Motherhood and Teaching: Radical Care

This essay is a personal reflection on how I leverage my positioning as a caregiver in my roles of a mathematician, teacher, and mother, to advance a vision for a more just and equitable society. I argue that care at home and in the classroom takes similar forms, and can be liberating instead of oppressive

Mathematizing Perceptions: Preservice Teachers’ Use of Mathematics to Investigate Their Relationship with the Community

Preservice teachers often hold deficit views about the students they will teach and their communities. These limiting beliefs can result in lower expectations of and poor outcomes for the students, and need to be addressed in all areas of teacher education, including mathematics courses. In particular, mathematics content courses for preservice teachers offer numerous opportunities for investigating social justice issues and challenging preservice teachers’ beliefs. The assignment described in this manuscript provides an example of the work that can take place in mathematics content courses for preservice K-8 teachers. As part of the assignment, preservice teachers used mathematics to investigate negative perceptions that their campus community has of the surrounding neighborhood. They wrote reflections and created mathematical arguments about household income, poverty rates, educational attainment, crime, and diversity in the neighborhood. Through working on the assignment many preservice teachers began to question their stereotypes about the community. Because of the preservice teacher interest in the topic, and because some problematic beliefs were displayed in the reflections, there is a need for similar assignments in this and other courses, in order to help preservice teachers see the strengths of diverse communities, instead of just their shortcomings

Making Art in Math Class During the Pandemic

For many of us, the pandemic has changed how we teach and how we support students. This manuscript highlights creativity as a way to support for student mathematical and emotional well-being. It describes the positive impact that creative assignments in a mathematics content course for preservice K-8 teachers had on students during the early days of the pandemic. The story is told by the instructor and two former students in the course

Justifying Euler\u27s formula through motion in a plane

In this paper we consider motion of an object in a plane to provide a mechanical interpretation of Euler\u27s formula. We believe that this approach contributes to a deeper and more intuitive understanding of Euler\u27s formula and can especially be useful for students learning it and encountering complex numbers for the first time. Euler\u27s formula can be introduced in many ways and using various approaches, but not all of these approaches help develop an intuition for where it comes from and why it works. We believe that the emphasis on physical interpretations and connections to motion can contribute to a more natural introduction and easier understanding of this fascinating formula. In this paper, we describe and consider motion in a plane, using it to give a detailed explanation of Euler\u27s formula. Also, our paper points to the need for an integrated approach to teaching mathematics and physics. In our opinion the interpretation of mathematical results based on the physical phenomena and processes has an important methodological and motivational role in the process of learning. We believe students will be more successful in using this and other formulas of mathematics if they understand them first

Mathematizing Perceptions: Preservice Teachers’ Use of Mathematics to Investigate Their Relationship with the Community

Preservice teachers often hold deficit views about the students they will teach and their communities. These limiting beliefs can result in lower expectations of and poor outcomes for the students, and need to be addressed in all areas of teacher education, including mathematics courses. In particular, mathematics content courses for preservice teachers offer numerous opportunities for investigating social justice issues and challenging preservice teachers’ beliefs. The assignment described in this manuscript provides an example of the work that can take place in mathematics content courses for preservice K-8 teachers. As part of the assignment, preservice teachers used mathematics to investigate negative perceptions that their campus community has of the surrounding neighborhood. They wrote reflections and created mathematical arguments about household income, poverty rates, educational attainment, crime, and diversity in the neighborhood. Through working on the assignment many preservice teachers began to question their stereotypes about the community. Because of the preservice teacher interest in the topic, and because some problematic beliefs were displayed in the reflections, there is a need for similar assignments in this and other courses, in order to help preservice teachers see the strengths of diverse communities, instead of just their shortcomings

From “Eye-opening” to Mathematical: Helping Preservice Teachers Look for Mathematics in Stories of Oppression

This article analyzes preservice teachers’ reflections about a visit to a campus event focused on injustice and oppression that they were required to attend as part of an assignment in a mathematics content course for preservice K-8 teachers. Prior to the assignment, the preservice teachers had had limited exposure to social justice-based mathematics contexts and extracting mathematics from the real-world. Their reflections provide valuable information about the types of social justice contexts preservice teachers find relevant, and the mathematical possibilities they see, on their own, in events such as this one

The influence of interactive learning materials on solving tasks that require different types of mathematical reasoning

The purpose of this study is to analyse the effects of the Interactive Learning Materials Triangle (iLMT) on the learning and knowledge retention of 12-year- old students. The iLMT is a digital version of the standard school learning materials in Serbia, and is characterized by a high degree of interactivity and immediate feedback during the learning process. We conducted an experiment to explore whether iLMT influences student success in solving mathematical tasks that require different types of mathematical reasoning. Based on previous extensive research by Lithner, 4 types of tasks are discussed: high relatedness answer, high relatedness algorithm, local low relatedness, and global low relatedness. The study involved 633 students and 13 teachers of mathematics, equally distributed in control and test groups. The main findings indicate that student success on a knowledge test for high relatedness answer and local low relatedness tasks for the test group was significantly higher than for the control group. On the knowledge retention test, students in the test group outperformed students in the control group at high relatedness algorithm and local low relatedness tasks. Our results also suggest that, even when learning materials are carefully digitalized with the use of available technological advantages, student success in global low relatedness tasks may still be lacking

The influence of interactive learning materials on solving tasks that require different types of mathematical reasoning

The purpose of this study is to analyse the effects of the Interactive Learning Materials Triangle (iLMT) on the learning and knowledge retention of 12-year- old students. The iLMT is a digital version of the standard school learning materials in Serbia, and is characterized by a high degree of interactivity and immediate feedback during the learning process. We conducted an experiment to explore whether iLMT influences student success in solving mathematical tasks that require different types of mathematical reasoning. Based on previous extensive research by Lithner, 4 types of tasks are discussed: high relatedness answer, high relatedness algorithm, local low relatedness, and global low relatedness. The study involved 633 students and 13 teachers of mathematics, equally distributed in control and test groups. The main findings indicate that student success on a knowledge test for high relatedness answer and local low relatedness tasks for the test group was significantly higher than for the control group. On the knowledge retention test, students in the test group outperformed students in the control group at high relatedness algorithm and local low relatedness tasks. Our results also suggest that, even when learning materials are carefully digitalized with the use of available technological advantages, student success in global low relatedness tasks may still be lacking

Engaging Teachers in the Powerful Combination of Mathematical Modeling and Social Justice: The Flint Water Task - National Council of Teachers of Mathematics

Two major challenges in mathematics teacher education are developing teacher understanding of (a) culturally responsive, social justice–oriented mathematics pedagogies and (b) mathematical modeling as a content and practice standard of mathematics. Although these challenges may seem disparate, the innovation described in this article is designed to address both challenges in synergistic ways. The innovation focuses on a mathematical modeling task related to the ongoing water crisis in Flint, Michigan. Through qualitative analysis of instructor field notes, teachergenerated mathematical models, and teacher survey responses, we found that teachers who participated in the Flint Water Task (FWT) engaged in mathematical modeling and critical discussions about social and environmental justice. The evidence suggests that integrating these 2 foci—by using mathematical modeling to investigate and analyze important social justice issues—can be a high-leverage practice for mathematics teacher educators committed to equity-based mathematics education. Implications for integrating social justice and mathematical modeling in preservice and in-service mathematics teacher education are discussed