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Prompting productive mathematical discussions
Dr Amie Albrecht University of South Australia
www.tinyurl.com/MatConf16-aa-discussions
@nomad_penguin
2016 MAT Annual Conference (14 May 16)
amiealbrecht.com
#MATConf16
Same. Different. Same.
More: Notice and Wonder
Ever Wonder What They’d Notice? (Annie Fetter’s NCTM 2011 Ignite Talk)www.youtube.com/watch?v=a-Fth6sOaRA&feature=youtu.be
@maxmathforum
Chapter 4 of ‘Powerful Problem Solving’ (but also just google ‘Notice and Wonder’)
#noticewonder#tmwyk (Talking Math With Your Kids)#wcydwt (What Can You Do With This?)
Activities for Sense Making with the
Mathematical Practices
Max Ray of The Math Forum @ Drexel
Powerful Problem Solving
Foreword by Susan O’Connell
Hidden Decision-Making in the Math Classroom (Or: ‘All What, No Why’?) (Annie Fetter’s Asilomar 2015 Ignite Talk)https://www.youtube.com/watch?v=LK2eXdYdHjs&feature=youtu.be
Prompts to help BUILD CURIOSITY
# @
# @WTF?
# @WTF?
#MTBoS
# @WTF?
#lessonstarter#mathphoto15#wcydwt#tmwyk
#MTBoS
More: MTBoS
To read the hashtag without joining Twitter: twitter.com/hashtag/mtbos
To find out more about MTBoS (it’s not just Twitter!): exploremtbos.wordpress.com
threeacts.mrmeyer.com @ddmeyer
threeacts.mrmeyer.com @ddmeyer
threeacts.mrmeyer.com @ddmeyer
Write down the first question that comes to mind
Write down the first question that comes to mind
• How many toothpicks does he have?
Write down the first question that comes to mind
• How many toothpicks does he have?• How many smaller triangles are in the larger triangle?
Write down the first question that comes to mind
• How many toothpicks does he have?• How many smaller triangles are in the larger triangle?• Does he complete the whole formation or does he stop in the middle?
Write down the first question that comes to mind
• How many toothpicks does he have?• How many smaller triangles are in the larger triangle?• Does he complete the whole formation or does he stop in the middle?
• How big does the triangle get? (In terms of number of layers.)
Write down the first question that comes to mind
• How many toothpicks does he have?• How many smaller triangles are in the larger triangle?• Does he complete the whole formation or does he stop in the middle?
• How big does the triangle get? (In terms of number of layers.)• How many toothpicks are used in each layer?
Write down the first question that comes to mind
• How many toothpicks does he have?• How many smaller triangles are in the larger triangle?• Does he complete the whole formation or does he stop in the middle?
• How big does the triangle get? (In terms of number of layers.)• How many toothpicks are used in each layer?• How long is it going to take?
Write down the first question that comes to mind
• How many toothpicks does he have?• How many smaller triangles are in the larger triangle?• Does he complete the whole formation or does he stop in the middle?
• How big does the triangle get? (In terms of number of layers.)• How many toothpicks are used in each layer?• How long is it going to take?• What is the perimeter of the entire triangle?
Write down the first question that comes to mind
• How many toothpicks does he have?• How many smaller triangles are in the larger triangle?• Does he complete the whole formation or does he stop in the middle?
• How big does the triangle get? (In terms of number of layers.)• How many toothpicks are used in each layer?• How long is it going to take?• What is the perimeter of the entire triangle?• What is the area of the entire triangle?
Write down the first question that comes to mind
• How many toothpicks does he have?• How many smaller triangles are in the larger triangle?• Does he complete the whole formation or does he stop in the middle?
• How big does the triangle get? (In terms of number of layers.)• How many toothpicks are used in each layer?• How long is it going to take?• What is the perimeter of the entire triangle?• What is the area of the entire triangle?• What is the end product going to look like?
Write down the first question that comes to mind
• How many toothpicks does he have?• How many smaller triangles are in the larger triangle?• Does he complete the whole formation or does he stop in the middle?
• How big does the triangle get? (In terms of number of layers.)• How many toothpicks are used in each layer?• How long is it going to take?• What is the perimeter of the entire triangle?• What is the area of the entire triangle?• What is the end product going to look like?• Is he going to clean the mess up afterwards?
Write down the first question that comes to mind
• How many toothpicks does he have?• How many smaller triangles are in the larger triangle?• Does he complete the whole formation or does he stop in the middle?
• How big does the triangle get? (In terms of number of layers.)• How many toothpicks are used in each layer?• How long is it going to take?• What is the perimeter of the entire triangle?• What is the area of the entire triangle?• What is the end product going to look like?• Is he going to clean the mess up afterwards?• Why is he doing this?
Write down the first question that comes to mind
• How many toothpicks does he have?• How many smaller triangles are in the larger triangle?• Does he complete the whole formation or does he stop in the middle?
• How big does the triangle get? (In terms of number of layers.)• How many toothpicks are used in each layer?• How long is it going to take?• What is the perimeter of the entire triangle?• What is the area of the entire triangle?• What is the end product going to look like?• Is he going to clean the mess up afterwards?• Why is he doing this?
Write down the first question that comes to mind
• How many toothpicks does he have?• How many smaller triangles are in the larger triangle?• Does he complete the whole formation or does he stop in the middle?
• How big does the triangle get? (In terms of number of layers.)• How many toothpicks are used in each layer?• How long is it going to take?• What is the perimeter of the entire triangle?• What is the area of the entire triangle?• What is the end product going to look like?• Is he going to clean the mess up afterwards?• Why is he doing this?
• How many rows does he create with his toothpicks?
Write down the first question that comes to mind
• How many toothpicks does he have?• How many smaller triangles are in the larger triangle?• Does he complete the whole formation or does he stop in the middle?
• How big does the triangle get? (In terms of number of layers.)• How many toothpicks are used in each layer?• How long is it going to take?• What is the perimeter of the entire triangle?• What is the area of the entire triangle?• What is the end product going to look like?• Is he going to clean the mess up afterwards?• Why is he doing this?
• How many rows does he create with his toothpicks?
Write down the first question that comes to mind
• How many toothpicks does he have?• How many smaller triangles are in the larger triangle?• Does he complete the whole formation or does he stop in the middle?
• How big does the triangle get? (In terms of number of layers.)• How many toothpicks are used in each layer?• How long is it going to take?• What is the perimeter of the entire triangle?• What is the area of the entire triangle?• What is the end product going to look like?• Is he going to clean the mess up afterwards?• Why is he doing this?
• How many rows does he create with his toothpicks?
Write down the first question that comes to mind
Act 1: The Hook
Act 1I: The Journey
Act III: The Resolution
threeacts.mrmeyer.com @ddmeyer
threeacts.mrmeyer.com @ddmeyer
threeacts.mrmeyer.com @ddmeyer
Act IV: The Sequel
mrkraft.wikispaces.com/Triangle+of+Toothpicks @nathankraft1
mrkraft.wikispaces.com/Triangle+of+Toothpicks @nathankraft1
mrkraft.wikispaces.com/Triangle+of+Toothpicks @nathankraft1
mrkraft.wikispaces.com/Triangle+of+Toothpicks @nathankraft1
mrkraft.wikispaces.com/Triangle+of+Toothpicks @nathankraft1
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CLIMBRIMEP
Copyright © 2014 Math for Love
What do you notice? What do you wonder?
mathforlove.com/games
Prompts to help BUILD CURIOSITY
No ‘right’ question
Prompts that ENCOURAGE RESPONSES
No single ‘right’ answer
Shade a quarter of a cross. Be as creative as you can!
Quarter of a cross
@nomad_penguin
@DavidKButlerUoA
5/4 = 1+1/4
5/4 = 1/2 + 3/4
5/4 = 2*(5/8)
5/4 = 1/2*(5/2)
@DavidKButlerUoA
@DavidKButlerUoA#QuarterTheCross
@Simon_Gregg#QuarterTheCross
Prompts with MULTIPLE APPROACHES
No single ‘right’ method
How many circles are in stage 10? …stage 100?
Inspired by visualpatterns.org
How many circles are in stage 10? …stage 100?
Inspired by visualpatterns.org
Sketch a graph.
Inspired by visualpatterns.org
Create a table.
Inspired by visualpatterns.org
How many circles are in stage 10? …stage 100?
Inspired by visualpatterns.org
Sketch a graph.
Inspired by visualpatterns.org
Create a table.
Inspired by visualpatterns.org
How many circles are in stage 10? …stage 100?
Inspired by visualpatterns.org
Sketch a graph.
Inspired by visualpatterns.org
Write an equation.
Inspired by visualpatterns.org
Prompts that stimulate DEEP THINKING
Procedural fluency↓
Conceptual understanding
Find the mean, median and mode:
5 3 6 3 3
Instead of:
nrich.maths.org/6267
Find the mean, median and mode:
5 3 6 3 3
Instead of:
Suppose that the mean, median and mode for five positive integers were:
mean: 4median: 3mode: 3
Would you be able to tell me the numbers?
Try:
nrich.maths.org/6267
Find the slope of the line passing through the points:
(3,5) and (8,4)
Instead of:
@MJFenton
Find the slope of the line passing through the points:
(3,5) and (8,4)
Instead of:
and
Use four different whole numbers (from 2 to 9)
to determine a line whose slope is least/greatest/closest to zero.
Try:
( , ) ( , )
@MJFenton
Use the numbers 1 through 9, exactly once each, to fill in the boxes and make three decimals whose sum is as close to 1 as possible.
Adding decimals
0.0.0.+
www.openmiddle.com @robertkaplinsky
Prompts that require PRECISE VOCABULARY
Prompts that start MATHS FIGHTS
Justify your position
@mr_stadel
General prompts
Even more resources
@nomad_penguin
www.tinyurl.com/MatConf16-aa-discussions
amie.albrecht@unisa.edu.au
www.amiealbrecht.com
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