Dec 2, 2010 - All students were exposed in both conditions to learning graphing by ... (correct answer) or 0 (incorrect answer), and a total score ranging from 0 to 11. ... requires interpretation skills and involves more dif culties than graph ...
Educational Media International
ISSN: 0952-3987 (Print) 1469-5790 (Online) Journal homepage: http://www.tandfonline.com/loi/remi20
Enhancing Mathematical Discourse: The Effects of E-mail Conversation on Learning Graphing Bracha Kramarski To cite this article: Bracha Kramarski (2002) Enhancing Mathematical Discourse: The Effects of E-mail Conversation on Learning Graphing, Educational Media International, 39:1, 101-106, DOI: 10.1080/09523980210131169 To link to this article: http://dx.doi.org/10.1080/09523980210131169
Published online: 02 Dec 2010.
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Date: 25 April 2017, At: 23:07
Enhancing Mathematical Discourse: The Effects of E-mail Conversation on Learning Graphing Bracha Kramarski, Israel
Abstracts This study investigated the effects of e-mail conversations between teachers and students on learning graphing. Participants were two classes of ninth-grade students (boys and girls) who were exposed to Excel software by using metacognitive instruction. One class (n=25) was exposed to e-mail conversation (EXCEL+E-MAIL) and the other class (n=25) was exposed to whole class conversation (EXCEL). Results indicated that the EXCEL+E-MAIL students signi cantly outperformed the EXCEL students on graph interpretation and graph construction. In particular, the effects were observed on students’ ability to explain mathematical reasoning. Furthermore, qualitative analysis of the e-mail messages indicated that the EXCEL+E-MAIL students used different levels of discourse in their e-mail messages than the EXCEL students. Améliorer le discours mathématique: effets des conversations électroniques sur l’apprentissage des graphes Cette étude porte sur les conversations e-mail entretenues entre enseignants et élèves et leurs effets sur l’apprentissage des graphes. Les participants ont été deux classes de neuvième année, garçons et lles, utilisant tous le logiciel EXCEL Une classe (25 élèves) a eu recours à l’e-mail et à EXCEL ( EXCEL + EMAIL) alors que les élèves de l’autre classe avaient la possibilité d’échanger directement entre eux, tout en utilisant EXCEL. Les résultats ont montré que les élèves EXCEL + E MAIL réussirent nettement mieux dans l’interprétation et la construction des graphes. Particulièrement dans leur habilité à expliquer les raisonnements mathématiques liés à l’activité et à éviter des erreurs de conception. De plus, l’analyse qualitative des messages électroniques a montré que les étudiants EXCEL+EMAIL ont utilisé des niveaux de discours différents de ceux employés par leurs camarades. Verbesserung des mathematischen Diskurses: Auswirkungen von Email Kommunikation auf das Erlernen von graphischen Darstellungen Diese Studie untersuchte die Auswirkungen von Email Kommunikation zwischen Lehrer und Schüler über den Lernprozess der graphischen Darstellung. Teilnehmer waren 2 Klassen der 9. Jahrgangstufe (Jungen und Mädchen), die das Excel Programm aufgrund von metacognitiven Anweisungen bedienen sollten. Eine Klasse (n=25) benutzte Email Kommunikation (EXCEL + EMAIL) und die andere Klasse (n=25) stützte sich auf die Kommunikation in der Klasse (EXCEL). Die Resultate zeigen, dass die Studenten mit dem EXCEL + EMAIL Programm den EXCEL Studenten hinsichtlich der Interpretation und Erstellung von Graphiken deutlich überlegen waren. Diese Studenten vermochten weitaus besser ihre mathematischen Thesen zu erläutern. Eine qualitative Analyse der e-mail Botschaften bewiesen, dass die Studenten des EXCEL + EMAIL Programms auf unterschiedlicheren Ebenen kommunizierten als jene, die nur das EXEL Programm benutzten.
In recent years, there has been increasing recognition in the mathematics education community of the social nature of mathematics activity and of the importance of communication within the practices of doing, teaching and learning mathematics (e.g. Burton and Morgan, 2000). Interest in mathematical language has gone beyond analysis of the mathematical symbol system and specialist vocabulary. The way in which language is used by teachers and students in classrooms is now a consideration as its in uence on the social identities and the views of mathematics that students construct (Pimm, 1987). Professional organizations have recognized the importance of engaging students in talking in the classroom, analysing the nature of mathematical talk and helping students to learn how to participate in oral mathematical discourse (NCTM, 2000). Although there is some interest in using writing as a means of learning, less attention has been paid to the nature of written mathematical texts or to Education Media International ISSN 0952-3987 print/ISSN 1469-5790 online © 2002 International Council for Education Media http://www.tandf.co.uk/journals DOI: 10.1080/0952398021013116 9
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EMI 39:1 – ICEM-CIME ANNUAL CONFERENCE TAIPEI
learning how to write mathematically. Yet, writing plays a crucial role in many mathematical practices. The question of how advanced technology can be used to enhance mathematical discourse is still open. Over the last decade, many experiments have been conducted on Computer-Mediated Communication (CMC). They consist of the use of CMC to deliver instruction, ranging from complete virtual campus to the mix of traditional lectures and CMC permitting exchanges between students and teachers (e.g. Deaudelin and Richer, 1999; Hiltz, 1988; Poling, 1994; Williams and Merideth, 1995;). The e-mail represents the most widespread device employed in educational contexts. On the one hand, e-mail allows asynchronous exchanges. It also permits one-to-one as well as one-to-many communication. Of these two, teachers should take advantage of one-to-one communication because it makes up for the lack of student–teacher interpersonal communication, inevitable in the classroom context. This type of communication seems particularly important to provide individual support to students. The purpose of the following study is twofold: First, to investigate the effects of e-mail conversation vs. whole class conversation among teacher-student on graphical learning; in particular, on interpreting graphs and constructing graphs. Second, to describe the e-mail discourse on different levels of interaction.
Method Participants Participants were 50 ninth-grade students (boys and girls) who studied graphing in two classes. One class (n=25) was exposed to Excel software embedded within e-mail conversation (EXCEL+E-MAIL); the other class (n=25) was exposed only to EXCEL software.
Treatments All students were exposed in both conditions to learning graphing by using Excel software and metacognitive instruction. In all classrooms, the unit of graphing was taught one hour a week for seven weeks. In particular, in all classrooms students studied: (a) presenting information by graphic representations and how to make decisions about the appropriate graph; (b) quantitative and qualitative methods of graph interpretation; and (c) drawing conclusions from graphs. The metacognitive instruction was based on the IMPROVE technique suggested by Mevarech and Kramarski (1997a). The metacognitive instruction utilized a series of four selfaddressed metacognitive questions: comprehension (e.g. what is the problem/task all about?); connection (e.g. how is this problem/task different from what you have already solved?); strategic (e.g. ‘what strategy/tactic/principle can be used in order to solve the problem/task?’, ‘why is this strategy/tactic/principle most appropriate for solving the problem/task?’ and ‘how can the suggested plan be carried out?’) and reection questions (e.g. ‘what are the dif culties/feelings during the solution process?’, ‘how can the solution be veri ed?’, ‘how can another approach be used for the solution?’). EXCEL+E-MAIL condition. For practising the graphing unit, the students were asked to send the teacher by e-mail the solution of seven graph tasks and to describe the solution process in writing. They were encouraged to use in their e-mail discourse the metacognitive questions based on the IMPROVE method (Mevarech and Kramarski, 1997a): comprehension, connection, strategic and re ection questions. They were also encouraged to ask the teacher for help when they encountered dif culties in understanding and to correct the graphs, if needed, after receiving feedback by e-mail from the teacher. In addition, the students were taught how to send/receive e-mails and how to send/open attachment les. Moreover, students were encouraged at any time to ask the teacher questions or send comments by e-mail. EXCEL condition. Under this condition, students studied the same as under the EXCEL+E-MAIL condition but they were not exposed to the e-mail discourse. Students were asked to deliver the solution of seven graph tasks with the solution process and re ection on their decisions about the graphing procedure.
Measurement Three measures were used in the present study to evaluate learning graphing: graph interpretation test, graph construction test and levels of discourse in written messages.
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Graph interpretation test. An 11-item test, adapted from the studies of Kramarski and Mevarech (1997), assessed students’ ability to interpret graphs, particularly linear graphs. The test included items that required qualitative and quantitative graph interpretation skills. This part involved open-ended items that asked students to give a nal answer and to explain their reasoning in writing. These 11 items required examinees to draw conclusions and make algebraic generalizations on the basis of a given graph. For each item, students received a score of either 1 (correct answer) or 0 (incorrect answer), and a total score ranging from 0 to 11. Two judges, who are experts in mathematics education, analysed students’ explanations. Inter-judge reliability coef cient was 0.88. Graph construction test. The test, adapted from the study of Mevarech and Kramarski (1997b), assessed students’ ability to construct graphs. According to Leinhardt et al. (1990, p. 12), ‘construction is quite different from interpretation. Whereas interpretation relies on and requires reaction to a given piece of data (e.g. a graph, an equation, or a data set) construction requires generating new parts that are not given’. Graph construction requires interpretation skills and involves more dif culties than graph interpretation (Mevarech and Kramarski, 1997b). The test is constructed of seven items, each representing a verbal description of a situation. The situations referred to increasing, decreasing, constant and curvilinear functions. Students were asked to transform the verbal descriptions into graphic representations. Students could choose any kind of representation and were allowed to construct the graphs freehand, without using a ruler. For each item, students received a score of either 1 (correct answer) or 0 (incorrect answer), and a total score ranging from 0 to 7. A graph was considered correct if it followed the Cartesian System conventions and correctly represented the situation described, regardless of the kind of graph used (e.g. histograms, bars or line graphs). Two judges, who are experts in mathematics education, scored students’ responses. Inter-judge reliability coef cient was 0.92. Levels of discourse in e-mailed messages/written solutions. Data from e-mailed messages/written solutions were collected and saved systematically as they were received by the teacher. Data were analysed by means of content analysis. Each e-mailed message/written solutions was divided into semantical units. Based on the Harri-Augstein and Thomas approach (1991), the category system was made up of three categories established in accordance with the three levels of discourse: tutorial, metacognitive and life. At the tutorial level, both learner and tutor talk about the learning objectives in order to develop a common language to discuss learning, and to enable the learner to obtain insights about his or her learning process (e.g. ‘temperature is the dependent variable’). At the metacognitive level of the task, the learner’s work is aimed at investigating his learning process (e.g. ‘we choose that graph because . . . ’; ‘hopefully this time I made no mistake’). At last, at the life level, the learner is relating his learning to his own life (e.g. ‘e-mail communication motivated me to understand graphing’). The data were double-coded by two researchers. Inter-judge reliability coef cient was 0.86.
Results Two kinds of analysis were used in the present study: a quantitative analysis for graph interpretation test and graph construction test, and a qualitative analysis for e-mailed messages/written solutions. The main purpose of the present study was to investigate the differential effects of learning graphing with Excel software embedded with e-mail conversation on students’ graph interpretation and graph construction, as well as on students mathematical discourse.
Graph interpretation A one-way Analysis of Variance (ANOVA) was carried out on the pre-test scores of graph interpretation, and then one-way Analysis of Covariance (ANCOVA) on the post-test scores with corresponding pre-test scores used as a covariant. Table 1 presents the mean scores, adjusted mean scores and standard deviations on graph interpretation by time and treatment. One-way analysis of variance (ANOVA) indicated no signi cant differences between conditions prior to the beginning of the study F(1,48)0.05. However, signi cant differences between treatment groups were found at the end of the study controlling for pre-treatment differences for graph interpretation (F(1,47)= 51.21, p1; p>0.05], but at the end of the study signi cant differences were found between treatments controlling for pre-treatment differences F(1,47)=3.6; p
