Deconstructing Math Questions

Please watch this presentation given by Dan Meyer at TEDxNYED in March 2010.

When I first watched this video a few months ago I immediately became fascinated by Dan’s deconstruction of the math textbook question. His approach of deconstructing the question and placing elements into layers struck a chord with me. Ever since then, I’ve been thinking about how deconstructing and layering a question could be applied to large-scale assessment.

A few years ago I would’ve had to give up on such an exploration. Until very recently, large-scale assessments were paper-delivered. Paper-based tests mean static presentation of item stimulus material, making it difficult to apply Dan’s techniques.

However, thanks to the two assessment consortia, computer-based assessment has arrived. Now I can explore ways to apply Dan’s techniques to test questions by making the stimulus (the question) interactive. I have been visualizing items where new information is presented under certain circumstances, perhaps when asked for by the student or after the student answers part of the question.

If you have seen an example of this, please share it. If not, I’d like to know whether you share my enthusiasm for creating test items that allow students to interact with the stimulus while answering the question.


Posted in Assessment, Mathematics, Uncategorized

Overview: NCTM’s Principles to Actions


I’m thankful that I attended this year’s NCTM Annual Meeting and Exposition because this year NCTM released a new book, called Principles to Action: Ensuring Mathematical Success for All. I attended two sessions about the book and became interested in its potential to become one of NCTM’s seminal works.

For over 20 years the National Council of Teachers of Mathematics (NCTM) had worked to bring about systemic change by defining the content, skills, and abilities that students needed to learn during before graduating high school. The need for NCTM to focus on defining those standards stopped when the National Governor’s Association commissioned the development of the Common Core State Standards for Mathematics.

Principles to Action is NCTM’s answer to the question, “What now?” They answered the question by defining the “conditions, structures, and policies that must exist for all students to learn” (NCTM, 2014). These six Guiding Principles for School Mathematics are reproduced, in whole, from page 5 of Principles to Action.

Teaching and Learning. An excellent mathematics program requires effective teaching that engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically.

Access and Equity. An excellent mathematics program requires that all students have access to a high-quality mathematics curriculum, effective teaching and learning, high expectations, and the support and resources needed to maximize their learning potential.

Curriculum. An excellent mathematics program includes a curriculum that develops important mathematics along coherent learning progressions and develops connections among areas of mathematical study and between mathematics and the real world.

Tools and Technology. An excellent mathematics program integrates the use of mathematical tools and technology as essential resources to help students learn and make sense of mathematical ideas, reason mathematically, and communicate their mathematical thinking.

Assessment. An excellent mathematics program ensures that assessment is an integral part of instruction, provides evidence of proficiency with important mathematics content and practices, includes a variety of strategies and data sources, and informs feedback to students, instructional decisions, and program improvement.

Professionalism. In an excellent mathematics program, educators hold themselves and their colleagues accountable for the mathematical success of every student and for their personal and collective professional growth toward effective teaching and learning of mathematics.

Clearly, NCTM plans to focus its immediate attention on the principle of teaching and learning. Almost half the book is focused on this one principle. None of the others received such detailed treatment. The sub-title for next year’s annual meeting, Reaching Today’s Students Through Innovative Teaching, reinforces their new focus.

What do you think of NCTM’s renewed emphasis on its core principles and, in particular, on teaching and learning? Leave a comment with your thoughts.


National Council of Teachers of Mathematics. (2014). Principles to action: ensuring mathematical success for all. Reston, VA: National Council of Teachers of Mathematics.

Posted in Education, Mathematics

This Week: NCTM National Meeting and Exposition


Later this week I’m privileged to be able to participate in this year’s NCTM National Meeting and Exposition. I haven’t attended this conference in many years and am very excited to be going to New Orleans. I expect the meeting to be an intense learning experience that I plan on sharing in future posts.

Last Friday I reviewed the list of presentations and developed a plan for how I want to spend my time. I plan on attending four or five sessions a day as well as spending time in the exhibition hall. I’ll be busy, but I don’t want to miss out on such a rare opportunity.

The sessions I’ll be attending can be organized under one of four themes.

  • Common Core State Standards for Mathematics (CCSS-M): I’ve selected sessions that focus on the CCSS-M and, in particular, the Standards for Mathematical Practice. Incorporating the practice standards into test items will be an important part of my work this year. So, I’m looking forward to hearing the latest ideas about the practice standards.
  • NCTM’s Principles to Actions: I discovered last week that this year’s meeting also marks the release of NCTM’s Principles to Actions: Ensuring Mathematical Success for All. I suspect that the ideas and recommendations contained in this book will heavily influence U.S. K-12 mathematics education for the next several years. I’m eager to learn what this book is all about.
  • Consortia Assessments: Both PARCC and Smarter Balanced are providing updates on their assessment programs. I must attend these briefings and listen for important information about the future of these programs.
  • Professional Development: Many of my projects this year revolve around teaching educators about what it takes to write high-quality items. I picked a few sessions that I believe will help me design and implement these programs. I’m looking forward to getting insights that will help me with a number of projects, including this blog.

If you plan on being in New Orleans, let me know by leaving a comment. Perhaps we can find time to meet and chat.

Photograph courtesy of

Posted in Mathematics