coding strategic behaviour in mathematical problem solving

CURRENT REPORT Coding strategic behaviour in mathematical problem solving Andri Marcou* London South Bank University, London, UK Research in mathematics education and educational psychology has revealed the crucial role of strategic behaviour for successful mathematical problem solving (MPS) (Pape and Wang 2003; Posamentier and Krulik 1998) and self-regulated learning (SRL) (Pintrich 1999; Zimmerman and Martinez-Pons 1986). Pape and Wang (2003) identified twelve categories of strategic behaviour such as self- evaluating, organising, planning and seeking information whereas Posamentier and Krulik (1998) focused on mathematics strategies like finding patterns and intelligent guessing and checking. Pintrich (1999) grouped the various SRL strategies into cognitive, metacognitive and resource management strategies and indicated their positive relationship to performance in various subjects. This study draws attention on both fields of MPS and SRL to suggest a coding scheme as a tool to analyse strategy use and self-regulation in MPS. The initial scheme consisted of various cognitive, self-regulatory, resource management and mathematics strategies allocated at each stage of MPS, ‘‘reading and analysing the text of the problem’’, ‘‘carrying out the plans’’, and ‘‘looking back’’ (Polya [1945] 1957). The coding scheme was piloted after the implementation of three studies which involved clinical interviews with students of Year 4 (age 8Á9), 5, and 6 while working on word MPS, either individually or in groups and these were video-taped, transcribed, and coded. As the process was going on, the coding scheme was revisited and transformed so as to include the most commonly used strategies at each stage of MPS. The final scheme consists of eight strategies at the first stage, six at the second stage and eight at the last stage of MPS. The scheme can be used by primary school students as a tool to regulate their strategic behaviour during word MPS, by teachers as a model to teach self-regulation in MPS and by researchers as a means to analyse students’ strategic behaviour. However, the scheme needs to be tested in terms of inter-rater reliability in order to be suitable to be used as a reliable tool for analysing primary students’ MPS behaviour and also to be evaluated as a teaching and learning tool when it is implemented in real classroom settings. References Pape, S., and C. Wang. 2003. Middle school children’s strategic behaviour: Classiﬁcation and relation to academic achievement and mathematical problem solving. Instructional Science 31: 419Á49. *Email: [email protected] ISSN 1479-4802 print/ISSN 1754-0178 online # 2008 British Society for Research into Learning Mathematics DOI: 10.1080/14794800801916929 http://www.informaworld.com Research in Mathematics Education Vol. 10, No. 1, March 2008, 99Á100

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CURRENT REPORT

Coding strategic behaviour in mathematical problem solving

Andri Marcou*

London South Bank University, London, UK

Research in mathematics education and educational psychology has revealed the

crucial role of strategic behaviour for successful mathematical problem solving(MPS) (Pape and Wang 2003; Posamentier and Krulik 1998) and self-regulated

learning (SRL) (Pintrich 1999; Zimmerman and Martinez-Pons 1986). Pape and

Wang (2003) identified twelve categories of strategic behaviour such as self-

evaluating, organising, planning and seeking information whereas Posamentier

and Krulik (1998) focused on mathematics strategies like finding patterns and

intelligent guessing and checking. Pintrich (1999) grouped the various SRL strategies

into cognitive, metacognitive and resource management strategies and indicated their

positive relationship to performance in various subjects.This study draws attention on both fields of MPS and SRL to suggest a coding

scheme as a tool to analyse strategy use and self-regulation in MPS. The initial

scheme consisted of various cognitive, self-regulatory, resource management and

mathematics strategies allocated at each stage of MPS, ‘‘reading and analysing the

text of the problem’’, ‘‘carrying out the plans’’, and ‘‘looking back’’ (Polya [1945]

1957). The coding scheme was piloted after the implementation of three studies

which involved clinical interviews with students of Year 4 (age 8�9), 5, and 6 while

working on word MPS, either individually or in groups and these were video-taped,transcribed, and coded. As the process was going on, the coding scheme was

revisited and transformed so as to include the most commonly used strategies at each

stage of MPS.

The final scheme consists of eight strategies at the first stage, six at the second

stage and eight at the last stage of MPS. The scheme can be used by primary school

students as a tool to regulate their strategic behaviour during word MPS, by teachers

as a model to teach self-regulation in MPS and by researchers as a means to analyse

students’ strategic behaviour. However, the scheme needs to be tested in terms ofinter-rater reliability in order to be suitable to be used as a reliable tool for analysing

primary students’ MPS behaviour and also to be evaluated as a teaching and

learning tool when it is implemented in real classroom settings.

References

Pape, S., and C. Wang. 2003. Middle school children’s strategic behaviour: Classification and

relation to academic achievement and mathematical problem solving. Instructional Science

31: 419�49.

*Email: [email protected]

ISSN 1479-4802 print/ISSN 1754-0178 online

# 2008 British Society for Research into Learning Mathematics

DOI: 10.1080/14794800801916929

http://www.informaworld.com

Research in Mathematics Education