NCTM Day 1

The sessions I attended and three things I want to remember from each one.

Incredible Math Tasks! Supporting the Productive Struggle in Learning Mathematics

Bill Barnes and Jenny Novak

- Five Practices for Orchestrating Productive Math Discussions by Stein and Smith

- Choose a learning target and find a task that matches it, then:

- anticipating, monitoring, selecting, sequencing and connecting

- Resources at Howard County Wiki

Building Middle Grades Ratio, Proportions, and Proportional Reasoning Essential Understandings

Travis Olson, Hannah Slovin, Melfried Olson

- Keala makes pizza at a rate of 3 pizzas in 5 minutes. Casey makes pizza at a rate of 4 pizzas in 9 minutes. Who is faster?

- You cut 2/5 of a piece of a board. The piece is ¾ of a foot long. How long is the whole board?

- Two solving methods I hadn’t thought about:

(2/5)x = 3/4 Scale up both sides by 2 ½ (2/5)x = (3/4)(5/2)

(2/5)x = 3/4 (1/5)x=(1/2)(3/4) 1x = (5)(1/2)(3/4)=(5/2)(3/4)

Developing Fractional Reasoning through Number Talks

Ann Dominick and Sherry Parrish

- Fractional Reasoning: Distinct numbers, parts of a whole, denominator, numerator, equivalence

- Comparing Fractions: benchmarks, unit fractions, distance from whole, compare numerators, compare denominators

- Whole # Multiplication: Partial products, doubling and halving, repeated addition, breaking factors into factors

Getting Students to Pose Powerful Questions

Jane M. Wilburne

- When you ask a question, you are more interested in finding an answer

- People don’t ask questions when they are angry/upset/troubled/victimized, other people around them have more knowledge/power --> intimidation, can’t formulate a question, haven’t felt supported in the past, lack of time

- Promoting classroom questioning: model questions, multiple platforms for students to ask and answer questions, invite questions, safe environment, plan for questioning (prompts)

Getting Students to Argue in Class with Number Sense Activities

Andrew Stadel

- Is the circumference of a Nalgene bottle greater than its height? Students improve their justification each time in first explaining to someone who agrees with them, second explaining to someone who agrees with them, and third convincing someone who disagrees with them, all while using the sentence frame: “I believe the circumference is {less than/equal to/greater than} the height of the bottle because _______”

- Each answer faces in a different direction, once they are done justifying, get the option to choose direction change

- Sentence frame for justifying prediction “I noticed ____, so I _____”

Tasks That Build the Essential Understandings in Middle Grades Algebra

Zandra de Araujo, Barbra Dougherty, Fay Zenigami

- Tasks:

• g - 227 = 543. g - 230 equals what?
• Write an equivalent expression for 5 - 7m
• d + 1 is less than d + 3. Is this always, sometimes, or never true?

- Flexibility, Reversibility, and Generalization problems

- Essential Understandings in Practice book coming out in the fall

Teachers as Designers: Mindset and Multidimensional mathematics in Classrooms

Jo Boaler

- even if you are not aware of making a mistake, your synapses will still fire because you are making a mistake (or possible because you are thinking hard?)

- pose the problem before teaching the method

- (first) week of school tasks

ShadowCon

Michael Pershan

(I sadly came in at the end of this, so he was the only speaker out of six that I saw)

- Problems with our hints: too vague, kill thinking, don’t have reasons, we improvise too much

- For better hints: add context, add reasons, be just specific enough. Example: If you’re dealing with lots of data it can help to make a table to help us notice patterns.

- Call to action: plan some hints, try them out in the classroom, and share them