Embracing Difficulties

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I just finished up chapter four in Making it Stick.  Parts of the chapter involve the topic of challenge and how it impacts memory.  Looking back at my K-12 experience, what I remember is often associated to how I felt during the experience.  The best experiences for me required an extensive amount of effort and perseverance that eventually led to a productive outcome.  Some of the more challenging experiences were also memorable.  I learned from both those positive and negative outcomes. It’s interesting that the experiences that I remember were either positive or negative.  I don’t have many so-so memories during school – they don’t stand out.

Chapter four emphasizes how difficulty can help students retain information for longer periods of time.  I’m going to interchange the terms difficulty and challenge for this post. Challenge triggers retrieval processes and encourages students to make connections to find a solution.  This is often termed “desirable difficulties” by the Bjorks.  Chapter four discusses the importance of generative learning.  Basically, generative learning places students in a situation where they solve problems without being explicit taught how to solve them.  Students are required to make connections and generate answers without repeating a process that was clearly taught by a teacher.  The responsibility is on the students to generate a solution.  When I first read this I wasn’t exactly sure about this idea.  I work with mostly elementary math students and some want to know exactly what and how to complete a task.  If they’re unsure students might say “you never taught us ______.” It takes a shift in mindset to take a risk and generate solutions based on prior knowledge.  In the end students might be absolutely right or wrong, but they took a risk and came up with a solution.  Praising the effort involved and reflecting on the journey is important.   When coming across open-ended tasks students need to understand that learning is a journey and challenge is part of that process.

Next year I’m planning on incorporating more opportunities for students to participate in generative learning.  I believe it first starts with creating an environment where students aren’t “spoon-fed the solution” and they have to think critically about the situation.  I find that students are more likely to check their answer for reasonableness with tasks like this.  That environment should encourage students to speak up, offer their ideas, use trial-and-error, make connections, and become aware that learning is a journey.  This culture and mindset takes time to build, but the dividends it pays throughout the year benefits all involved.

I’m staring to to take a look at next years plans. Currently there’s one task for each unit that’s designed for generative learning.  Sometimes I have students work on these tasks in groups, while other times it’s independent work.  These types of tasks are often open-ended and may have multiple solutions.  They also involve a hefty time commitment and can reach multiple math standards within one tasks.  Over the summer I’m planning on finding additional ideas using MARS and Illustrative Mathematics resources.

Next steps: At the end of each task I’d like to have a class conversation about the task.  Have a regular reflection component can bring additional connections.  I’m planning on continuing to have students journal about these experiences throughout the year.  I’m also hoping that these types of tasks translate into students being more willing to take additional ownership for creating and monitoring their math identities.

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2 thoughts on “Embracing Difficulties

  1. “They also involve a hefty time commitment and can reach multiple math standards.” You bet! Soon I’ll be writing about my summer school math experience with James Tanton’s Pinwheel Area problem. This is a challenging task along the lines of finding the area of the shaded region. It took 45 minutes to discuss and solve. The students had individual think time before working in a group, and not one had a strategy to get started. I’ll link my post here when I write it, but briefly, it required continuous teacher intervention. Constant questioning beginning with, “What shapes do you see?” In the end students solved the task with teacher questioning, but it was so worthwhile. In this case I think perseverance is directly related to a student’s mathematical toolbox and his/her ability to transfer knowledge.

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    1. I watched the Pinwheel video and that fits the bill for a task that’s open-ended and requires connecting multiple math concepts. It takes a learning curve and a certain amount of perseverance to tackle problems like this – not to mention intentional questioning techniques from the teacher. It’s not something that all students are familiar with. I like the idea of having students work individually first and then head to groups to discuss possible next steps. I might even give them some type of anchor chart paper or another medium to show their thinking throughout the process. I’m looking forward to hearing about the experience through your post. I’m filing this task away and thinking about using it with my classes at some point next year.

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