Uncovering the Perception of Difficulty: Personalized Learning in Pre-Calculus – Part 1

David Buller

David Buller has been teaching high school mathematics and computer science in Madison, CT for 18 years. Prior to teaching, David spent 15 years working in the information technology arena, where he utilized many of the skills and strategies he now teaches. David and his wife are the proud parents of three grown children, and currently reside in CT with their black lab, “Solo.”

Lead-in by Allison Zmuda

David Buller immediately caught my attention — he candidly and openly reflected with me on whether personalized learning would be a good fit for him or his math students. We talked about some of the struggles he was having with his pre-calculus students and started imagining time-effective ways to have students provide him a window into how they were approaching problems, feeling about the work, and degree of self-direction/self-advocacy when they were struggling.

At the end of the first hour, we began to create a plan to test out the waters of revealing their thinking to David. There were a few incredible moments along this early journey:

  • David is all in. While it is not brand new practice for him to ask these questions, he never had an opportunity to do this for all of his students using conversational writing.
  • The compassion and insight of David’s comments on each student’s reflection is incredibly powerful. His students see first-hand that he cares about their success and is genuinely interested in making it possible for all students.
  • David continues to iterate by testing out other possible questions and actions to personalize learning based on their feedback.
  • This is a strong example of how self-discovery can be integrated into the classroom through reflective questions that help the students reveal their approach to problem solving and how that impacts their learning.

Guest post by David Buller: Part 1 of 3

For the past 17 years, I’ve tended to equate improving my teaching practice with increasing my content knowledge and finding better, more innovative ways of sharing that content with my students. I’ve embraced graphing software, smartboards, polling software, homemade video lessons, robots – you name it – and, frankly, I believe much of it has had a positive impact on student learning.

But this past summer, I was presented with an opportunity to try something very different; something that promised to shift the focus from my teaching habits to my students’ learning habits.

Where to Begin?

Allison had spent the prior year helping a small group of my colleagues bring personalized learning into their classrooms and I was offered the chance to be part of the “innovation lab.” To be completely honest, my initial reaction was to pursue the low-effort path of featuring a class that already had a high degree of personalized learning: a project-based computer science class.

It was only after speaking at length with Allison that I began to get excited about the potential of introducing personalized learning into a traditional upper-level math class.

During that conversation with Allison, she suggested that we start with something relatively quick and easy for my students to do that would start them down the path of reflecting on their habits, behaviors, and perceptions associated with learning math.

A few areas I was interested in better understanding and addressing were:

  1. an increase in the level of “irrational confidence”
  2. students’ perception of the impact of effort on performance
  3. students’ attribution of blame or credit when they struggle compared to when they succeed.

The Perception of Difficulty

As I started to play out possibilities with Allison, I became intrigued by the perception of difficulty and how that might impact the success of individual performance. It was also important to me that we didn’t turn the class into a writing lab. I know that some people like math largely because it doesn’t require an extensive amount of writing.

Allison proposed an idea that I immediately liked for its simplicity, immediate impact, and potential. The next day, just prior to displaying the night’s homework, I gave them the following written instructions:

From now on:

  1. after you complete each homework problem, please label it as easy or hard.
  2. record the start and end time of when you work on your homework
  3. record whether or not you answered the problem correctly

This will not be shared with the class, so please be honest.

The next day, I added,

Jot down any observations regarding:

  1. the impact of your perception on focus on accuracy/precision for the remaining problems
  2. the impact of the time of day on your ability to engage in homework

And with those words, our journey into personalized learning had begun.

My next blog post outlines how students responded to this challenge.

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