By Michael Wiernicki, posted November 23, 2015 –
I recently had the opportunity to sit with a sixth-grade
teacher who had some deep concerns about some of her students who were
struggling with their basic facts, mainly multiplication. Her worries were
written all over her face: “How can I get these students to know their facts
and get them through the sixth-grade curriculum by May?”
Her worries were valid, and she is certainly not alone. I’ve
had similar conversations with teachers in high school as well as elementary
school. To teach mathematics, the problems we give to students must be
memorable. Although this may not be easy (it’s much easier to hand students a
deck of flash cards or give them a 5-minute speed test), it is worth the
effort. If we want to fill mathematical gaps, we need to help students develop understanding.
With understanding, connections are made, and the mathematics becomes
memorable.
To be clear, there’s nothing wrong with practice. Even drill
can have a place. But what are we drilling? If it’s memory, forget it (no pun
intended). Memorization will fail unless connections are made through building understanding.
If we’re drilling strategy, then we’re on to something. But before we get to
drill, we’ve got to have some investigation and some purposeful, memorable
practice.
Through discussion, we came up with a plan to help these
students develop their understanding of multiplication, make the facts
memorable, and not lose sight of the sixth-grade content (and even preview some
seventh-, eighth-, and ninth-grade content . . . shhh).
We began by showing students this picture:
We asked the students what they noticed. Before sharing their
thoughts with the class, we asked them to first talk with some group members
about their ideas. When it was time to share, all students were engaged. A
sample of what they noticed will appear in the comments section one week after
this post. In the meantime, please share
in the comments. What do you notice?
The students noticed more and more as the discussion
progressed. Each time students shared, we had them explain what they were
noticing so that everyone could understand. We thought it was very important
for these students to realize that they were capable of not only noticing
mathematics but also explaining the mathematics they saw. The teacher was
impressed as she heard these often-struggling math students use mathematical
language, communicate with a high degree of precision, notice patterns, and
explain number relationships.
This sharing took a lot more time than we planned, but it
was worth it for the engagement and mathematical discussion we got in return.
As we wrapped up the discussion, some students asked
questions; this was perfect because we were going to ask them what they were
wondering about. There were not as many “I wondered about” as “I noticed,” but students
were still a bit curious about the picture itself. I will discuss these student
wonderings in the comments next week. In
the meantime, please share in the comments. What do you wonder?
The focus of this first lesson was to get students talking
and get them to realize that they really are capable of making sense of
mathematics, using mathematical descriptions of the arrays in the picture (not
just color), and asking mathematical questions. We did not have time to allow
students to answer any of the questions they had, but we did continue it the
next day. The next post will detail that.
Mike Wiernicki, mjwiernicki@gmail.com,
is a math specialist in Georgia. He tweets at @mikewiernicki and blogs
about teaching mathematics at http://mikewiernicki.com.