Three modes of STEM integration for middle school mathematics teachers

Of the four subjects in an integrated science, technology, engineering, and mathematics (STEM) approach, mathematics has not received enough focus. This could be in part because mathematics teachers may be apprehensive or unsure about how to implement integrated STEM education in their classrooms. There are benefits to integrated STEM in a mathematics classroom though, including increased motivation, interest, and achievement for students. This article discusses three methods that middle school mathematics teachers can utilize to integrate STEM subjects. By focusing on open‐ended problems through engineering design challenges, mathematical modeling, and mathematics integrated with technology middle school students are more likely to see mathematics as relevant and valuable. Important considerations are discussed as well as recent research with these approaches.     

Empirically supporting school STEM culture—The creation and validation of the STEM Culture Assessment Tool (STEM‐CAT)

School STEM Culture—an aspect of culture within a school community—is defined as the beliefs, values, practices, and resources in STEM fields as perceived by students, parents, teachers, and administrators and counselors within a school. This study validates the STEM Culture Assessment Tool (STEM‐CAT), an instrument intended to advance the use of the School STEM Culture construct within the research community. Internal consistency was determined through the use of Cronbach's alpha and factor analyses, and the instrument was found to be a reliable measure of School STEM Culture. The instrument can be used in future research to quantify School STEM Culture to determine if interventions change the culture of a school to further STEM education.     

High school students' use of representations in physics problem solving

Findings from physics education research strongly point to the critical need for teachers’ use of multiple representations in their instructional practices such as pictures, diagrams, written explanations, and mathematical expressions to enhance students' problem‐solving ability. In this study, we explored use of problem‐solving tasks for generating multiple representations as a scaffolding strategy in a high school modeling physics class. Through problem‐solving cognitive interviews with students, we investigated how a group of students responded to the tasks and how their use of such strategies affected their problem‐solving performance and use of representations as compared to students who did not receive explicit, scaffolded guidance to generate representations in solving similar problems. Aggregated data on students' problem‐solving performance and use of representations were collected from a set of 14 mechanics problems and triangulated with cognitive interviews. A higher percentage of students from the scaffolding group constructed visual representations in their problem‐solving solutions, while their use of other representations and problem‐solving performance did not differ with that of the comparison group. In addition, interviews revealed that students did not think that writing down physics concepts was necessary despite being encouraged to do so as a support strategy.     

“Do we teach subjects or students?” Analyzing science and mathematics teacher conversations about issues of equity in the classroom

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.     

Supporting disciplinary and interdisciplinary knowledge development and design thinking in an informal,pre‐engineering program: A Workplace Simulation Project

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.     

A study of early career teachers’ practices related to language and language diversity during mathematics instruction

The role of language in mathematics teaching and learning is increasingly highlighted by standards and reform movements in the US. However, little is known about teachers’, and especially early career teachers’ (ECTs) practices and understandings related to language in mathematics instruction. This multiple case study explored the language-related understandings and practices of six ECTs in diverse elementary classrooms. Using iterative cycles of analysis, we found that all ECTs regularly attended to students’ mathematical vocabulary use and development. Yet, there was variability in ECTs’ focus on how to teach mathematical vocabulary, expectations for students’ precise use of mathematical terminology, and the use of multiple languages during instruction. These findings indicate that ECTs need more targeted support during teacher preparation and early career teaching in order to better support all students’ language development in the mathematics classroom.     

Critical perspectives of the ‘new’ difference equation solution method of Rivera-Figueroa and Rivera-Rebolledo

Recently, claims of a ‘new and straightforward’ method of solution to second-order linear difference equations have appeared in the mathematics education literature from Rivera-Figueroa and Rivera-Rebolledo. The claim of novelty is based on an assumption that ‘since the equation is worked in its canonical form’, the method within this context must be new. In addition, the assertion of straightforwardness is based on the position that ‘the solution comes naturally’ through this method, rather than artificially. In this article, we subject these claims and assumptions to closer scrutiny, examination and analysis. We note that the method has been published before, and we present the method in a more succinct form. We also discuss how the method can be extended to solve difference equations with non-constant coefficients, illustrating this via a discussion of an example.     

从一个习题到十个命题

从一道熟知的微积分习题,可以导出十个相关的命题.通过这一讨论过程,试图表明什么是创造性学习,以及如何进行创造性学习.     

水资源持续利用的多目标决策模型的建立

可持续发展战略的实施,资源的可持续利用是关键.针对日趋短缺的淡水资源,根据多目标决策理论,以同时追求经济、环境、社会效益为主要目标提出了其可持续利用的多目标决策模型,并举例说明了模型的应用,旨在为决策者提供淡水利用规划的依据.