1. Teaching through the Mathematical Processes
Session 5: Assessing the
Math Processes

3. Retention Timeline Pink: time students retain procedures
years
Pink: time students retain procedures
Yellow: time students retain concepts
Blue: time students retain math processes

4. “Five Minute University”
“What are we teaching?”

5. Reflecting on the Mathematical Processes
Father Guido’s “5 minute university”
Think, Pair, Share
Reflect on the connections between the Mathematical Processes and Father Guido’s comments.

6. Assessing the Processes
Assessment vs Evaluation vs Reporting

7. What is Classroom Assessment?
One possible answer:
Classroom Assessment refers to the collection of information teachers use to monitor students’ learning, provide feedback and to make appropriate adjustments to instruction Exploring Classroom Assessment in Math NCTM 1998

8. Mathematics Processes Rubric

9. Mathematics Processes Rubric
Think → Pair → Share
Reflecting
Problem Solving
Reasoning and Proving
Selecting Tools and Computational Strategies
Communicating
Connecting
Representing

10. Opposite Sides
Agree / Disagree / Don’t Know!
The distance around a tennis ball can is less than the height of the can.
Justify your answer with your group.
“don’t know”s explore further.

11. = 3 diameters
h = 3 balls
C =  diameters
The distance around a tennis ball can is less than the height of the can.

12. Tennis Ball Can Problem
What MP were used in solving the problem?
What rubrics could be used to assess the MP with this problem?

13. How do we effectively teach math processes?
Teach the curriculum expectations
Doing investigations and solving rich problems
Ask questions and provide feedback related to the processes
Explore the TIPS lessons found on the LMS website, that demonstrate how lessons can be adjusted to focus on particular processes.

14. Students learn content
and problem solving
strategies by
solving problems
and sharing solutions.

15. Problem Selection
Consider each of the following problems to answer the question:
“Which problems are best suited to which Mathematical Process?”

16. Combination of Functions Card Game

17. Volume of Three Dimensional Shapes
Develop, through investigation (e.g. using concrete materials) the formulas for the volume of a pyramid, a cone and a sphere

18. Temperature Problem
The inhabitants off Xenor use two scales for measuring temperature. On the A scale, water freezes at 0° and boils at 80°, whereas on the B scale, water freezes at -20° and boils at 120°. What is the equivalent on the A scale of a temperature of 15° on the B scale?
(1970-J-16)

19. Painted Cube Problem
A 10 x 10 x 10 cube made up of small cubes is dipped into a bucket of red paint and removed.
How many small cubes will have 3 faces painted?
How many small cubes will have 2 faces painted?
How many small cubes will have 1 face painted?
How many small cubes will have 0 faces painted?
Generalize your results for an n x n x n cube.

20. Painted Cube Problem… Graphically
Graphically, using Excel...

21. Painted Cube Problem… Graphically
Geometrically, using cubes and patterns...
1 face painted
3 faces painted
2 faces painted
(n – 2)X(n – 2)
“square”
(n – 2)
8 Corners
6 Faces
12 Edges
N3 = 8
N2 = 12(n – 2)
N1 = 6(n – 2)2

22. Dart Board Problem
This dart board is designed with a square inside a circle and a square outside the same circle.
Assign numerical values of 2, 5 and 8 to the three coloured regions on the dart board such that regions with smaller areas are assigned higher scores.
Justify your solution.

23. Which mathematical processes will you use during this investigation?
Problem Solving
Representing
Reflecting
Reasoning and Proving
Connecting
Selecting Tools and Computational Strategies
Communicating

24. Problem Solving Activity
In pairs, explore different solutions to one of the problems on the previous pages
As a table, share your solutions and note:
the grade level(s) appropriate to each solution Explain?
the variety of “Tools” used
the different problem solving strategies employed
the Mathematical Processes accessed (10 minutes)

25. Assessing the Math Processes
Fishbowl Activity
Half the groups “solve” one of the problem
The remaining groups observe fishbowl style and assess the math processes they observe using the given rubric.
The observing group may attempt to identify other processes that become apparent in the solving activity.
Groups switch roles.

26. Graffiti
Rotate through each station and answer the following question.
“What have I learned about this topic?”: ______________________________
Repeat the rotation to read all the comments.

27. Home Activity
Brainstorm ideas of how to creatively remember and present some of your learning.