Overview of Class Comments about notebooks Introduction to algorithms Modeling standard addition algorithm with bundling sticks Planning for teaching of mini-problem Wrap up

Comments About Notebooks Different methods of organization Sections, typing & gluing things in Important to do (keep doing): Thoroughly complete assignments Make connections to work in field To try more of: Rereading and annotating your previous work Keeping track of other’s ideas(possibly w. attribution) Making more nuanced observations of students Avoid making assumptions or making overly broad comments about what students know or don’t know -- e.g., the student understands (or doesn’t know) place value

Using Different Approaches to Add 49 + 37 = 9879 + 3958 = Which method was easiest for you to use on each calculation?

Algorithms for Adding and Subtracting Multi-Digit Numbers A well defined step-by-step procedure for solving any given case of a (usually computational) problem in a finite number of steps. (“Mindless:” You can program a machine to do it.) Examples: Standard algorithms for multi-digit addition, subtraction, multiplication, division. Bisecting a line segment with ruler and compass. Etc.

Different Kinds of “Algorithms” “Conventional” or “standard” algorithms Traditionally taught in school May vary across countries, times General, reliable, efficient (“compressed”), “opaque” “Alternative” algorithms (often not really algorithms) Transitional Useful for particular types of cases More transparent (meaning of the steps is clear)

Alternative algorithm Conventional algorithm Alternative algorithm (Partial Sums)

In Your Notebook… What stood out from today’s work? Any important mathematical issues? Any teaching ideas?

Mini-Problem Assignment Start planning for mini-problem in class today Teach mini-problem Practice moves/questions we have been working on Audiotape & collect any artifacts Professional Practice Piece Choose a 3-5 minute segment of tape where you try moves/questions we have been working on Complete “question track” form List 5 key questions, purposes, and student responses in light of your purposes Improve 3 of the 5 questions, supporting your work with principles On October 13 bring: audio recording, artifacts, 4 copies of question track form

Planning to teach a Mini-Problem (Part 1): Analyze the Task Think about the core mathematical ideas and how students might approach the task: Do the problem yourself. What other solutions or solution methods are there? How do you think students will solve the problem? What challenges are they likely to encounter? What are the main mathematical ideas that you want to emphasize through the problem?

Planning to teach a Mini-Problem (Part 2): Plan the Discussion Setting up the problem Monitoring student work Launching the discussion Orchestrating the discussion Concluding the discussion

Mini-Problem Groups #1: Karla, Lindsay, Meaghan, Diana, Aimee, Justine, Lani #2: #3: Wendy, Julie, Melanie (or #4), Jessica S #4: Jessica T, Graham, Olou, Michele, LesLeigh, Kristy, Brian #5: Alyson, Rob S, Dawn, Dave, Gordon, Chrystal, Lee, Lori #6:

Plan to Teach Your Mini-Problem What is your purpose for doing this problem? Think about the core mathematical ideas and how students might approach the task: Do the problem yourself. What other solutions or solution methods are there? How do you think students will solve the problem? What challenges are they likely to encounter? What are the main mathematical ideas that you want to emphasize through the problem? Use the checklist to plan the discussion

Wrap Up Please leave notebooks Comment cards Assignments Finish planning mini-problem and teach it on scheduled date Reading: Strands of Mathematical Proficiency from Adding It Up (page at a time on web; copies in Study Hall) PSSM process standards (requires NCTM trial membership) Try to model an alternative algorithm (example from Everyday Math) using bundling sticks Please leave notebooks Comment cards