ED2652 Lecture 3: Mathematics Lecture 3
Mathematics One: Number and Algebra
Lecture Three – Week Three
Common Fractions
• Six Important Messages
o Two of these messages are important to keep in mind about the teaching and learning fractions
▪ Fractions are an important part of the mathematics ‘curriculum’
▪ Fractions are a challenge to teach and learn
o Four of these messages are key ideas in developing an understanding of fractions
▪ Developing the idea that the size of the unit/whole determines what the fraction “looks” like is
essential
▪ Multiple representations of fractions are required
▪ Common fraction understanding is based on the part/whole concept (partitioning) and fractions
are about equal parts
▪ The bigger the denominator the smaller the parts
• Seigler, Fazio, Bailey & Zhou (2012)
o “Poor fraction knowledge in elementary school predicts low mathematics achievement and algebra
knowledge in high school, even after controlling for general cognitive abilities, knowledge of whole
number arithmetic, and family education and income. High school algebra teachers recognize this relation;
they rank students’ fraction knowledge as among the largest impediments to success in their course.”
• Are Fractions Challenging?
o “No area of school mathematics is as mathematically rich, cognitively complicated, and difficult to teach as
fractions, ratios and proportion”
▪ Smith (2002, p.3)
o The inappropriate application of while number schemes
▪ Seeing the numerator and denominator as separate whole numbers
▪ This student sees the denominator as the larger number
• Hiebert (1999)
o Explored the difficulty in building conceptual understanding after a procedural approach has been taught
• What are the language difficulties inherent in talking about fractions?
o Use of ordinal numbers – we talk about thirds, fifths and sixths, etc.
o Lack of consistency in the use of ordinal numbers – halves not “twoths,” and quarters not fourths
o The variety of names we have for fractions - one half is also five-tenths, zero point five (0.5) and fifty
percent (50%), as well as two-quarters, three-sixths, four-eighths, and so on
o A “fraction” usually refers to “any little bit”, but 9/2 is also a fraction.
▪ You can actually have a fraction greater than one (Improper fractions)
▪ Not always about being smaller
• The different Models
o Region models
▪ 2D and 3D
o Area Models – same areas but not necessarily the same shape
o Length Models – Strings, paper strips, etc
o Set Models – Counters etc
▪ Set Models can be ‘whole part’ or ‘part whole’
find more resources at oneclass.com
find more resources at oneclass.com
