The Who, What, When, & Why in Growing Deep Mathematical Understanding

Who:  ALL--Every student deserves the opportunity to tackle problems with a high

level of cognitive demand.

What:  Multi-layered math problems with multiple entry points that promotes deep thinking.

When:  Embedded within the math workshop on a regular basis.

Why:  To promote deep understanding and coherency around math.

Going into this school year one personal goal I had for myself was to dedicate professional development and coaching support at the buildings I serve (Hawthorne, Hillcrest, and Lowell) to deepening mathematical understanding through rich tasks. The types of tasks we focused on were those that offered cognitive levels that were low floor and high ceiling. This meant the task should have an entry point that allows all students, at every level, the opportunity to access the problem. These ultra engaging tasks are called 3-Act Math Tasks. Originally created by Dan Meyer, these tasks have transformed the way we think about math exploration, inquiry, and mindset. These types of tasks can single handedly infuse a sense of wonder in our students and leave them wanting more. So what are these 3-Acts?

Act 1 is the set-up or the hook...and, in my opinion, the most exciting part.  This is where the teacher presents the chosen problem that will help meet the day’s learning target.  Here, students are given an opportunity to discuss what they notice in the problem and what they continue to wonder.  They will have an opportunity to estimate. They will have a chance to determine their own course of action.

Act 2 is where the students collect the necessary data and make attempts at solving the problem presented in Act 1.  They will determine what information is needed and the most effective method of solving. This is where the collaboration occurs.

Act 3 is the reveal and reflection.  Here, students will share the various strategies they used and the solutions they came up with.  This is also the time when the answer is revealed and students are given the opportunity to reflect on their process and celebrate their successes and failures.

When asked, “Why 3-Act Math Tasks?”, the answer is fairly simple...our students thrive when given the opportunity to determine their own path while appropriately struggling through the process.  Additionally, these types of tasks:

• Provide an opportunity for estimation and reasonableness.
• Build new knowledge from prior knowledge.
• Encourage multiple approaches.
• Honor diversity.
• Create situations which require students to engage in mathematical modeling.
• Build relational understandings among mathematics concepts.
• Shift student ideas about justification of thinking and answers.​

After having the esteemed pleasure of working alongside some of the best educators in our system, I have become even more fond of what these tasks have to offer us and the students we service.  Through modeling and co-facilitating, I have been able to see the direct impact these experiences have had on our students in terms of deepening their mathematical thinking and increasing their love of mathematics.