# PER-SERVICE ELEMENTARY TEACHERS' SITUATIONAL STRATEGIES IN DIVISION

# 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.

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