Understanding Numerical Operations in Preschool

1. Understanding Numerical Operations in Preschool Developed by Carmen Davis, Hoa Ly, Ryan Ratajski & Johari Sykes Camden City School District

2. Standard 4.2 Children demonstrate an initial understanding of numerical operations. Match The Cards Select a piece of paper from the bag provided on your table. Try to find a member of the group with the matching halfof the phrase. After matching the phrase, take this opportunity to talk to your partner about some things you know about numerical operations.

3. Today’s Objectives • To define numerical operations, giving teachers a deeper understanding of what the math content means. • To describe how this standard translates into practice during small group times, large group times, and as a choice embedded in classroom centers. • To highlight math practices that can be used while teaching about numerical operations. • To accentuate that the quality of the teacher-child interactions is key to enhancing children’s outcomes as they develop an initial understanding of numerical operations.

4. 2004: Math Expectation 1Children demonstrate an understanding of number and numerical operations Preschool Teaching Practices Make materials and books that promote number exploration accessible to the children. Encourage children to compare numbers frequently through questions and graphing. Integrate purposeful counting experiences throughout other learning opportunities. Encourage and support individual attempts to learn to count numbers. Encourage counting to 30+.

5. 2004: Math Expectation 1Children demonstrate an understanding of number and numerical operations Preschool Teaching Practices (cont’d.) Provide children opportunities to use estimation skills during daily activities by asking interesting and relevant questions. Model addition for children by using counting to combine numbers. Model subtraction for children by using counting to separate numbers. Foster one-to-one correspondence throughout the day.

6. 2004: Math Expectation 1Children demonstrate an understanding of number and numerical operations Preschool Learning Outcomes 1.1 Demonstrates understanding of one-to-one correspondence. 1.2 Spontaneously counts for own purposes. 1.3 Learns to say the counting numbers. 1.4 Discriminates numbers from other symbols in the environment. 1.5 Recognizes and names some written numerals.

7. 2004: Math Expectation 1Children demonstrate an understanding of number and numerical operations Preschool Learning Outcomes (cont’d.) 1.6 Compares numbers in different. 1.7 Uses estimation as a method for approximating an appropriate amount. 1.8 Adds two groups of concrete objects by counting the total. 1.9 Subtracts one group of concrete objects from another by taking some away and then counting the remainder.

8. What does “numerical operations” mean for our preschoolers?

9. Numerical OperationsPreschool Learning Outcomes 4.2.1 Represent addition and subtraction by manipulating up to 5 objects: (a) putting together and adding to (e.g., “3 blue pegs, 2 yellow pegs, 5 pegs altogether.”); and (b) taking apart and taking from (“I have four carrot sticks. I’m eating one. Now I have 3.”). 4.2.2 Begin to represent simple word problem data in pictures and drawings.

10. Number Sense + Numerical Operations = Number & Operations • Counting (1, 2, 3…one-to-one correspondence) • Quality (sense of number; three fingers = 3; subitizing) • Order (sequence – first, second, third…) • Numerals (seeing numbers and what they represent)

11. Number Sense + Numerical Operations = Number & Operations (cont.) • Comparisons (more/less; more/fewer) • Combining operations (adding) • Separating operations (subtracting) • Sharing operations (dividing) • Set-Making operations (multiplying)

12. Numerical OperationsPreschool Learning Outcomes 4.2.1 Represent addition and subtraction by manipulating up to 5 objects: (a)putting together and adding to (e.g., “3 blue pegs, 2 yellow pegs, 5 pegs altogether.”); and (b)taking apart and taking from (“I have four carrot sticks. I’m eating one. Now I have 3.”). 4.2.2 Begin to represent simple word problem data in pictures and drawings.

13. Numerical OperationsWhat Preschoolers Can and Cannot Do • Preschoolers typically: • Believe that two sets of objects have the same number if the objects are close to one another. • Solve subtraction problems before they can solve addition problems. • Think about small numbers without having the physical objects. • Preschoolers typically do not: • Understand mathematical words in abstract thinking without the use of real objects present. • Connect the idea on large quantity schema. • Easily keep track of what they have counted or not counted.

14. Teaching Practices and Classroom Environments that Make the Difference

15. Preschool teachers will: • Model addition for children by using counting to combine numbers (e.g., “Maria has two blocks and Justin has three. There are five blocks altogether: 1, 2, 3, 4, 5.”). C: I hit all them pins down, but I can pick them back up. T: Why would you do that? C: Because if I pick one up, then it’s one and then if I pick up this one, it’s two of them. (counts) 1, 2, 3, 4, 5, 6, 7, 8. It’s eight of them still down. T: This is a number sentence. How many children are here? C: (counts) 1, 2, 3. 3. T: Plus how many children? C: One. T: Equals… C: (counts) 1, 2, 3, 4. Four kids. It’s four. T: Can you find that card in your hand? C: Yes. (selects the number 5 card and holds it up) T: How many green stripes do you have? C: (counts) 1, 2. T: How many yellow stripes do you have? C: (counts) 1, 2, and one glitter one, too. T: Good. So how many do you have in total? That means altogether. C: (counts) 1, 2, 3, 4, 5. I got five stipers!

16. Video #1

17. Scaffolding Activity • What did you see and hear in this clip? Use the checklist to guide a discussion at your table. • How does this teacher’s activity support Standard 4.2.1: Represent addition and subtraction by manipulating up to 5 objects? • Then, as a group, use the 5 objects in the brown bag to modify the activity seen in the clip or to develop a new activity. Think about children in the group who might be at earlier stages of understanding and/or children with more advanced thinking. • To debrief, we’ll have one person from each group sum up the group’s discussion and another person from each group describe the activity developed by the group.

18. Materials to Use Play people Linking cubes Counting bears Collections of natural objects

19. Preschool teachers will: Develop addition and subtraction stories with small groups of children using story mats and flannel board scenes with small quantities of objects and pictures/drawings.

20. Preschool teachers will: Use fingers, chalk, wipe-off markers and/or whiteboard technology to tell and draw addition and subtraction stories with small groups of children.

21. Preschool teachers will: Provide writing materials and/or handheld devices with appropriate applications in classroom centers so that children can choose to view, solve, and create addition and subtraction stories. Figure 1 Figure 2

22. Let’s try it! • Represent this math problem • With pictures • With objects • By acting it out

23. Video #2

24. Assessing Your Current Practice

25. From Preschool to Kindergarten • Do you know what the Common Core asks of children in kindergarten? New Jersey Preschool Teaching and Learning Mathematics Standards Aligned to the Common Core Mathematics Standards for Kindergarten – DRAFT

26. Making It Happen

27. References • The Creative Curriculum for Preschool - Volume 4 Mathematics by Juanita V. Copley, Candy Jones, and Judith Dighe • The Young Child and Mathematicsby Juanita V. Copley

28. Resources for Further Use • http://www.naeyc.org/positionstatements/mathematics NAEYC/NCTMposition statement on Early Childhood Mathematics: Promoting Good Beginnings • Teaching and Learning Math: The Learning Trajectories Approach by Douglas H. Clements and Julie A. Sarama • http://www.youtube.com/watch?v=wV85P07K1mUThe Building Blocks of Math: Lessons from Research, featuring Dr. Doug Clements