Imagine that a teacher requires some advice from you as a mental health consultant.
The teacher bought a toy that all the children like to play with.
The school mathematics we envision is more fulsome, and uses problems as the basis for exploring the mathematical ideas of the curriculum, building skills and understanding, and builds more flexible and capable mathematical thinkers.
As a child, perhaps you had a “problem of the week” to solve, perhaps on Fridays.
Having a process for solving problems helps to keep efforts focused and eliminate becoming stalled.
For over 30 years, with NCTM reforms, we have been talking about “teaching through problem-solving”, rather than teaching *about* problem-solving. I am not sure “teaching through problem-solving” is all that well-defined.As a teacher, it is helpful to observe those moments when children have problems and help them think about ways to solve their own problems.Anticipate problems before they escalate and help children identify possible solutions.Engaging with a word problem was your reward for getting through four days of worksheets and homework.You faithfully highlighted the key words, and went to work.What do we mean when we say “mathematics problems”?Any worthwhile mathematics task or question could be considered a problem.We who are, broadly speaking, constructivist teachers need to answer for how kids will do enough math, to be good at math, in problem-solving classrooms, but that’s a topic for another post. Somewhere, on a dusty shelf, you might have an old binder full of problems.That binder might be organized by problem-solving strategies, like: working backwards; solve a simpler problem; or make a table or chart.Solving problems is not really something that can be taught like that.That approach could be characterized as “teaching about problems”, or “teaching how to solve problems”.