Understanding a problem is much more important than simply getting the correct answer. This statement definitely applies to fractions, a topic that can even get us adults confused at times. I ask my students to prove their answers by drawing pictures, using number lines, or decomposing. Students may also use words to explain their thinking. I understand that the process of explaining ones' work is not the way we learned growing up, where the emphasis was on answering as many questions as possible instead of actually understanding why the process worked; however, if your child really understands a skill or concept and does not just learn tricks to help get the answer easily, he/she will be a much better thinker and reasoner, and will do much better down the road when problems (and school in general) becomes more and more complicated.
The following are two examples of students using different strategies to show how they arrived at their answers.
The following are two examples of students using different strategies to show how they arrived at their answers.
With the above being said, I am not saying tricks and shortcuts do not have a place in fourth grade. I only mean to say that these tricks should not be taught at first; it would mean so much more to the student if they could discover the tricks themselves! Tricks do not help students learn and comprehend the process or skills that are being taught. Once students are taught a shortcut, they tune me out completely because they have an easy way to find the answers. Students who are only taught tricks and who do not understand why those tricks work will not do well in my class or down the road when math becomes more challenging.