An unexpected opportunity for reflection...

Recently, while reading an article from the September issue of Teaching Children Mathematics, a journal for elementary math education published by the National Council of Teachers of Mathematics (www.nctm.org), I read something that made such a connection for me that I had to share it.

The article, titled, "Warning Signs!", outlined three teacher moves that the authors identified as moves that tend to precede a teacher taking over a student's thinking:

     Warning Sign #1 - Interrupting the child's strategy
     Warning Sign #2 - Manipulating the tools
     Warning Sign #3 - Asking a series of closed questions

While the entire article was an excellent read, my personal connection was related to warning sign #2, manipulating the tools. In the scenario provided, a teacher took over control of the pencil while working with an individual student. This shifted the focus from the student's strategy to the teacher's strategy.

Students using colored tiles to represent multiplication

As I read this, I immediately thought of a recent math professional development session in which I was modeling a lesson for a group of teachers. As students were working with tools (colored tiles) to represent arrays for multiplication, I would physically move the manipulatives for the students when I noticed confusion. As I read the article, I began wondering if I could have used questioning to get the students to identify their misunderstandings and self-correct.

I also reflected on the brain research tied to this - that students need to be the ones physically manipulating objects. In the book, Brain Matters: Translating Research into Classroom Practice, Pat Wolfe (2001) discusses the three levels of learning: concrete, representational, and abstract. She states, “Many of our strongest neural networks are formed by actual experience” (p. 138). An example of an experience relevant to math instruction is the use of manipulatives.  Manipulatives increase understanding of math concepts and motivate students to learn math.  The research of Eric Jensen (1998) adds that physical movement, such as hands-on activities and the manipulation of objects, promotes student learning.


So what are some alternates to these warning signs? What can we do to move students forward? The article suggests:

• Slow down: Allow the child to finish before intervening.
• Encourage the child to talk about the strategy so far.
• Ask questions to ensure the child understands the problem and how his or her strategy relates to that situation.
• Ask whether trying another tool or another strategy would help.

You can read the entire article HERE with a subscription.