At first, counting helps
When learners are first getting used to addition, counting helps. In fact, an important early addition learning step involves counting. Educators distinguish between two counting strategies for addition: “Counting all” vs. “counting on”. Imagine a learner who is using concrete items like beads or dots to find 4 + 3. The learner can solve the problem by pointing at every item in both sets, like this: “1, 2, 3, 4 … 5, 6, 7.” This strategy is called “counting all”. Or the learner can start at the number of items in the first set and count on from there, like this: “There are 4 here. So adding 3 more, the answer will be 5, 6, 7.” The transition from counting all to counting on is a key step in mathematical development (Secada et al., 1983).
Some ways to add are more powerful than counting
Many powerful strategies for addition do not involve counting all or counting on. The addition games and activities here will help learners start using these strategies. When learners are playing the addition games, stopping to count, no matter whether they are counting all or counting on, is a clue that they can benefit from going back to review earlier material.
No matter where an individual’s level is, there is some game or activity that individual can use without having to stop to count. Learners who stop to count in addition should go back to one of these — unless they are still as young as 6 or 7. At these ages, children are still getting comfortable with addition, and counting to add benefits them (Jay and Betenson, 2017). After spending enough time counting, however, children are ready to move on to addition strategies that do not require stopping and counting. These children benefit from learning how to add without having to stop and count. (Newton, 2016, p. 56; Davenport, 2019, p. 15-16).
Selecting games for learners who are still counting
Learners who need review because they are still counting might need to go back earlier within the same section, or they might need to go back to the Number Properties section. The Number Properties games help learners build knowledge about numbers to make addition, subtraction, multiplication and division easier. To figure out exactly where to move learners, give them an assessment.
Emotional support for learners
Learners who are told that they should use earlier games may feel frustrated initially. But when they are at an appropriate level, they will make faster progress, and will enjoy the feeling of competence that comes from success.
Of course, you have the power to improve learners’ motivation and support them emotionally with your words. If a learner is stopping too often to count, you don’t need to use negative language. (Examples of negative language: “This game is too hard for you, try an easier one” or “You’ve got to go back, you’re not ready for this yet.”) Instead, you can support this learner by using positive language like “Here, try this game. You’ll learn faster.” Then, when they are playing confidently, you can give them positive feedback, like “You seem really confident with this material.”
Occasional counting is OK, even with fingers
When a learner is just starting to work with a new concept in a new game, it’s OK for them to check the new concept by counting. But if the learner doesn’t regain comfort and start playing without counting pretty soon, that learner probably needs to try earlier games.
When learners are trying out a new concept, you may see them occasionally using their fingers to keep track of certain numbers. As long as they are using a strategy other than counting to solve the problems, occasionally using fingers is probably not a cause for concern. A good way to check on strategy is to ask “How did you figure out that answer?”
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References
Davenport, Linda Ruiz, Connie S. Henry, Douglas H. Clements, and Julie Sarama. 2019. No More Math Fact Frenzy. Portsmouth, NH: Heinemann.
Jay, Tim, and Julie Betenson. 2017. “Mathematics at Your Fingertips: Testing a Finger Training Intervention to Improve Quantitative Skills.” Frontiers in Education 2(22) doi: 10.3389/feduc.2017.00022 .
Newton, Nicki. 2016. Math Running Records in Action: A Framework for Assessing Basic Fact Fluency in Grades K-5. New York, NY: Routledge.
Secada, Walter G., Karen C. Fuson, and James W. Hall. 1983. “The Transition from Counting-All to Counting-On in Addition.” Journal for Research in Mathematics Education 14(1): 47-57.
August 18, 2020