Word Problems in Context.

Unfortunately, too many word problems found in textbooks tend to be artificial and constructed to meet the math being taught at that moment.  The unfortunate side effect to this is students look for the math to apply rather than starting with the word problem itself.

Lets look at the process involved in solving real world problems starting with the context rather than the math.

We are given a mathematical problem in context.  From that we formulate the mathematical application and its uses to the real world problem.  This includes taking the situation and translating it into a form which we can identify the mathematics needed to solve it. The next step is to use any mathematical formulas, processes, procedures, reasoning, facts or tools required to find the solution.  The final step is to interpret and or evaluate the answer to determine if the solution is reasonable.

This is directly opposite of the normal way of doing things where we teach some math, have them practice the math, finally applying the math in a situation where the math has already been set up for the student.

We as math teachers can step away from the textbooks, to provide open ended real texts and real situations so students  have a chance to make connections between math and its use in the real world.  We can provide students with those messy problems and help them learn to extract the information needed to identify the mathematics needed to solve it, and when students stumble, use that to determine what needs to be taught.

As part of providing these types of experiences, there has been a creation of authentic tasks which require students to demonstrate their knowledge by applying it to real world problems.  A good task bridges the gap between the classroom and understanding its applications outside of the classroom.

Tomorrow, I'll be discussing how a good authentic or real world task is built. Let me know what you think.