Reflecting on Mathematics Instruction

Now that we’ve completed year 2 of using the Go Math textbook series, we should have a sound familiarity with the program. We’ve had plenty of time to explore the various technology-based and print-based features, and hopefully had the chance to make some notes along the way as to what worked best with what lesson (i.e., Interactive Student Edition, Math on the Spot Videos, using manipulatives, etc.). I recently had the privilege to attend a presentation by Dr. Matt Larson, President of the National Council of Teachers of Mathematics (NCTM), as well as one of the coauthors of the Go Math series. Dr. Larson had brought up some really thought-provoking points in the area of K-12 mathematics instruction.

As quickly became apparent in year one, Go Math presents many different strategies to solving standard mathematics problems revolving around the four basic operations. Questions immediately arise as to how necessary it is to teach all of those strategies, and/or do our students have to master each one. According to Dr. Larson, we must not confuse mathematical standards with research-informed instructional strategies. Being able to multiply is the standard; using an area model as an alternate to the standard algorithm is an instructional strategy. Although it is not necessary for every student to master every presented strategy, it is imperative to expose students to all strategies in an effort to provide multiple methods to achieve an answer and build deeper conceptual understanding. “We should emphasize visual representations or models as a means to build understanding; not as “alternate, different, or new algorithms" (Larson, 2017). We need to go further than simply guiding students through a series of “steps.”

Refer to the comparison below. The left is a standard multiplication algorithm; the right is an area model representing the multiplication problem. Imagine this is the work of two students, and they are explaining their work (whether verbally or in writing); which explanation most likely would demonstrate a truer understanding of multiplication?

As you reflect on this year and think forward to next, think about how we can move past the worksheet consisting of 20 computational problems, and design more authentic tasks to challenge student thinking, increase engagement, develop deep conceptual understanding, and squash the common belief that mathematics is only for students who can quickly recall basic facts from memory.

Informational Text Resources

Many of us have been using ReadWorks and Newsela as online resources for current informational text articles. There's another resource - Tween Tribune - that is very similar the other two. The website is funded by the Smithsonian Institute and 100% free. Articles are leveled by Lexile levels, as well as self-scoring quizzes also customized by Lexile. Tween Tribune is also available en Espanol.

Notes from Mr. Scotto

As we prepare for year-end evaluations, I encourage to reflect on your teaching (4A).

Have you taken the time to: