Building thinking and problems solving skills is an important math objective. However, drill in thinking and problems-solving does not seem to return improved student performance for the time and effort that is expended.
Ongoing stories with math problems embedded in them is a great strategy. However, these are more difficult to write than Daily Oral Language (DOL) or Daily Oral Vocabulary (DOV) stories. The reason that these are more difficult to write is that any story line can be used for grammar, punctuation, spelling or vocabulary; but math problems require a “dedicated to math” story line.
Of course, the strategy of asking math questions in every content area subject could also be considered Daily Oral Math. Lessons for every subject should include math questions, even if you have to come up with them “off the cuff.”
While asking questions about real numbers is better than asking questions about make up numbers, there is a place for “What if?” math questions whenever you don’t have time to find some numbers. It is better to ask “What if?” and include numbers than to teach a lesson that doesn't include number questions.
What are these number questions?
If it has to do with numbers, math, problem-solving, analysis; it is appropriate.
There isn't a single academic or non-academic subject that cannot be improved with math questioning.
And, the corollary is also true...Any class that does not include mathematical problem solving, charts, graphs, statistics, patterns, etc.; did not reach its full potential.
The strategy of repetition (drill and practice) to move concepts from short-term memory into long-term memory is flawed because the same kind of problems are assigned. When stimuli are uniform, constant, similar; attention lags.
This is the “Doctor’s Office of Yesteryear” syndrome. In the old days, a doctor’s office reeked of alcohol and medicine smells. When you arrived, the smell was almost unbearable. But, as you sat there, the awareness of the smell receded. However, once you left, the impact of the smell returned.
This same principle occurs with repetition of lots of the same type of math problem. Instead of maximizing learning, the uniformity (and boredom) drops the stimuli out of awareness.
Math is the premier subject for integrating with other content area classes. In fact, if teachers practiced the integration of math in every other subject, the habits that they developed would make the integration of technology much easier.
Here are two other models of integrated math and...<