Wednesday, September 6, 2017

A linear function unit that I finally like

There are tons of things I'm excited about this school year, but a craft of pain and love has been the development of a pretty cool intro unit to our co-taught Algebra class.  The goal is to build a base for an understanding of functions that we will explore in depth all year.  We start with linear because they are used to it (I'm pretty sure that the goal of 8th grade is to pound lines into brains), but everything in this unit is a launching point for something else.

I like the daily variety -- students graph conceptually (with Desmos sliders), read stories, write stories, create equations, make tables and examples, create patterns, interpret patterns, and have to constantly use words to explain what is going on.  It is inspired by a ton of cool resources that we've stumbled on in the Math Twitter-Blog-osphere, especially Visual Patterns.  It builds up throughout the unit until the last two sections put the pieces all together as prep for a two-giant-question test.  Each section has short quizzes with retakes to demonstrate complete mastery.

Besides being a base for normal mathy things like quadratic functions, it also introduces elements of the Bootstrap Algebra curriculum.  Bootstrap is a free programming environment + curriculum designed specifically for teaching math.  It is exciting because it involves students making their own video games, but it also offers an efficient way to teach a deep intuition around what functions do and how they work.  It uses a custom-design programming language and environment based on Scheme, a "functional language".  This is different than most languages used in school and industry (C, Java, Python) because it prevents anti-math statements common in software development like x = x + 1 from creating math misconceptions (amongst a bunch of other benefits).  The main developer, an amazing guy named Emmanual, has a deep understanding of both software and effective math instruction.  If you think you like Bootstrap, I recommend the in-person workshops to really build up a sense of purpose and a vision for implementation.

The unit is broken into seven sections that bridge different forms of linear functions:
A: Tables to Graphs (graph points in Desmos, match a y=mx+b line to the points with sliders)
B: Visual Patterns to Words (analyze a pattern for rate of change, starting point, and create stories)
C: Words to Tables & Examples (read a story, work through Bootstrap example cases, fill a table)
D: Words to Visual Patterns (create a structured pattern from a story)
E: Words to Equations (work through a simplified Bootstrap design recipe and create an equation)
F: Visual Patterns to Tables, Words, & Equations (review pattern -> everything else)
G: Words to Visual Patterns, Examples, Tables, & Equations (review story -> everything else)

Feel free to borrow/adapt any of it if you wish.  Email me (rockychat3 at gmail) if you want a set of A/B/C quizzes and a test to go with it.  And please, comment or email me if you make it better -- no hogging good ideas.  The example stories are definitely a weak spot.

Note that graphing is only briefly introduced at the start and then goes largely ignored.  In our 3rd unit of the year, we explore the different forms of writing equations and spend a ton of time creating graphs in the most intuitive manner from each form (of point-slope, 2 points, slope-intercept, parallel/perpendicular to something).

Also note that sections are named after dinosaurs, because, why not?  And only one of them is made up due to the fact that real dinosaurs that start with F are not things you want 9th graders to try to pronounce.

4 comments:

  1. Hi Andy! We are planning to implement Bootstrap this year, and I found your blog from the Bootstrap teacher forum. Thank you for not hogging your good ideas!

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