Our work this week has been focused on the subskills that our research linked to counting on. Jackie and I chose to take our students out together, three at a time, so that one of us could work with the students while the other videotaped and we would both get to witness what the students were doing.
In the groups we worked with we identified students who used the strategy of counting on and those who did not yet employ the use of this strategy. When we first took the students out, we presented them with an addition problem and asked them to solve it. We did not provide any manipulatives, and all of the problems had sums greater than 10 so the students could not hold both addends up on their fingers at the same time. After the students gave an answer, we asked them to share how they solved their problem and asked them what number they started with and how many more they added on. Our goal in having students solve this initial problem was to see who was already using the counting-on strategy. Since some students demonstrated use of this strategy, we continued on to test the subskills to see if the students would also demonstrate these because our research claimed that they were linked to counting on. We also continued on with the subskills for those who did not demonstrate the strategy already in order to see if work with the subskills would lead them to discovering the strategy of counting on.
The first subskill our research linked to counting on was the ability to identify the first addend does not need to be counted out because its quantity is stated in the problem. To test this, we placed a number of counters out in a line in front of the student, then placed a card above the counters telling how many were there. We then pointed at the last counter in the line and asked what count it would receive if we had counted all of the counters. All of the students who demonstrated an ability to count-on were also able to identify that the count given to the last counter was the same as the number on the card placed above them. Although students sometimes needed to be reminded that they did not need to count the counters to give the count of the last counter, all of the students we worked with were able to demonstrate this skill.
The other subskill we worked on with the students was the ability to identify that the first count when adding a second addend is the count given to the first addend plus one more. To test this, we placed a plus sign down next to the first counters and addend and then placed more counters out along with another card above them. We then pointed to the first counter in the second addend and asked what count the students would give it if we were adding. This question often took prompting in terms of asking “what is x and one more?” but this also may have just been due to initial confusion of students not being sure what was being asked of them, because many of them wanted to think of the second group of counters as a separate entity at first and give the first counter a count of 1. We observed all students eventually demonstrating this skill, as well. For these students who were already counting on and demonstrated knowledge of the subskills, the next step may be to have students discover that counting-on from the larger number is a more efficient use of time when adding. We witnessed a small handful of students who could count on already doing this when given the addition problem alone, but using the counters and practicing the subskills only encourages counting on from the first addend. For students who demonstrated the subskills but did not yet count-on, we hope to continue work on the subskills to see if this will lead to counting on in the future.
Posted on April 26th, 2014 by Jessica Bacon
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