One of the most challenging topics in a typical math class is the learning of fractions and their operations. Why does Johnny (Jenny) struggle with the concepts of fractions, decimals, and percentages? I believe that these ideas are not taught effectively in most elementary classrooms. Teachers tend to move quickly through the lessons at this time in elementary school (usually 3rd or 4th grade), and tend to treat fractions as an abstract idea.
When learning to speak, infants are taught to point to an object and repeat the word that the adult speaks. These nouns become the buiding blocks of language, and numbers and counting is done the same way.
Primary grade students learn to count objects in their world, moving on to basic number pattern ideas and labels such as multiples of 5 and 3, and the concepts of odd and even. But these are whole number ideas, and partial numbers (fractions and decimals) tend to be introduced on paper as an abstract idea. In other words, teachers should be repeatedly showing students what a third of something is, or how to cut things up into equal pieces, etc.
I am not saying that this is avoided in elementary school, just that students are not given enough exposure to those ideas. Students should not be doing worksheets where they practice adding fractions with unlike denominators until they can draw pictures of these fractions, or show how to cut them up into equivalent pieces. The concrete learning idea of manipulating objects to show a mathematical idea needs to be embedded into the minds of young learners before they can practice similar math ideas on pencil and paper. This curriculum piece tends to be skipped or rushed in most elementary classrooms.
Students who are not ready to move on to do fraction work (or decimals or percentages) are either unsuccessful the rest of their math careers, or memorize the algorithms and get stuck later in higher level math courses.
Either case requires extra help to survive high school or college math curriculum because the developmental phases in mathematics cannot be avoided. If a student didn’t understand a fundamental concept such as fraction operations, they will not be successful in learning topics that use these ideas, such as solving equations, graphing linear relationships, or manipulating precalculus problems.
So, if you are a parent of a child who struggles in math, take a look at how your son or daughter expresses the ideas of fractions. Ask them to show you what 2 thirds looks like, or what 8.6 means, or to make a model of what percent 8 out of 10 represents. Can they do it?
If not, find a quality online math tutor who can diagnose the developmental phases of what your child has missed in the classroom. A highly skilled, experienced teacher can help fill in those gaps in learning, make it fun, and help your child to once again rediscover their math confidence!