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Introducing #PSCatCIPLC

My math methods class at the University of Wisconsin-Stout heralds the idea of problem-based learning as a method of instruction for math

Although I like to think of my classroom as collaborative and student-centered, my approach to teaching mathematics could be described as teaching for problem-solving. Skills are introduced first and then students will be asked to apply those skills in more challenging situations.

Monday, Oct 18th, will mark my first attempt at what the book "Elementary and Middle School Mathematics: Teaching Developmentally," ( Van De Walle, Karp, Bay-Williams) would describe as problem-based learning.

Here is the problem adapted from the book, "Natural Learning and Mathematics" by Rex Stoessiger.

My thoughts pre-lesson:

Van de Walle, et al. contend that in order for problem-based learning to be successful individual accountability, shared responsibility and group flexibility must be in place. My students already do a great job collaborating with their peers. It is a small tight-knit class and they enjoy helping each other out. The climate of individual accountability when working with partners has already been established as students know anyone could be called on to explain the thinking of his/her group.

I'm excited to implement problem-based learning.

One key advice for teachers is LET GO. Too often teachers jump in when students are struggling. However, productive struggle is part of learning and the task of thinking should be placed on the student.

I'm excited to implement problem-based learning in my classroom.

Updated November 17th - Lesson Highlights

Post Lesson Reflection

Positives

The lesson exceeded my expectations in a variety of ways.

  • Increased Engagement - After restraining myself from jumping in right away, students quickly got to work on the problem. They asked high-level questions to their partner, like “How many sequences do we have to try to prove this rule?” They made connections to science class, “We just need one solid example of the rule not working to reject the hypothesis.” They tried negative numbers and decimals. I had complete 100% engagement.

  • Reception - Students seemed primed and ready to think algebraically. Although one group was able to visually illustrate a proof of the rule (adding the first term + the last term = the sum of the middle terms, and thus are able to multiply the sum of the first and last by 2), no group had an algebraic proof. But attempting the problem first, struggling with their own thinking, inspired a thirst for knowledge. Everyone was very receptive when I explained how to think of the problem algebraically. I think they were better able to see the purpose and usefulness of algebra.

  • Extension - I was amazed at how far students were able to extend the problem...on their own. I was ready to move onto the next lesson when students started asking, “Is there a rule for 5 consecutive numbers?” They developed a universal rule, “Every time you increase the sequence by one number you have to increase the multiplier by one half.” That quote was an unintended consequence of that lesson. Looking back at my 7th grade self, I do not think I would have ever been able to develop that rule by myself.

Things to improve

  • Discussion - As you can tell from the video, the discussion got a little wild and animated. Possibly the high level of engagement is inversely proportional to standard discussion decorum. Sometimes discussions can be heated, as in real life, but in the classroom we should strive to maintain civility.

  • Expectation of help - This is not a spoon-fed lesson. Students were required to take ownership over the problem-solving process. I did limited thinking for them. This shift caught some students by surprise.

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