What is my mission? What do I want students to be able to do and understand mathematically once they leave HS? Those are questions I ask each week before I sit down to plan - the global question before what I want them to be able to do with a specific skill.
I know that I want all my students to be ready for college and career -- but what does that really look like? Once you get beyond that truly basic premise of "math ready" what do we want? I want innovative, problem solving students who don't accept the world around them without through questioning it! Students who engage, attempt, FAIL, revise and retry. I want projects that require that - and when they appear I have to remind myself to grab them - otherwise I get worried about what they may miss.
When is the last time an average adult had to factor a second order polynomial, or use the quadratic formula? I know some jobs do.... But I was an engineer for 12 years prior to teaching and only a few times did I need specific higher level math, but what I did do was problem solving, data analysis, experimentation and logic thinking. It was trying and FAILING, revising and retrying. The skills that higher level math requires (when we keep the cost of errors low and let students do the work) - so math prepares us for those challenges!
Yet as a teacher it is easy to get caught in teaching all the things - all the details. My tact has changed dramatically over the past decade - number one college bound students must place into college mathematics period (no remedial), and then second students must practice the soft skills of the math practices. Teaching the focus of a parabola is not important, likewise matrix operations - the important part is the soft skills it takes to understand. Now full-disclosure I only teach focus for a single day in Pre-Calculus and matrix operations in Pre-Calculus only - why? Because unless you are on a STEM path those things, while good, are not as good as doing other soft projects.
Schools have the tendency not to make leaders, or challengers of the status quo but the opposite. That is why a big part of my year is built around projects where I require the students to work with limited information, to learn skills that I do not show - I was reading Poke the Box by Seth Godin and he talked about how schools actually drive-out kids drive to initiate.
And I agree our schools are still based on a sorting system - rule followers are rewarded, and - well - in most rooms vice versa. The world is not orderly and does take turns - those that push hardest while maintaining ethics get there first and get the spoils. We need to encourage free thinkers, get all students to be disobedient enough to be innovative - scary - but we need students to question us (my favor joke now is don't trust me, verify me).
Students must engage, try, fail and revise - but as any teacher will tell you, often students don't try unless they know the way to the solution. That is not preparing them. That is because they have to be taught on how to engage and revise; they need to hear that the wrong answer is not the end, just a step. Rarely do my students get the math in the assigned projects correct, but if they support their position and do well they all get 100%! If they don't support their position - they revise - then they get a 100%! We work together, I model, they revise - not engaging is not an option.
As leaders we must embrace our roll to change what teaching looks like - and the first step is not to utter - it is not in the curriculum. If it teaches soft skills - it is more important than half the math we teach - so grab it.
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