# 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.

## Purposeful Questioning with High Cognitive–Demand Tasks

We share ideas for preparing for and enacting high-cognitive demand tasks in ways that support students in articulating and justifying their ideas. We offer strategies for developing and posing several types of purposeful questions: (1) eliciting thinking, (2) generating ideas, (3) clarifying explanations, and (4) justifying claims.

## Opportunities for Redefining Unconventional Units

This article highlights the importance of re-defining units unconventionally with fractions. We provide three examples of tasks Grade 5 students engaged in; we highlight the creative ways that they flexibly re-defined units and engaged deeply with fractions. We offer suggestions for supporting unconventional units for promoting conceptual understanding of fractions.

## Classroom Rules Reimagined as the Rights of the Learner

The article describes how one fifth-grade teacher helped her students to exercise their Rights of the Learner (e.g., to be confused; to claim a mistake; to speak, listen, and be heard; and to write, do, and represent what makes sense) as they learned to graph and interpret non-linear data.

Mathematical paradoxes often produce awe and wonder in the mathematics classroom. In this classroom episode, I share a paradoxical task, based on Simpson's Paradox, and its power as an intervention for a child diagnosed with ADHD. The Paradox leveraged his strengths to help him build understandings in proportional reasoning.

## Evaluating Videos for Flipped Instruction

Teachers who are flipping instruction face the challenging task of selecting or creating high-quality videos for their students. This article presents a framework for evaluating videos and describes the benefits of including interactive features and considering options beyond lecture videos.

The hammer-and-nail phenomenon highlights human tendency to approach a problem using a tool with which one is familiar instead of analyzing the problem. Pedagogical suggestions are offered to help students minimize their mathematical impulsivity, cultivate an analytic disposition, and develop conceptual understanding.

## Batman Reimagined

Inspired by the “Batman Equation” of 2011, this article presents a challenging and engaging process for graphing complicated designs from just a single parametric equation pair. Reinforces numerous analytic geometry skills. Works in popular graphing software such as Desmos or GeoGebra, or even graphing calculators.

## Teaching Proportionality through Robotics

This article shares the learning experienced by my seventh-grade students during a lesson incorporating LEGO robotics into my mathematics class. I provide evidence of my students' learning, which represents how LEGO robotics can benefit students in the mathematics classroom to support engagement and development of understanding.

## Constructing and Unpacking Diagrams in Geometry

By having students practice constructing diagrams for geometric theorems, teachers can develop students' understanding of mathematical claims, vocabulary, and notation methods. This practice can also strengthen students' ability to interpret mathematical diagrams and recognize their limitations.

## Digital First: Not Just an Add-On

This manuscript will highlight MTLT's digital first philosophy, which is not just an add-on to the mathematics, but a partner, working hand in hand with the mathematics to enhance the experience.

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 enrichment and differentiation in the elementary grades, equivalent equations in the middle grades, and assessment retakes in high school.

## Then: The Timing of Algebra 1

This article briefly describes the timing of the first concentrated study of algebra over the 100 years of NCTM, from a 9th-grade course taken by only about 1/5 of students to a course taken by virtually all students, with almost half taking it in 8th grade.

## Now: Reclaiming Mathematics for Solving Today's Issues

As educators, we can attest to how students are the best litmus test for the relevance of our subject matter. To close the gap between an abstract idea or the means to a good grade, we must contextualize our teaching within the issues most prevalent in our students' minds.

## Problems to Ponder

Problems to Ponder provides 28 varied, classroom-ready mathematics problems that collectively span PK-12, arranged in order of grade level. Answers to the problems are available online.

## GPS: Little Straw, Big Impact

In this growing problem solvers article, readers explore their impact on the environment with their use of straws through measurement and geometry. The sequence of tasks spans grades P-12 and we invite readers to explore real world contexts with mathematics.

## Pythagoras's Quilt

A quilt design repeating the use of Pythagoras's Theorem provides a variety of questions we can begin to ponder.

## Hook Line Sinker

The Hook-Line-Sinker eBook aims to utilise rich tasks as the core learning in mathematics rather than a selection of “one-hit-wonders”. The featured resources intend to provide teachers with a starting point for sparking student curiosity, developing the need to learn, and consolidating learning in multiple ways.

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: mtlt@nctm.org

Editorial Board

Editor-In-Chief

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

Stephanie Dean, Managing Editor

Mary E. Donovan, Editorial Coordinator

Eleanore Tapscott, Director Of Publications

Scott Rodgerson, Art Director

Tristan Coffelt, Sr. Copy & Production Editor

Luanne Flom, Copy & Production Editor

Christine A. Noddin, Publications Coordinator

Contact the editorial staff publications@nctm.org

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.

Editorial:

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.

Resources

Author Toolkit

Calls for Manuscripts

Student Work Release