I love it when my students struggle! OK – before you think I am a cold-hearted teacher I’m not talking about that kind of struggle. I’m talking about productive struggle as part of the learning process. And this came to light when I started my fraction division unit. But before we jump into the math, let’s talk a little about struggle.
Productive struggle is the part of the learning process where the learning really happens and takes hold. It’s when answers can’t be quickly or readily found and we have to grapple with the concepts we know to grow and learn more. Productive struggle is good for us, it’s good for our students.
My Introduction to Struggle
Back in 2014, I set out on a mission to make math more than just equations and solutions. Inspired by Wendy Ward Hoffer’s ‘Minds on Mathematics,’ I was introduced to the concept of struggle. I was intrigued by the book and wanted to know more. I did some digging that summer and learned so much that would not only make me a better teacher but would make my students better learners.
In an article titled Why Struggle is Essential for the Brain – and Our Lives, Jo Boaler states that “Neuroscientists have found that mistakes are helpful for brain growth and connectivity and if we are not struggling, we are not learning. Not only is struggle good for our brains but people who know about the value of struggle improve their learning potential.” She goes on to say that “once we stop the charade of knowing everything, and embrace knowing less, with a willingness to sit with uncertainty, unexpected things happen.”
After being introduced to the concept of struggle as part of the learning process, I knew I wanted this for my students. In an online article about productive struggle found on the Houghton Mifflin Harcourt website, productive struggle is defined as this: “When students expend effort to grapple with perplexing problems or make sense of challenging ideas, they engage in a process of productive struggle—effortful practice that goes beyond passive reading, listening, or watching—that builds useful, lasting understanding and skill.”
Incorporating Struggle in My Classroom
After being inspired by Wendy’s book I knew that I wanted to incorporate the concept of “struggle” in my classroom. As we approached a new unit on dividing fractions I was ready to give it a try.
Allowing Students to Struggle
As the fraction division unit approached, I decided to take a different approach. Prepared with a fascinating problem, I threw my students into the world of fraction division without giving them the usual step-by-step guide. The challenge was to solve the following:
The decision to let them figure it out without the usual introduction and lesson of “how to” complete these problems led to some initial resistance, but it was a necessary step.
What happened next was just as you’d expect. The classroom echoed with the groans of students longing for the safety net of a direct solution. I mean, pure begging was taking place to have the answers given straight to them. But I’m proud to say I gave out some tough love, and I stood my ground. Instead of step-by-step assistance, I encouraged them to get creative by drawing, measuring, or doing whatever it took to try to solve the problem.
Once they realized that I wasn’t going to give them what they wanted, they started to dig into the problem. Some students dove into intricate drawings, visualizing the problem spatially. Others grabbed a yardstick, measuring every 5 3/4 inches. Then, there was the group using calculators as markers, which was an out-of-the-box approach that somehow worked for them.
The Outcome
As the struggle continued, something amazing happened. Some students triumphed in finding solutions. They used different methods and some took multiple attempts, but they did it. They used the knowledge they had, applied it to something new, and did not give up. And let me tell you, the pride and self-confidence beamed across their faces that day.
I didn’t want to stop the flow, so when students conquered the first problem, I gave them a second problem.
I let them use the entire class period this first day to work on one or both of these problems.
The dynamics in each class were different, but one thing remained the same. Every student dove into math at a new level that day. They pushed themselves to move through the fear and into the productive struggle of learning. The outcome was memorable and impactful. Every class had its unique story from different approaches and different paces. The struggle, far from being a roadblock, turned out to be the key to unlocking their thinking abilities.
Diving Deeper into Fraction Division
Once we completed the introduction problems my students were hooked. They were ready to dive into everything related to dividing fractions. Honestly, it was the best “hook” for a unit I have ever had.
Introducing the Steps with a Math Wheel
From there were dove even deeper into the concepts of dividing with fractions. We started working on the steps using the Dividing Fractions Math Doodle Wheel. A note-taking format that they were familiar with that chunked the steps into digestible pieces while adding a burst of color to help with memory.
Something amazing happened as we worked our way around the math wheel. At each step, students were able to give examples of how they did that step when they were trying to solve the introduction problems. They might not have known the official name or term to describe what they were doing but through the math wheel, they were able to make that connection.
After we finished our notes, I gave my students time to add some color to the math wheel while also working on the practice problems around the wheel. It is the perfect way to reinforce the notes and steps. If you’d like to learn more about using math wheels, I go deeper into the benefits of math doodle wheels in my blog post Your New Favorite Note-Taking Strategy.
Diving Deeper in the Unit
The math doodle wheel was just the starting point for teaching fraction division! We worked through the nine lessons in our unit on fraction division. I utilized the Dividing Fractions Math Curriculum Unit as the guide. This unit focuses on all the skills my students need to become pros at dividing with fractions. This unit covers least common multiples, greatest common factors, and how to divide fractions by whole numbers, whole numbers by fractions, and fractions/mixed numbers by fractions.
Inside the resource, there are PowerPoint slideshows to go along with each lesson. These are editable so you can make changes if needed to fit the needs of your classroom. The unit provides clear visuals to show the fractions in model form before moving on to the computation.
I have my students follow along on their interactive note pages which allows them to apply the concept immediately. Each note page includes this section called “You Try It” where they practice problems to reinforce what was learned.
Throughout the unit, we went back to those initial challenge problems. They gave us a common experience to refer back to. Students had a better understanding of the challenges that might be involved but were no longer afraid to try something new.
Try it Out for Free
Are you excited about trying out the concept of productive struggle in the classroom? Maybe you need some extra practice with dividing fractions? I can help you with both! Inside the Free Math Resources Center, I have a variety of resources you can use in your classroom. One of those is my Dividing Fractions Problem of the Week. But there’s so much more! Inside you’ll find a wealth of resources that you can use in your class! All you need to do is sign up with your email address. I’ll send you the password, and voila! You’ll have access to all the free resources and trainings.
Additional Fraction Division Resources
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