In this study, we investigated prospective secondary mathematics teachers’ development of a meaning for the Cartesian form of complex numbers by examining the roots of quadratic equations through quantitative reasoning. Data included transcripts of the two sessions of classroom teaching experiments prospective teachers participated in, written artifacts from these teaching sessions, and their answers to pre-and-post written assessment questions. Results point toward prospective teachers’ improved meanings regarding the definition of complex numbers and the algebraic and geometrical meanings of the Cartesian form of complex numbers. Implications for mathematics teacher education include providing specific tasks and strategies for strengthening the knowledge of prospective and in-service teachers.

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## Exploring Prospective Teachers’ Development of the Cartesian Form of Complex Numbers

### Gülseren Karagöz Akar, Merve Saraç, and Mervenur Belin

## Understanding Algebraic Expressions Through Figural Patterns

### Casey Hawthorne and John Gruver

This instructional sequence develops your students’ meaningful understanding of algebraic expressions.

## Harnessing the Power of a Single-Number Number Talk

### Alison Williams and Lisa Lamb

Easy to implement, this strategy has a powerful positive impact in mathematics classrooms.

## Making Sense of Algebraic Expressions in Context

### Isabel White, Michael Foster, and Joanne Lobato

Explore three challenges that students faced and how they made progress.

## Crack the Code

### Karen Zwanch and Bridget Broome

This game teaches algebraic generalizations through differentiated play in pairs, small groups, or as a whole class and uses manipulatives to bridge numerical and algebraic thinking.

## GPS: Iterating and Partitioning

### Daniel K. Siebert and Monica G. McCleod

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.

## Developing Skills with Visual Representations

### Ruthmae Sears

This article describes how visual representations can help develop students’ reasoning and proof skills.

## Exploring Relative Size with Relative Risk

### Surani Joshua, James Drimalla, Dru Horne, Heather Lavender, Alexandra Yon, Cameron Byerley, Hyunkyoung Yoon, and Kevin Moore

The Relative Risk Tool web app allows students to compare risks relating to COVID-19 with other more familiar risks, to make multiplicative comparisons, and to interpret them.

## Revising Word Problems to Address UDL and Standards

### Noah Brown, Jonathan D. Bostic, Timothy Folger, Laura Folger, Tiara Hicks, and Shay Nafziger

Mathematics assessments should allow all students opportunities to demonstrate their knowledge and skills as problem solvers. Looking at textbook word problems, we share a process for revising them using Universal Design for Learning.

## Take a Seat at the Equation Café

### Sandra Vorensky

Design projects to encourage your students’ self-efficacy and motivate mathematics learning by helping them apply their prior knowledge from real-world experiences.