If students have learned the basic facts, what else will they be able to do?

Edward C. Rathmell
University of Northern Iowa

Students, who have just rotely memorized the basic facts without being able to justify their answers or explain their thinking, will not be as adept at using their knowledge in new situations. On the other hand, when students have learner efficient thinking strategies, they can use that same thinking in many different situations. For example, if they can count on, they can easily solve 68 + 3 almost as easily as 8 + 3. Similarly, 28 + 6 is not much more difficult than 8 + 6. The thinking strategies are powerful ways for them to solve many problems with larger numbers. In other words, these students will be much better at mental computation.

Students, who understand the part-part-whole concepts, will be able to write number sentences that make sense to them based on parts and wholes. And they will be able to easily determine whether to add or to subtract when they attempt to solve a word problem. If they know both parts, they simply add to find the whole. If they know the whole and one part, they subtract to find the other part. This provides them a powerful way to solve addition and subtraction word problems.

Perhaps the most important attribute of students, who have met the goals described above, is the mathematical power that they develop. They feel confident that they can make sense of numbers. They are competent because they can accurately solve basic fact problems and many other problems as well. And they have developed the perseverance to try to make sense of problems involving numbers. They do not quit trying to solve a problem just because they do not remember the answer. These students have the mental tools to be successful in mathematics.

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