How do we calculate? How do we learn math in a different way than we learn reading? Why are some people “readers” and some people “math” people? Or is that even true? These are the questions which lead me to explore chapter 19 of The Brain and Learning. (Jossey/Bass, 2008)
In reading Math Skills by James P. Byrnes (ch19, Jossey Bass), I learned that the neuroscience behind math achievement is far behind the psychological research in that area. The author suggests that because of this we should base our instructional choices on the psychological perspective until more neuroscience studies have been conducted. (p. 324) Byrnes goes on to make several suggestions for instructional choices. A few especially stood out to me and warrant mention.
The first is that “instruction at all levels should be consistent with the “Math 2000″ recommendations of the National Council of Teachers of Mathematics (1998).” (p. 324) I was curious if there was an updated recommendation by the NCTM and in reviewing their website I was correct in my assumption that they are now recommending the Common Core State Standards in math. In a comparison paper by Achieve.org, they outline the similarities of the CCSS and the NCTM Focal Points. Their conclusion was this –
Overall, the CCSS are well aligned to the Focal Points. Policymakers can be assured that in adopting the CCSS, they will be setting learning expectations for students that are similar to those set by the Focal Points. There are, however, a number of important differences in the placement and priority of topics as detailed in this document. These differences will require careful consideration in building curriculum, planning instruction, providing professional development and developing assessments during the implementation of the CCSS in states. The CCSS, like the Focal Points, place a priority on focus and coherence, seeking to set forth rigorous learning outcomes that will prepare students for later success. (www.achieve.org/files/CCSSandFocalPoints.pdf)
The next point Byrne makes is that “one of the best ways to instill knowledge in students is to have them solve structurally similar problems and consider how these problems are similar (Gick & Holyoak, 1983: Sweller & Cooper, 1985)(p. 324) In addition he states, “exercises should be designed to promote an accurate meta-cognitive understanding of when an answer is sensible and correct, and when it is not.” (p. 324) This is key in my instruction with my students and something I am constantly encouraging them to ask themselves. We practice ways to approach problems, underline the key numbers and words in word problems, and ask ourselves “what am I trying to solve for in this problem?”. After solving, students ask themselves, “does my answer make sense?” and “how can I check my answer?”. They then use strategies such as estimation and/or checking their answer with the opposite operation to be able to be sure they are correct and their answer is reasonable. For my struggling math students this is very difficult. They struggle to determine and explain if their answer is reasonable much in the same way my struggle readers have difficulty accurately answering comprehension questions or finding text evidence to support their answers.
Finally, Byrne concludes that “there is no substitute for extensive practice”. (p. 324) Students need as much practice as possible both in problem solving and to overcome making “a variety of procedural errors”. He sums it up saying, “the best approach involves embedding practice within meaningful, goal-directed activities.” (p. 325) I achieve practice in my classroom in many ways including; early work, problem of the day, morning question, math groups, practice, math games, Reflex, and IXL. We use the idea of coming back to the concept again and again throughout the day so that by the time they sit down with homework at night it is the fourth or fifth time they have seen that type of problem that day. Hopefully, this is working to help the students build a schema on how to solve similar problems consistently.
The Jossey-Bass Reader on the Brain and Learning. San Francisco: Jossey-Bass, 2008. Print.