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.

edit:

I better not slack off. Lisa and Meg both called me out. http://www.teachesmath.com/?p=765 and http://www.megcraig.org/?p=394. Stay focused Glenn!

I love the cohesion and big picture that you are proposing. One of the toughest things for many students is to see how today’s work has anything to do with last week’s or last month’s. For me, this answers your fourth question directly. If this sequence helps to cement connections, then that is reason enough.

A couple of clarifying questions… The repeat of 1 and 2 is because you spend more time solidifying linear relationships? This sequence is intended for Algebra 2 I assume?

Looking forward to thinking through the details that go with this big picture plan. Thanks!

Yes, I teach algebra 2, but I repeat 1 and 2 (lines and absolute value) so that I can solidify the knowledge through something they already are familiar with (but definitely do not remember or understand well enough to master at the level needed.) The other reason is that I want to push this into algebra 1 as well. I really believe this IS the heart and core of algebra, and if I can write enough down perhaps it can be seen as a complete curriculum starting with algebra 1 through trig and beyond. We just layer more things on top of this core in trig and calc.

That’s my initial thoughts at least. Stay tuned!

Thanks Glenn…this is really getting my mind working! Can’t wait for part II! 🙂

[…] WANT TO HEAR YOUR PhD EXCUSES),UPDATE: Glenn has shared part one of his ONE MATHS blog posts here! these are my big three goals for Algebra II this […]

I’ve been thinking about helping kids to make connections as well (after all, it was the theme of this year’s USCOTS). Interested in hearing more about how you incorporate this into your classroom, how students respond, and the impact you think it has.

I’m thinking of prompting kids to explain what connections they are making with new material.

Amy,

I will keep you apprised of the posts. This has changed how I teach Algebra so much, and as I have developed the idea over the last couple of years the ideas have helped learners. The questions are richer and deeper. The only struggle I have had this year is in the reviewing. The learners struggle with an entry point, and I have not made it clear enough that you can enter the maths at any selected point, not just at a particular form or particular type.