Why are fractions such a problem?

In tutoring over the last few years, I’ve seen errors in one kind of math problem more than any other. This is common to students who struggle with math and those who get excellent math grades. It is true of 8th graders and high school seniors. The topic that challenges many students of all achievement levels is fractions.

Fractions are introduced as numbers by third grade. Then, in fourth through eighth grades, students work with equivalent fractions, adding/subtracting, then multiplying/dividing fractions, and working with ratios and proportions. The concepts build, so that by the time a student enters high school, s/he is expected to be comfortable with all of these ideas.

The topic of fractions actually represents a number of different ideas: 1/2 is a number on the number line midway between 0 and 1, and it is also 1 of 2 equal parts that make a whole. The idea that a number can represent a relationship rather than a single quantity (i.e., 1/3 of 60 is not the same as 1/3 of 3) is huge.

Add decimals and percentages - which are other representations of fractions - to the mix and students have a lot to think about. After years of dealing with numbers as solid, exact, precise, unyielding entities where there is one and only one right answer, the concept that a fraction represents a different quantity in a different context is difficult for many to understand.

Students need the time and support to explore each concept. And it is important that they don’t just memorize an algorithm and get by. Without a solid understanding of fractions, students struggle with high school math. So, it is important that students’ questions are answered, and that they get help with homework if necessary, and that they get as much time as they need to work through this complicated concept. The energy teachers, families and tutors put into middle grade math is well worth the effort. Your high school math student will be happier and more successful because of it!