Today I took a glass and a jug of water into the classroom and asked students to pour a certain fraction into the glass.
I started the lesson by writing these fractions / numbers on the white board:
1/2, 1/4, 1/3, 3/4, 2/4, 2/3, 1, 0
and asked students to arrange them from highest to lowest
No one seemed to be able to do it so I introduced my glass of water teaching aid early into the lesson. Most of the students could manage pouring 1/2, 1/4, 3/4, 1 (and 0) but for the others many had difficulty. They couldn't do it.
I then asked if anyone could come out the front and show how to do 2/3 rds or 3/4 by drawing on the white board. With some assistance - this took a while - one student showed the rest of the class how to split the glass into the correct number of equal parts and then shade in the desired number of parts. Eventually everyone seemed to get it, by that I mean everyone could explain in words about dividing the glass into (denominator) equal parts and then shading in (numerator) number of parts
I then moved onto doing fifths and eighths and it seemed to be understood. Students could say what to do in words.
Going back to my original question, some students could now arrange the fractions in their correct order. But there was still some confusion. One student asked: "Why is 2/3 great than 2/4?". I dealt with that by asking someone to show 2 glasses on the white board, one with each of the fractions.
At this stage I haven't broached anything such as lowest common denominator. I see that as an algorithm that produces a correct answer without understanding.
... studies in Australia, Papua New Guinea and Malaysia showing that most primary school children do not link what they learn about fractions in mathematics classrooms with situations involving fractional quantities in their personal worlds. For example, many children who correctly answered pencil-and-paper fraction questions such as 5/11 x 792 = q could not pour out one-third of a glass of water, and of those who could, only a small proportion had any idea of what fraction of the original full glass of water remainedThis is part 5 of a series about teaching fractions and meta-dialogues:
- Nerida Ellerton and M. A. (Ken) Clements
- Fractions: A Weeping Sore in Mathematics Education
"a dialogue with students which involves meta cognition (thinking about their own thinking) and meta-conceptions (students thinking about their own knowledge and understanding of concepts)"earlier posts:
meta-dialogues are hard to establish
initiating a meta-dialogue
fractions in real life
redefining power relationships in the classroom