Simple activities can be thought-provoking. Allowing students an opportunity to consider all of the aspects and approaches to a what may seem like a straightforward problem can be used as a demonstration to show that each student possesses a unique capacity for problem solving. As discussed in the Dan Meyer TED Talk, being less helpful to students may benefit them by allowing them the opportunity for discovery. Real life, practical questions are often the most engaging. Their basis in reality and not formulas or arithmetic may engage even the least inclined students. In order to accomplish this however, it is recommended that "noise" be removed from problems, as this extraneous information may detract from the focus of the problem at hand. Assignments should never be rooted in formulas as this does not teach any of the underlying critical thinking and understanding of problem solving. This "black box" approach to arithmetic generally provides all but one piece of information for a given formula, and asks students to simply plug the values in for the answer. Students have become focused on finding "the answer" as a result, despite the fact there is almost never a single correct method for any exercise.
My experiences as a univeristy-level teaching assistant in chemistry highlighted how misconceptions about mathematics are ingrained in students. The focus of student questions and discussion dealt with a single value, such as a mass, or volume, or pH, and how exactly their solution matched an answer key. Students often neglected consideration for the process by which they got their answer (beyond using a formula that they were familiar with) and rarely considered whether their reasoning or solution were logical. It was obvious that students were always taught in a very singular, traditional approach where methodology was downplayed and students were all expected to think and learn in a very monochromatic way.
