Methods: Examines textbook reading of 11 beginning undergrad students from perspectives of working tasks in the passages read, the writing style of US math textbooks, and reading comprehension literature. (227)
Students selected from precalc class and two sections of Calc I. Identified good readers. 11 elected to participate, no minorities. Volunteers select when they read section of textbook. Encouraged to think aloud. (234) Students all good readers according to ACT scores (241)
All interviews audio-recorded and transcribed. Noted how students read various sections of the textbooks (i.e. exposition, definitions, theorems, and worked examples) (235)
1. Did the students exhibit characteristic responses of good readers, that they would support the judgment that they were good readers?
2. Could students read effectively? Could they carry out straightforward tasks? Could they carry out straightforward tasks associated with the reading soon, often immediately, after reading passages explaining, or illustrating, how the tasks should be carried out, and with those passages still available to them?
3. Student difficulties in working tasks traceable to the writing style?
4. What kinds of mathematical difficulties did students encounter in working the tasks in, or arising from, their reading? (232)
Findings: Barton and Heidema (2002) and Shuard and Rothery (1988) talk about mathematical writing and how it can pose difficulties:
1. Reading math requires reading from right to left, top to bottom, bottom to top, or diagonally
2. The writing in mathematics textbooks has more concepts per sentence, per word, and per paragraph than other textbooks
3. Mathematical concepts are often abstract and require effort to visualize.
4. The writing in mathematics textbooks is terse and compact — there is little redunancy to help readers with meaning
5. Words have precise meanings, which students often do not fully understand. Students’ concept images of them — mental links to such things as relevant examples, nonexamples, theorems, and diagrams of them, may be thin.
6. Formal logic connects sentences so the ability to understand implications and make inferences across sentences is essential.
7. In addition to words, mathematics textbooks can contain numeric and non-numeric symbols.
8. The layout of many mathematics textbooks can make it easy to find and read worked examples while skipping crucial explanatory passages.
9. Mathematics textbooks often contain complex sentences which can be difficult to parse and understand. (229-230)
- Typically there is a repeated pattern consisting of first presenting a bit of conceptual knowledge, such as a definition or theorem or perhaps some less formal mathematical assertions, followed by closely related procedural knowledge in the form of a few worked examples (tasks), and finally, as a self-test students are invited to work very similar tasks themselves (230)
- Students can master reading narrative texts but does not suffice for precise, concise text with no redunancy (Snow 2010: p 450)
- All students in study have difficulty completing straightforward tasks. (237)
- Could not trace any student difficulties to the writing style of the textbook (238)
- Difficulties working tasks: a) Insufficient insensitivity or inappropriate response to their own confusion or error b) inadequate or incorrect prior knowledge c) insufficient attention to the content of the textbook. (238)
- A major factor in effective reading is sensitivity to their own confusion and errors and appropriate response to them (242)
- Future research:
- How would mathematicians react under similar conditions?
- Which beginning undergrads read or do not read, which parts do they read and why? (242)
- To become effective readers of mathematics, students would need to learn to recognize their own errors and to appreciate that careful re-reading of a task can be very productive (244)