The sample of student work I obtained this week was a
worksheet the students completed for homework as an extension from the previous
day’s lesson on square numbers. I took a picture of one of the lower level math
students’ completed worksheet to analyze. The worksheet had 3 sections. The
second section built off the first section and the final section was “practice”
of math procedures multi-digit addition, subtraction, and multiplication. The
first section required the student to solve number sentences to find square
number equivalent. For example, one question was 4*4= ___ and MJ filled in the
blank with 16, which is the correct answer. Another format for the questions in
this section was 52= ___. MJ correctly completed this section of the
worksheet. The second section asked students to provide the number model for
two rectangular arrays then determine which one of the arrays represents a
square number and explaining their choice. MJ struggled with this section of
the worksheet. She gave the correct number model for both arrays, but struggled
to determine which array represented a square number and why the array
represented a square number. The third section of “practice” was 4 questions of
multi-digit basic math; 2-digit by 2-digit multiplication, 4-digit plus 4-digit
addition, and 3-digit minus 3-digit and 4-digit minus 4-digit subtraction. MJ
was very successful with this section and showed all of her work for this
section.
MJ’s
answers on this worksheet reveals that she has an understanding of how to solve
for square numbers, but does not fully understand what it actually means for a
number to be square. This gap in her understanding is evidenced by the fact
that she identified the wrong number as a square number and her explanation of
why the array represented a square number used addition instead of
multiplication to prove the number was square.
To
advance MJ’s mathematical understanding I would ask her to verbally explain to
me what it means for a number to be square because she may simply be struggling
to write down clearly her thought process. If she is unable to clearly explain
this concept, which I suspect she will struggle with, I would then have her work
through a series of equations to determine the pattern and connection between
squaring a number and a square number (ex. 42 and 16.)
I like the way the two problems / tasks you describe are scaffolded in a way that allows for insight into the students' understanding. Obviously, 5^2 = 25 is good, but may not reveal all that the student really understands or thinks about square numbers.
ReplyDeleteTalking to the student is a good way to obtain more understanding, but you might also think of a task that allows her to continue to explore the array idea. What about having students complete the arrays and then compare their responses and defend their reasoning? What about asking students to create a representation for square numbers and then to compare those representations?