Inside Teaching Math

I recently created a real-world lesson about taking off consecutive percents vs. taking off the same discount in one step (20% then 20% again vs. 40% off the original price). I often call this stacking percents. Rather than go through a normal lesson day of notes, examples and practice and then do this activity the next day – I decided to try using this lesson to teach students about the difference. The results were mixed but positive overall.

The big point of the lesson is trying to get students to see that taking the discount off in two steps will get a different result compared to taking it off in one step. This lesson had students take a more inquiry based approach (which I will be writing on plenty in the future) as most students assumed that the discounts would result in the same price.

Doing it through the activity allowed them to find out which one saved more and conjecture about why it saved more. This worked out really well for my moderate to advanced students and not quite as well for my low students. This is partially my fault as my low students were struggling to find the percent discounts as I did not properly scaffold this skill for them – definitely something I will change in the future. I like this method of approach for students that have a firm grasp of content as it allows them to explore the learning possibilities themselves. I will continue to experiment with this approach and see what role it can take in an every-day class environment.

Today in preparation to correct a test I had students go through and identify which problems on a test were difficult and describe to me why they were difficult. I think this is a really important skill to grab a hold of as it makes you a better learner. If you can identify what is challenging about a problem, then you can narrow your focus on what to look at, ask questions about, or study.

The problem is I have discovered this is a skill I need to teach to my students. First, I think students are often over confident in what they find challenging. They are quick to assume they got something right – especially on multiple choice tests. Secondly, they have difficult putting into words why a problem is difficult. They can act like it should be assumed that because they are not able to do the problem then of course they cannot tell my what’s difficult about it. They equate knowing what’s difficult or challenging with knowing how to solve. This is a problem.

Students need to recognize what they know about a problem, how to try it, and then when they can’t come up with a right answer they need to recognize where the difficulty lies. What is the hurdle that they cannot get over. Even if it’s as simple as ‘I know I am solving the proportion right, so I must be setting it up wrong” or “I am unsure if this is the correct number for the denominator.”

We need to get students to question themselves – not to the point of self doubt, but to make a more complete learner.

In Learning To Love Math Dr. Willis mentions a study that asked students to draw a typical classroom learning experience and then draw a learning experience they liked. When drawing a typical learning experience most students drew a teacher at a board and often didn’t include themselves in the drawing at all. This is quite the contrary to drawing a learning experience they liked where they predominately drew themselves as the focal point.

I find myself constantly battling the direct instruction, teaching at a white board (whether it is interactive or not) mentality. It is how I learned and I learned pretty well. It is how all my friends learned and a lot of them were even better than me. I think the problem is that direct instruction works. I know I can get certain results with it and it is comfortable to me. If I want to go beyond those results – or better yet – engage my students in a profound way, the focus needs to be off of me in the front of the room and shifted to make the student the center of the learning.

Teacher turns facilitator.

How would this look fully realized?

I think groups, stations, experiments, etc. aren’t answers but rather pieces. Forming them to make a unique math classroom experience is something we must all experiment with. Resisting what is easy and natural is the start. What do you think?

I get why best practices are important and why we talk about them and attempt to get teachers to use them. I however feel that there is an inherent danger with labeling best practices. It can seem as if you do not use one of them or several of them then you are not a good teacher. This is besides the point that every book or person you meet has a different definition of what are THE best practices for teaching math. We need to face it there each teach is very different from the next and more importantly each student is very different from the next. Focusing less on labeling and more on discovering new and innovative ways to teach math is far more important in my opinion. It should be our job not to implement “best practices” but attempt to try out as many practices as possible to see what works best for the current group of students you have and what works best for who you are as a teacher. We are not robots.

All that being said, we should be doing everything we can to continue to learn, get better, and discover ways to make our classroom and instruction the best it can be. That is hopefully what this blog will assist in doing for me and anyone else reading.