The first time that I took kids outside to measure the heights of buildings and poles using sunlight, shadows and mirrors, they thought that I had surely lost it. They had never been outside of their district printed worksheets and the idea that math could be just as physical as science was alarming. For me, it was instructional.
For starters, I learned that tasks such as this work best when the expectations are clearly defined. I also learned that experience, even when imperfect, can serve to better prepare students for the math within it as long as they are owning the learning.
For years, the students that entered my classroom had only “learned” math through duplication of teacher-led problems. They were not questioned about any individual thought and would wait with intent for the answer to appear so that they could write it down. Poor kids…those answers never appeared! They wanted a guide…a pattern to duplicate, which only gave the perception of mastery in my opinion.
Students could not express why something worked or what it meant because their only connection to the math that they were doing was that there was a definitive answer….period. Solving for a solution was the focus. There was no in between.
Comparing relationships was like pulling teeth. As a matter of fact, the most common comparison was that one was one answer and one was the other. When asked what else they noticed about a problem, you could literally hear a pen drop in the room. There was no connection because there was no understanding…just a collection of scattered memorized facts.
The act of experience is important for students to understand math beyond black and white. Experience brings the how and why something works and informs greater depth of understanding because it stems from the perceptions and ideas of the students themselves. On the teacher’s part, it’s a deliberate setup for student interaction. It’s also a time to take a back seat and allow their thoughts to occur.
I’ve fallen prey to the Three Act lesson, created by Dan Meyer. It involves presenting the experience in a visual, non wordy kind of way and allows students to think in terms of meaning and not in terms of finality. The reflective aspect is what makes learning such as this work. It’s a shift in thinking on both the part of the teacher and the student. We are no longer the deliverers of what is right or wrong. Students make inferences, explore and reflect as to how their perceptions relate to the problem itself.
Math should be about where and how it fits into the lives of students. Real problems should be presented in real ways and not just read in a book, worksheet or on an ipad but experienced in their purest form.
Below are few of my favorite resources by amazing members of my PLN.
See HERE for more 3 Act Math Tasks
Jose Vilson’s Math Lesson on the Economic Conditions of the March on Washington (real data, real problems)