86 ( n = 86) eighth-grade students. The treatment group conducted fieldwork with naturalists and collected data for a professional biologist studying horseshoe crab speciation and a mock survey. The comparison group studied curriculum related to horseshoe crabs in the science classroom. A series of measures related to self-efficacy, interest, outcome expectations, choice goals, and content knowledge were given to participants before and after the intervention. It was hypothesized that students would report higher motivational beliefs regarding science and show higher levels of achievement following the intervention than the comparison group. Support was shown for most of the hypotheses. In addition, path analyses indicated that students' motivational beliefs influence content knowledge and outcome expectations, which in turn affect their career goals. These results have implications for incorporating authentic fieldwork within a formal school structure as an effective method for promoting student achievement and STEM career motivation. [ABSTRACT FROM AUTHOR]