Reading Comprehension of Mathematical Texts by Osterholm

Posted on September 21, 2012 by

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Österholm, Magnus. “Characterizing Reading Comprehension of Mathematical Texts.” Educational Studies in Mathematics 63, no. 3 (2006): 325–346.
Methods:
  • This study compares reading comprehension of three different texts: two mathematical texts and one historical text. The two mathematical texts both present basic concepts of group theory, but one does it using mathematical symbols and the other only uses natural language. A total of 95 upper secondary and university students read one of the mathematical texts and the historical text. Before reading the texts, a test of prior knowledge for both mathematics and history was given and after reading each text, a test of reading comprehension was given (325)
  • Two major questions are addressed:

    1. How can reading comprehension of mathematical texts without sym- bols be characterized compared to reading comprehension of texts from other subject areas? Is there a significant difference caused by some properties of the subject areas themselves, or is the main component of the comprehension process for these texts the general literacy skills?
    2. How is reading comprehension affected by the use of symbols in mathematical texts? Can the reading of texts with symbols be seen as a part of the content-specific component of the literacy skills, or are the gen- eral literacy skills more important and dominating factors in the reading process? (330)

Findings:

  • The results reveal a similarity in reading comprehension between the mathematical text without symbols and the historical text, and also a difference in reading comprehension between the two mathematical texts. This result suggests that mathematics in itself is not the most dominant aspect affecting the reading comprehension process, but the use of symbols in the text is a more relevant factor. (325)
  • This finding suggests that there is a need for more explicit teaching of reading comprehension for texts including symbols. (325)
  • there seems not to be much research done about the more detailed use of mathematical texts in learning situations (Fenwick, 2001; Love and Pimm, 1996), but more research that focuses on other aspects of mathematics textbooks (see Turnau, 1983). For example, in the Swedish research community there are studies about the solving of textbook exercises (Lithner, 2004), about the role of the textbook as a part of the curriculum (Johansson, 2003), and about differentiation in mathematics textbooks (Bra ̈ndstro ̈m, 2005). (326)

  • content literacy refers to the ability to read, understand and learn from texts from a specific subject area, as it is also defined by McKenna and Robinson (1990) (329)
  • For example, the type of texts used in this study focus on conceptual understanding, and perhaps different results would emerge if texts are used that present and explain a procedure or an algorithm of some sort. Symbols can be said to have both a semantic meaning (like ordinary words) and an operational meaning, and one strength of symbols is the fact that the one “who can detach the semantic component of the symbols at will can work much more quickly with the symbols” (Pimm, 1989, p. 183). Such a detachment of the semantic component could perhaps be fatal when reading the text with symbols used in this study, but might be beneficial when reading a text that focuses on procedures. Thus, one way to explain the differences between the mathematical texts observed in this study can be that the students are expecting procedural descriptions when mathematical symbols are used in the text, and thereby they are reading the text in a different manner than other types of texts. (341)

  • This study only shows an existence of a difference between reading comprehension of mathematical texts with and without symbols, but exactly what is causing this difference needs to be studied in more detail. The possibility that the students read the texts differently has been mentioned, but another possibility is that they are reading the texts in a too similar way, in that symbolic expressions and natural language do not follow the same syntactical and grammatical rules (Ernest, 1987) and therefore need to be read differently (341)
Posted in: Math