ABSTRACT
When students first learn about subtraction, they learn to subtract each digit of the subtrahend from its counterpart in the minuend:
To compute this, they simply subtract 2 from 5 and 1 from 7. However, this straightforward strategy does not work all the time. When a digit at a lower place value of the subtrahend is larger than its counterpart in the minuend (e.g., 22−14, 162−79), students cannot conduct the computation directly. To subtract 49 from 62, they need to learn subtraction with regrouping:
Subtraction, with or without regrouping, is a very early topic anyway. Is a deep understanding of mathematics necessary in order to teach it? Does such a simple topic even involve a deep understanding of mathematics? Would a teacher’s subject matter knowledge make any difference in his or her teaching, and eventually contribute to students’ learning? There is only one answer for all these questions: Yes. Even with such an elementary mathematical topic, the teachers displayed a wide range of subject matter knowledge, which suggests their students had a corresponding range of learning opportunities.
