INTERPRETATION OF GRAPHS: READING THROUGH THE DATA

2003

In current social contexts there are various situations in which people participate in graphing activities. The school has an important role in the teaching of graphing knowledge to citizens. Several researchers have stressed critical sense as an important aspect of the data handling process. This paper reports on a pilot study exploring some tasks in which primary school teachers might approach graphing, using critical sense as an important element. Analysis of the results suggests factors, which may be significant in the design of such tasks.

Several studies investigated the interpretation of graphs as pedagogical issue. The studies of Curcio (e.g. Curcio, 1987) presented three levels of students’ responses: reading the data, reading between the data and reading beyond the data. Watson’s (e.g. 1997) studies suggest a hierarchical schema of classification of interpretation based on three tiers. We presented the idea of Critical Sense in graphing as a skill to analyse data and its interrelations rather than simply accepting the initial impression given by the graph. This paper discusses about convergent and divergent aspects among the authors referred above.

Although the creation of graphs to display data has been part of the school curriculum for some time, the call in the new Australian Curriculum for " numeracy across the curriculum " provides both the opportunity and challenge to link the skills of graph creating with the understanding of context in order to produce meaningful interpretation of the messages held in graphs. This paper reports on classroom experiences of and follow-up interviews with 12 grade 5/6 students who were introduced to the software TinkerPlots to assist in graph creation. The focus is on their success at graph creation and interpretation in contexts that provide potential links to other subjects in the school curriculum. Implications for the curriculum and teaching are drawn from the students' experiences.

Eurasia Journal of Mathematics, Science and Technology Education

Choosing graphs to display quantitative information is a component of graph sense. An important aspect of pre-service elementary teachers' content knowledge; ability to choose appropriate graphs in applied contexts is investigated in this study. They were given three scenarios followed by four graphs representing the same quantitative data. They rated the appropriateness of each graph and indicated the reasons for their choices. Results showed that pre-service elementary teachers can recognize the situations appropriate for bar graphs, pie charts, and line graphs and match the suitable graphs to these situations. However, they had limited knowledge of scatterplots and did not recognize the situations for which they are typically used. Implications of findings for elementary pre-service teacher education programs are drawn.

This paper discusses a research study that focused on middle grades students' abilities to read and to move between different graphical representations before and after instruction. The data analyzed were collected from a group of 76 sixth grade students who were in 3 different mathematics classes in a middle school located in central North Carolina. The ways that students made sense of information presented through graphical representations and made connections between related pairs of graphs were investigated. General conclusions indicate that students need to talk more about graphs, including talking about the structure of graphs and how this informs the statements that can be made about: (1) the information depicted by the graphs and/or (2) the predictions or inferences that can be drawn from the graphs. Contains graphs and questions used on written pre- and posttests. Contains 26 references. (MKR)

Abstract. Considering the wide utilization of graphs in different contexts of the contemporary society, curriculum makers around the world have included graphing as a topic in all levels of school mathematics in order to strengthen the social role of the school curriculum. This inclusion has been justified as a way to provide opportunities for students to use mathematical and statistical tools learnt in school to understand out-of-school uses of data. This paper discusses some aspects of the socio-historical origins of graphs and some current contexts in which they are used, as well as pedagogical implications. Resumo. Considerando a ampla utilização de gráficos em diferentes contextos da sociedade contemporânea, curriculistas de diversas partes do mundo incluíram o ensino de gráficos como tópico de todos os níveis escolares. Essa inclusão tem como objetivo a atualização o papel social de conteúdos escolares relacionados a Matemática e a Estatística. Além disso, essa inclusão tem sido justificada como uma maneira de proporcionar oportunidades para os alunos usarem ferramentas matemáticas e estatísticas para interpretar e compreender dados em situações em situações cotidianas fora da escola. Este artigo discute alguns aspectos das origens sócio-históricas de gráficos e alguns contextos atuais nos quais eles são usados, incluindo implicações pedagógicas de tais reflexões. Keywords: interpretation of graphs; historical aspects related to graphs; mathematics education; statistics education. Palavras-chave: interpretação de gráficos; aspectos históricos de gráficos; educação matemática; educação estatística.

2012

This study focused on middle grades students ’ reasoning in response to questions about a bar graph. There were three levels of questions, and responses were coded to identify knowledge of structural components of graphs, accuracy of graphical-perception tasks, and development of graph schema. At each grade level, students (N=76 in grade 6; N=71 in grade 8) were taught by a single teacher who had been certified as a statistics educator. The teachers taught an experimental graphing unit, with a paper-and pencil task administered before and after the unit. Students seemed to learn to coordinate the components of graphs, performed graphical-perception tasks more accurately, and developed more coherent graph schema. There was some evidence to support the existence of a (perhaps developmental) sequence of reasoning strategies. This study investigated the ways that students in the middle grades (grades 6-8 in USA) interpret data presented in a bar graph. Of particular interest was the nat...

2015

The preliminary results of an empirical research (n 150) on teachers ’ comprehension of graphical representations of data are presented. A questionnaire consisted of 10 graphical representations with three questions each (in multiple choice format) was used in order to reveal what teachers comprehend of various formats of graphs and diagrams that represent data collected by small statistical surveys and projects. In most of the displays, teachers exhibited major difficulties predicting from the graph (“reading beyond and behind the data”) while they were proficient at extracting specific values (“reading the data”) and computation types of questions (“reading between the data”). Findings of a similar research on pupils ’ understanding of graphs are used in comparison with the results. Implications for teacher preparation are discussed.

Science Educator, 2015

AbstractThis study focuses on pre-service science teachers' interpretations of graphs. First, the paper presents data about the freshman and senior pre-service teachers' interpretations of graphs. Then it discusses the effects of pre-service science teacher training program on student teachers' interpretations of graphs. The participants in the study were 117 pre-service science teachers. Fifty-six of the participants were freshman. The data of the study were gathered with a questionnaire adapted from Aoyama (2007). The questionnaire includes two graphs each based on a different context, and having four questions about the interpretation of the graphs. The participants' interpretations of graphs were analysed in five levels. The levels were listed from low to high level: Idiosyncratic, Basic Graph Reading, Rational/Literal, Critical, and Hypothesising and Modelling. The results of this study reveal that pre-service science teacher can read values and trends in graphs...

2012

Graphs as representational tools are very important in all disciplines especially in mathematics. They are useful for summari zing sets of data, obtaining and interpreting new information from complex data. The purpose of this study is to investigate pre-service mathematics teachers' graphing skills. The participants are 32 pre-service mathematics teachers from a public university. Graphing tasks and questions corresponding to the interpreting, modeling and transforming components of the graphing skill (Kwon, 2002) were used in gathering written data and interviews conducted with selected participants. It is concluded that students have problems in modeling and transforming tasks but they can extract information from graphs so they are better in interpreting tasks.