Mathematicians are painfully aware that fresh knowledge is unreliable and it is necessary to mercilessly hunt down and fix errors before it becomes useful. In contrast, there is very little error correction in K-12 math. Instead they rely on repetition to eventually overcome misunderstanding.
The Issue for discussion is: how can we encourage more error-correction in K-12 math?
Barriers
- Teachers (in the US at least) are taught to encourage students and appreciate what they can do rather than point out flaws. Frequently this means giving credit for “knowing” even when the “knowledge” is nonfunctional.
- Low requirements for correctness, grading curves, extra credit — in short all the methods teachers use to disconnect credit from performance — often leave students not realizing there are problems, and certainly not feeling any urgency about fixing them.
- Teachers are discouraged from telling students too directly that they have done something wrong. This is considered suppressing creativity, or forcing thinking into arbitrary “approved” channels.
- Students do not understand (and are not taught) the difference between being told they are wrong and being told they are stupid. This discourages efforts at correction. It also means that when disfunctionality becomes obvious it is taken as personal failure.
- Texts and teaching methods are rich with distractions and content is diffused. They almost seem designed to invite errors rather than avoid them. This is tolerable only because lack of error correction hides the fact that current texts increase the burden of errors.
- Error correction requires focused individual attention. In classroom settings this is dependent on cooperation (good behavior) of other students.
Urgency
The US math curriculum has much more repetition than that of other countries and there are frequent calls to reduce it. However error correction may be more common in these other countries — as it was in the past in the US — and increased repetition may be a compensation for decreased error correction. If so then eliminating repetition will be unsuccessful unless it is accompanied by an increase in error correction.
Hope
Computer-based tests and practice problem may help:
- Having computers tell students they have made a mistake avoids emotional and personal problems.
- Separating assessment and instruction reduces the tension that exists between them when the teacher is responsible for both. Teachers can focus on teaching.