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Why are Fractions so Difficult?

According to research, there are a number of reasons students struggle with fractions.

They include:

  • It is important for teachers to help students see how fractions are like and different from whole numbers.

Think about it:

Mike is offered the choice of a third of a pizza or a half of a pizza. Because he is hungry and likes pizza, he chooses the half. His friend Jane gets a third of a pizza but ends up with more than Mark.

How can that be?

Misconception 2

Students may think that 2/3 means any two parts, not equal sized parts.

EX: Students may think that the following shape shows ¾ green rather than ½ green.

Chapter 15 : Developing Fraction Concepts

Misconception 3

Misconception 1

Students think that a fraction such as 1/5 is smaller than a fraction such as 1/10 because 5 is less than 10.

  • Teachers should use lots of visuals and contexts that show parts of a whole for them to understand the concept. For example ask the students if they would want to go outside for ½ an hour, ¼ of an hour, or 1/10 of an hour. Students may be told that fractions are the reverse-the bigger the denominator the smaller the fraction.

Ana Cardarelli

Cecilia Candelaria

Students think that the numerator and denominator are separate values and have trouble seeing them as a single value. (Cramer & Whitney, 2010)

  • Finding fraction values on a number line or ruler can help students develop this notion.
  • Using the phrases “three out of four” or “three over four” should be avoided.
  • Instead say “three fourths”.

EX: It is hard for them to see that ¾ is one number.

Some common misconceptions about fractions are the following:

References

Fractions are sometimes written in an unusual way.

There are many meanings to fractions.

Instruction does not always focus on a conceptual understanding of fractions.

  • Van De Walle, J., Karo, K. S. and Bay-Williams, J. M. (2013). Elementary and Middle School Mathematics: Teaching Developmentally. (8h Ed). Upper Saddle River, NJ: Prentice Hall.
  • Cramer, K. & Whitney, S. (2010). Learning rational number concepts and skills in elementary school classrooms. In D.V. Lambdin & F.K. Lester, Jr. (Eds.), Teaching and Learning mathematics: Translating research for elementary school teachers (pp. 15-22). Reston, VA: NCTM
  • Siebert, D. & Gaskin, N. (2006). Creating, naming, and justifying fractions. Teaching Children Mathematics, 12(8), 394-400

Misconception 4

(Part/whole, quotient, ratio, etc.)

(1/4, 1.5, 12/4, 3:5, etc.)

Students incorrectly use the operation “rules” for whole numbers to compute with fractions.

EX: ½ + ½= 2/4

Students tend to overgeneralize their whole number knowledge.

Students struggle with fractions because they use what they know about whole numbers to solve problems with fractions.

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