Still a work in progress…
Over the past couple of years, I have begun to read blogs discussing education and, more specifically, math education. I have been surprised to discover blog comments that actually formed productive conversations (although they still sometimes contain subtle and not-so-subtle personal attacks). The challenge is forcing myself to actually sit down and read these blog entries and the ensuing comments. The mental exhaustion resulting from a day of teaching (and all the other challenges that a school day brings) can be difficult to overcome. Yet, one advantage of blogs and online presentations over in-person professional development sessions is that you can experience them when you are most up to the task. One of these newly discovered blogs that I have been following is that of Dan Meyer. I have found great value in both the entries and the comments that follow, especially since there is a fair amount of overlap between the content in Mr. Meyer’s class and the 8th Grade Math Georgia Performance Standards.
Following the administration of the state standardized test at my school, I have had more flexibility to try teaching in a more “high-risk, high-reward” manner. I utilized several of the ideas from Dan Meyer’s “What Can You Do With This?” blog entries, including “What Can You Do With This: Italian Job,” “Who Cares? – The Wager,” “What Can You Do With This: Water Tank,” and “What Can You Do With This: The $6400 Question.” My focus was on better engaging my students and giving them problems without a clear, easily obtainable resolution. Real-life problems can rarely be solved by looking at an example problem and following the exact same procedures. So why were we taught this way as students? Why do we continue to teach this way now that we are educators? Just look at the accepted observation that there is no one-size-fits-all reform strategy in education as a real-world example. Every school has a different student population and unique challenges to overcome.
One day I introduced a lesson based on a challenge presented by Dan Meyer (The Wager from “Who Cares?”). I played about 20 seconds of a video clip created by Dan Meyer of a transparent tank filling up with water at the beginning of class. I asked each group of students to predict how long it would take to fill the tank. Their guesses ranged from ten minutes to a few hours. The fill/drain a water tank problem is a pretty easy, if unexciting, application of linear equations to a real-world situation. Yet, by allowing the students to actually see the tank and having them make a prediction, the plan was to engage the students in the process of discovering the answer. After the students made their predictions, I abandoned the water tank problem and moved on to something completely different. In each one of my classes, eventually a few of the students made a comment along the lines of “you never told us how long it took to fill the tank.” Sometimes the comment came only a few minutes after we had moved on. Other times, it came much later. More convincing evidence of the students’ level of engagement in the exercise came at the end of the lesson when I played the rest of the video. With their focus on the screen, you would have thought they were watching a summer blockbuster at the movie theater, not a tank filling with water in a classroom.
I used the engagement of the students to invest them in solving a problem that involved some critical thinking. When we revisited the problem, I avoided the temptation to hold the students’ hands through writing a linear equation to represent the situation. Instead, I simply asked them to come up with a justified answer to the question of how long it would take to fill up the tank. Some students’ answers included a rate of change and/or linear equation. Most of the answers didn’t. All of them experienced the struggle, including failure, that it takes to solve a real problem, and the first group was able to make a connection between the content covered earlier in the year and a problem they had not seen before.
It seems intuitive that the engagement and critical thinking that results from discovery learning would benefit students. However, there is also research to support the value of discovery learning. Kevin Hall, one of the commenters on Dan Meyer’s blog, directed readers’ attention to “Practice Enables Successful Learning Under Minimal Guidance,” Journal of Education Psychology (2009).
Hall also referenced the article “What Needs to Develop in the Development of Inquiry Skills,” Cognition and Instruction (2000), to support the effectiveness of project-based learning.