By Dane Ehlert, posted October 26,
2015 –
In this post, we’ll shift our focus to course content.
Specifically, 3 Act Math can help promote growth mindset. For more on what 3
Act Math is and how to use it, click here.
LOW
FLOOR, HIGH CEILING
One big reason why these tasks are helpful is the fact that there
is a low entry point. Jo Boaler talks about this. It’s crucial for
allowing students at every level to be able to enter a problem. Here’s the set up (video).
After playing the video, ask, “Which way will be faster?” and
students simply write down a guess. This is great because all students, no
matter what their confidence level, can take a guess. This is the low floor
that Boaler is looking for. I’ve seen some of the least confident students get
very involved with these types of problems because of the low entry point and the
high intrigue level.
MULTIPLE METHODS OF PROBLEM SOLVING
Another crucial component is the fact that there are multiple
routes to a reasonable solution. This is important because students begin to
develop growth mindset when they can see different avenues to success.
Act 2 is where multiple methods occur in the lesson. Students are given information
after some discussion that has taken place about what might be needed to solve
the problem. For example, we need to know the speed of the person on the
stairs (video).
After the necessary information is received, the students work in
groups to solve the problem. Almost always, different methods are used
throughout the room. Here are some possibilities for this lesson.
As you can see, a variety of problem-solving tools can be used.
This is awesome because it allows for good discussion, formative assessment,
and personal dialogue between teachers and students. All of this can help
encourage growth mindset.
WHEN IT’S ALL WRONG (OR RIGHT?)
After students work on the problem and present their work, it’s
time to reveal the actual
result for Act 3.
The reveal not only is exciting but also allows for a
great opportunity to discuss the imperfection of mathematical models in real
life and encourages learning from mistakes. Many times, the actual result is
different from students’ calculations even if they didn’t make computation errors.
For example, many students will not get the exact time for the stairs because
of other factors at play. Did the speed change during the descent? What about
the time to go around the turns? This problem provides a chance to analyze the
influences in real life that don’t always allow for a perfect “right” answer.
In addition, students can be encouraged to share possible mistakes they made
and how they could correct them. This is important because they need to
continually be shown that mistakes are valued in our classrooms.
A STUDENT’S STORY
My favorite reason for using these tasks is the students
themselves. I have to mention one individual whose story inspired me to never
take these problems out of the curriculum.
I had a junior in my freshman algebra class last year because he had
failed the course twice. On the last day of school, the student came to see me.
“Mr. E, I just want to say thank you. I’ve always
struggled with math, but this year I finally got it.”
What struck me the most was the student discussing his previous
struggles with math. This was surprising because he was brilliant
mathematically. Every time we did an open-ended problem in class, I was blown
away by his thought process, visuals, and reasoning. It was incredible to
witness, and the other students were in awe, as well. We could all see that
this student had an amazing ability to reason mathematically.
I told him he was brilliant, and it showed in his work. His
response is why I will always use these tasks.
“Well, yeah, I was good at those problems because
they’re real life. They just make sense.”
What he was saying is that he was able to have the space to
demonstrate his thinking in a way that he’s never had before. He, along with so
many other students, just needed a different outlet to express his thinking.
Whenever it came to traditional work and assessment, this student was near the
class average. It wasn’t always easy to see his thinking come out. When we
opened up the tasks, his ability shone in a way that was easy for everyone to
see. I want these types of students in our classrooms to have an opportunity to
show their math potential in this way. I know that there are countless students
who have “always struggled with math” but just need the opportunity to show that
they really are “math people.”
Check out the following list for great 3 Act/open-ended lessons.
You can also see problems in action with student work and
outstanding insight at Clayton Edwards's blog.
Dane Ehlert, dane@whenmathhappens.com, is a secondary math teacher in Texas.
He tweets at @DaneEhlert and blogs at whenmathhappens.com.