The step-by-step design sets up students to succeed
Learning with these games happens incrementally, one small step in each game. Small steps make success easier, so the incremental design makes frequent learning successes likely. Succeeding in learning gives learners confidence and motivates them to continue. All in all, the incremental design results in faster progress for learners.
This small-step approach is innovative. Consider the progression of games in the Addition section. Many curricula ask children to learn the facts 3 + 4 = 7, 4 + 5 = 9, 5 + 6 = 11, 6 + 7 = 13, 7 + 8 = 15, and 8 + 9 = 17 all at the same time, by using a newly introduced strategy with a name like “Doubles Plus One” or “Near Doubles”. To apply “Doubles Plus One” to 6 + 7, a child must already have 6 + 6 = 12 in accessible memory; must notice that 6 + 7 is close to 6 + 6; must decide to apply the 6 + 6 knowledge to the 6 + 7 problem; must analyze 6 + 7 with respect to 6 + 6 to see that the exact difference between the two expressions is 1; and, finally, must add that 1 to the sum of 6 + 6 to arrive at the answer, 13.
This strategy is a powerful one that children unquestionably need to learn. However, the whole sequence of thought processes required by this strategy is a lot to ask them to perform all at once, especially when they are still just getting used to thinking about numbers in arithmetic expressions. It should not be surprising that some children fail to pick up on the strategy when it is presented all at once in this way.
Here, an addition game series breaks the process of learning this strategy into manageable steps. The first game in this series, “Change 3 + 4 into 3 + 3 + 1” focuses on the single fact 3 + 4 = 7. In this game, learners use cards showing three dots or four dots. A hint in the rules says, “With 3 + 4, notice how the four dots are the same as three dots plus one more. Imagine that the three is going together with the other three. That leaves just one dot left over. That’s one way to see why 3 + 4 is the same as 3 + 3 + 1.” With this visual aid, learners who already know that 3 + 3 is 6 — which includes almost all students learning addition, since the first few “doubles” facts such as 3 + 3 = 6 tend to stick in memory very easily (Bay-Williams and Kling, 2019, p. 25) — pick up quickly on this new way of thinking about 3 + 4. Subsequent games walk learners through using related strategies to find 4 + 5, 3 + 5, 5 + 6, 5 + 7, and 3 + 6. By playing these games, children come to see that similar strategies can be applied to many expressions. That idea is then put to use in the games that come afterward, which teach learners how to add 9 to other single-digit numbers (relatively easy, since 9 is just one away from 10), then how to add 8 (a bit harder than adding 9), then 7 and finally 6 (the trickiest addends for many learners). This small-step approach is used consistently throughout all of the games.
Next section: Learners get to experience success
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References
Bay-Williams, Jennifer, and Gina Kling. 2019. Math Fact Fluency: 60+ Games and Assessment Tools to Support Learning and Retention. Reston, VA: ASCD and the National Council of Teachers of Mathematics.
July 14, 2020