If the games and activities are being used to supplement a curriculum in progress, the curriculum itself may include many ways for learners to practice the concepts. The situation is different if your curriculum does not stress practice, or when learners are working outside a curriculum to catch up with their peers. In this case, they may need extra ways to practice the concepts.
One extra way for learners to practice is with worksheets that you create for them. More ways to practice are listed below.
Workbooks
Workbooks with arithmetic problems can be found in bookstores and online.
While your learner is using a workbook, you should check in from time to time to make sure that he is using an appropriate strategy to solve the problems.
For example, if the games have recently helped a learner to start adding without counting one by one, it is critical to make sure that she does not fall back to a counting-one-by-one strategy during workbook practice.
A learner who is ready to add without counting will not be helped by repeatedly rehearsing a counting strategy. In fact, repeated rehearsal of the counting strategy may prevent this learner from progressing. Instead, he should be applying the strategies he has learned in the games. Similarly, if learners are doing multiplication problems, they should be applying the ideas about the multiplication facts that they have learned in the games.
You can help learners by showing them how the workbook problems are similar to what they did in the games, and asking them to practice using the same strategies with the workbook problems.
Free online worksheets
Many free worksheets are available online. See tips for workbooks, above.
A workbook/worksheet tip that learners enjoy
Tip: Tell learners to cross out any problems where they already know the answer from memory. They don’t even have to write the answers to those problems. When they use their own self-knowledge to cross out problems they don’t need to solve, they are essentially creating their own individualized worksheets.
Telling learners they can skip worksheet facts they already know lets them focus on what they need to learn.
It also motivates them. When you tell learners they don’t have to spend time writing down answers they already know, the implicit messages are “Your time has value” and “You can be trusted.” Learners of all ages appreciate hearing these messages.
Of course, this tip only works when the point of an assignment is learning. During assessments, students should answer all the questions.
Electronic apps for arithmetic practice
A wide variety of electronic applications for arithmetic practice are available. Arithmetic practice apps are like workbooks in that it is important for you to check in on learners to see how they are getting their answers.
Electronic apps: What to watch out for
A “perverse incentive” is an incentive with an undesirable result that the designers did not intend. Some electronic applications give learners a perverse incentive to obtain answers by counting (or by skip-counting, for multiplication) instead of by using non-counting strategies.
When does this happen? It happens when an application puts time pressure on learners. Some applications do this by giving the learner more positive reinforcement for quicker correct answers than for slower correct answers. Others do it by making learners answer before time runs out.
Time pressure can be a problem because it hampers strategy practice. Ultimately, practicing non-counting strategies leads to quick arithmetic skills. But at first, practicing non-counting strategies requires a little thinking time. This means that when an application puts time pressure on learners, it is giving them an incentive to avoid using non-counting strategies and revert to counting.
These concerns do not mean that you should avoid all electronic apps. But if your learner has been using an app and does not seem to be progressing, this information may help you identify the problem.
Meaningful real-world applications
It is especially helpful whenever learners can make a connection between a mathematical concept they are learning how to use and a real-life situation that is personally significant. This is something you can help them do in conversation.
Is there some real-world situation they already care about? Through conversation, you may be able to find a way to get them to transfer their learning from the games to this meaningful real-world situation.
Next section: Pairing learners
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August 18, 2020