Mathematics Teacher: Learning and Teaching PK-12

MTLT reflects the current practices of mathematics education, as well as maintaining a knowledge base of practice and policy in looking at the future of the field. Content is aimed at preschool to 12th grade with peer-reviewed and invited articles.


We discuss how discourse actions can provide students greater access to high quality mathematics. We define discourse actions as what teachers or students say or do to elicit student contributions about a mathematical idea and generate ongoing discussion around student contributions. We provide rubrics and checklists for readers to use.

The complexity of understanding unit fractions is often underappreciated in instruction. We introduce a continuum of children's understanding of unit fractions to explore this complexity and to help teachers make sense of children's strategies and recognize milestones in the development of unit-fraction understanding. Suggestions for developing this understanding are provided.

Too often, statistical inference and probability are treated in schools like they are unrelated. In this paper, we describe how we supported students to learn about the role of probability in making inferences with variable data by building models of real world events and using them to simulate repeated samples.

We present a Scratch task we designed and implemented for teaching and learning coordinates in a dynamic and engaging way. We use the 5Es framework to describe the students' interactions with the task and offer suggestions of how other teachers may adopt it to successfully implement Scratch tasks.

Transferring fundamental concepts across contexts is difficult, even when deep similarities exist. This article leverages Desmos-enhanced visualizations to unify conceptual understanding of the behavior of sinusoidal function graphs through envelope curve analogies across Cartesian and polar coordinate systems.

The Asked & Answered department shares excerpts from discussion threads on the online MyNCTM community. In this issue, featured threads highlight responses to members' questions related to mathematical depth in preschool, spiral review in the upper elementary grades, ideas for differentiation in middle school, and projects for high school algebra.

“It's a YouTube World” (Schaffhauser, 2017), and educators are using digital tools to enhance student learning now more than ever before. The research question scholars need to explore is “what makes an effective instructional video?”.

Debate and discussions have often been staples of humanities classrooms. However, as Elham Kazemi states “everything we know about student learning and classroom practice tells us that classroom conversations are crucial to mathematics learning.” Let's explore ways to incorporate short debates into everyday math lessons.

Welcome to Mathematics Teacher: Learning and Teaching PK-12, NCTM’s new journal that reflects the current practices of mathematics education, as well as maintains a knowledge base of practice and policy in looking at the future of the field. Content is aimed at preschool to 12th grade with peer-reviewed and invited articles. MTLT is published monthly. Contact:

Editorial Board


Angela T. Barlow, University Of Central Arkansas, Conway

Associate Editors

Thomasenia Lott Adams, University Of Florida, Gainesville

Rick Anderson, Eastern Illinois University, Charleston

Wendy Bray, Florida State University, Tallahassee

Roger Day, Illinois State University, Normal

Clayton Edwards, Grundy Center Middle School, Iowa

Randall Groth, Salisbury University, Salisbury, Maryland

Alison Langsdorf, Weston Public Schools, Wayland, Massachusetts

Sandra Madden, University Of Massachusetts–Amherst, Amherst

Cathy Martin, Denver Public Schools, Denver, Colorado

Rebecca Robichaux-Davis, Mississippi State University, Starkville

Aaron Rumack, The College Board, Chicago, Illinois

Department Editors

Lisa Bejarano, Harrison School District, Manitou Springs, Colorado

Matt Enlow, Dana Hall School, Wellesley, Massachusetts

Josh Hertel, University Of Wisconsin La Crosse, La Crosse, Wisconsin

Megan Holstrom, Independent Consultant, Whitmore Lake, Michigan

Steve Ingrassia, Newbury Local Schools, Newbury, Ohio

Susie Katt, Lincoln Public Schools, Lincoln, Nebraska

Megan Korponic, Denver Public Schools, Denver, Colorado

Cheng-Yao Lin, Southern Illinois University Carbondale, Carbondale, Illinois

Kelly Hagan Mccormack, Wayland Middle School, Wayland, Massachusetts

Wayne Nirode, Miami University, Miami, Florida

Asli Özgün-Koca, Wayne State University, Detroit, Michigan

Molly Rawding, Fiske Elementary School, Lexington, Massachusetts

Erik Tillema, Indiana University, Indianapolis, Indiana

Journals Staff

Chris Asher, Managing Editor

Mary E. Donovan, Editorial Coordinator

Eleanore Tapscott, Director Of Publications

Scott Rodgerson, Art Director

Aisha Jamil, Sr. Copy & Production Editor

Maryanne Bannon, Luanne Flom, Larry Shea, Copy & Production Editors

Christine A. Noddin, Publications Coordinator


Contact the editorial staff

To submit a manuscript

To subscribe

MTLT features three types of articles:

Front and Center article: Submissions should be 3500 to 5000 words and must touch on a topic that spans pre-K–12. When submitting, choose the Manuscript Type category “All grades PK–12.” This article should try to appeal to the wide range of MTLT readers.

Feature article (grade-band specific): Submissions should be 3000 to 3500 words and focus on a narrow grade band (PK–2, 3–5, 6–8, 9–10, 11–12). When submitting, choose the grade-band category that fits your article.

Focus article (grade-band specific): Submissions should be 1000 to 1500 words and focus, as well, on a narrow grade band (PK–2, 3–5, 6–8, 9–10, 11–12). This tier allows authors to share a single, well-developed idea. When submitting, choose the grade-band category that fits your article.

MTLT Submission Guidelines

Submit to Departments

Writing for a department is a great way to begin writing for our profession. Department articles are often drawn from your daily interactions with students. If it is of interest to you and your students, it is likely to also be of interest to MTLT readers. The departments described below offer opportunities for you to share your problems and ideas.


An editorial allows readers to raise a significant issue or advocate a point of view about some aspect of teaching or learning mathematics. It can involve a narrow grade band or address a topic of interest to pre-K–12 educators.

Subject matter could include such topics as curriculum, pedagogy, assessment, mathematics teacher education, educational philosophy, research implementation, structure of the educational system, special teacher needs, or special student needs.

Word count: 1000 - 1500.

Letters to the Editor:

Readers are invited to respond to an article or department that is featured in MTLT.

Word count per letter: 250.

Problems to Ponder:

Readers are asked to submit individual problems or groups of problems (and answers only, not solution strategies) that are grade-band specific, much like those that appeared in TCM’s Math by the Month, MTMS’s Palette of Problems, and MT’s Calendar).

When submitting, click on specific grade band(s).

Growing Problem Solvers (GPS):

Send in your rich task or tasks that can potentially span four points along the pre-K–12 learning trajectory (elementary, intermediate, junior high, and high school) and can elicit higher-order thinking.

Each task should be a low-floor/high-ceiling task with multiple entry points, allowing for a variety of solution strategies and reaching many different learners. A teacher page will explore the math and potential instructional strategies.

If you have used a rich task in your classroom and have had to extend it, contribute to this discussion. No solutions will be provided.

Word count: 1000 (Teacher page 500 words, each task 250 words).

For the Love of Mathematics:

The last page of the journal will be visual and fun, engaging, and inspiring. This reader-driven department is intended for the teacher, rather than for direct use with students.

Items sent to the editor may include a photograph, combined with a funny or engaging mathematical question; an original cartoon that is humorous or reflective; a puzzle; Math Circle prompts; a poem or vignette; original artwork; or general celebratory items, such as Pi Day or Metric Week. Submission of student work within these guidelines is also welcome. How do you show your love of mathematics?

Word count: 350.

Ear to the Ground

Ear to the Ground features voices working in various corners of the mathematics education world. Readers hear from book authors, conference presenters, bloggers, and others and get accompanying digital enhancements to keep up-to-date on current happenings in mathematics education. Contributors are invited by the editors.

Where to Submit

All submissions to MTLT must be made to the ScholarOne: MTLT submission site. Limit your article or submission to the TOTAL word count listed above, including references and figures, where applicable. You are encouraged to include such digital components as a video clip, audio file, Livescribe™ file, SMART Board™ file, or other form of multimedia to enhance the submission. Authors are encouraged to use applications and software in their articles, however, such use does not imply NCTM endorsement of any product or developer.


Author Toolkit

Calls for Manuscripts

Student Work Release

Photographer Copyright Release

Video Permission

The Mathematics Teacher: Learning and Teaching PK-12 is available to individuals as part of an NCTM membership or may be accessible through an institutional subscription.

The Mathematics Teacher: Learning and Teaching PK-12 (MTLT), an official journal of the National Council of Teachers of Mathematics (NCTM), reflects the current practices of mathematics education, as well as maintaining a knowledge base of practice and policy in looking at the future of the field. Content is aimed at preschool to 12th grade with peer-reviewed and invited articles.

MTLT is published twelve times a year and presents a variety of viewpoints. Learn more about MTLT.