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

Retention Timeline Pink: time students retain procedures 0 2 4 6 8 10 years Pink: time students retain procedures Yellow: time students retain concepts Blue: time students retain math processes

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

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.

Assessing the Processes Assessment vs Evaluation vs Reporting

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

Mathematics Processes Rubric

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

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.

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

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

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.

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

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

Combination of Functions Card Game

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

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)

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.

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

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

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.

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

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)

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.

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.

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