What's the Mechanism?


Sunday morning I continued my reading of Principles to Actions. This book, released by the National Council of Teachers of Mathematics, describes what a high-quality mathematics program is supposed to look like. The illustration in the chapter about curriculum (page 76) is an excellent example of how a small group of teachers improved the organization and instruction of one topic within their curriculum.

If I were in that group of teachers, I would want to figure out a way to get our ideas in front of textbook writers and curriculum designers. The teachers' work improves upon the sequencing of instruction presented in the textbook so that it is in better alignment with the Common Core State Standards for Mathematics and in better alignment with effective methods for teaching the concepts. These improvements could help the textbook publisher when they go to write the next edition. This leads me to the title question of this post, "What's the mechanism for getting the word back to publishers?"

I work in assessment development rather than textbook development. However, I have the same question because, in my experience, I rarely get feedback from the marketplace about our work. For custom-developed assessments, our client provides ongoing feedback that we incorporate before releasing a test or an item bank to the field. However, for product development, there is little client feedback until after a product launch.

Have you tried to report something back to either a textbook publisher or an assessment publisher? What was your experience? What was the result? I'm curious to learn whether or not publishers are responsive to good ideas presented to them from educators.



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 Mathematics

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