Mathematical problem solving strategies used by pre-service primary school teachers Zsoldos-Marchis Iuliana Babes-Bolyai University This research was supported by Babes-Bolyai University, contract number GTC_34070/2013

Introduction  Developing mathematical problem solving skills is one of the main goals of school education.  For solving mathematical problems successfully is important to master more problem solving strategies.  Primary school teachers should know those strategies which are more suitable for their pupils’ age.

Research design Aim of the research  to study what mathematical problem solving strategies pre-service primary school teachers use Research sample  43 Pre-school and Primary School Pedagogy speciation students:  23 second year, 20 third year  41 female, 2 male

Research design Research tool  A problem sheet with 2 problems  Problem 1. In the following table there is a number in each cell, which we cover by different geometrical shapes: under the same geometrical shapes there is the same number, under different geometrical shapes there are different numbers. We have written near each row the sum of the numbers from that row; under each column the sum of the numbers from that column. Which number should be instead of the question mark?  Problem 2. In the garden there are 58 roses, white and red. How many red and how many white roses there are in the garden, if we know that there are three more red roses than four times the white roses?

Results: Problem 1 Strategy Number of students who solved correctly who solved incorrectly Use an ideaDiscovering the idea that the sum of the columns are equal with the sum of the rows 70 Solve an equationWriting a system of equations and solving it 02 Writing a system of equations and calculating the value of the required sum based on these relation 20 Writing a system of equations without solving it 01 Using the relations between the three unknowns without symbolic notations 10 Guess and checkGuessing the values of the three variables 017

Results: Problem 1  Use an idea. the sum of the rows are equal with the sum of the columns, i.e. 8 + ? + 6 = , from where it follows that we should write 10 instead of the question mark 7 students – 7 correctly

Results: Problem 1  Solve an equation  Writing the relations between the unknowns and calculating the value of the required sum based on these relations Using the symbols from the problem 1 student – 1 correctly2 students – 2 correctly Using symbolic notation

Results: Problem 1  Solve an equation  Writing a system of equations and solving it 3 students – 0 correctly

Results: Problem 1  Guessing the value of the unknowns 17 students – 0 correctly

Results: Problem 2 Strategy Number of students who solved correctly who solved incorrectly Solve an equationWriting an equation and solving it 142 Writing a system of equations and solving it 193 Guess and checkGuessing the values of the two variables 20 CalculatingCalculating the values of the two unknowns using simple operations 21

Results: Problem 2  Solve an equation  Writing an equation and solving it  Writing a system of equations and solving it  Guess and check  Calculating 16 students – 14 correctly 22 students – 19 correctly 2 students – 2 correctly 3 students – 2 correctly

Conclusions  In case of a problem, which could be considered as a routine problem for using equations or system of equations, students prefer algebraic methods instead of arithmetical methods.  The research results highlight the necessity of developing pre-service primary school teachers’ problem solving skills by enlarging the set of problem solving strategies they know and can easily apply.