NCTM 2018 #SlowMath_ Looking for Structure and Noticing Regularity in Repeated Reasoning

Looking for Structure and Notici Noti cing ng Regularity in Repeated Repeated Reasoning

Jennifer Wilson Wilson

Jill Gough

Black Mountain, NC @jwilson828 http://easingthehurrysyndrome.wordpress.com

Trinity School, Atlanta, GA @jgough http://jplgough.wordpress.com

http://bit.ly/slowmathmp78 http://bit.ly/slo wmathmp78

● Name ● Building/Location ● Course(s) ● Your school year, in one word ... ● One outcome you hope for

● How do you give your learners the opportunity to look for

and make use of structure, to look for and express regularity in repeated reasoning reasoning?? ● How might you give your learners the opportunity to look

for and make use of structure, to look for and express regularity in repeated reasoning reasoning??

All students students need time to think before responding to a teacher’s question, talking with a partner, or following a classmate’s strategy presented to the whole group. Grace Kelemanik, Amy Lucenta, Susan Janssen

Kelemanik, Grace, Amy Lucenta, Susan Janssen. Creighton, and Magdalene Lampert.Routines Lampert.Routines for Reasoning: Fostering the Mathematical

Add a reflective pause because because our extroverts need to learn to listen. Our introverts need to learn to talk.

Cain, Susan. Quiet . New York: Broadway, 2013. Print.

9ax+9b–6=21 Based on the equation above, what is the value of ax+b? A. B. C. D.

3 6 8 12

“SAT Practice Tests.” SAT Suite of Assessments, Assessments, 24 Apr. 2017,

9ax +9b–6=21 Based on the equation above, what is the value of ax +b? A. B. C. D.

3 6 8 12


Which of the following expressions is equal to 0 for some value of x? A. B. C. D.

| x x–1|–1 | x x+1|+1 |1– x|+1 | x x–1|+1


Which of the following expressions is equal to 0 for some value of x? A. B. C. D.

| x x–1|–1 | x x+1|+1 |1– x|+1 | x x–1|+1


If x2+14 x=51 and x>0, what is the value of x+7?


+7? If x2+14 x=51 and x>0, what is the value of x +7

+49=51 =51+49 +49 x2+14 x+49 +7)2=100 ( x +7


r a e Y e h t f o h c t a C L F N NFL. “Odell Beckham Jr. Makes Catch of the Year! | NFL.” YouTube YouTube,, YouTube, 24 Jan. 2015,

L F N | e c i t c a r P e m a g e r P

bit.ly/ccsssmp

SMP 7: I can look for and make use of structure.

SMP 7: I 7: I can look for and make use of structure.

@jgough Contemplate then Calculate Primer, BPE Boston Teacher Residency.

Which shaded region is larger? Explain your reasoning.

One Square

The Sides and Areas of Tilted Squares

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If the two triangles above are congruent, equilateral triangles, which is greater, the total area of the three red regions red regions or the total area of the six purple purple regions? regions? https://brilliant.org/100day/day37/


What fraction of the regular octagon is shaded red red?? https://brilliant.org/100day/day33/


What is the area of the blue figure? https://brilliant.org/100day/day72/


If the two triangles triangles above are congruent, congruen t, equilateral triangles, which is which is greater, the total area are a of the three red regions red regions or the total area of the six purple purple regions? regions? What fraction of of the regular octagon is shaded red red??

https://brilliant.org/100day/day37/ https://brilliant.or g/100day/day37/


https://brilliant.org/100day/day37/

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e c n a D D T s i w e L y a R d n a h c t a C d e d n a h e n

BreedingEntrtainment. “Odell Beckham One Handed Catch Pregame Routine. And Ray Lewis TD Dance

Research on expertise suggests the importance of providing students with learning experiences that specifically enhance their abilities to recognize meaningful patterns of information.

Bransford, J. D., Brown, A. L., & Cocking, R. R. (2001). How people learn: Brain, mind, experience and school. Washington, D.C.: National Academy Press.

Algebra Talk: Solve Each Equation

bit.ly/ccsssmp

SMP 8: I can look for and express regularity in repeated reasoning.

Visible Learning for Mathematics

If students know where they are going and how they’ll know when they get there, they are better able to set their own expectations, self-monitor, and predict or self-report their own achievement. EFFECT SIZE FOR SELF-REPORTED/STUDENT EXPECTATIONS =1.44 Hattie, John A. (Allan); Fisher, Douglas B.; Frey, Nancy; Gojak, Linda M.; Moore, Sara Delano; Mellman, William L.. Visible Learning for

Using multiple representations representations in instructional materials can facilitate self-explanations. Thus, if you have students self-explain a certain concept or procedure, try to include diagrams or technology-enhanced representations like simulations to help students generate self-explanations and learn with understanding. ~Jennifer L. Chiu, Michelene T.H. Chi Chiu, J. and Chi, M. (2014). Supporting self-explanation in the classroom. In V. A. Benassi, C. E. Overson, & C. M. Hakala (Eds.). Applying science of learning in education: Infusing psycholo gical gical science into the curriculum . Retrieved from the Society for the Teaching of Psychology web site:

Prompting self-explanations may help students use multiple representations in complementary, constraining, or constructing roles to fill in missing pieces or revise their understanding. ~Jennifer L. Chiu, Michelene T.H. Chi

Chiu, J. and Chi, M. (2014). Supporting self-explanation in the classroom. In V. A. Benassi, C. E. Overson, & C. M. Hakala (Eds.). Applying science of learning in education: Infusing psycholo gical gical science into the curriculum . Retrieved from the Society for the Teaching of Psychology web site:

Although solving a problem could be a measure of some kind of transfer of the conceptual knowledge, conceptual items should be included if one is interested in the direct impact of self-explaining. ~Jennifer L. Chiu, Michelene T.H. Chi

Chiu, J. and Chi, M. (2014). Supporting self-explanation in the classroom. In V. A. Benassi, C. E. Overson, & C. M. Hakala (Eds.). Applying science of learning in education: Infusing psycholo gical gical science into the curriculum . Retrieved from the Society for the Teaching of Psychology web site:

Multiple studies show that including incorrect solutions or examples in study materials can be particularly helpful for learning with self-explanation: recognize gaps in understanding or repair faulty information, whereas explaining correct examples may be more likely to reaffirm students' existing understanding. ~Jennifer L. Chiu, Michelene T.H. Chi Chiu, J. and Chi, M. (2014). Supporting self-explanation in the classroom. In V. A. Benassi, C. E. Overson, & C. M. Hakala (Eds.). Applying science of learning in education: Infusing psycholo gical gical science into the curriculum . Retrieved from the Society for the Teaching of Psychology web site:

What's My Rule?, Rule?, TI



Labeling Tick Marks on a Number Line

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Deep practice is built on a paradox: struggling in certain targeted ways — operating at the edges of your ability, where you make mistakes — makes you smarter. ~Daniel Coyle

Coyle, Daniel (2009). The Talent Code: Greatness Isn't Born. It's Grown. Here's How. (p. 18). Random House, Inc. Kindle

Or to put it a slightly different way, experiences where you’re forced to slow down, make errors, and correct them —as you would if you were walking up an ice-covered hill, slipping and stumbling as you go— end up making you swift and graceful without your realizing it. ~Daniel Coyle Coyle, Daniel (2009). The Talent Code: Greatness Isn't Born. It's Grown. Here's How. (p. 18). Random House, Inc. Kindle

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Looking for Structure and Notici Noti cing ng Regularity in Repeated Repeated Reasoning

Jennifer Wilson Wilson

Jill Gough

Black Mountain, NC @jwilson828 http://easingthehurrysyndrome.wordpress.com

Trinity School, Atlanta, GA @jgough http://jplgough.wordpress.com

http://bit.ly/slowmathmp78 http://bit.ly/slo wmathmp78

NCTM 2018 #SlowMath_ Looking for Structure and Noticing Regularity in Repeated Reasoning

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