## Thursday, November 5, 2015

### Multiple Representations: Midpoint and Endpoint Socrative Practice

One value I push and is a common thread throughout my lessons is the idea of multiple representations. I think, far too much in education, we teach kids "the easiest way", which may be the easiest way for you, or for most kids, but it could very well be the most difficult method for others. I make every attempt to analyze math topics from multiple perspectives.

If I am a strong algebra student/equation solver, how would I best understand this concept?

If I am a strong visual student/grapher, how would I best understand this concept?

If I am a strong tactile student/manipulative-user, how would I best understand this concept?

I know lots of philosophies put emphasis on catering to the different types of learners (visual, kinesthetic, auditory), but that's not exactly what I'm trying to do here. You see, I am an auditory learner - very auditory. In fact, a specialist "tested" me and said I was the highest auditory result he'd ever seen. Evidently I'm weird - nobody that knows me well is shocked.  But you see, it's a beautiful thing. In a way, we are all weird. We all learn differently. Some of us are about the minutiae - detail people. Some of us are big picture visionaries. How do these types best learn? I don't think we necessarily can have a perfectly ironed-out answer here. However, we should give students choices in how they can approach a problem

When I taught midpoint and endpoint this year, I stressed using reasoning and these multiple approaches to arrive at an answer. Students were taught how to find midpoint and endpoint (1) algebraically, (2) graphically, and (3) on a number line with marker manipulatives. Some kids heavily preferred the algebraic approach. Some initially avoided the algebra like the plague. The great thing is - by the end of the lesson set - students saw how all the methods were interwoven. Because of students' strength in one approach and the interconnectivity, these initial strengths eventually translated into a gradual strengthening of their approaches in other, more weak, methods.

To facilitate this type of practice, I used Socrative (I'm a huge Socrative fan) and a strategically assembled worksheet.

Socrative Code (if you'd like to use this activity): SOC-18350734

Here is the handout. For each problem kids had to (1) specify if the problem was an endpoint or midpoint problem (I know this is obvious, but this question seems to help the kids focus), (2) prove the calculation algebraically, (3) prove the solution on number lines, and (4) prove the solution on the coordinate plane.