Fractions in Math Class aren't the Same as Fractions in Real Life - or are they?

Seems like a silly question, but to some kids it is reality. 

At Mathnasium, we have the opportunity to work with a lot of students, all with their individual level of math understanding.  Starting in 4th grade, fractions can be the make or break topic for future success with math.  Fractions often start the decline in a student’s attitude towards math. 

When we assess students in 4th grade or higher, we find many students can add, subtract, multiply and divide fractions.  Their computation is competent, but is it understood?  During the assessment we ask students to rank fractions from smallest to largest.  We include the numbers 0 and 1.  More often than I would like to see, students place all the fractions before the number 0.  When I ask, “Would you rather have half a candy bar or no candy bar?”, I either receive a very puzzled look or I receive the “That’s different” response.  I also receive the “Fractions are really small” as an answer to why they placed the fractions as being less than zero.

3 Steps of learning:  Exposure, Competency and Mastery

Too often the 1st step, exposure, is skipped and the 3rd step, Mastery is not attained.  Once a student is competent they are moved on to the next topic.  Unfortunately, without previous exposure or reaching mastery, competency is often not maintained.

For example, children first learn their ABCs by singing and repeating the sounds – orally.  This is a mental process exposing the student to letters.  They are not expected to understand the meaning of the letters.  When first learning to count, the order is:

1) The child hears the words “Zero, one, two,…” without having any idea of the meaning.

2) At a later time the child uses objects and forms the notions of quantity and order.  It is at a much later time that the child learns to read and write numbers on a printed page.

If we waited until the child can read and handle physical objects before beginning to teach the words “zero, one, two…” it would be a much slower process. 

To help understand fractions students need to hear and say fractions before they are expected to understand how to write and compute with fractions.  What can parents do?

1. - Have the students count by fractions just like you had them count by ones.  One-fourth, 2 fourths, 3 fourths, etc.  One third, two thirds, 3 thirds, etc.
2. - Use fractional language in your daily life.  It doesn’t need to be a math lesson and it may seem awkward but it will have a lasting impact:
   • I have 7/8’s of a tank of gas
   • I only have an eighth of a tank of gas
   • Here is 1/12th of the pizza
   • I baked 2 dozen cookies, let’s take a third of them with us
   • Talk about the measuring cups you are using – there are 4- ¼ cups – in a whole cup,etc
   • Use an analog clock and use the phrase “a quarter after” or “a quarter to”
   • Relate fractional parts like when giving them a quarter say, “Here is a fourth of a dollar” or with a dime, “Here is a tenth of a dollar”.
3. - Relate fractions to things they love:
   • Music -  point out the meaning of a quarter note, a half note and a dotted half note
   • Sports -  talk about batting averages, shooting percentages, etc

Exposure to learning begins and continues at home.  Even if you didn’t like math as a child (please don’t tell your children that) you do a lot of daily math and you can do this!  The more you expose your child to fractions, the more you will help your child.  

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