I pretty-much taught math the way that I did back when I taught a higher-level eighth grade class:

- I front-loaded the vocabulary using a TPR for variable, equation, graph, table and linear relationships. They used social media to discuss things in life that have linear relationships.
- I gave the students a scenario: They had to raise money for a field trip by selling junk food at a school dance. They did quick research on the cost of bags and decided how many they would buy and how much they needed to raise.
- They worked in partners to determine a variable.
- They solved it however they wanted: pictures, tables, multiplying, dividing, estimating, etc. Although the district discourages us to do this, I let them use calculators. I didn't want computation to be a distractor.
- After solving it, they looked at the correct answer and checked if they had it right. Many of them modified their approaches and wrote a shared "common mistakes" document together as a class on Google Drive
- Different pairs compared and contrasted their approaches to the answer algebraically, in graphs, in tables, through repeat addition, etc. In this phase, they also were asked to "prove" their answers using other methods.
- They created their own word problems, graphed the answers (using online graphing), created tables, solved it algebraically and wrote reflections based upon a menu of questions that included the efficiency of methods, the relationships between approaches and how they solved it themselves.

Some of the students still asked for additional algorithms and I offered them as a practice. However, in looking at their student work, I feel like math became accessible again. I have no idea how they'll do on the test, but I watched them become better problem-solvers. And ultimately that's what I want students to become: deep-thinking problem-solvers.

This sounds awesome, John. "I have no idea how they'll do on the test,..." This bums me out, because there may be an assessment problem. If the goal, or part of the goal, is to become "deep-thinking problem-solver," the assessment needs to address that. The linear relationships are important, but they will forget a lot of that. Practice problem solving...40 year learning there!

ReplyDeleteI'm sure you've heard of Dan Meyer (if not... @ddmeyer). What do you think of his approach to teaching math?

ReplyDeleteMany of his ideas are ones I've used for years (back when I taught math intervention): what can you do with this, treating a word problem like a story, etc.

DeleteMy real issue has been with the time that I have and the standards themselves.