Geometry Students’ Arguments About a 1-Point Perspective Drawing

The practice of formulating and justifying claims is a fundamental aspect of doing mathematics, and in geometry, students’ use of diagrams is integral to how they establish arguments. We applied Toulmin’s model to examine 23 geometry students’ arguments about figures included in a 1-point perspective drawing. We asked how students’ arguments drew upon their knowledge of 1-point perspective and their use of the diagram provided with the problem. Students warranted their claims based upon their knowledge of perspective, both in an artistic context as well as from experiences in everyday life. Students engaged in multiple apprehensions of the diagram, including using the given features, adding features, or measuring components, to justify claims about the figures. This study illustrates the importance of students’ prior knowledge of a context for formulating arguments, as well as how that prior knowledge is integrated with students’ use of a geometric diagram

Geometry Students’ Arguments About a 1-Point Perspective Drawing

The practice of formulating and justifying claims is a fundamental aspect of doing mathematics, and in geometry, students’ use of diagrams is integral to how they establish arguments. We applied Toulmin’s model to examine 23 geometry students’ arguments about figures included in a 1-point perspective drawing. We asked how students’ arguments drew upon their knowledge of 1-point perspective and their use of the diagram provided with the problem. Students warranted their claims based upon their knowledge of perspective, both in an artistic context as well as from experiences in everyday life. Students engaged in multiple apprehensions of the diagram, including using the given features, adding features, or measuring components, to justify claims about the figures. This study illustrates the importance of students’ prior knowledge of a context for formulating arguments, as well as how that prior knowledge is integrated with students’ use of a geometric diagram

Geometry Students’ Arguments About a 1-Point Perspective Drawing

The practice of formulating and justifying claims is a fundamental aspect of doing mathematics, and in geometry, students’ use of diagrams is integral to how they establish arguments. We applied Toulmin’s model to examine 23 geometry students’ arguments about figures included in a 1-point perspective drawing. We asked how students’ arguments drew upon their knowledge of 1-point perspective and their use of the diagram provided with the problem. Students warranted their claims based upon their knowledge of perspective, both in an artistic context as well as from experiences in everyday life. Students engaged in multiple apprehensions of the diagram, including using the given features, adding features, or measuring components, to justify claims about the figures. This study illustrates the importance of students’ prior knowledge of a context for formulating arguments, as well as how that prior knowledge is integrated with students’ use of a geometric diagram

Interpretations of slope through written and verbal interactions between a student and her tutors in algebra 1

There is an ongoing need to support students’ learning of linear functions, and the study of slope makes up a foundational component of this learning. We applied techniques from systemic functional linguistics to document the meanings that were established through spoken interaction between a student and her tutors during discussions of slope. We found that, while fraction notation gave the student and tutors a common reference point to discuss slope, it also masked important differences in how the student interpreted slope compared to her tutors. The findings of this analysis imply the need not only to attend to how students quantify slope, but also whether students recognize slope as an attribute of a line.Existe una necesidad continua de apoyar el aprendizaje de los estudiantes sobre las funciones lineales y el estudio de la pendiente es un componente fundamental de este aprendizaje. Aplicamos técnicas de lingüística funcional sistémica para documentar los significados que se establecieron a través de la interacción oral entre una alumna y sus tutores discutiendo la pendiente. Descubrimos que, aunque la notación de fracciones le dio a la estudiante y a los tutores un punto de referencia común para discutir la pendiente, también ocultó diferencias importantes en cómo la estudiante interpretó la pendiente en comparación con sus tutores. Los resultados de este análisis implican la necesidad no solo de atender la forma en que los estudiantes cuantifican la pendiente, sino también si los estudiantes reconocen la pendiente como atributo de una línea

Computing as a mathematical disciplinary practice

© 2019 Elsevier Inc. In this paper, we make a case for computing as a mathematical disciplinary practice. We present results from interviews with research mathematicians in which they reflected on the use of computing in their professional work. We draw on their responses to present evidence that computing is an inherent part of doing mathematics and is a practice they want their students to develop. We also discuss the mathematicians’ perspectives on how they learned and teach computing, and we suggest that much needs to be explored about how to teach computing effectively. Our overarching goal is to draw attention to the importance of the teaching and learning of computing, and we argue that it is an imperative topic of study in mathematics education research