As a child, perhaps you had a “problem of the week” to solve, perhaps on Fridays.Engaging with a word problem was your reward for getting through four days of worksheets and homework.
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.
Our students are sensitive to pseudo-context, as they should be.
Problems about pizza or cookies are far too common, and often not problematic enough.
The mathematical world is an interesting place to be, and to live.
Our students need to be shown that it is our world, too.Mathematics is about question asking as much as it is about question answering.Worthwhile mathematics tasks are those that get students thinking about big and important mathematical ideas.Worthwhile mathematics tasks are those that get students to think about mathematics that is interesting, useful, or beautiful. The mathematical world is interesting enough, sometimes.It is a world of thought, or visualization, and representation, and then bringing those representations into being, through speech, and on paper.Young children are wired to try and try again to accomplish a goal that matters to them.By the time they are in the upper elementary grades, however, they often do not show this same perseverance in math problem-solving.Consider this definition of “problem-solving”: Wieman/Arbaugh Sure, but many things in the world are “problematic”, the behavior of celebrities, and politicians, for example. A definition that perhaps begs the question: what is “problematic”?A teaching through problem solving approach means using problems, questions, or tasks that are intellectually challenging and invite mathematical thinking through both mathematical content and mathematical processes in our students.“It is important to understand that mathematics is to be taught through problem solving.Any worthwhile mathematics task or question could be considered a problem.A problem is something that gets students thinking. A problem sparks more questions, a problem sparks more questions until the sparks make a raging fire.