Some may wonder why there are all the steps and detail in the Guided Solutions? It looks like a lot of work for students who are not doing well in math and may already have some resistance. Wouldn’t it be easier for them and more time efficient if we just explained the answers clearly?

Maybe your students are different, but the students we’ve worked with who are not doing well tend to miss important details and fail to derive some of the needed implications from the given information. They also fail to make logical connections on their own, even when the solutions are explained to them.

In order to get more out of the given in a geometry problem, it’s helpful to understand the problem (what are students trying to solve) and think about some of the possible routes to a solution (definitions, postulates, theorems, procedures). It’s also helpful to be able to ask questions of the given (what information do they have or can they reasonably derive). Asking these questions can open up the given and remind students of solution paths. It is this latter experience that is behind the guided solution approach.

Why guided solutions?
1. It is how we teach and tutor anyway.  Rather than telling what we know, we guide student discoveries as they build their mathematical thinking, their skill and knowledge.
2. It models the kinds of questions a student can ask of a diagram.
3. It models looking for connections between different parts of the given.
4. It models a path from the given to the solution.
5. It models an approach for stimulating students’ emerging sense of mathematical curiosity and logic.

Depending on the need, you can break the lesson down into logical and accomplishable sub-lessons, so the students feel a sense of success each step of the way. Or when doing the whole lesson, don’t show them all of the questions at once. Succeeding with each individual question and consequently seeing the diagram open up before them, is a motivator to keep going. While for other students, seeing all of your guiding questions up front, finding patterns in the questions as you ask them, and realizing at the end that they did get through all of them, can make the process less daunting in the future.

Students who know that the answers will eventually be given to them have less of a need and so are less motivated to develop their own analytical skills. To the extent that analytical reasoning is developed through guiding and not telling, future problem-solving becomes more efficient. The long-cut in the beginning is the short-cut in the long-run.