No Heads or Tails: Promote Students’ Sense Making and Perseverance
By Tim McCaffrey, posted May 9, 2016 –
Think of the last word problem you gave your students. Did
any of your students—
If so, then keep reading because this blog post is for you
and your students. The following steps are the secret to unlocking students
sense making and perseverance in solving real-word problems:
Step 1: Remove the question and ask
students to write down what they know for sure.
Two large storage tanks, T
and W, contain water. T starts losing water at the same time additional water
starts flowing into W. The graph below shows the amount of water in each tank
over a period of time. Assume that the rates of water loss and water gain continue as shown.
Removing the questions and asking student to write down what
they know for sure allows all students to access the task. It also allows
students to focus on making sense of the information rather than on the question.
Allow students to convince one another of the information
they know for sure. As you travel from group to group, you will learn what
students know and possibly some of their misconceptions as well.
Step 2: Ask students to write down
question(s) that make sense to ask.
Given time to make sense of the information and discussing
it with peers, students can now write down questions that make sense to them. Have
students share their question(s) in groups and possibly vote on the most
interesting one. Record the students’ questions and the question(s) that you
want your students to address. Here is the kicker, “You can choose any question
we came up with as a class. However, you also have to do my question as well.” This
will allow buy-in and give students ownership of the question of their choice
as well as the teacher question.
For our prompt above, here is my question: In three different ways, find when the
amount of water in the two tanks is the same.
Step 3: Collect data as students work on their
This is probably one of the most important steps because these
data will be used to make your next move. In other words, depending on how
students are responding to the task, you may need to—
Step 4: For those students who finish
early, give an extension question.
We all have those students who need an additional push. Having
a few extension questions in your back pocket is valuable to keep all students
engaged and thinking. Here would be my simple extension: Assume that the
rates of water loss and water gain are not constant. How does that change your
This is called a Tailless
word problem because the tail (question) has been cut off. It’s amazing how
much a task can be opened up by making such a simple adjustment. The next time
you pose a word problem to your students, chop off the question and unlock
sense making for your students. Next post, we will discover how Headless problems
reinforce sense making and perseverance.
Tim McCaffrey is the founder of Agree
or Disagree?, writes at http://timsmccaffrey.com/, and tweets at @timsmccaffrey. He currently serves as the mathematics coordinator
for grades 6–12 in Fontana, California. He desires to help coaches and
administrators implement sound mathematical practices that will help students
become deep thinkers.