Arbitrary and necessary - Nov. 6

 

Arbitrary names and labels are developed within a community. I think it is important to recognize that students come from many different communities and the labels or names that they are used to are just as effective at describing a particular shape or idea. This reminds me of conversations we have had in our LLED class about literacy and how students who are ELL have a background of knowledge in other languages and should be able to use that in conveying ideas. As teachers, we need to think about what we are assessing and give our students multiple modes to communicate their understanding. 

The author describes necessary parts of education as being things that students could figure out, that don't have to be taught like conventions or names. This makes me think of the thinking classroom and how the belief that students can actually figure out a lot of the content in the curriculum is the foundation for that pedagogy. Students are given very short lessons and then prompted to figure out a lot of things. 

One example from my practicum was how the teacher introduced the idea of radians as another way to measure angles and talked briefly about how it was developed but did not give any direct conversion between the two. The students then had to figure out how to convert in groups. I had never seen this done before, I had only seen teachers present 180/pi and then have students practice. It was so excited to students use their understanding of ratios to figure out the conversions.

There is an important discussion started here about what are we trying to teach students and the significance of doing math not just learning arbitrary steps or conventions. The skills developed in figuring things out are so much more valuable. The competencies we want students to develop can not be taught with the "recipe" format of teaching because to learn problem-solving, students need to work through things and use multiple strategies to get there.