Number Talks with Preservice Teachers 3


Number Talks with Preservice Teachers Using Landmark Numbers

My preservice teachers and I were engaged in a Number Talks (NT) involving Landmark Number to strengthen their mental math capacity. My goal is for this NT is to give my students opportunities calculated basic math problems without relying on paper pencil computation and to gain knowledge on NT strategies.  Since we have been working with place value learning using manipulatives, models, and other tools, I thought it was befitting to have NT with the emphasis on landmark numbers.

The Common Core State Standards (CCSS) or College and Career Readiness Standards (CCRS) calls for the formal teaching of US algorithm for addition and subtraction in grade four. Therefore, preservice teacher should be aware of the different instructional strategies that lends itself to development of place value understanding. This include using place value to add and subtract two and three digit numbers.

I presented the following sequence of cluster problems:

11 + 10

11 + 20

11+ 30

11 +33

We started with the first problem 11 +10.  Two students shared their thinking and justification of their answer. Student One is a male student. Student Two is a female student. Student One started the conversation by solving the problem by justifying his reasoning:

Teacher: How did you get 21? You can’t say you just know.

Student One: I added 10 + 10 and then added 1 +0)

Teacher: Where did you get 10 + 10?

Student One: I got ten from the 1 in 11.

Teacher: This 1? (pointing to the 1 in the ones place)

Student One: No the first in the tens place.

Teacher: Is this a 1?

Student One: No, that is a 10.  So I took the 10 from 11 and the other 10 and added them together.

Teacher: You decomposed 11 into 10 +1 and 10 into 10 +0?

Student One: Yes. Then I added 10 + 10 + 1. That gives you 21.

My goal for student one to realize that numbers greater than ten can be expressed as 10 ones + some other one which build place value understanding in kindergarten (K.NBT. 1)

Student Two: I just simply staked the numbers on top.

Teacher : How did you stake them?

Student Two: I put 11 (on top) + 10 (on botton).

Teacher: Then what did you do?

Student Two: I added 1 +0 =1 and 1 + 1=2

Teacher: Is are these 1? (Pointing to the number in the tens place)

Student Two: No, no, those are tens. Ok 10 + 10 is 20. So, the answer is 21.

Notice, I did not allow this student to say the numbers in the tens place are ones.

It is essential that correct mathematical terms. This is part of attending to precision. Students who are mathematically proficient uses precise language to communicate effectively. At the elementary level student use correct meaning of symbols and carefully formulated explanations (corestandard.org, 2016)


Also when looking at the actual scribing, I wanted to emphasize the importance of using the properties at the elementary level to develop algebraic thinking in younger students. There are various algebraic properties that apparent with this NT. Including using the associate property to rearrange number to add more efficiently. Properties of addition allow student to be more flexible and fluid with adding numbers.  The goal of preservice teacher education is to equip future teachers with the knowledge and application for successful mathematics teaching, and in turn, will allow their future students to become mathematically proficient.

Reference

Common Core State Standards (2016). Standards for mathematical practice. Retrieved from corestandards.org.
Parish, S. (2010). Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K 5, Updated with Common Core Connections. Sausalito, CA: Math Solutions

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