To 3-Act Math or to not 3-Act Math?

Recently, I was tutoring and a student asked me for help with what I found to be an interesting question.

"There are 2 stools, one 3-legged and one 4-legged. One of the stools wobbles slightly.

• Which one is it? How do you know?
• Suppose that each stool is placed on a flat surface that is slightly sloped. Do you expect either of the stools to rock side to side? Explain why or why not. 

 Life experience led me to the correct answer yet I had to think for a moment to consider how to help the student understand the underlying concept that any 3 points make a plane.

Concurrently, I was thinking that a much better way of presenting this question to the students would be during an inquiry activity. It would allow students to discuss their ideas with one another and collaborate in order to make a precise statement defending their position. It would allow students to make a connection between "real-life" and mathematics - an opportunity to understand that there is a mathematical explanation for an what many students may have already observed during their lives. It demonstrates that people use math to explain the world around them. This idea also has applications such as the use of tripods.

I thought more about the question as I drove home and considered how I might have introduced this to students and what tools I may provide to them in order to experiment and get them interested in the task at hand. I turned to my PLN for ideas and posted the question and asked "Could this be improved? How could tech be integrated?"

A conversation followed between myself, +Jeremy Bell, and +Kyle Pearce. They both offered suggestions. The conversation then turned to whether or not the concept warranted the creation of a 3 Act Math Task or not. I would argue that this is an opportunity for students to have a math talk about a concept that is pretty simple, yet difficult to explain without mathematics vocabulary. Perhaps I view this activity as one that could be done at the beginning of the semester in Geometry. It could be used as an opportunity for the teacher to demonstrate to the students how to engage in math talks and share ideas. Also of emphasis could be that learning will take place through inquiry and discovery activities. This is a significant change for many students as they have been taught in a more traditional direct instruction model.

I also understand the other side of the argument. The same idea may be conveyed through a quick demonstration or even an explanation. The concept is not one that is of great focus in Geometry. It may be wasted time to create a 3 Act Math Task for this small concept and it may be a waste of time to have students work through a process.

So the question stands. Do you think that a 3 Act Math Task is an effective way to help student uncover the idea that 3 points always make a plan, or is it wasted time and resources for this particular topic?

Mini Goals

Lately I have been working hard to try to stick to a workout schedule. With the start of the school year (yes in AZ it starts at the end of July or beginning of August) it means my wife will be going back to work and I will once again have the pleasure (or duty - depending on the day) of transporting our three year old to daycare a preschool. Sticking to a workout schedule becomes more difficult. I also tutor at Grande Sports Academy, a residential soccer program, three nights per week. So the schedule gets more hectic and getting up with the alarm at 5 gets tougher.

While running earlier this week I found myself wanting to take a walking break after running just over a mile. With another 1.5 miles to go, I was having a sort of internal struggle over whether or not to take a short walking break. My hip was hurting, I was out of breath, and my allergies were causing issues beyond the normal. The struggle led me to keep setting mini-goals. Keep running to the next intersection, then the stop-light, then catch that guy that is walking, then to the corner in front our house. Before I knew it, the run was over and I never did take a walking break. I find myself doing this when I work out. One more set of 10 burpees, 15 more seconds planking, 3 more sprints, etc. I break down a workout that seems overwhelming into a series of mini-goals. This helps me keep from giving in to the aches, pains, or lack of motivation.

Amid the argument in my head, I began to realize that this strategy can apply to other areas of life. I specifically thought about using this strategy in education. Instead of being overwhelmed by a larger goal you may have (integrate technology, implement problem-based learning, etc.) break a larger, long-term goal into one mini-step at a time.

As a trainer this is something that I sometimes fail to do. I fail to help participants break an overwhelming task into smaller more attainable mini-goals. This is one great weakness that I see in the model of PD that I am sometimes asked to deliver. One-time, all-day PD sessions often have excellent content, strategies, resources etc. However, they truly lack in follow-through and support. Fortunately many schools are beginning to ask for follow up support as their teachers implement the new _______________ that has been presented. It is more effective and it seems that teachers are much more willing and able to truly change their teaching when this support is provided.

My goal is to be more cognizant of what my long-term goals are and work to create mini-goals that lead me to the finish line. Although, if you are a runner you know that one finish line leads to another start.

What are your long-term goals and what are some mini-goals that will help you get there?