Mathematical problem solving strategies used by pre-service primary school teachers

Mathematical problem solving strategies used by pre-service primary school teachersZsoldos-Marchis IulianaBabes-Bolyai UniversityThis research was supported by Babes-Bolyai University, contract number GTC_34070/2013

IntroductionDeveloping 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 designAim of the researchto study what mathematical problem solving strategies pre-service primary school teachers useResearch sample43 Pre-school and Primary School Pedagogy speciation students:23 second year, 20 third year41 female, 2 male

Research designResearch toolA problem sheet with 2 problemsProblem 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 1StrategyNumber of studentswho solved correctlywho solved incorrectlyUse an ideaDiscovering the idea that the sum of the columns are equal with the sum of the rows70Solve an equationWriting a system of equations and solving it02Writing a system of equations and calculating the value of the required sum based on these relation20Writing a system of equations without solving it01Using the relations between the three unknowns without symbolic notations10Guess and checkGuessing the values of the three variables017

Results: Problem 1Use an idea. the sum of the rows are equal with the sum of the columns, i.e. 8 + ? + 6 = 9 + 8 + 7, from where it follows that we should write 10 instead of the question mark

7 students 7 correctly

Results: Problem 1Solve an equationWriting the relations between the unknowns and calculating the value of the required sum based on these relations

Using the symbols from the problem1 student 1 correctly2 students 2 correctlyUsing symbolic notation

Results: Problem 1Solve an equationWriting a system of equations and solving it

3 students 0 correctly

Results: Problem 1Guessing the value of the unknowns

17 students 0 correctly

Results: Problem 2StrategyNumber of studentswho solved correctlywho solved incorrectlySolve an equationWriting an equation and solving it142Writing a system of equations and solving it193Guess and checkGuessing the values of the two variables20CalculatingCalculating the values of the two unknowns using simple operations21

Results: Problem 2Solve an equationWriting an equation and solving itWriting a system of equations and solving itGuess and checkCalculating

16 students 14 correctly22 students 19 correctly2 students 2 correctly3 students 2 correctly

ConclusionsIn 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.