1. Teaching Young Learners with the Ohio Early Mathematics Standards in Mind Sponsored by the Ohio Department of Jobs and Family Services in collaboration with the Ohio Department of Education Module One

2. Overview of Seminar Module 1 Module 1 What are Standards, benchmarks and indicators?What are Standards, benchmarks and indicators? Supporting Children’s Early Concepts of NumberSupporting Children’s Early Concepts of Number Module 2 Module 2 Early Addition and SubtractionEarly Addition and Subtraction Patterns and Algebraic ReasoningPatterns and Algebraic Reasoning Module 3 Module 3 Geometric Reasoning through Children’s PlayGeometric Reasoning through Children’s Play Teaching Mathematics through Activity – Measurement & Data AnalysisTeaching Mathematics through Activity – Measurement & Data Analysis

3. Themes for the Sessions Play Play Inquiry & projects Inquiry & projects Home-school connections Home-school connections Adaptations for diverse learners Adaptations for diverse learners Integration across the curriculum Integration across the curriculum The connected nature of mathematical knowledge The connected nature of mathematical knowledge Role of conversation and questioning Role of conversation and questioning 3 levels of representational thinking 3 levels of representational thinking

4. Overview of Module 1 What are the Ohio Early Learning Content Standards? What are the Ohio Early Learning Content Standards? What are the benefits of using standards? What are the benefits of using standards? What are some of the challenges of using standards? What are some of the challenges of using standards?

5. What are the Ohio early learning content standards? How do standards, benchmarks, and indicators relate to one another? How should teachers think about using them? The Ohio Standards

6. Imagine… The Teacher as gardener The Teacher as gardener The Learner as the growing plant The Learner as the growing plant Standards as a grower’s guide Standards as a grower’s guide Early content standards as roots Early content standards as roots Environment and circumstances as sun, water, soil, geography… Environment and circumstances as sun, water, soil, geography…

7. We all begin young and full of potential Seeds and seedlings need much care. The younger the plant, the greater the need for careful observation and responsiveness. The child as learner needs similar support and responsiveness.

8. We need strong roots… The roots of the plant develop first and are critical to further growth, but they also continue their importance throughout the life of the plant.

9. an appropriate environment… The sunlight, temperature, water, proximity and types of other plants, soil, fertilizer, and other environmental factors influence the development of the plant. A child’s environment influences the development of his or her math thinking

10. …and a gardener who knows our unique needs. A grower’s guide is a generic guide for how MOST plants grow. It provides benchmarks in the life of a plant, and it gives assistance to the novice gardener. It can’t predict with certainty all the specific needs of one particular plant. A skilled gardener adjusts directions in order to create the best environment for her particular plant.

11. There are many plants and many learners.

12. Ideas to Keep In Mind… We can’t depend on a guide to provide the schedule of care for each day. We can’t depend on a guide to provide the schedule of care for each day. Too much of a good thing can be damaging. Too much of a good thing can be damaging.

13. Ideas to Keep In Mind (Cont.) … What worked with one plant will not necessarily work with another; individualization is important. What worked with one plant will not necessarily work with another; individualization is important. Patience is important for the gardener. Patience is important for the gardener.

14. The standards are like the The standards are like the grower’s guide. grower’s guide. Teachers make educated judgments about necessary conditions for math learning. Each child is different. Teachers make educated judgments about necessary conditions for math learning. Each child is different. We reap benefits when we opt not to push children too hard or too quickly. Teachers need patience and direction. We reap benefits when we opt not to push children too hard or too quickly. Teachers need patience and direction. Using the Standards Wisely

15. What is an early math standard? Standards are what we expect students to know and be able to use as they progress through school. Standards are what we expect students to know and be able to use as they progress through school. Standards outline the foundational content and processes in mathematics. Standards outline the foundational content and processes in mathematics.

16. Standards are both content and process Number, number sense and operations Number, number sense and operations Measurement Measurement Geometry and spatial sense Geometry and spatial sense Patterns, functions and algebra Patterns, functions and algebra Data analysis and probability Data analysis and probability Mathematical processes Mathematical processes

17. What is an indicator? Indicators are specific skills and understandings that students demonstrate across the grade levels Indicators are specific skills and understandings that students demonstrate across the grade levels These indicators let us know that the student is making progress toward the benchmarks These indicators let us know that the student is making progress toward the benchmarks

18. What are benchmarks? Benchmarks are particular indicators that are “grouped” in developmental chunks to indicate where students should be by a particular grade. Benchmarks are particular indicators that are “grouped” in developmental chunks to indicate where students should be by a particular grade. For early childhood math, the benchmark is second grade. For early childhood math, the benchmark is second grade.

19. Number, Number Sense and Operations Standards (by grade 12) Students will demonstrate number sense, including an understanding of number systems and operations and how they relate to one another. Students will demonstrate number sense, including an understanding of number systems and operations and how they relate to one another. Students compute fluently and make reasonable estimates using paper and pencil, technology-supported and mental methods. Students compute fluently and make reasonable estimates using paper and pencil, technology-supported and mental methods.

20. 2 nd grade benchmark for number standard There are 13 indicators that a student has reached the 2nd grade standard for number, number sense, and operation. There are 13 indicators that a student has reached the 2nd grade standard for number, number sense, and operation. For example: recognize, classify, compare and order whole numbers For example: recognize, classify, compare and order whole numbers Model, represent and explain subtraction as comparison, take-away, and part-to- whole Model, represent and explain subtraction as comparison, take-away, and part-to- whole

21. Mathematical Processes Standard Students use mathematical processes and knowledge to solve problems. Students apply problem- solving and decision-making techniques, and communicate mathematical ideas. Students use mathematical processes and knowledge to solve problems. Students apply problem- solving and decision-making techniques, and communicate mathematical ideas. Problem solving, Communication, Connections, Representation, & Reasoning and Proof Problem solving, Communication, Connections, Representation, & Reasoning and Proof

22. Benchmark for process standard Example indicator (there are 9 all together): Use a variety of strategies to understand problem situations, e.g., discussing with peers, stating problem in own words, modeling problems with diagrams or physical materials, identifying a pattern. Use a variety of strategies to understand problem situations, e.g., discussing with peers, stating problem in own words, modeling problems with diagrams or physical materials, identifying a pattern.

23. Achieving Balance Children construct their own knowledge through play Teachers provide lots of time for free play with math materialsTeachers provide lots of time for free play with math materials Teachers place math related materials in every part of the roomTeachers place math related materials in every part of the room With Intentional Teaching, teachers can pay attention to curriculum standards and benchmarks as they prepare environments With Intentional Teaching, teachers can pay attention to curriculum standards and benchmarks as they prepare environments Teachers plan math experiences based on the standards, with developmental levels and culture in mind.Teachers plan math experiences based on the standards, with developmental levels and culture in mind. Teachers assess where children are and provide next step experiencesTeachers assess where children are and provide next step experiences

24. Backmapping How do we know we are providing experiences that support students’ progress toward the benchmark? How do we know we are providing experiences that support students’ progress toward the benchmark? We backmap!! We backmap!! Backmapping is a regular routine where you look back at curricular experience and ask: which indicators have we been supporting? Backmapping is a regular routine where you look back at curricular experience and ask: which indicators have we been supporting?

25. BREAK TIME

26. Early number Concepts What understandings are young learners developing as they are developing their concepts about number? How do you support these early competencies?

27. Early number -- sorting Free sorting activities – what are they? Free sorting activities – what are they? Teacher’s roles: providing sortable materials, conversation/questioning Teacher’s roles: providing sortable materials, conversation/questioning “ What did you find?” “What kinds of groups did you make?” “How did you put them together in different groups?” “I see you sorted them into colors!”

28. Structured Sorting Activities “In the Loop”: The leader (adult or child) places one piece in the loop. Everyone else finds pieces from their pile to add to the loop “In the Loop”: The leader (adult or child) places one piece in the loop. Everyone else finds pieces from their pile to add to the loop “Guess my rule”: The leader places several pieces in a loop – everyone else guesses what s/he is thinking “Guess my rule”: The leader places several pieces in a loop – everyone else guesses what s/he is thinking

29. As early number concepts develop further Classification – sorting according to attributes Classification – sorting according to attributes Patterns Patterns Comparisons of sets (more than & less than) Comparisons of sets (more than & less than) Ordering Sets (smallest to largest) Ordering Sets (smallest to largest)

30. As early number concepts develop further (Cont.) Conservation - Conservation is the recognition that the number, length, quantity, mass, area, weight, and volume of objects and substances are not changed by transformations in their appearance. Conservation - Conservation is the recognition that the number, length, quantity, mass, area, weight, and volume of objects and substances are not changed by transformations in their appearance. Beginning to recognize how many in a small set without counting Beginning to recognize how many in a small set without counting

31. Early Counting Concepts and Skills What do you see when children count? How is learning to count similar to learning to read?

32. Seven Candies While watching the children, notice what they do to count the candies While watching the children, notice what they do to count the candies What do they show us about their understanding of number and counting What do they show us about their understanding of number and counting Take notes about individual children’s: Take notes about individual children’s: StrategiesStrategies Physical behaviorsPhysical behaviors Knowledge and competenciesKnowledge and competencies Misunderstandings or limited experienceMisunderstandings or limited experience

33. Seven Candies

39. Developing Early Concepts of Number What do you do to foster children’s early development of counting?

40. Components of Early Number Knowledge - Counting Principles Production of numbers (standard list of counting words) Production of numbers (standard list of counting words) One-to-one correspondence (one object for each number) One-to-one correspondence (one object for each number) Ordering or seriation (small to largest) Ordering or seriation (small to largest) Cardinality principle (last number is the number in the set) Cardinality principle (last number is the number in the set) Which object in the set you start with doesn’t matter Which object in the set you start with doesn’t matter Conservation– number stays constant even if objects are rearranged Conservation– number stays constant even if objects are rearranged

41. Groups of 5 counters are arranged in the following 3 patterns. Discuss the students’ knowledge of counting principles on each of the following slides Groups of 5 counters are arranged in the following 3 patterns. Discuss the students’ knowledge of counting principles on each of the following slides

42. A conversation with Stephen T: Are there more red, blue, or yellow counters? T: Are there more red, blue, or yellow counters? S: More blue. S: More blue. T: How do you know? T: How do you know? S: I can tell by looking. S: I can tell by looking. T: How many of each? T: How many of each? S: One, two, three, four, five... five red. One, two, three, four, five...five blue. One, two, three, four, five...five yellow. S: One, two, three, four, five... five red. One, two, three, four, five...five blue. One, two, three, four, five...five yellow. T: Five of each? T: Five of each? S: Yes. S: Yes. T: Do you still think there are more blue? T: Do you still think there are more blue? S: Yes, I can just see there's more blue. S: Yes, I can just see there's more blue.

43. A conversation with Rebecca T: Are there more red, blue, or yellow counters? T: Are there more red, blue, or yellow counters? R: They're the same. R: They're the same. T: How do you know? T: How do you know? R: I counted them. R: I counted them. T: How many of each? T: How many of each? R: One, two, three, four, five...Five red. Five blue. Five yellow. R: One, two, three, four, five...Five red. Five blue. Five yellow. T: Five of each? T: Five of each? R: Yes. R: Yes.

44. Counting Principles: Stephen T: Here are some blocks in a row. Start with this one on the end and count them. T: Here are some blocks in a row. Start with this one on the end and count them. S: One, two, three, four, five, SIX. There are six blocks. S: One, two, three, four, five, SIX. There are six blocks. T: What if you start at the other end of the row and count them? T: What if you start at the other end of the row and count them? S: One, two, three, four, five, SIX. There are six. S: One, two, three, four, five, SIX. There are six.

45. Counting Principles: Rebecca T: Here are some red blocks in a row. Start with this one on the end and count them. T: Here are some red blocks in a row. Start with this one on the end and count them. S: (Touches each of the 5 blocks) One, two, three, five, six. Six red blocks S: (Touches each of the 5 blocks) One, two, three, five, six. Six red blocks T: Now count these blue blocks. T: Now count these blue blocks. S: (Touches each of the 4 blocks) One, two, three, five. Five blue blocks. S: (Touches each of the 4 blocks) One, two, three, five. Five blue blocks.

46. Counting Principles: Sally T: Here are some blocks in a row. Start with the one on this end and count them. T: Here are some blocks in a row. Start with the one on this end and count them. S: One, two, three, four, five, six. There are six. S: One, two, three, four, five, six. There are six. T: What if you start at the other end of the row and count them? T: What if you start at the other end of the row and count them? S: I already counted them! There are six! S: I already counted them! There are six!

47. Counting Principles: Brenda T: Here are some red blocks (4) in a row. Start with this one on the end and count them. T: Here are some red blocks (4) in a row. Start with this one on the end and count them. S: (Points to each but says two numbers with each point) One, two, three, four, five, six, seven, eight. Eight red blocks. S: (Points to each but says two numbers with each point) One, two, three, four, five, six, seven, eight. Eight red blocks.

48. Number Standard Age 3 Counts Collection of 1 to 4 items Counts Collection of 1 to 4 items Begins to understand cardinality Begins to understand cardinality Group recognition for collections of 1 to 3 Group recognition for collections of 1 to 3 Adds and subtracts non-verbally low numbers Adds and subtracts non-verbally low numbers Age 6 Counts and counts out collections up to 100 using groups of 10 Counts and counts out collections up to 100 using groups of 10 Group recognition for patterned collections of up to 6 items Group recognition for patterned collections of up to 6 items Adds and subtracts using counting-based strategies such as counting on for numbers and totals less than 10 Adds and subtracts using counting-based strategies such as counting on for numbers and totals less than 10