Using diagrams as tools for the solution of non-routine mathematical problems

Pantziara, Marilena; Gagatsis, Athanasios; Ηλία, Ιλιάδα

doi:10.1007/s10649-009-9181-5

Cited by 55 publications

(30 citation statements)

References 29 publications

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“…In the study, it was seen that these mistakes stemmed from inaccurate drawing of the figure or inaccurate interpretation of an accurate drawing. This finding is coherent with those in the studies by Hong (1993Hong ( , 1995 and Pantziara, Gagatsis, and Elia (2009).…”

Section: Findings and Discussionsupporting

confidence: 93%

Determining the Errors of Primary School 5th Grade Students in Non-Routine Problem Solving

Ulu¹,

Tertemiz²,

Peker³

2016

Journal of Theoretical Educational Science

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ABSTRACT:The aim of this study is to determine the errors of 5th grade students in non-routine problems. In this study, descriptive survey method was used and clinical interview method was used in order to determine the source of the errors of 5 th grade students in non-routine problems. The study group of descriptive survey model was composed of 467 primary school 5 th grade students in 13 classes in 7 different primary schools in the city of Kütahya chosen according to cluster sampling method, while the study group of clinical interview method was composed of 70 students chosen among those who had made the error themes determined. As a result of the research, it was determined that the students made mostly comprehension-related errors (45.50%); this comprehension based errors mostly resulted from miscomprehension (27.28%), followed by irrelevant operation (10.42%) and incomplete comprehension (7.39%). It was also determined that the errors stemmed from the following: performing the strategy (5.72%), reading (3.77%), performing the operation (2.62%) and choosing the right strategy (2.36%), respectively.Keywords: Mathematics, 5 th grade students, non-routine problem, mistake types, sources of the errors Extended AbstractPurpose and Significance: This study deals with mistakes in non-routine problems due to the facts that they require high level thinking skills, that more mistakes are seen both in student solutions and in teacher solutions and that the rate of utilization by teachers is low. During problem solving process, an individual is supposed to make sense of the problem during and after reading because without making sense of the problem, it is thought that individuals will come up with meaningless conclusions by using the numbers in the problem randomly. Problem solving skill is a complex process requiring use of information, and in this process students firstly need language skills. Because no studies have been encountered in Turkey about the relation between language skills and problem solving strategies, it is aimed in the study to determine the source of the mistakes of primary school students in non-routine problems. In this context, answers for the following questions are sought:1.How is the distribution of the mistakes of primary school 5th grade students in non-routine problems according to mistake types? * This paper is a part of corresponding author's unpublished doctoral dissertation. ** Corresponding Author: Assist. Prof. Dr., Dumlupınar University, Kütahya, Turkey, mustafa.ulu@dpu.edu.tr *** Assoc. Prof. Dr., Gazi University, Ankara, Turkey, tertemiz@gazi.edu.tr **** Prof.Dr., Afyon Kocatepe University, Afyonkarahisar, Turkey, peker@aku.edu.tr Ulu, M., Tertemiz, N., & Peker, M. (2016 What are the reasons for primary school 5th grade students to make mistakes in non-routine problems? Citation InformationMethods: In the research, descriptive survey and clinical interview methods were used together. Survey models are research approaches that aim to describe a former or an existing case as it is....

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Section: Findings and Discussionsupporting

confidence: 93%

Determining the Errors of Primary School 5th Grade Students in Non-Routine Problem Solving

Ulu¹,

Tertemiz²,

Peker³

2016

Journal of Theoretical Educational Science

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“…This goes to show dominance of algebraic thinking that is routinely used in most mathematical problems albeit unaware (Ketterlin-Geller & Chard, 2011;Milgram, 2007;Vogel, 2008). The results also show that learners performed better in a question with a diagram because diagrams simplify complex situations and illustrate abstract concepts (Kidman, 2002) and make problems easier (Pantziara, Gagatsis, & Elia, 2009). Perhaps diagrams should be used considerably when teaching problem solving because they are a resource to facilitate analysing and understanding a problem and teachers should expose learners to a variety of solution strategies.…”

Section: Discussionmentioning

confidence: 96%

Mapping a Group of Northern Namibian Grade 12 Learners' Algebraic Non-routine Problem Solving Skills

Mogari

Lupahla

2013

African Journal of Research in Mathematics, Science and Technol

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This article investigates the algebraic non-routine problem-solving skills of grade 12 learners of a high-achieving school in northern Namibia. The school was selected on the basis of its outstanding results and sound management style. The study followed a descriptive survey design that involved a written test to examine learners' problem-solving skills together with the solution strategies used, and structured learner interviews to get their views about the choice of strategies for solving non-routine problems. The assessment framework of the learners' problem-solving skills was based on the Trends in International Mathematics and Science Study (TIMSS) scales for Polya's problem-solving model. The results showed that learners were more successful in answering the question with a diagrammatic illustration, suggesting that the use of diagrams makes it easier to understand the problems. A significant number of learners' algebraic problemsolving skills function at or below level 2 of TIMSS scale. The algebraic strategy was the most preferred solution strategy and there were learners who encountered difficulties with the language used in the questions.

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“…Die Lösungsraten sind jedoch höher unter den Kindern, die im Problemlöseprozess Zeichnungen anfertigen (vgl. Müller 1995;Veloo und Lopez Real 1994;Bender 1980aBender , 1980b Pantziara et al (2009) und van Dijk et al (2003, in deren Studien mit Kindern der 5. und 6. Jahrgangsstufe die vorgegebenen grafischen Diagramme die Lernenden teils an der Lösung der Aufgabe hinderten.…”

Section: Forschungsbefundeunclassified

Grafisches Darstellen zu Textaufgaben fördern – eine Interventions- und Evaluationsstudie in der 3. Jahrgangsstufe

Ott

2018

J Math Didakt

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Darstellungen sind für Erkenntnis-und Kommunikationsprozesse in der Mathematik und im Mathematikunterricht wesentlich. Im Sachrechnen werden grafische Darstellungen hauptsächlich als Bearbeitungshilfen verwendet und erforscht. Studien zur Förderung der Nutzung grafischer Bearbeitungshilfen zeigen kein einheitliches Bild. Forschungsergebnisse zu einem Unterricht, der von Kindern selbstgenerierte grafische Darstellungen im Sachrechnen als Erkenntnis-, Kommunikationsund Reflexionsmittel verwendet, mit dem Ziel, die Entwicklung der grafischen Darstellungsfähigkeiten der Kinder zu fördern, gibt es bisher nicht. Hierauf fokussiert die vorliegende Studie. Dabei wird untersucht, inwieweit sich eine dementsprechende Intervention auf die Darstellungsfähigkeiten der Kinder und die Lösungsraten zu Textaufgaben auswirkt. Die Ergebnisse zeigen, dass die Schülerinnen und Schüler der Interventionsgruppe bei relativ gleichbleibendem Abstraktionsgrad signifikant häufiger als Kinder aus Kontrollgruppen mathematisch passende grafische Darstellungen der mathematischen Struktur anfertigen. Die Lösungsraten verbessern sich kontinuierlich, der Unterschied ist jedoch nicht signifikant. Das Beachten der korrekten mathematischen Struktur einer Textaufgabe in der grafischen Darstellung kann jedoch als Voraussetzung für eine mögliche Nutzung als Bearbeitungshilfe betrachtet werden.

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Using diagrams as tools for the solution of non-routine mathematical problems

Cited by 55 publications

References 29 publications

Determining the Errors of Primary School 5th Grade Students in Non-Routine Problem Solving

Determining the Errors of Primary School 5th Grade Students in Non-Routine Problem Solving

Mapping a Group of Northern Namibian Grade 12 Learners' Algebraic Non-routine Problem Solving Skills

Grafisches Darstellen zu Textaufgaben fördern – eine Interventions- und Evaluationsstudie in der 3. Jahrgangsstufe

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