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NAEYC Conference
Preschoolers and ECE teachers
as mathematicians:
Playing with early math concepts
through games and 'math talk'
Teresa Gonczy
Friday, Nov 20th, 1-2:30pm
© Teresa Gonczy 2015 – NAEYC National Conference – Orlando, FL
Who am I?
Teresa Gonczy
* Graduate Student studying Early Math Learning
* Owned an early learning center in LA
* Run the @earlymath Twitter community
Who are you?
Teachers – Directors – Researchers – Etc
Preschool – Infant/Toddler - Kindergarten
Math Problem Solving
Let's get into
thinking & playing mode! :-)
Math Problem Solving
The Smallest Candy Store Problem
* Take a few minutes to try it out yourself
* Then collaborate with 3-4 people
* Write out your combined ideas on paper
(document your solutions)
Math Problem Solving
The Smallest Candy Store Problem
* What were some of the strategies you used?
Math Problem Solving
The Smallest Candy Store Problem
* What made this problem interesting
or unusual?
Math Problem Solving
The Smallest Candy Store Problem
* How did working on this problem make you feel?
Math Problem Solving
The Smallest Candy Store Problem
* How could you modify or adapt the problem
into one that your students could work on?
Math Problem Solving
Exercises versus Problems
* one right answer * multiple solutions
* memorizing rules * figuring it out
* working alone * collaborating
* doing it in head * using materials
* only use numbers * use shapes, etc
Math Problem Solving
* Guess & check
* Make a list/table
* Look for a pattern
* Draw a picture/model
* Solve a simpler problem
* Work backwards
* Act it out/use manipulatives
* Change your point of view
* Try special cases
Why Math in ECE?
Research shows that early math skills are just as
predictive, and possibly more predictive, of later
academic success than early literacy skills.
And yet most preschool classrooms devote much
more time to literacy than to math.
Duncan, G.J., Dowsett, C.J., Claessens, A., Magnuson, K., Huston, A.C., Klebanov, P., Pagani, L.S., Feinstein, L., Engel, M., Brooks-Gunn, J., Sexton, H.,
Duckworth, K., and Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43(6).
NCTM & NAEYC Joint Position
Statement Recommendations
4) Use curriculum and teaching practices that strengthen
children's problem solving and reasoning processes
as well as representing, communicating,
and connecting math ideas
6) Provide for children's deep and sustained interaction
with key mathematical ideas
8) Provide ample time, materials, and teacher support for
children to engage in play, a context in which they explore
and manipulate mathematical ideas with keen interest
Why Early Math Games?
Early math isn't about worksheets or flashcards.
It is seeing patterns in the world, playing games,
building with blocks, and 'talking math'.
Why Early Math Games?
Math games are fun and effective!
Researchers found that the more board games
children played, the better they performed on
various early math tasks.
Ramani GB and Siegler RS. 2008. Promoting broad and stable improvements in low-income children’s numerical knowledge through playing with number board
games. Child Development 79(2):375-394 - See more at: http://www.parentingscience.com/preschool-board-game-math.html#sthash.xvbOeAdk.dpuf
Math Games
Let's look at some math game ideas.
Think about...
* what specific math skills are being developed?
* what non-math skills are being developed?
* how could you create this game in your
classroom with basic materials?
Math Games
Image and activities from http://kidsactivitiesblog.com/6415/early-math-activities-2
Math Games
Image and activities from http://kidsactivitiesblog.com/6415/early-math-activities-2
Math Games
Think about...
* what specific math skills are being developed?
* what non-math skills are being developed?
* how could you create this game in your
classroom with basic materials?
Math Games
What does the research say about
some very effective math games?
Math Games Research
Early math skill:
Moving from logarithmic thinking
to linear thinking
Ramani GB and Siegler RS. 2008. Promoting broad and stable improvements in low-income children’s numerical knowledge through playing with number board
games. Child Development 79(2):375-394 - See more at: http://www.parentingscience.com/preschool-board-game-math.html#sthash.xvbOeAdk.dpuf
Math Games Research
The Great Race Game
Ramani GB and Siegler RS. 2008. Promoting broad and stable improvements in low-income children’s numerical knowledge through playing with number board
games. Child Development 79(2):375-394 - See more at: http://www.parentingscience.com/preschool-board-game-math.html#sthash.xvbOeAdk.dpuf
Math Games Research
Moving from logarithmic thinking
to linear thinking -
The Great Race Game
The Great Race Game is...
* not color based
* not circular track
* straight track with evenly-spaced numbers
Siegler, R. S. & Ramani, G. B. (2009). Playing linear number board games ­ but not circular ones ­ improves low­income preschoolers’ numerical understanding.
Journal of Educational Psychology, 101, 545­560.
Math Games Research
Moving from logarithmic thinking
to linear thinking -
The Great Race Game
How you count matters!
Count on!
“You were on 4. You spun to move
two more spaces. 4... 5... 6
Now you're on 6.”
Laski EV and Siegler RS. 2014. Learning from number board games: You learn what you encode. Dev Psychol. 50(3):853­64. ­ See more at:
http://www.parentingscience.com/preschool­math­games.html#sthash.G1eVH9KD.dpuf
Math Games Research
Moving from logarithmic thinking
to linear thinking -
The Great Race Game
You can create in your classroom -
Individualize for each student and their interests
Laski EV and Siegler RS. 2014. Learning from number board games: You learn what you encode. Dev Psychol. 50(3):853­64. ­ See more at:
http://www.parentingscience.com/preschool­math­games.html#sthash.G1eVH9KD.dpuf
Math Games Research
Subitizing & the Approximate Number System
Daniel C. Hyde, Saeeda Khanum, Elizabeth S. Spelke. Brief non­symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in
children. Cognition, 2014; 131 (1): 92 DOI: 10.1016/j.cognition.2013.12.007
Math Games Research
Daniel C. Hyde, Saeeda Khanum, Elizabeth S. Spelke. Brief non­symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in
children. Cognition, 2014; 131 (1): 92 DOI: 10.1016/j.cognition.2013.12.007
Math Games Research
Subitizing & the Approximate Number System -
* Saying how many after a quick showing
* Comparing two quantities
Without Counting!
Daniel C. Hyde, Saeeda Khanum, Elizabeth S. Spelke. Brief non­symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in
children. Cognition, 2014; 131 (1): 92 DOI: 10.1016/j.cognition.2013.12.007
Math Games Research
Subitizing & the Approximate Number System -
In the classroom...
* dots on paper plates
* objects hidden by cloth
Daniel C. Hyde, Saeeda Khanum, Elizabeth S. Spelke. Brief non­symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in
children. Cognition, 2014; 131 (1): 92 DOI: 10.1016/j.cognition.2013.12.007
Math Games Research
Spatial Training
Yi Ling Cheng, Kelly S. Mix. Spatial Training Improves Children's Mathematics Ability. Journal of Cognition and Development, 2012; 120919075341007 DOI:
10.1080/15248372.2012.725186
Math Games Research
Spatial Training
Yi Ling Cheng, Kelly S. Mix. Spatial Training Improves Children's Mathematics Ability. Journal of Cognition and Development, 2012; 120919075341007 DOI:
10.1080/15248372.2012.725186
Math Games Research
Spatial Training -
* Blocks & tangram shapes
* Mental rotation
* Fitting blocks into shapes
* Playing with puzzles
Yi Ling Cheng, Kelly S. Mix. Spatial Training Improves Children's Mathematics Ability. Journal of Cognition and Development, 2012; 120919075341007 DOI:
10.1080/15248372.2012.725186
Math Games Research
Spatial Training -
Using spatial language (in, on, above, etc)
is also very important!
Pruden SM, Levine SC and Huttenlocher J. 2011. Children's spatial thinking: Does talk about the aptial world matter? Developmental Science (14): 1417­1430. ­
See more at: http://www.parentingscience.com/spatial­intelligence.html#sthash.8R3JvZfG.dpuf
Math Talk Research
Not only spatial talk -
Lots of different types of
math talk are helpful
Pruden SM, Levine SC and Huttenlocher J. 2011. Children's spatial thinking: Does talk about the aptial world matter? Developmental Science (14): 1417-1430. -
See more at: http://www.parentingscience.com/spatial-intelligence.html#sthash.8R3JvZfG.dpuf
Math Talk Research
Math talk from preschool teachers
is associated with the growth of
preschoolers' math knowledge
Klibanoff, R.S., Levine, S.C., Huttenlocher, J., Vasilyeva, M., & Hedges, L.V. (2006). Preschool Children's Mathematical Knowledge: The Effect of Teacher
"Math Talk". Developmental Psychology 42-1, 59-69.
Math Talk Research
What is math talk?
Klibanoff, R.S., Levine, S.C., Huttenlocher, J., Vasilyeva, M., & Hedges, L.V. (2006). Preschool Children's Mathematical Knowledge: The Effect of Teacher
"Math Talk". Developmental Psychology 42-1, 59-69.
Math Talk Research
What is math talk?
* counting (with object names)
* cardinality (how many in a set)
* spatial (in – on – over – etc) & shapes
* comparisons (same – different)
* basic calculations (one and another is two)
* fractions ('half of a cookie')
* equivalence and non-equivalence
* ordering items ('first', 'next', 'last')
* recognizing number symbols
Klibanoff, R.S., Levine, S.C., Huttenlocher, J., Vasilyeva, M., & Hedges, L.V. (2006). Preschool Children's Mathematical Knowledge: The Effect of Teacher
"Math Talk". Developmental Psychology 42-1, 59-69.
Research into Classroom
So how do we take what the research says
and bring it into our classrooms?
Let's Create!
We don't need to buy games!
We can create our own games with
basic materials,
and we can customize the games
to our curriculum topics and
our students' interests.
Let's Create!
* Decide on a theme
(curriculum topic, student interest, etc)
* Choose a type of game & make a prototype
(linear race game, subitizing & ANS,
spatial training, or your own idea!)
* Write out 3 possible 'math talk' questions
you could ask or sentences you could say
with your children
Let's Create!
Presentation of Games
Conclusion
* I used to think... Now I think...
* What new idea or activity are you going to take
into your classroom next week?
Contact
Teresa Gonczy
teresaeg@gmail.com
Twitter @earlymath
Slides will be available
on my blog at
www.teresaeg.com/blog

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NAEYC - Early Math Talk

  • 1. NAEYC Conference Preschoolers and ECE teachers as mathematicians: Playing with early math concepts through games and 'math talk' Teresa Gonczy Friday, Nov 20th, 1-2:30pm © Teresa Gonczy 2015 – NAEYC National Conference – Orlando, FL
  • 2. Who am I? Teresa Gonczy * Graduate Student studying Early Math Learning * Owned an early learning center in LA * Run the @earlymath Twitter community
  • 3. Who are you? Teachers – Directors – Researchers – Etc Preschool – Infant/Toddler - Kindergarten
  • 4. Math Problem Solving Let's get into thinking & playing mode! :-)
  • 5. Math Problem Solving The Smallest Candy Store Problem * Take a few minutes to try it out yourself * Then collaborate with 3-4 people * Write out your combined ideas on paper (document your solutions)
  • 6. Math Problem Solving The Smallest Candy Store Problem * What were some of the strategies you used?
  • 7. Math Problem Solving The Smallest Candy Store Problem * What made this problem interesting or unusual?
  • 8. Math Problem Solving The Smallest Candy Store Problem * How did working on this problem make you feel?
  • 9. Math Problem Solving The Smallest Candy Store Problem * How could you modify or adapt the problem into one that your students could work on?
  • 10. Math Problem Solving Exercises versus Problems * one right answer * multiple solutions * memorizing rules * figuring it out * working alone * collaborating * doing it in head * using materials * only use numbers * use shapes, etc
  • 11. Math Problem Solving * Guess & check * Make a list/table * Look for a pattern * Draw a picture/model * Solve a simpler problem * Work backwards * Act it out/use manipulatives * Change your point of view * Try special cases
  • 12. Why Math in ECE? Research shows that early math skills are just as predictive, and possibly more predictive, of later academic success than early literacy skills. And yet most preschool classrooms devote much more time to literacy than to math. Duncan, G.J., Dowsett, C.J., Claessens, A., Magnuson, K., Huston, A.C., Klebanov, P., Pagani, L.S., Feinstein, L., Engel, M., Brooks-Gunn, J., Sexton, H., Duckworth, K., and Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43(6).
  • 13. NCTM & NAEYC Joint Position Statement Recommendations 4) Use curriculum and teaching practices that strengthen children's problem solving and reasoning processes as well as representing, communicating, and connecting math ideas 6) Provide for children's deep and sustained interaction with key mathematical ideas 8) Provide ample time, materials, and teacher support for children to engage in play, a context in which they explore and manipulate mathematical ideas with keen interest
  • 14. Why Early Math Games? Early math isn't about worksheets or flashcards. It is seeing patterns in the world, playing games, building with blocks, and 'talking math'.
  • 15. Why Early Math Games? Math games are fun and effective! Researchers found that the more board games children played, the better they performed on various early math tasks. Ramani GB and Siegler RS. 2008. Promoting broad and stable improvements in low-income children’s numerical knowledge through playing with number board games. Child Development 79(2):375-394 - See more at: http://www.parentingscience.com/preschool-board-game-math.html#sthash.xvbOeAdk.dpuf
  • 16. Math Games Let's look at some math game ideas. Think about... * what specific math skills are being developed? * what non-math skills are being developed? * how could you create this game in your classroom with basic materials?
  • 17. Math Games Image and activities from http://kidsactivitiesblog.com/6415/early-math-activities-2
  • 18. Math Games Image and activities from http://kidsactivitiesblog.com/6415/early-math-activities-2
  • 19. Math Games Think about... * what specific math skills are being developed? * what non-math skills are being developed? * how could you create this game in your classroom with basic materials?
  • 20. Math Games What does the research say about some very effective math games?
  • 21. Math Games Research Early math skill: Moving from logarithmic thinking to linear thinking Ramani GB and Siegler RS. 2008. Promoting broad and stable improvements in low-income children’s numerical knowledge through playing with number board games. Child Development 79(2):375-394 - See more at: http://www.parentingscience.com/preschool-board-game-math.html#sthash.xvbOeAdk.dpuf
  • 22. Math Games Research The Great Race Game Ramani GB and Siegler RS. 2008. Promoting broad and stable improvements in low-income children’s numerical knowledge through playing with number board games. Child Development 79(2):375-394 - See more at: http://www.parentingscience.com/preschool-board-game-math.html#sthash.xvbOeAdk.dpuf
  • 23. Math Games Research Moving from logarithmic thinking to linear thinking - The Great Race Game The Great Race Game is... * not color based * not circular track * straight track with evenly-spaced numbers Siegler, R. S. & Ramani, G. B. (2009). Playing linear number board games ­ but not circular ones ­ improves low­income preschoolers’ numerical understanding. Journal of Educational Psychology, 101, 545­560.
  • 24. Math Games Research Moving from logarithmic thinking to linear thinking - The Great Race Game How you count matters! Count on! “You were on 4. You spun to move two more spaces. 4... 5... 6 Now you're on 6.” Laski EV and Siegler RS. 2014. Learning from number board games: You learn what you encode. Dev Psychol. 50(3):853­64. ­ See more at: http://www.parentingscience.com/preschool­math­games.html#sthash.G1eVH9KD.dpuf
  • 25. Math Games Research Moving from logarithmic thinking to linear thinking - The Great Race Game You can create in your classroom - Individualize for each student and their interests Laski EV and Siegler RS. 2014. Learning from number board games: You learn what you encode. Dev Psychol. 50(3):853­64. ­ See more at: http://www.parentingscience.com/preschool­math­games.html#sthash.G1eVH9KD.dpuf
  • 26. Math Games Research Subitizing & the Approximate Number System Daniel C. Hyde, Saeeda Khanum, Elizabeth S. Spelke. Brief non­symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children. Cognition, 2014; 131 (1): 92 DOI: 10.1016/j.cognition.2013.12.007
  • 27. Math Games Research Daniel C. Hyde, Saeeda Khanum, Elizabeth S. Spelke. Brief non­symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children. Cognition, 2014; 131 (1): 92 DOI: 10.1016/j.cognition.2013.12.007
  • 28. Math Games Research Subitizing & the Approximate Number System - * Saying how many after a quick showing * Comparing two quantities Without Counting! Daniel C. Hyde, Saeeda Khanum, Elizabeth S. Spelke. Brief non­symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children. Cognition, 2014; 131 (1): 92 DOI: 10.1016/j.cognition.2013.12.007
  • 29. Math Games Research Subitizing & the Approximate Number System - In the classroom... * dots on paper plates * objects hidden by cloth Daniel C. Hyde, Saeeda Khanum, Elizabeth S. Spelke. Brief non­symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children. Cognition, 2014; 131 (1): 92 DOI: 10.1016/j.cognition.2013.12.007
  • 30. Math Games Research Spatial Training Yi Ling Cheng, Kelly S. Mix. Spatial Training Improves Children's Mathematics Ability. Journal of Cognition and Development, 2012; 120919075341007 DOI: 10.1080/15248372.2012.725186
  • 31. Math Games Research Spatial Training Yi Ling Cheng, Kelly S. Mix. Spatial Training Improves Children's Mathematics Ability. Journal of Cognition and Development, 2012; 120919075341007 DOI: 10.1080/15248372.2012.725186
  • 32. Math Games Research Spatial Training - * Blocks & tangram shapes * Mental rotation * Fitting blocks into shapes * Playing with puzzles Yi Ling Cheng, Kelly S. Mix. Spatial Training Improves Children's Mathematics Ability. Journal of Cognition and Development, 2012; 120919075341007 DOI: 10.1080/15248372.2012.725186
  • 33. Math Games Research Spatial Training - Using spatial language (in, on, above, etc) is also very important! Pruden SM, Levine SC and Huttenlocher J. 2011. Children's spatial thinking: Does talk about the aptial world matter? Developmental Science (14): 1417­1430. ­ See more at: http://www.parentingscience.com/spatial­intelligence.html#sthash.8R3JvZfG.dpuf
  • 34. Math Talk Research Not only spatial talk - Lots of different types of math talk are helpful Pruden SM, Levine SC and Huttenlocher J. 2011. Children's spatial thinking: Does talk about the aptial world matter? Developmental Science (14): 1417-1430. - See more at: http://www.parentingscience.com/spatial-intelligence.html#sthash.8R3JvZfG.dpuf
  • 35. Math Talk Research Math talk from preschool teachers is associated with the growth of preschoolers' math knowledge Klibanoff, R.S., Levine, S.C., Huttenlocher, J., Vasilyeva, M., & Hedges, L.V. (2006). Preschool Children's Mathematical Knowledge: The Effect of Teacher "Math Talk". Developmental Psychology 42-1, 59-69.
  • 36. Math Talk Research What is math talk? Klibanoff, R.S., Levine, S.C., Huttenlocher, J., Vasilyeva, M., & Hedges, L.V. (2006). Preschool Children's Mathematical Knowledge: The Effect of Teacher "Math Talk". Developmental Psychology 42-1, 59-69.
  • 37. Math Talk Research What is math talk? * counting (with object names) * cardinality (how many in a set) * spatial (in – on – over – etc) & shapes * comparisons (same – different) * basic calculations (one and another is two) * fractions ('half of a cookie') * equivalence and non-equivalence * ordering items ('first', 'next', 'last') * recognizing number symbols Klibanoff, R.S., Levine, S.C., Huttenlocher, J., Vasilyeva, M., & Hedges, L.V. (2006). Preschool Children's Mathematical Knowledge: The Effect of Teacher "Math Talk". Developmental Psychology 42-1, 59-69.
  • 38. Research into Classroom So how do we take what the research says and bring it into our classrooms?
  • 39. Let's Create! We don't need to buy games! We can create our own games with basic materials, and we can customize the games to our curriculum topics and our students' interests.
  • 40. Let's Create! * Decide on a theme (curriculum topic, student interest, etc) * Choose a type of game & make a prototype (linear race game, subitizing & ANS, spatial training, or your own idea!) * Write out 3 possible 'math talk' questions you could ask or sentences you could say with your children
  • 42. Conclusion * I used to think... Now I think... * What new idea or activity are you going to take into your classroom next week?
  • 43. Contact Teresa Gonczy teresaeg@gmail.com Twitter @earlymath Slides will be available on my blog at www.teresaeg.com/blog