Algebra

A classroom study was conducted to understand how to engage in responsive teaching with 18 seventh grade students at three stages of units coordination during a unit on proportional reasoning co-taught by the first author and classroom teacher. In the unit, students worked on making two cars travel the same speed. Students at all three stages of units coordination learned to do so, as reported elsewhere (Hackenberg et al., 2023). This paper focuses on the practice of inquiring responsively in small groups.

Professional development (PD) for mathematics teachers often emphasizes transformative instructional change. However, a more modest, incremental approach may offer a higher likelihood of success in ways that complement transformational efforts. This Editorial discusses the potential advantages of incremental PD where teachers make small but meaningful improvements to their practice over time. We explore the differences between transformational PD and incremental PD as evidenced by the articles in this Special Issue.

This article presents results from a design experiment intended to develop students’ understanding of linear functions and rates of change in a linguistically diverse ninth grade classroom. The intervention focused on fostering classroom discussions. Students’ pre-post assessment gains were higher in the redesigned classrooms than in the pre-intervention classrooms. Additionally, multilingual students who were classified as English Learners (ELs) made larger gains than their non-EL peers, and the majority of student learning gains occurred on conceptually-focused items.

The Transition to Algebra (TTA) curriculum seeks to quickly give students the mathematical knowledge, skills, and confidence to succeed in a standard first-year algebra class and to show them that they can explore mathematics and actually enjoy it. TTA is a full-year algebra support curriculum that can run concurrently with first-year algebra.

Seeds of Algebraic Thinking are sub-conceptual resources coming from life experience that students call upon when responding to mathematical prompts. This site includes resources students could activate when thinking about groups and sets, equality, proportionality and ratio reasoning, and functions.

This site provides three online activities focused on covariational reasoning as a foundation for middle school students to build more abstract algebraic knowledge. These tasks provide students with opportunities to understand static points, understand dynamic points, and make sense of different amounts of change.

In this paper, we share the design and impact of a set of two-hour online mathematics professional development modules adapted from face-to-face video-based materials. The “Video in the Middle” (VIM) modules are aligned with principles of authentic e-learning and can be combined in a variety of ways to form professional development pathways that meet the unique needs of a wide range of professional learning settings and contexts. VIM modules aim to support teacher noticing of student thinking and increase their mathematical knowledge for teaching.

We investigate the algebraic discourse of secondary mathematics teachers with respect to the topic of equation solving by analyzing five teachers’ responses to open-ended items on a questionnaire that asks respondents to analyze hypothetical student work related to equation solving and explain related concepts.

The purpose of the Reasoning Language for Teaching Secondary Algebra (ReLaTe-SA) project is to understand teachers' use of reasoning language for teaching concepts and procedures in middle and high school algebra. Previous studies on algebra and algebraic reasoning have investigated other aspects, including students’ conceptions and discourse. The link between students' discourse and conceptual understanding has been explored (Chesnais & Constantin, 2020; Reinhardtsen, 2020). However, less is known about middle and high school teachers' language in the algebra classroom.

The researchers conducted a qualitative analysis of the perceptions of school personnel and pre-service teachers about an Algebra I tutoring program for students with learning disabilities. The researchers surveyed and interviewed the participants about the effectiveness of the program for the mathematics learning of the students with LD at the school and as a learning experience for the pre-service teachers. The school personnel indicated there was a mutually beneficial relationship between the tutors and the school.