NCTM Days 2 & 3

Three(ish) things I want to remember from the sessions I went to on Friday and Saturday

Building Student Understanding of the Mathematical Practices through IN-formative Assessment

Matt McLeod, Mary Wedon (EDC) 

 - Assessing students’ use of structure (MP7) through computation problems. In directions, write “avoid unnecessary computation”

- "Hidden Meaning" questions

- ex: 36(6⁵) is equivalent to 6⁷. Explain or show why this is true.

- "Chunking" questions

- ex: Simplify the following: 8(99²-4)+3(99²-4)-11(99²-4)

Fake-World Math: When Mathematical Modeling Goes Wrong

Dan Meyer

- There are 5 steps of modeling. Students do a lot of steps 3 and 4 in textbooks. We should be doing a lot more of 1, 2, and 5. Students don’t need to do all 5 steps every time you do modeling. Celebrate what students are contributing at each level through praise, one clap, etc.

            1. Identify the variables

            2. Formulate models

            3. Perform operations

            4. Interpret results

            5. Validate conclusions

- When modeling, we need to be honest about whether the math “works.” Have a discussion why the predicted height in cups with all accurate computation isn't the actual height in cups.

- Set up situations that require knowledge that students don’t have yet. This creates a need for a “bigger boat” (Jaws reference) before we give it to them.

Investigating the Pythagorean Theorem and Its Proofs

Robyn Carlin

- What is the definition of “proof” in the common core? Is it enough for students to be looking at examples and then making generalizations?

Reasoning Revisions Revolution

Patrick Callahan and Jessica Murk

- In having students work on problems you don’t know the answer to, you authentically cede authority and model reasoning and revision

- After having students/groups write and revise their own rules, having all students write the same rule down at the end defeats the purpose

- With peer feedback, the authority shifts from teacher to student. Feedback expectations:

            - it takes practice

            - giving feedback is not the same as being mean

            - think about what you would find helpful

            - avoid opinions

            - be specific

- Bongard problems

What do my students know? How do they know it?

Barbara Dougherty and Jeanette Olson

- Encourage students to show their thinking rather than show their work. In doing so you open the door for valuing logical reasoning over structured algorithms.

- Challenges of open response questions in progress monitoring:

            - students couldn’t explain

            - hard to score

            - students often skipped

- In multiple choice, options have different point values based on complexity of thinking required for the (wrong) option

Bringing the Standards for Mathematical Practice to Life In Classrooms

Ruth Parker

- Daily objectives are too fragmented of a way to learn math. Instead, there should be 6 to 8 units of study a year where you are looking at the same math on the first and last day of the unit (see Phil Daro on grain size). Then, students should be able to answer “what are you trying to figure out right now?” instead of “what math are you learning today?”

- Big mathematical ideas are never fully mastered. They deepen in complexity over time. Therefore, learners should encounter:

• fragile understandings
• periods of cognitive dissonance
• mistakes as sites of learning
• states of not knowing… yet

- Can You See? (Teacher starts by asking questions, then turns it over to the student)

            - 2/5?

            - 2/3?

            -1 divided by 2/3 ?

- Number Bracelets

- a way for students to gain addition fluency

- after doing an example or two, ask students to come up with their questions and explore them