Prospective Teachers’ Learning in Geometry: Changes in Discourse and Thinking

This study investigates changes in prospective teachers’ levels of geometric thinking and the development of their geometric discourses in the classification of quadrilaterals. To examine prospective teachers’ thinking about geometry, this study connects Sfard’s discursive framework to another, namely the van Hiele theory. Findings of the study reveal discursive similarities and differences in participants’ geometric discourses within the same van Hiele level, as well as changes in geometric discourse as a result of changes in levels of geometric thinking. The study also investigates the usefulness of a discursive framework in providing rich descriptions of prospective teachers’ thinking processes

Discourse Perspective of Geometric Thoughts

Sasha Wang revisits the van Hiele model of geometric thinking with Sfard’s discursive framework to investigate geometric thinking from a discourse perspective. The author focuses on describing and analyzing pre-service teachers’ geometric discourse across different van Hiele levels. The explanatory power of Sfard’s framework provides a rich description of how pre-service teachers think in the context of quadrilaterals. It also contributes to our understanding of human thinking that is illustrated through the analysis of geometric discourse accompanied by vignettes.https://scholarworks.boisestate.edu/fac_books/1446/thumbnail.jp

Understanding Prospective Teachers’ Levels of Geometric Thoughts: Insights from a Discursive Analysis

The study investigates the characteristics of prospective teachers’ geometric discourses at the van Hiele model of thinking (1959/1985), using Sfard’s (2008) discursive framework. In this report, I align two prospective teachers’ pre- and post- van Hiele geometry test (Usiskin, 1982) results with the analyses of their geometric discourses from clinical interviews, to illustrate changes in geometric discourse when a student’s test results showed no change in van Hiele levels, and changes in geometric discourse when a student developed her thinking to the next van Hiele level. Revisiting the van Hiele model of thinking, complemented with a discursive lens, helped to understand learning as change in discourses, as prospective teacher develop thinking toward a higher van Hiele level

Identifying Similar Polygons: Comparing Prospective Teachers’ Routines with a Mathematician’s

This paper reports two prospective teachers\u27 and a mathematician\u27s ways of identifying similar triangle and hexagons through the analysis of routines, a characteristic of geometric discourse. The findings show that visual recognition was a common approach for the mathematician as wells as the two prospective teachers. However, when asked for justification, their routines of identifying similar polygons diverged. The paper also discusses the implication of classroom discourse practices to enhance prospective teachers\u27 communication and reasoning skills while learning geometric concepts such as similarity

How Do They Know It Is a Parallelogram? Analysing Geometric Discourse at Van Hiele Level 3

In this article, we introduce Sfard\u27s discursive framework and use it to investigate prospective teachers\u27 geometric discourse in the context of quadrilaterals. In particular, we focus on describing and analysing two participants\u27 use of mathematical words and substantiation routines related to parallelograms and their properties at van Hiele level 3 thinking. Our findings suggest that a single van Hiele level of thinking encompasses a range of complexity of reasoning and differences in discourse and thus a deeper investigation of students\u27 mathematical thinking within assigned van Hiele levels is warranted

Navigating the Seas of Mathematics Education: New Waves in Research to Improve Student Learning

This issue focuses on research in the domain of mathematics education. Although mathematics has been a subject of study for many centuries, mathematics education is a relatively new field of scholarly inquiry, having been established as an independent field of research only in the early twentieth century. The most significant milestone was the establishment of the International Commission on Mathematical Instruction (ICMI) in 1908. Since 1969, ICMI has organized the International Congress on Mathematical Education, a quadrennial international meeting whose aim is to present the current states and trends in mathematics education research and in the practice of mathematics teaching at all levels

How Do U.S. and Chinese Biology Students Compare in Explaining Energy Consumption Issues?

This qualitative study investigates how biology majors explain energy consumption issues. In particular, we focus on two energy consumption activities that account for about two-thirds of global carbon dioxide emissions in 2011: burning fossil fuels for transportation and using electricity. We conducted in-depth clinical interviews with twenty U.S. students and twenty Chinese students. We compared these two groups of students in terms of two aspects of explanation: 1) naming scientific terms in the explanation, and 2) explaining an energy consumption issue. Regarding naming, we examined the frequency of naming different terms of scientific concepts and principles in students’ explanations. Regarding explaining, we developed a rubric that differentiates three levels of explaining: informal explanations that are based upon intuitive ideas (Level 1), school science explanations that are based on alternative conceptions about matter and energy (Level 2), and scientific explanations that demonstrate the scientific understanding of concepts/principles about matter and energy (Level 3). The results revealed that scientific terms appeared most frequently in scientific explanations (Level 3), but they also appeared in many school science explanations (Level 2) and in some informal explanations (Level 1). We further describe how scientific terms were used in explanations at different levels. We found although Chinese students named scientific terms more frequently and demonstrated a better performance in explaining, they still produced more informal explanations and school science explanations than scientific explanations. In general, the results suggest the importance of promoting students’ abilities to use scientific terms correctly and meaningfully in explaining real-world environmental events in both countries

Energy and Carbon Considerations of Fine-Tuning BERT

Despite the popularity of the `pre-train then fine-tune' paradigm in the NLP community, existing work quantifying energy costs and associated carbon emissions has largely focused on language model pre-training. Although a single pre-training run draws substantially more energy than fine-tuning, fine-tuning is performed more frequently by many more individual actors, and thus must be accounted for when considering the energy and carbon footprint of NLP. In order to better characterize the role of fine-tuning in the landscape of energy and carbon emissions in NLP, we perform a careful empirical study of the computational costs of fine-tuning across tasks, datasets, hardware infrastructure and measurement modalities. Our experimental results allow us to place fine-tuning energy and carbon costs into perspective with respect to pre-training and inference, and outline recommendations to NLP researchers and practitioners who wish to improve their fine-tuning energy efficiency.Comment: EMNLP 2023 Findings; First two authors contributed equally; 12 page

Elementary School Student Development of STEM Attitudes and Perceived Learning in a STEM Integrated Robotics Curriculum

Robotics has been advocated as an emerging approach to engaging K-12 students in learning science, technology, engineering, and mathematics (STEM). This study examined the impacts of a project-based STEM integrated robotics curriculum on elementary school students’ attitudes toward STEM and perceived learning in an afterschool setting. Three elementary school teachers and 18 fourth to sixth graders participated in an eight-week-long program. Quantitative and qualitative data were collected and analyzed, and showed students’ attitudes toward math improved significantly at the end of the robotics curriculum. Three specific areas of learning were identified, including STEM content learning and connection, engagement and perseverance, and development and challenge in teamwork. The findings also identified the opportunities and challenges in designing a STEM integrated robotics afterschool curriculum for upper elementary school students. Implications for future research studies and curriculum design are discussed