One one hand, we have our old way of mathematics: introducing a concept and its vocabulary, teaching strategies, students completing work and then (maybe...) applying to a contextual problem to extend their learning. Imagine the motivation, ownership, and learning if this process was flipped on its head.
First, students develop ideas through a real-world problem or task. Engagement is high and so is cognitive demand. The teacher provides contextual information and tools, but no clear and tried path. No math word or strategy. Students work on their own and with a partner or group--they develop ideas all around the problem. Some students show misconceptions they have about number, some draw models, some develop diagrams, some use mathematics concepts they already know to solve. Answers are both wrong and write. As a class, a rich discussion is held. What happened? Which strategies worked? Which one's didn't? The teacher provides vocabulary and draws out key concepts and mistakes to be learned from. This is known as the "developing" phase.
Next, where does the learning go? Students have many ideas about their new concept, but have not been afforded time to use all the strategies. Teachers will share a targeted concepts--i.e., today, remember what Suzy Q. explained to us yesterday about how she used place value? Let's use that concept to see if it will help us on our task today. Another launch of an engaging task, more work with more focus on a strategy and concept, another rich discussion. Students are solidifying ideas about mathematics--this is the "solidifying" phase.
Finally, students have developed and solidified all important ideas about their mathematics topic. They are ready to work on their accuracy and fluency. The teacher launches a problem string, mathematics game, or task that requires repeated reasoning. The students work and re-work the tasks, focusing on using strategies flexibly and attending to the correct answers in problems. This is the "practicing" stage, and marks the end of the mathematics task cycle.
The math task cycle is powerful when teachers use it in the classroom, and can be used to ensure all students have access to deep conceptual understanding. No more "I'm not a math person..." All students can be successful in mathematics through the learning cycle.
Join me next time for a deeper dive into planning for learning in the three stages!
Yours,
Ms. M
