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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]

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]

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]

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]

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]

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]

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 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]

Investigates the effects of a dynamic instructional environment and visualization on eight-grade students' construction of the concepts of reflection and rotation. Basis of the theoretical framework of the dynamic instructional environment; Use of the computer to discover the properties of reflection and rotation.

Describes a science and math activity plan for school children. Science and math skills which can be learned from the exercise; Prerequisite skills; Hands-on activities on astronomy; Activity procedure.

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]