Mid-April, that time of year where teachers and students start to see the finish-line of the school year. Everyone feels the burdens…state testing, class distractions, covering all the “material”….teachers have a lot on their plate. But it’s also a great time to reflect upon the past year, work in teams to consider best-practice, and plan changes for next year. Two intriguing blog posts by Grant Wiggins this week should be required reading for all secondary math teachers.

First, Grant Wiggins rants against courses we call algebra 1. What could be wrong with Algebra 1? We all took it, we all agree kids “need” it, and isn’t a proven gate-keeper to college success?

Algebra, as we teach it, is a death march through endless disconnected technical tools and tips, out of context. It would be like signing up for carpentry and spending an entire year being taught all the tools that have ever existed in a toolbox, and being quizzed on their names – but without ever experiencing what you can craft with such tools or how to decide which tools to use when in the face of a design problem.

Amen, brother. In algebra, we move from the unit of linear functions, to the unit on systems of equations, to the unit on exponents, then the unit on polynomials. At the end of each unit, we duitfully give the unit test, get some number score back, then move on to the next unit. We have trained students to think this way: that algebra means mastering one skill, then the next. How often do we provide rich tasks which allow students to reflect upon their cumulative skills set? I appreciate the work of many math folk out there to change the nature of Algebra 1 from a rigid sequence of skills to a course which encourages application and reflection, driven by interesting, authentic problems. Some examples of outstanding math educators working to promote inquiry in math class are listed at the end of this post.

For many special education students, chunking is a device used to “help” students in algebra. By continued pounding of square pegs into round holes, using worksheets of similar problems (i.e. solving a one-variable equation, with variables on both sides), students can achieve temporary, recordable “success”. The students most in need of seeing auhentic problems are often those least likely to move past the chunking, and into authenticity. Fortunately, to help sort out the madness, Grant Wiggins provided a second great article of required reading for math teachers this week:

Grant Wiggins on turning math classes into bits of disconnected microstandards.

What’s so harmful about taking a broad subject like Algebra and breaking it into pieces? What is the consequence?

Take a complex whole, divide into the simplest and most reductionist bits, string them together and call it a curriculum. Though well-intentioned, it leads to fractured, boring, and useless learning of superficial bits.

Hallelujah! Make sure you check out Grant’s driver-ed analogy for the full effect. More ammunition for us to develop math courses rich with interesting, relevant tasks, where algebra is the tool, not the star of the show.

Fortunately, there are many educators out there working to develop tasks which develop algebraic thinking, and encourage the use of algebra as the tool, rather than the exercise. Keep them in your toolbox for future planning.

Dan Meyer: the king of perplexity. If you aren’t visiting Dan’s blog at least semi-regularly, then start now. And check out his spreadsheet of tasks for the math classroom. In the same theme, visit Timon Piccini, and his many on-point 3-act tasks.

Sam Shah: Sam leans more towards the pre-calc, calc end of the math spectrum, but I apprecaite Sam’s constant self-reflection and great ideas for engaging kids in math discussions.

Kate Nowack: sometimes task-oriented, sometimes ranting on policy, but always interesting.

NCTM’s reasoning and sense-making task library has a number of problems around which algebraic ideas can be wrapped.

You can add me…always trying to reframe the question so that students get why they are learning Algebra in the first place.

Amy

Ms. Zimmer Teaches in Mathland

What do you do when students’ IEPs demand tasks broken down? That’s a struggle I’ve had – when the whole point of the reframing of my question is to get students to think through what they need to do to process a solution, those mandated-chunkers have lost out on the whole experience.

I have the same struggle, and I’m afraid I don’t have a snappy answer. In conversations wih many of my special ed teacher colleagues, they understand the need to expose students to more complex tasks, yet are bound to produce data evidence. So, segmented quizzes become the norm. I think somebody could make some good money by providing measurable tasks which provide multiple options for different learners.

Challenge accepted!!

Reblogged this on evangelizing the [digital] natives and commented:

I always know when I’m being most guilty of breaking down Algebra skills too far because I’ll hear things like, “Man, we do somethin’ new EVERY DAY.”

[No, this is completely connected to what we did yesterday, and the day before that].

If you’ve ever noticed your students have “lost” their equation solving skills because you “spent so long graphing,” you might be a skill chunker.