I have been in college for 14 years. I tell my kids that puts me in 26th grade. In that time I have taken a ton of math and statistics courses and in all of them similar approaches to homework were used. It goes like this…
Learn the material then do the homework.
I took a class on Geometry teaching methods last semester and a whole new world was opened to me.
Everyone knows that every student comes into the classroom with prior knowledge from different areas of their lives. Many people will also agree that effective instruction includes making connections to this prior knowledge. In order to make these connections in the traditional approach we usually try to choose homework problems in the major or content area of the student’s studies. I think the majority opinion about math and statistics of my students when they enter my classroom is some proof that this isn’t working. If we were making connections with students effectively I believe that the attitude about the subject(s) would be much better.
So, what was shown to me in the class I took was, if you put the problems first and let the students work themselves through the process using the “regular†knowledge they have coming in you will make a much more secure connection with the previous knowledge that they have. For example, the first lecture in my statistics course is on how to organize and summarize data. In the past I have just started in assuming that, since much of the information is common sense, the students will not have trouble. Then I am always surprised when, and I think it’s because it is a scary statistics class, the students don’t seem to get it very easily.
So, this summer I am trying out the backwards approach. On the first day of class I had the students get into groups and I handed out data sets, both qualitative and quantitative. Before showing them anything I gave them the task of organizing and summarizing the data. It was amazing! Every group in both of my classes started out down the path that I was going to show them, all on their own. After a whole-class discussion we moved on to the slides. These students are just turning in their first exam but I had NO questions on this part of the material and that is a first for me in 6 years of teaching.
I have used a similar approach for introducing probability and it also went well. I am now going to look at all of my classes and see what I can do to incorporate this method and see how it goes. I really do think I’ve been turned on to a wonderful shift in thinking. I’ll keep you posted!