Understanding Children’s Thinking Through Number Talks Sue Dolphin

Number Talks are an approach to developing facility with computation that engages children in thinking about numbers and allows them to add, subtract, multiply and divide using the mathematics that is meaningful to them, rather than following procedures that are not. Kathy Richardson Fold paper in half. Part 1 – Respond begin day 1. Part 2 – end day 2

What is a Number Talk? a short daily routine (5-15 minutes) where the teacher poses intentionally selected problems for students to solve using the mathematics they know and understand. ongoing conversations about mathematics that give children the opportunity to develop mathematical competence over time.

98 + 46

55 + 98

298 + 34

NUMBER TALK PROCEDURE The teacher presents the problem and allows the students think time. The students figure out the answer and use “thumbs-up” signal. The students share their answers and defend solutions by explaining their thinking. The class agrees on the answer to the problem. The steps are repeated for additional problems.

The National Council for Teachers of Mathematics states that: "Computational fluency refers to having efficient and accurate methods for computing. Students exhibit computational fluency when they demonstrate flexibility in the computational methods they choose, understand and can explain these methods, and produce accurate answers efficiently.” Principles and Standards for School Mathematics, NCTM, Reston, VA 2000, p.152

Essential Elements of a Number Talk A safe environment Problems of various levels of difficulty that can be solved in a variety of ways Concrete and representational models Interaction Self-correction

What do you see? pumpkin The next 3 slides presents a word, such as pumpkin. Ask the participants what they see when they hear the word pumpkin. Something like this?

What do you see? bear

What do you see? seven This time “seven” comes up. What do you see? something like this? – “7” We want students to see the quantity. The numeral itself could be anything – it represents a quantity. Just like the letters B E A R have no meaning in of itself – they represent a real object.

What Tools/Models Help Students Develop Computational Fluency?

Visual flashcards: Dot Cards Toothpick Cards Number Shape Cards Color Tile Arrangement Cards Pattern Block Arrangement Cards

Unifix Cube Towers Hundred Grids and beyond

Number Composition and Decomposition to 20 Place Value: Tens and Ones Developing an Understanding of Core Number Concepts through Number Talks Counting Number Relationships Number Composition and Decomposition to 20 Place Value: Tens and Ones Place Value: Hundreds, Tens and Ones

Videos & discussion Here

What is the Role of the Teacher? Provides a safe environment Selects problems Provides wait time Values everyone’s thinking Records, clarifies, restates Asks questions

The teacher asks questions… Who would like to share their thinking? Who did it another way? Who solved it the same way as Billy? How did you figure that out? What is the first thing your eyes saw, or the first thing your brain did?

The teacher notices who… Counts all? Counts on? Sees groups? Composes and decomposes Uses benchmarks? Sees relationships? Uses strategies? Just knows?

Learning How Numbers Work • Numbers are composed of smaller numbers. 6 = 4 + 2 • What we know about one number can help us figure out other numbers. “I know 3 and 3 is 6 so 3 and 4 must be 7.” • Numbers can be taken apart and combined with other numbers to make new numbers. “I broke up the 6 into 4 and 2. I put the 2 with the 8 to make a 10 and then I have 4 more which is 14.” .

Teaching elementary mathematics does not mean bringing children to the end of arithmetic…Rather, it means providing them with a groundwork on which to build future mathematics. Liping Ma, Knowing and Teaching Elementary Mathematics, p. 117

Remember: Keep it short, 5 to 10 minutes Do number talks daily Be intentional Begin instruction where the children begin counting by 1s If it’s too difficult, make the numbers smaller