Curricular Micro-Teach October 15th

 

Battle Ground Schools Response

 Stop 1:

I find the negative public views of mathematics to be a very interesting topic. It is something that I hear regularly among every social environment I've observed (progressive, conservative, older, younger, mathematicians, scientists, non-mathematicians). One worry that I have for mathematics education reform is that it will never see positive results as long as these negative public views persist in such a widespread way.

 Stop 2:

Something that I've been thinking about since we read Skemp's writing on relational vs instrumental understanding is that sometimes we might mistake one for the other. In particular, I was reflecting on my work with students learning introductory algebra concepts and I keep wondering what kind of understanding a student is exhibiting when they are successfully doing algebraic manipulation. It often seems almost entirely instrumental (when I'm solving for x in an equation like 10=(5+x)/2, I never think about graphs and stories. I just step by step move terms and coefficients to one side until x is alone.). But maybe there is something relational about it that I'm missing. However, maybe there isn't... This feels connected to another thought that I had regarding relational understanding ; Relational understanding being 'relational' demands that it forms an understanding by 'relating' various other understandings, does this mean that there must be some small foundation of instrumental understanding (or some other kind of understanding) that exists before there is anything to relate to anything else?

 Stop 3:

My final stop/question is really for my own sanity as a future as a math educator. I've learned throughout my science education that research on highly social topics that are steeped in charged public opinion and politics are *exceptionally* difficult to do quality research on, so how do math educators do their research? Why should I believe any of the results that are being published in this field?

Lockhart's Lament Response

I remember reading this when I was in high school and I thought that it was a cool different perspective on mathematics. At the time, I really disliked all of my math classes. They were all chores, too easy, not interesting, but I loved playing around with numbers and other 'math' ideas. So Lockhart's Lament really spoke to my experiences. 

There is definitely a distinction to be made between some mechanical skills that we call mathematics and the creative problem solving / exploration that Lockhart seems to think of as mathematics. I believe that there is an important distinction there and that these different ideas should be taught differently.

I also believe that the reason that most of secondary school mathematics is taught is historical rather than reasoned. I don't believe that most people need to learn much trig or algebra. This is one reason to dismantle and re-envision mathematics education and move towards a system where the creative 'puzzle' kind of math is an optional sort of course open to anybody that wants to participate. However, as long as mathematical skills remain correlated with high-status, high-pay careers it is likely beneficial (and important for equity) to try to keep that door open for everybody. That being said, I think it would be so fun to teach a 'puzzles / problem solving' course.

In comparison with Skemp, Lockhart seems to pull lots of ideas, like the analogy with music, from Skemp's article. Where Skemp says that math should be taught more relationally, Lockhart agrees that relational understanding is a positive outcome, but the exploration that gets you there is the valuable part.