Menu
  • Teachers, Textbooks, and Big Ideas in Math

    Posted By John Woodward, Ph.D. | Jun 07, 2017
    NUMBERS-blog-2017

    American educators have a well-honed way of thinking about curriculum. Typically, district committees compare and then adopt a curriculum to meet specific goals or guidelines. More recently, curriculum adoption in math has been driven by state or national standards.

    Full story
  • Site-Based Math Professional Development: Where to Begin?

    Posted By John Woodward, Ph.D. | May 24, 2017
    iStock-508210504-blog

    Rita Bean’s and Diane DeFord’s article about instructional coaching offers a highly sensible list of dos and don’ts for working with teachers in their classrooms. Crafted from what is clearly a great depth of experience, Bean and DeFord apprise the reader immediately of the highly political nature of coaching. For example, if coaches communicate explicitly or implicitly that they are there to “fix them and their classrooms,” then the chances of a successful working relationship plummet dramatically.

    Full story
  • How Should Principals Take the Lead on Math Professional Development?

    Posted By John Woodward, Ph.D. | May 10, 2017
    iStock-179113206-blog

    Professional development researchers have told us for a long time principals need to be instructional leaders. That prescription entails visible support for new instructional strategies as well as the need for persistence, follow-up, and even the use of data to sustain or refine new practices. Unquestionably, all of this is important. But where does a principal start today in a world awash with new teachers, many of whom struggle to teach to state or national standards? As co-authors of the K-8 mathematics professional development program, NUMBERS, Michele Douglass, Mary Stroh and I have done a lot of thinking about how principals can orchestrate successful change.

    Full story
  • The Problem with Word Problems Might Be the Way They Are Taught

    Posted By John Woodward, Ph.D. | Mar 22, 2017
    JWProblem2-blog

    Traditional algebra word problems have a bad rap and for good reason. Students are hardly enamored with content of the typical word problem, and its relevance to the real world is questionable at best. Amdahl and Loats (1995) captured this sentiment in their amusing tour of beginning algebra: “Folks who write math books live very different lives from you and me. They seem to spend a lot of time on trains, for example, which leave cities you and I rarely visit, in hopes of meeting their buddies on trains at destinations in-between….They launch rockets across rivers, build bridges, and agonize over how tall various trees are. After a couple of years of math classes, you’ll be uncomfortable hiking through the woods without your calculator handy.” (p. 104)

    Full story
  • The Future of Work: Robots, Artificial Intelligence, and What They Mean for Math Education Today

    Posted By John Woodward, Ph.D. | Mar 01, 2017
    iStock-612375398-blog

    Much has been said about the state of American manufacturing in the last year, and a series of recent reports present an intricate picture that takes us beyond some of the confusion and common misconceptions. Except for the understandable decline in manufacturing during the recent recession, manufacturing productivity since 2000 has been surprisingly robust. Ball State University’s report even suggests that growth in manufacturing going forward is steady and on an upward path. With all of the news of outsourcing in areas such as textiles, furniture, and apparel, how can this be?

    Full story
  • Show Me What You Know—The Power of the Graphic Organizer

    Posted By Bea Moore Luchin | Nov 02, 2016

    Graphic organizers are powerful tools that support conceptual development, language development, and skills acquisition when used appropriately. In the mathematics classroom, they can serve as powerful vehicles that facilitate discussion, provide formative assessment data, and allow students to demonstrate their thinking in creative ways.

    In order to achieve success with the use of graphic organizers, the teacher has to select the appropriate organizer, understand it, plan for how the organizer will be used to promote thinking, and develop appropriate questions and tasks.

    Full story
  • Exploring Formative Assessment in the Mathematics Classroom

    Posted By Bea Moore Luchin | Sep 14, 2016
    formative-assessment-blog

    Formative assessment is an important tool to take full advantage of, especially in this transitional era of implementing more rigorous standards.

    When correctly incorporated into classroom practice, the formative assessment process provides information needed to adjust teaching and learning while they are happening. The process serves as practice for the student and a check for understanding during the learning process. The formative assessment process guides teachers in making decisions about future instruction. 

    Full story
  • What did you learn today?

    Posted By Bea Moore Luchin | Apr 20, 2016
    learn1

    As we implement higher standards across the country, it has become increasingly important that we identify and use a variety of strategies to assess student learning so that the appropriate interventions may be provided. 

    One strategy is to encourage students to reflect on their reasoning and justify their work.  The idea of justifying your work in mathematics has to go beyond the use of inverse operations to “prove” that the calculation was correct. This way of checking is not justification since it does not address the student’s use of metacognition—the thinking about thinking—that goes beyond the use of an algorithm and takes you into their decision-making processes.

    Full story
  • How to Unlock the Language of Math for Your Students

    Posted By Bea Moore Luchin | Mar 30, 2016
    rsz_signs

    I’d like to take you on another journey along the road of the language of mathematics with a stop at the intersection of “math concepts and symbolic notations.”

    Sometimes the mathematics conversation is just as confusing to students as this collection of signs is to a driver in an unfamiliar situation. There appears to be a variety of symbols used to identify the different types of roads in the area, just as we have a variety of concepts, operations, and relations that are conveyed through symbolic notations. 

    To further complicate the issue, in math we sometimes have a variety of symbols used to convey the same concept or idea. Imagine the student’s dismay when he or she is not familiar with a new symbolic notation that is being used but is familiar (and perhaps proficient) with a different notation. This can certainly be a blow to some students’ math confidence.

    Full story
  • Put Thoughtful Research into Practice for Struggling Math Learners

    Posted By John Woodward, Ph.D. | Mar 23, 2016
    iStock_000021749706-300px

    In my previous blog, I argued for a dual topic approach to curriculum design. The framework outlined in that blog is based on a variety of research. Some of this research is drawn from psychology and studies of human learning. These involve the development of automaticity and controlling cognitive load. Other design elements are associated with what we have learned over the years from international research, particularly the way successful countries focus on fewer topics with greater depth in their math curricula. Still other research is a synthesis of what we believe are best instructional practices in remedial and special education.

    Full story