Inside a kindergarten classroom with Augustana students

It Takes Two

In the kindergarten classrooms this week, Jackie and I have been continuing work with our students on counting on strategies. We are continuing practice for students who do not yet utilize the strategy of counting on for addition, and for those who have been using the strategy we are practicing the strategy with the goal of helping the students discover that it is more efficient to count on from the larger addend.
This week, we had two new sets of materials to help us work with the students. One of the materials was a container which held three dice, two of which were numbers 1-6 and the other was either an addition or subtraction sign. We also had a set of addition and subtraction flash cards which had numbers on one side and dots on the other.
We used the dice with students who did not have their addition facts for addends 1-6 memorized. The students would shake the container and then read the math problem that resulted. We had white boards for the students to write the problem out, and we then asked them how they would solve their problem. Many students said that they wanted to draw dots on the white board or use their fingers in order to represent the addition problem. Since most of the sums that resulted from the problems were less than 10, we found that many of the students would want to hold up both addends on their fingers and then count all in order to solve the problem. If they chose to draw dots, they would represent both addends and then count all in order to solve. We let the students solve the problems counting all the first time if this was the strategy they chose, but the next time they began using counting all as a strategy we would prompt them by questioning whether they needed to count the first addend or if they already knew how many they had. A good visual seemed to be when the first addend was five and the students chose to use their fingers. The students already know that holding one hand represented five without having to count each finger, so they did not need to count the first addend. We even heard students thinking out loud, saying “I already know that I have “x”…” when referring to the first addend. For these students, we focused on counting on from the first addend instead of counting on from the larger.
For students who could have performed the dice addition in their heads, we used the addition and subtraction flash cards. Since the cards had dots on the back, we started by having the first addend represented by a number card and the second represented by dots, hoping to prompt students to start at the first number and then count up the number of dots to find the sum. After students were demonstrating this, we flipped the second addends over so the number side was showing for both addends. At this time, we started placing the larger addend second. If students did not choose the larger addend to count on from, we would ask the students if the reverse of the addition problem gave them the same answer. We then modeled by counting on from the larger addend, and asked if this seemed easier or took less time. Many of the students would note other students in the group using the counting on from the larger strategy and would then use this same reasoning when solving their own problems. It will be interesting to see if the practice with the strategies in both situations will result in a change in strategy when we work with the students next week.

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