Algebraic Thinking and Proportional Reasoning, Day 1 (7/17/17)

Welcome back for week two! Today we welcomed several friends returning from last week, as well as several participants who completed Week 1 last summer, and are now back for week 2.

We began the morning with the “Walk the Graph” activity. Beth brought us to the physics lab, where motion detectors and computers were set up.  We touched on a lot of ideas that will show again this week, although in less formality.  During discussion we saw how distance from the detector, speed of motion, and direction of motion could all be visible in the graph. We also discussed a few graphs that could not be generated at all – they required someone to be in multiple positions at the same time.

Next, we moved back to the Math room and discussed Block 0, an overview of Week 2. A key point to remember is that the material we’re covering in week 2 is probably not directly applicable to what you teach in your classroom. These activities will really challenge you – don’t be afraid to ask for support from your peers or from the discussion leaders when you need it. These tasks are definitely not meant to be used (in their current form) with your students!

Next we tackled the “Sliding Snail” problem. Many people incorrectly concluded that it would take 24 hours for the snail to reach the top of the ramp (12 feet). However, after some discussion, most people realized that the snail would actually pass 12 feet earlier than 24 hours – because as soon as he gets to the top, he won’t slide down anymore. Participants shared their solutions, including tables of values and graphs. Lin showed how to use technology (in this case, the app Geogebra – https://www.geogebra.org/ ) to show a graph.

Next we moved into thinking about even numbers and odd numbers. We extended the thinking we used with counters to think about divisibility and remainders.

After lunch, we considered processes – We discussed the idea that some processes are interchangeable (add 6 to the input vs. add the input to 6) while others are not (subtract 6 from the input vs. subtract the input from 6).

Homework:

Math Homework:

Try to find the process that makes Mathemagic Trick #2 work. (See Block 1 page 12).

Hint: For any number that is a multiple of 99, the sum of the digits will equal 18.

Pedagogy Homework:

Read Principles to Action: “Pose Purposeful Questions” (p. 35-41) and “Elicit and Use Evidence of Student Thinking” (p. 53-57)

In your notebook, write a response to these three prompts:

  1. In questioning small groups of students working on a problem, a teacher noticed that when she asked a “focusing” question, the students continued to look at their work and continued to engage in their own dialogue. When she asked a “funneling” question, the students looked up at the teacher. Comment on these observations.
  2. If Nursen came to your classroom during math time, would she see you using a funnelling pattern of questioning or a focusing pattern of questioning?
  3. Suppose a student presented you with the following piece of work. What questions could you ask that would elicit the student’s thinking?

Screen Shot 2016-08-03 at 2.22.52 PM

Leave a Reply

Your email address will not be published. Required fields are marked *