Kay and LeSage (2009) (2009) conducted a literature review of research on use of student response systems in university courses (typically Science, Technology, Engineering, and Mathematics courses) and categorized benefits into classroom environment, learning, and assessment. The objectives of the proposed session are to discuss how using Google Forms will benefit those three above categories. Examples of Google Forms used to gather data, receive in-the-moment feedback to students and instructors, engage students' learning, and assess their learning will be shared throughout the paper. Limitations of Google Forms will also be discussed. This session can be beneficial to all K-College educators.
Engaging with mathematical modeling can support learners to collaboratively explore mathematics in integrated ways as well as generate mathematical ideas and representations that may be useful in everyday life. Although several studies provide diverse insights into teaching and learning mathematical modeling, research has yet to be conducted on the mathematical modeling learning opportunities available to secondary mathematics preservice teachers (PTs) in mathematics and education courses in teacher education programs. This study investigates the mathematical modeling learning opportunities reported by 48 instructors and ten focus groups of 37 PTs.Multiple data sources (e.g., interview transcripts, syllabi, tasks, and exams) collected from universities were used to achieve triangulation in this case study of secondary preparation programs. When asked about mathematical modeling, both PTs and instructors reported rich examples of mathematical modeling from the opportunities afforded by their respective programs. Both also reported modeling experiences that were not mathematical modeling, such as word problems, representations, or demonstrations. Along with the study's particular themes and examples, common mathematical modeling opportunities recalled by PTs and instructors are elaborated in our findings. This study intends to begin a discussion of possible pathways for providing rich opportunities for PTs to engage in mathematical modeling.
K E Y W O R D Salgebra, learning processes, math/math education, teacher education, teachers and teaching
U.S. students have consistently demonstrated poor performance in spatial reasoning in standardized testing (e.g., National Assessment of Educational Progress). One possible reason is students' lack of conceptual understanding of measurement concepts (length, area, volume, capacity). This paper describes different ways that mathematics textbooks written for future elementary teachers define meanings of measurement concepts, especially the meaning of measure, area, and the measurement process (generally and for area). We base the analysis of definitions and construction of complete definitions using several definitions of each concept from mathematics textbooks written for future elementary teachers (e.g., Beckmann, 2012; Sowder, Sowder, & Nickerson, 2010). Although not one mathematics textbook provided a complete definition, together the definitions present a detailed and in-depth look at the measurement process and area measurement.
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