PER-SERVICE ELEMENTARY TEACHERS' SITUATIONAL STRATEGIES
IN DIVISION
Anu Laine, University of Helsinki; Sinikka Huhtala,
Helsinki City College of Social
and Health Care; Raimo Kaasila, University of Lapland; Markku S. Hannula,
University of Turku & Erkki Pehkonen, University of Helsinki
Here we will present some preliminary results of our research project on
pre-service
primary teachers’ views of mathematics (the project financed by the Academy of
Finland; project #8201695). We have collected survey data of 269 pre-service
primary teachers in the beginning of their mathematics studies . Here we will
concentrate on teacher students’ understanding of division. Division is an
essential
arithmetical operation , and there are many misconceptions connected to it. These
might be: “You must always divide the bigger number by the smaller one” (e.g.
Hart,
1981) or “You can operate with the digits independently : 84÷14=81 because 8÷1=8
and 4÷4=1” (Anghileri, Beishuizen & van Putten, 2002).
Understanding of division with decimal numbers was measured by task 16.8÷2.4.
About half of the students (51 %) could do the calculation . Students used
different
approaches in solving the problem . Using quotitive division and “trial and
error” or
“ repeated addition ” had usually led to the right answer. “Operating with the
digits
independently” had caused the most common wrong answer 8.2 and “dividing in
half” led to answer 8.4.
Task “Solve 7÷12 by using long division algorithm” measured among other things,
whether students divided the numbers in right order . 16 % of students divided 12
by
7. In task “Write a word problem to task 6 ÷ 24 and solve it ” students seemed to
be
able to write a word problem little better than to calculate the task . The most
common
wrong answer was 4. Another usual answer was 0.4. Although tasks 7÷12 and 6÷24
were much alike students solutions varied . Situational strategies in solving
division
tasks seem to depend at least on numbers , problem structure and different
concrete
situations (cf. De Corte & Verschaffel, 1996).
Our data suggest that mathematical understanding that students have in division
is
inadequate for teaching division for understanding. During teacher education it
is also
important that elementary teacher students become conscious of the difficulty of
division and of the different misconceptions people have in division so that
they can
better teach division for their pupils.