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

2. 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

3. Using Different Approaches to Add= =
Which method was easiest for you to use on each calculation?

4. 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.

5. 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)

6. Alternative algorithm
Conventional algorithm
Alternative algorithm
(Partial Sums)

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

8. 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

9. 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?

10. 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

11. 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:

12. 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

13. 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