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Mathema'cs in the TK Classroom
Kim Bambao, Martha Drinkwater, and Andrea Meyers San Mateo County Office of Education
Gail Oshima San Mateo Park School, San Mateo
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Outline • Why Early Math Ma8ers • What Does Quality Instruc'on Look Like? • Planning Math Ac'vi'es & Socio-‐Emo'onal Development
• Math Talks • Resources
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Why Early Math Ma8ers
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Why Early Math Ma8ers: Duncan et al., 2007
In 2007, Duncan et al. examined 6 longitudinal data sets to look at the links between school readiness and later academic achievement. – Controlled for mother’s education, socio-economic
status, and other variables
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Why Early Math Ma8ers: Duncan et al., 2007
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Why Early Math Ma8ers: Duncan et al., 2007
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Why Early Math Ma8ers: Duncan et al., 2007
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What Does Quality Support of Early Mathema'cs Look Like?
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What does it look like?
• Flexible…thinking on your feet is really important… – Something might not work for one group, but it will for another
– Something might not work at one point in 8me, but it will for another
– Being able to change ac8vi8es to adapt to children’s place in development (and the day) is essen8al!
• For this you need… – Mathema8cal content knowledge – Knowledge of mathema8cal development – Pedagogy – Classroom management skills
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What does it look like?
• Developmental…providing instruc8on that matches students’ needs… – What do they know? – What are they working on? – What’s next?
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What does it look like?
• Progressions… – Successively more sophis8cated ways of thinking about a topic that can follow one another as children learn about and inves8gate a topic (Duschl et al, 2007)
– A picture of the path students typically follow as they learn…a descrip8on of skills, understandings and knowledge in the sequence in which they typically develop (Masters & Forster, 1996)
– Requires support
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Preschool Founda'ons Number Sense
Kindergarten CCSS Coun'ng and Cardinality
Children expand their understanding of numbers and quan''es in their everyday environment PK. N.S. 1.1 Recite numbers in order to twenty with increasing accuracy
Know number names and the count sequence K. CC. 1 Count to 100 by ones and by tens K. CC. 2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1)
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Preschool Founda'ons Number Sense
Kindergarten CCSS Coun'ng and Cardinality
Children expand their understanding of numbers and quan''es in their everyday environment
Know number names and the count sequence
Vocabulary: count, number words (i.e., one, two, three, etc. from 1-‐100), count by, count from, number, next number, how did you figure that out? What it looks like: • While playing hide-‐and-‐seek, Ezra counts to twenty before looking for the
other children. • When asked to count as high as she can, Melia counts to 50. • When asked how old he is, Kenji answers, “I’m five, and then I’ll be six, seven,
eight, nine, ten!
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Preschool Founda'ons Number Sense
Kindergarten CCSS Coun'ng and Cardinality
Children expand their understanding of numbers and quan''es in their everyday environment
Know number names and the count sequence
Big Ideas: • Students learn to recite numbers before they can apply one-‐to-‐one concepts to
coun'ng objects or understand cardinality (i.e., the last number counted represents the numerosity of the set).
• Encourage students to slow down as they count. Aaer students have had experiences coun'ng from one, have them start coun'ng in the middle of the coun'ng sequence to encourage conceptual understanding of the order of numbers.
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Preschool Founda'ons Number Sense
Kindergarten CCSS Coun'ng and Cardinality
Children expand their understanding of numbers and quan''es in their everyday environment
Know number names and the count sequence
Instruc'onal Issues: • An important goal in early mathema'cs instruc'on is that students achieve fluency
with the coun'ng sequence. Students may learn a short sequence of numbers (“fourfivesix”) and not understand that they are separate numbers (similar to the “lmnop” issue when learning the alphabet).
• Numbers eleven through fiaeen may be difficult for students to learn as they do not follow the pa8ern (number followed by –teen) of sixteen through nineteen. Use discussions about how these numbers are kind of funny—calling a8en'on to the irregularity of these number names may make it easier for students to remember that they do not follow the regular number naming pa8ern.
• Saying the counAng numbers is someAmes referred to as verbal or rote counAng and does not indicate an understanding of object counAng with one-‐to-‐one correspondence.
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Preschool Foundations Number Sense
Kindergarten CCSS Counting and Cardinality
Children expand their understanding of numbers and quantities in their everyday environment
Know number names and the count sequence
Activities: Using a puppet (George), tell the students a story about how George has a hard 'me remembering how to count. Tell them that you would like them to help George figure out when his coun'ng isn’t right. Ask the students to raise their hands when they hear George make a mistake and to remember George’s coun'ng mistake. In George’s voice, count to ten, skipping or repea'ng one number in the sequence. Call on the students who raise their hands to describe George’s mistake. Ask ques'ons to make sure that students thoroughly describe the mistake and how George can fix his mistake. MP2, MP3, MP4, MP6
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CDE TK Framework
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Draa Mathema'cs Framework Chapters hVp://www.cde.ca.gov/ci/ma/cf/draY2mathfwchapters.asp
Bambao, Drinkwater, Meyers, & Oshima: Mathematics in the TK Classroom
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TK Students In Ac'on
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What does it look like?
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Video Clip
Bambao, Drinkwater, Meyers, & Oshima: Mathematics in the TK Classroom
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What does it look like?
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Video Clip
Bambao, Drinkwater, Meyers, & Oshima: Mathematics in the TK Classroom
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What does it look like?
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Video Clip
Bambao, Drinkwater, Meyers, & Oshima: Mathematics in the TK Classroom
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What does it look like?
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Video Clip
Bambao, Drinkwater, Meyers, & Oshima: Mathematics in the TK Classroom
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Planning Ac'vi'es
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Socio-‐Emo'onal Development and Mathema'cs
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Socio-‐emo'onal and Mathema'cal Development: Self-‐regula'on
• Mathema8cs ac8vi8es almost always require self-‐regula8on skills – Raising hand during mathema8cs discussions – Taking turns during games – Paying aVen8on to the instruc8ons and the problem
• Mathema8cal solu8ons to conflicts – Fair-‐sharing – Timed turns
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Socio-‐emo'onal and Mathema'cal Development: Discussion
• Group – Teacher-‐facilitated/modeled – Rich in mathema8cal vocabulary
• Teacher-‐student – Open-‐ended ques8ons that require explana8ons and mathema8cal vocabulary
• Student-‐student – Collabora8on – Sharing problem-‐solving strategies
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Socio-‐emo'onal and Mathema'cal Development: Persistence
• Real problems • Encouragement • Pride in persistence
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Loca'on
Group Size
Vocabulary
Scaffold Down
Scaffold Up
Common Core
Founda'ons
Assessment
Materials
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TK Math Talks
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Bambao, Drinkwater, Meyers, & Oshima: Mathematics in the TK Classroom
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Number Talks
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Bambao, Drinkwater, Meyers, & Oshima: Mathematics in the TK Classroom
Number Talks give TK students the opportunity to:
• Inves8gate mathema8cal rela8onships
• Communicate different ways of making sense of the math they are seeing
• Explore different mathema8cal strategies
• Listen to and respond to each other’s mathema8cal thinking
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Number Talks: What does it look like in TK?
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Tools: Dot images, Five-‐Frames and Ten-‐Frames, Rekenreks— star8ng with smaller numbers
Time: About 5-‐10 minutes Group Size: 5-‐10 students Format: • Show the “problem”
• Wait for students to come up with an answer(s)
• Ask students for their answer(s): “How many dots do you see”? All answers are acknowledged and considered respecgully.
• Call on students to explain their answer(s): “How do you see them? How did you get seven?”
• Keep students focused on number discussion and help students to communicate their math thinking for beVer understanding
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Video: Number Talks
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Video clip
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Number Talks in TK helps students to:
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• Build number sense
• Subi8ze
• Develop one-‐to-‐one correspondence and cardinality
• Decomposing and composing numbers
• Communicate and ar8culate how they solve the math problem
• Listen and learn from each other
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Kim: [email protected]
Martha: [email protected]
Andrea: [email protected]
Gail: [email protected]
Ques'ons?
Bambao, Drinkwater, Meyers, & Oshima: Mathematics in the TK Classroom
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References • Duncan, G. J., Claessens, A., Huston, A. C., Pagani, L. S., Engel, M., Sexton,
H., . . . Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428-‐1446.
• Duschl, A., Schweingruber, H., & Shouse A. (Eds.), (2007). Taking science to school: Learning and teaching science in grades K-‐8. Washington, DC: Na8onal Academies Press.
• Masters, G. & Forster, M. (1996). Progress Maps (Part of the Assessment Resource Kit). Melbourne: Australia: The Australian Council for Educa8onal Research
• Parrish, Sherry (2010). Number Talks Helping Children Build Mental Math and ComputaLon Strategies. California: Math Solu8ons
• Romano, E., Kohen, D., Babchishin, L., & Pagani, L. S. (2010). School readiness and later achievement: replica8on and extension study using a na8on-‐wide Canadian survey. Developmental Psychology, 46, 995-‐1007
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Resources • California Kindergarten Association
– http://www.californiakindergartenassociation.org/
• Common Core Progressions – http://ime.math.arizona.edu/progressions/
• CA TK – http://www.tkcalifornia.org/
• Preschool CA – http://www.preschoolcalifornia.org/
• Common Core – http://www.corestandards.org/Math
• Preschool Foundations – http://www.cde.ca.gov/sp/cd/re/documents/preschoollf.pdf
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