exploring the kinds of questions that
math teachers ask during instruction.
At the same time, I was researching the
various phases of student development
in each strand of mathematics.
1 The
two universes collided. I started to see
the potential for using questioning as
a way to differentiate instruction in a
classroom with groups of students at
different levels.
What emerged was the delineation
of two core techniques for differentiating instruction in mathematics in a
meaningful but manageable way—using
open questions and parallel tasks. Each
technique enables students to enter into
a mathematical conversation from different access points—one by using a
wide net and the other by being deliberately, but thoughtfully, focused.
Students may initially be uncomfortable
Open Questions
An open question is just what it sounds
like—a single question that is broad
enough to meet the needs of a wide
range of students while still engaging
each one in meaningful mathematics.
Consider, for example, this question:
“If someone asked you to name two
numbers that are easy to multiply,
which numbers would you choose and
why?” As long as the word multiply is
familiar, any student can contribute.
Let’s look at some student responses:
Student 1: I would choose 2 and 5 because
I know that 2 x 5 = 10.
with ambiguity in a subject that has,
until now, seemed so clear-cut.
Student 3: I would choose 4 x 9 because
you could just double 2 x 9 to get 18 and
then double that. Eighteen doubled is
two 10s and two 8s, so that’s 20 and 16,
which is 36.
Student 4: I would choose 4 x 25 because
I know 4 quarters make a dollar, and
that’s 100.
Student 2: I would choose 45 x 100
because 45 x 100 means 45 hundreds.
That means you write 45 in the hundreds
place in a place value chart, so it’s actually
4,500.
Student 5: I would choose 1 x 34,782
because if you multiply by 1, you don’t
have to do anything; it’s just the other
number.
Thousands
Thousands
Hundreds Tens Ones
45
Á
Hundreds Tens Ones
5 00
That single question about multiplication ends up reinforcing a wide
range of mathematics concepts: place
value; working with money; and several
properties of multiplication, including
multiplying by 1 and the notion that
multiplying by 4 is the same as doubling twice.
Open questions also provide choice,
one of the elements implicit in differen-
tiating instruction. Students can answer
in a way that is suitable for their level.
And everyone benefits from different
perspectives when they hear other stu-
dents respond. The open question is
both accessible to and enriching for all.
