By Ian Whitacre and
Donna Wessenberg, posted December 19, 2016 —
In our
previous
post, we detailed our thoughts on the differences between strategies and
algorithms and what those differences mean for instruction. In this post, we’ll
visit with Ms. Donna Wesenberg, who teaches kindergarten in Central
Florida. Her class is a place where students are encouraged to be creative, to
experiment, and to explain their thinking when solving story problems. They
find their answers in many different ways. It’s a place where students are
encouraged and expected to generate their own strategies for solving problems.
Wesenberg introduces problem
solving in a way that students feel comfortable with being inventive and different.
“I like to explain to my students that math is like going home. Do we all get
into our homes the same way when we go home? No! Some people go through the
front door, some through the garage, and others through a sliding door, back
door, side door, bathroom door to the pool, or even a window when the doors are
locked. The goal is to get into the house, and we all achieve that goal.
Solving math problems is no different.” This approach helps students to feel
comfortable with their inventive strategies being different than those of their
neighbors. We celebrate their creative thinking.
Wesenberg has always been
interested in problem solving:
I have always liked the problems
that challenged students to think. When math was about doing a worksheet, my
class was not engaged. Teaching math was hit and miss. The curriculum felt dry and
not in touch with my class culture. But every time students were given the
opportunity to be creative or the problem was about something that interested
them, I found my class engaged.
Wesenberg finds that when
students draw pictures and come up with their own ways of solving problems, they
engage in more complex thinking. She took her problem-solving instruction to
the next level after she participated in professional development in cognitively
guided instruction (CGI) along with colleagues at her school. Their grade-level
team meets weekly to discuss story problems and students’ strategies. They note
the progress that their students are making, and they anticipate how students’
thinking can develop. Wesenberg relates her students’ problem solving to
algebraic thinking:
Students naturally break numbers
down into smaller numbers that make sense to them. By giving students the
creative license, they are naturally making connections and are able to explain
their thinking.
Even in kindergarten, Wesenberg has
her students solving equal-groups story problems (such as problems about three bags
of candy with the same number of candies in each bag). Wesenberg related a
realization that she had about teaching through problem solving:
It is hard at first to sit back
and not butt in. I started to tell a student she was doing a problem wrong,
when I decided to change my mindset and ask her to explain what she was doing.
I was amazed, because what I saw and what she was doing were too different
things. Once she explained her thinking and her picture, I found out she had
the correct answer within what she did. It did not matter if it made sense to
me, what mattered was it made sense to her.
Wesenberg’s students continue to
surprise her, as they grow more knowledgeable and excited about math. She finds
that shy students are coming out of their shells and explaining their thinking.
She also finds that her students are eager for more mathematical challenges.
Wesenberg’s class is just one
example, and teaching through problem solving is not limited to the primary
grades. Some teachers at each grade level are making these kinds of changes in
their classrooms; others have been teaching this way for many years.
The standards refer to students
solving problems in a variety of ways. For example, K.OA.2 states, “Solve
addition and subtraction word problems, and add and subtract within 10, e.g.,
by using objects or drawings to represent the problem.” Teachers like Wesenberg
understand this statement as a goal and have confidence in their students’
abilities to achieve that goal. She does not interpret it as a mandate that she
train her students in particular procedures for using objects or drawings to
represent problems, because she knows that students’ sense making comes in the
choices that they make. When students
are given step-by-step procedures, the message they receive is that sense
making is not their responsibility. Someone else has already figured out the
right way to do this, and they just need to follow along and remember how.
Problem solving requires figuring out what to do and how to do it without being
given step-by-step instructions.
Ian Whitacre is a faculty member
in the School of Teacher Education at Florida State University in Tallahassee.
He studies how children think about math, and he collaborates with teachers to
improve mathematics teaching and learning. Donna Wessenberg is a mother of
three and a kindergarten teacher at English Estates Elementary School in Fern
Park, Florida. She has been a teacher for eleven years, two of those years
teaching fifth grade and eight years teaching kindergarten. She has a Masters
of Elementary Education from the University of Phoenix and a Bachelors in Fine
Arts from the University of South Florida.