## Reflection: Letters & Postcards, Day 2 of 2 - Section 1: Student Presentations

I am totally committed to class discussions.  Students need to learn how to make conjectures and how to critically examine them.  They learn confidence as well as humility by putting their ideas before their peers to be either accepted or rejected on their merits.  They learn to listen to one another and to learn from one another.  Once everyone has had a chance to ask questions, propose explanations, the truth of the matter should be visible for all to see.

Should be.

Like any teaching method, class discussion and Socratic questioning don't always work.  Learning is an incremental process, and I have to remind myself that while every student will learn something from the discussion, none of them can be expected to learn everything.  The attached student work is a good example of the kind of finished product I'm thinking of.  In many ways it's very good, but it still reveals some misunderstanding on the part of the student.

***

Today, I had an opportunity to work one-on-one with a handful of students who were seriously struggling.  These students were simply stuck and had no way to move forward without some very direct intervention.  With these students, I focused entirely on making sense of the graphical solution.  They needed help understanding how verbal expressions were turned into algebraic inequalities; they needed help graphing these inequalities; they needed help understanding what their graph meant.  At this point, I wasn’t as concerned with finding the optimum solution as I was with understanding what was different about the various feasible solutions.  At times, it's important to scaffold your instruction by focusing on the most important concepts, rather than the flashy or "neat" ones.  In this case, that meant interpreting the model in context.

The limits of discussion.

# Letters & Postcards, Day 2 of 2

Unit 1: Modeling with Algebra
Lesson 5 of 15

## Big Idea: Systems are useful mathematical models for situations with a several of constraints. Time is money!

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45 minutes

### Jacob Nazeck

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