Do the Math—Explore Mathematical Content to Enhance Instruction

  • Do the Math—Explore Mathematical Content to Enhance Instruction

    By Zachary Champagne and Michael Flynn, posted March 14, 2016 –

    As two educators who have attended and led a myriad of online and face-to-face professional development experiences, we have come to realize that we get the most from these experiences, both in the moment and over time, when we are challenged to engage in the mathematics. We understand, and probably both held the position at one time, that this may seem trivial to elementary school mathematics educators. However, it has become clear to us that engaging and exploring the mathematical ideas embedded in our content standards is essential to becoming better consumers of information and practitioners in the classroom.

    We would like to pose one simple idea—Doing the math is important and can lead to a fundamental understanding of important mathematical ideas. First, we would like to explain what we mean when we say, “Do the math.” We will then pose our opinions and share experiences about why we think this is important. In our follow-up blog entry, we will pose two examples of math problems that are worth engaging in to deepen an understanding of two topics in the Common Core State Standards for Mathematics in elementary school.

    When we say we are interested in doing the math, we mean just that. We, as educators, should be “genuinely curious” about the math that we teach. We should try out problems that are connected to the work our students are doing and look for connections to future content, explore a variety of models, and discuss our ways of thinking with our peers in an effort to push our own thinking forward.

    Thinking about the mathematics with which our students will engage is critically important for a variety of reasons:

    • It allows us to reflect on the prerequisite skills and concepts necessary to engage with the math.
    • It lets us consider a variety of pathways into the problem and the different representations.
    • It helps us anticipate pitfalls and places where students may get off track.
    • It deepens our understanding of the content.
    • It presents an opportunity to interact as learners with our colleagues as we genuinely explore the content.

    We have had experiences with this work in different situations. One experience that stands out was an opportunity to consider models and contexts for dividing fractions that gave us a much stronger understanding of what it means and looks like to divide a fraction by a whole number and a whole number by a fraction (5.NF.B.7.a), interacting with the content from the standpoint of a learner through an authentic learning experience. We found this work made us better educators because we had an enhanced sense of how our students experience this work. Gaining a deeper understanding of the content and ability to anticipate potential roadblocks for our students allowed us to develop and plan better learning sequences.

    So, at this point you may be asking yourself, “What does this look like?” Well, first and foremost, it is not necessarily just grabbing a problem from the textbook or curriculum materials that your students will be using. This may be useful in some instances; however, we found that asking authentic questions as learners is a good way to start. Building on the example above, perhaps that learning experience could begin with a such a question as, “What does a visual fraction model look like for dividing a fraction by a whole number?” Or perhaps the question is, “What is a good story context for dividing a fraction by a whole number?” After that comes the difficult part: finding a good problem or model to help with understanding that content. We don’t claim to have all the answers here.

    Your Turn 

    Now it’s your turn. What is your view of doing the math as a means of professional development? If there is a particular math problem that has recently challenged you, tell us about it. In our next post, we will offer two example problems that groups of teachers may wish to explore.

    We want to hear from you! Post your comments below or share your thoughts on Twitter @TCM_at_NCTM using #TCMtalk.


    2016-03 Champagne aupic2016-03 Flynn aupic

    Zachary Champagne is an Assistant in Research at the Florida Center for Research in Science, Technology, Engineering, and Mathematics (FCR-STEM) at Florida State University. Previously he taught fourth and fifth grade mathematics in Jacksonville, Florida, for thirteen years. He is currently interested in learning how young students think about mathematics and how to help them understanding that mathematics makes sense. He tweets at @zakchamp. Michael Flynn is the Director of Mathematics Leadership Programs at Mount Holyoke College in South Hadley, Massachusetts. Previously he taught second grade in Southampton, Massachusetts, for fourteen years. He is currently interested in how primary and elementary school students develop algebraic reasoning and how teachers can support that work. He tweets at @mikeflynn55.

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