On semiotics and jumping frogs : the role of gesture in the teaching of subtraction

Abstract

I had asked the five-year-old children to suggest ‘frog jumps’ on the class number line. To model subtraction the frog, ‘Freddie’, is placed on the line and then jumps back the number subtracted. Giannis has suggested that Freddie starts on the number 1. MTF [Places frog above the number 1 on class line] He didn’t go very far! [Laughs] Now let’s see what Giannis is going to say [pause] Giannis [Smiles]Two! MTF He jumps back[pause] Two?! [Puts out two fingers] Let’s see what happens if Freddie jumps back two. One, two! [Moves frog back one jump, then another. Mimics the frog falling half way to the floor] Child 1 Woo! David Aaah! MTF [Moving the frog toward the floor] What happens to Freddie? Sven He fell off! [Smiles] Children [Smile] He falls off / he fell off. Dragan [Smiles] He jumped in the water. This vignette is taken from a series of lessons I carried out with a group of young children in Malta as part of a teaching/research experience. The frog jumps—which were key to the children’s learning about subtraction—are the focus of this article. As a teacher-educator, I teach elementary mathematics education to pre-service teachers, and frequently have contact with in-service teachers. One of my main areas of interest is language, and in my discussions with practitioners, I encourage them to give explicit attention to mathematical language. I wished to try out this recommendation for myself through a teaching/research experience in order to ‘practise what I preached’ and to be in a better position to reflect on this aspect of mathematics education. One of the classes I taught for this purpose included Giannis and the other children featured in the vignette above [excerpt].