• 6–8 Session
In this research-based, practice-oriented presentation we explore the benefits of creating productive struggle with desirable difficulties to help students shake up naïve or loose thinking and to construct “new” knowledge by encouraging transfer of related knowledge to new situations.
Not everyone wants to be a mathematician, but everyone can want to think like one. It can be argued that what really matters most is not how many answers you know, but what you do when you don’t know the answers. We must help people construct their own “new” knowledge, and, through modelling, apply that knowledge in ways different from the situation in which it was learned.
Sometimes learners express a reluctance to look at mathematics in an alternative way to their initial exposure to the topic. Pleas of “You’re going to confuse me!” may actually signal an unrecognized confusion that is ALREADY present.
Using the principle that “No matter what IT is, the chances of finding IT are dramatically increased if you’re looking for IT” we will explore techniques to encourage and reinforce modeling mathematics as a way of thinking and reasoning. The concepts we explore are like the colored glass at the end of a kaleidoscope. They may form a pattern, but if you want something new, different, and beautiful, you’ll have to give them a twist or two. You follow your intuition. You experiment with a variety of approaches. You rearrange things, look at them backwards, and turn them upside down. You ask “what if” questions and look for hidden analogies. You may even break existing rules or create new ones.
There are many benefits to be gained through productive struggle with desirable difficulties that are designed to encourage reasoning and discourse as well as enhancing both long-term retention and transfer. Out of apparent chaos and confusion, the effective use of productive struggle can bring about the emergence of a deeper understanding and appreciation of the mathematics we encounter and interpret every day.
To help develop instructional strategies which enable all students to engage in reasoning and discourse about quantitative ideas.
To help in understanding how mathematical ideas interconnect and build on one another to produce a coherent knowledge base of number, geometry, and data analysis.
To recognize and apply quantitative reasoning to solve problems, including within contexts outside of the “apparent” mathematics.