Developing teacher content understanding by integrating pH and logarithms concepts

Logarithms are notorious for being a difficult concept to understand and teach. Research suggests that learners can be supported in understanding logarithms by making connections between mathematics and science concepts such as pH. This study investigated how an integrated chemistry and mathematics lesson impacted 29 teachers’ understanding of the logarithmic relationship and pH. Pre- and post-test data indicated 23 teachers improved their understanding of logarithms and 28 improved their understanding of pH, suggesting that teacher educators in both science and mathematics context can use this approach to foster better understanding with their teachers and ultimately school students. Our analysis also identified professional development components and teacher characteristics associated with gains in understanding of pH and logarithms, which mathematics and science teacher educators can use to strategically adapt and implement the lesson within other teacher education settings.     

Beyond the professional development academy: Teachers' retention of discipline‐specific science content knowledge throughout a 3‐year mathematics and science partnership

The Teacher Academy in the Natural Sciences (TANS) provided middle school (U.S. Grades 6–8) teachers (N = 81) with intensive professional development (PD) in chemistry, geosciences, and physics, with teachers enrolled in one scientific discipline per year. Because some teachers were retained and rotated into different disciplines, the TANS program investigated retention of science content 1–2 years beyond an instructional year. All teacher participants exhibited significant gains (p < .001), in chemistry, geosciences, or physics content, between their incoming knowledge and the 10‐day summer academy's conclusion. Chemistry and geosciences content were retained until the end of the PD year. Physics participants reported a significant loss (p < .001), although gains from teachers' incoming knowledge were still significant. When retention was measured beyond the instructional year, only the geosciences content was retained. Chemistry and physics gains were not retained, with no significant differences between incoming teachers' knowledge and content 1–2 years post instruction. Our research indicates that science content support is needed after PD programs, and importantly, that the support differs between scientific disciplines.     

同伴指导影响师范生课堂教学基本技能的实验研究

为了找寻训练师范生课堂教学行为的有效策略，对某师范大学的38名师范生进行教育实验，探讨了教师单向指导训练策略和同伴相互指导训练策略对师范生课堂教学行为变化的影响。结果表明，相比教师单向指导策略，同伴相互指导策略能激发全体师范生的积极主动性，是一种低消耗、高效率的训练师范生教学基本技能的有效策略。     

Locally logical mathematics: An emerging teacher honoring both students and mathematics

This case study explores the mathematics engagement and teaching practice of a beginning secondary school teacher. The focus is on the mathematical opportunities available to her students (the classroom mathematics) and how they relate to the teacher's personal capacity and tendencies for mathematical engagement (her personal mathematics). We use a mathematical process-and-action approach to analyze mathematical engagement and then employ the teaching triad—mathematical challenge, sensitivity to students, and management of learning—to situate mathematical engagement within the larger context of teaching practice. The article develops the construct of locally logical mathematics to underscore the cogency of mathematical engagement in the classroom as part of a coherent mathematical system that is embedded within a teaching practice. Contributions of the study include the process-and-action approach, especially in tandem with the teaching triad, as a tool to understand nuances of mathematical engagement and differences in demand between written and implemented tasks.     

STEM Teachers' Planned and Enacted Attempts at Implementing Engineering Design‐Based Instruction

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.     

“Beyond an acronym,STEM is…”: Perceptions of STEM

Although STEM is at the forefront of many educational initiatives, little is known about various professionals’ perceptions of STEM. This mixed‐methods study surveyed 164 preservice teachers, inservice teachers, administrators, informal educators, and STEM professionals. Quantitative and qualitative questions on the survey elicited participants’ perceptions of STEM, STEM support, and STEM careers. Quantitative analysis revealed that profession influenced understandings of STEM, importance of STEM, support for STEM, and perceptions of STEM career opportunities. Qualitative analysis provided rich explanations for the differences in perceptions among professions. This study suggests that science teacher educators need to ensure preservice teachers have understandings of STEM and STEM careers, K‐16 educators need to emphasize the current importance of STEM, and administrators and policymakers need to align visions of STEM with curriculum and pacing guides so teachers feel supported in their STEM endeavors.     

课堂提问在大学数学教学中的意义

课堂提问是一种有效的教学组织形式,它既是重要的教学手段,又是完美的教学艺术.这篇文章以高等代数的教学为例,阐述了大学数学教学中课堂提问的重要意义.希望对年轻的教师能有所启迪和帮助.     

Computational estimation skill of preservice teachers: operation type and teacher view

Despite the importance of computational estimation skill for the improvement of number sense, little research exists on preservice teachers’ estimation skills and their view on estimation in the US context. This study examined the computational estimation skill of 58 preservice elementary teachers (PSTs) and its relationship to their views of the meaning of estimation and the importance of teaching it. Three sets of instruments were used: an estimation task, a computational task, and a belief survey. Results indicated that PSTs performed differently depending on the types of operations on the estimation test. It was also found that different types of problems elicited different strategies. Furthermore, the intervention of the study, along with five other factors were found to significantly correlate with estimation skills. The five factors include PSTs’ mathematical knowledge, their reported confidence about estimation skills, their self-reported knowledge about calculator use in instruction, their views of estimation in teaching mathematics, and their definition of estimation. A negative correlation was documented for the knowledge of calculator use in instruction, and positive correlations were present for other factors. Implications are discussed in accordance with these findings.     

Engineering design and the development of knowledge for teaching among preservice science teachers

The goal of this article is to inform professional understanding regarding preservice science teachers’ knowledge of engineering and the engineering design process. Originating as a conceptual study of the appropriateness of “knowledge as design” as a framework for conducting science teacher education to support learning related to engineering design, the findings are informed by an ongoing research project. Perkins’s theory encapsulates knowledge as design within four complementary components of the nature of design. When using the structure of Perkins’s theory as a framework for analysis of data gathered from preservice teachers conducting engineering activities within an instructional methods course for secondary science, a concurrence between teacher knowledge development and the theory emerged. Initially, the individuals, who were participants in the research, were unfamiliar with engineering as a component of science teaching and expressed a lack of knowledge of engineering. The emergence of connections between Perkins’s theory of knowledge as design and knowledge development for teaching were found when examining preservice teachers’ development of creative and systematic thinking skills within the context of engineering design activities as well as examination of their knowledge of the application of science to problem‐solving situations.     

Exploiting the potential of primary historical sources in primary school: a focus on teacher’s actions

Integrating history of mathematics in classes could be a hard task with young pupils. Indeed, original historical sources have a language that is far from the modern one. Such texts represent cultural artefacts that can give access to mathematical knowledge. The teacher can exploit such potential acting as a mediator between the mathematical signs of the source and those signs that are accessible to students. Through a case study, we investigate the role of the teacher in the process of semiotic mediation during a collective discussion. The analysed intervention is made of two phases: firstly, students work collaboratively and secondly, the teacher mediates a discussion aimed at institutionalizing the knowledge. During the discussion, working on a text from Tartaglia’s translation of Euclid’s Elements, a group of fifth graders constructs a definition of prime numbers. Referring to the Theory of Semiotic Mediation, we analyse the role of the teacher in building up semiotic chains linking students’ productions to an institutionalized knowledge emerging from the collective discussion. We highlight how teacher’s focalization on students’ words allows the progress of the discussion: the potential of the historical text is exploited fostering a definition that is close to culturally shared mathematics.