Abstract
This chapter analyzes interpretations of a graph of motion by bilingual adolescents using multiple representations of motion: a written story, a graph, and an oral description. The chapter uses a socio-cultural conceptual framework, complex views of language and academic literacy in mathematics, and assumes that mathematical discourse is multi-modal and multi-semiotic. Data from a bilingual classroom and transcript excerpts illustrate the multimodal and multi-semiotic nature of mathematical language. The analysis describes how pairs of students interpreted stories of bicycle trips using multiple modes, sign systems, and texts. The analysis examines how multiple modes provided tools for students to make sense of mathematical ideas and how inter-textuality functioned as students negotiated the mathematical meaning of motion through multiple texts (graphs, written questions, written responses, and oral discussions). We describe how four pairs of eighth-grade bilingual students interpreted horizontal segments on a distance versus time graph as they answered questions using a story about a bicycle trip. While students shifted between two interpretations (moving and not moving) of the three horizontal segments above the x-axis, pairs interpreted the segment located on the x-axis as representing the biker not moving. We examine how students shifted among alternative interpretations of the horizontal segments and describe how the graph and the written text mediated these student interpretations.
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Notes
- 1.
While the student pairs worked together on the task, the first author observed silently and then asked follow-up questions in order to clarify student responses and understand students’ assumptions about the goals of the task.
- 2.
This paper reports on the peer-discussion sessions for four pairs. The classroom data are analyzed elsewhere (Moschkovich 2008).
- 3.
With the exception of one utterance by one pair.
- 4.
Transcript conventions are provided in Appendix.
- 5.
We note that students used the labels for segments in multiple ways. In the beginning of their discussions, students sometimes used the labels to refer to the interval and other times to refer to the end points. By the second discussion session, all pairs were using the labels of the segments to refer to intervals rather than endpoints.
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Acknowledgements
This manuscript is based upon work supported in part by the National Science Foundation under Grant No. 0424983 to CEMELA (Center for the Mathematics Education of Latinos/Latinas) and Grant No. REC-0096065 to the first author (Mathematical Discourse in Bilingual Settings). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. We would like to thank the Chèche Konnen Center at TERC, the participating students, and the classroom teacher.
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Appendix: Transcription Conventions
Appendix: Transcription Conventions
Timing | ||
Equal sign | = | Indicates the end or beginning of two ‘latched’ utterances that continue without an intervening pause.Where necessary, can be combined with brackets. |
Timed pause | (1.8) | Measured in seconds, this symbol represents intervals of silence occurring within and between speakers’ utterances. |
Delivery | ||
Period | . | Indicates a falling pitch or intonation at the conclusion of an utterance that may or may not mark the completion of a grammatically constructed unit. |
Question mark | ? | Rising vocal pitch or intonation at the conclusion of an utterance that may or may not have the grammatical structure of a question. |
Exclamation point | ! | Marks the conclusion of an utterance delivered with emphatic and animated tone. The utterance itself may or may not be an exclamation. |
Comma | , | Indicates a continuing intonation with slight upward or downward contour that may or may not occur at the end of a grammatical phrase. |
Hyphen | - | An abrupt halt between syllables or words. |
Colon(s) | : | One or more colons indicate sustained enunciation of a vowel, consonant, or syllable. |
Capitalization | Represents speech delivered more loudly than surrounding talk. | |
Other | ||
Parentheses | ( ) | Talk for which transcriber doubt exists. |
Double parentheses | (( )) | Transcript annotations Translation italicized |
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Moschkovich, J., Zahner, W., Ball, T. (2017). Reading Graphs of Motion: How Multiple Textual Resources Mediate Student Interpretations of Horizontal Segments. In: Langman, J., Hansen-Thomas, H. (eds) Discourse Analytic Perspectives on STEM Education. Educational Linguistics, vol 32. Springer, Cham. https://doi.org/10.1007/978-3-319-55116-6_3
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