Developing problem solving skills is a fundamental part of learning math. This article explores the issues around teaching problem solving in the math classroom, pointing out that students learn problem solving skills slowly but that problem solving skills should be integrated in to every math class. It also recommends using “Worthwhile problems” instead of simple ones for teaching both mathematical concepts and problem solving skills. For a similar idea, see my post about Dan Meyer’s Patient Problem Solving.
National Council of Teachers of Mathematics. (2014). Why is Teaching With Problem Solving Important to Student Learning? Brief. from National Council of Teachers of Mathematics: http://www.nctm.org/news/content.aspx?id=25713