I tried to do a 180 blog, and made it to 90. I really don’t know how people like Justin Aion and Sam Shah do it. It is very difficult to find something to day for 180 days without it sounding boring and forced. They pull it off though. That is amazing.
Knowing I can’t pull of the 180 thing isn’t bad, however. I know I can do topics, and I have a topic I really want to crystallize for myself (as well as others.) I have really been toying with the idea of “one maths” the last three years, and I convinced / forced one of my fellow teachers in my building to start doing it as well. The results are amazing. The connections between the different topics are astounding, and the learners see them, are motivated by them, and create further connections as well. To see why the connections are so important, one just needs to read this “Math with Bad Drawings” post. The connections are vital.
Some tools I will use regularly in class.
1. The Three Essential Rules – from day one, these are the only “rules” I will ever talk about. Log “rules”? Nope, don’t have them. Those are shortcuts to understanding why the properties of logs work. Exponent rules? Nope, nothing more than shortcuts. The only rules we will ever explicitly say are these three: Additive Identity, Multiplicative Identity, and balancing equations. How I implemented them can be found here.
2. Desmos.com – This is the first website I load every morning as I get ready for my day. It is essential to visualizing and discussing function families. The main difficulty I have with desmos is I have so many ‘files’ created it is hard to find them all! That is a great problem to have I think.
3. My structure of functions: This is how I organize the entire year. We move from topic to topic, but as we move, the connection to the prior topic is constantly referred to and stressed.
This list is the core of the connections I want to explore and develop this summer.
Some things I want to make explicit for myself.
1. How to connect this list to the CCSS standards and Essential Understandings explicitly.
2. How to connect each step to prior knowledge in a stronger way.
3. How to connect each step with the breadth of knowledge required (for example, quadratics have many ways to solve).
4. Finally, why in the first place! It seems odd to put the why at the end, but I think it is easier to think about the why once it is all laid out. Does this curriculum have an advantage over the standard “textbook” curriculum? Anecdotal evidence suggests yes, but it needs to be better explained before others can weigh in.
It is a large project, but well worth doing. I think it will really make me understand the mathematics better, and enhance my teaching tremendously.