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.

# Browse

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

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

## Building Coherence and Progression on Sound Frameworks

### Travis Lemon and Scott Hendrickson

A robust framework can support teachers and their students’ learning.

## Using Series to Construct Pythagorean Triples

### Darien DeWolf and Balakrishnan Viswanathan

This article provides a series-focused approach to computing Pythagorean triples.

## Are We Preparing Agents of Change or Instruments of Inequity? Teaching Toward Antiracist Mathematics Teacher Education

### Joel Amidon, Anne Marie Marshall, and Rebecca E. Smith

The authors began this work with the understandings that (a) there is no “neutral” when it comes to the teaching of mathematics, and (b) mathematics teacher educators need to do something to help produce teachers of mathematics that develop students’ relationships with mathematics and push against the inequities that exist both within and outside of the classrooms in which they will teach. In response, the authors created, deployed, and studied a learning module in an attempt to enact antiracist mathematics teacher education. The learning module activities, the findings about the learning from the prospective teachers who engaged in the module, and messages for mathematics teacher educators who want to engage in this work are shared.

##
Teaching Is a Journey: What Did I *Really* Mean?

### Karla Bandemer

This department provides a space for current and past PK-12 teachers of mathematics to connect with other teachers of mathematics through their stories that lend personal and professional support.

## “Reflections on High-Quality Math Instruction”

### Blake E. Peterson, Douglas L. Corey, Benjamin M. Lewis, Jared Bukarau, and Introduction by: Wendy Cleaves

From the Archives highlights articles from NCTM’s legacy journals, previously discussed by the *MTLT* Journal Club.

## 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.

## Mathematical Wonders and Reasons Abound in the Seasons

### Maria Franshaw

Mathematics abounds in the beauty of the seasons. Where you live, work, or travel, how do you engage with and explore the wonders of math in our natural world?

## Symbiosis: Social and Emotional Learning & Mathematics Learning

### Ruthmae Sears, Jennifer Bay-Williams, James C. Willingham, and Amanda Cullen

Social and Emotional Learning and the Standards for Mathematical Practice have a mutually beneficial relationship and develop mathematically proficient and confident students.

## Math Chat Opportunities Abound!

### Alice Aspinall

This article describes how fortuitous mathematical moments should be noticed, encouraged, embraced, and capitalized upon.