I am currently in a course titled "teaching reading in a content area." While there are plenty of examples of different strategies that can be used in different subject areas, there are little suggestions for mathematics, due in part I am guessing to our book author's unfamiliarity with the subject. A little is discussed on how to approach textbook reading with your students (involving pointing out the structure and function of different aspects of the book, which is of course important), but I am feeling very wanting.

These are some of the ways I know that reading comprehension can affect math class performance. In an answer I would be hoping for ways to address any or all of these. Additionally, mentioning other ways that reading comprehension can affect math ability would be something I'm interested in as well.

  • Straightforward: Not knowing how to read the textbook (or not knowing when to read the textbook) affects a student's independent learning ability. This applies to all classes, but I'd argue particularly math, since it seems that students expect teachers to talk them through everything and if they don't catch something, it's out of sight out of mind. (This comes from a lot of tutoring: many students don't bring their textbooks to the tutoring center I am at and those who do seemed stunned that the formulas are in the book)
  • Content (mathematical) vocabulary. This is something I believe most of us already focus on since definitions are at the heart of mathematics. However, we all know a student can memorize a definition without having understanding of the concept behind it. Perhaps this can be summed up as "making meaning of mathematical ideas."
  • Comprehension of "word problems" and turning "words" into mathematical diagrams/formulas-- if a student cannot decode their word problems, they cannot do them. This was evident in a remedial geometry course I taught for the first time last year, where it took me until mid-course to realize that some of my students' reading skills affected their ability to learn math (it was the first course I ever taught). The question I posed was, nearly verbatim: "A church has a 6" stair leading to its entrance. They want to build a wheelchair ramp to the stair. The maximum legal angle for wheelchair ramps is 6 degrees from the ground. How far out horizontally from the stair will the ramp reach? Make sure to draw the stair and the ramp." One particularly struggling student drew a stair, but did not even draw a ramp. Does this signify defeat or lack of comprehension?
  • Comprehension of causative statements. The "If...then" relationship tends to be a challenge to effectively convey as evidenced by even upper-division math students struggling in proofs courses with it. While this may in part be due to difficulty in logical reasoning skills, this may also be tied to lack of clear exposure to "If...then" and "cause...effect" instruction in language learning.

To recap: What are ways that reading comprehension (at the lower, decoding level AND the higher, reading for meaning level) can be addressed meaningfully in a math classroom? What are other ways that poor reading comprehension can affect mathematical performance?

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    If this is how you actually worded the problem, I would have had difficulty also. For one thing, "stair" is singular, so it sounds like you're talking about one stair step. Also, does 6" refer to the vertical height of the stair(s), the horizontal length of the stair(s), or the diagonal length? Also, "build a wheelchair ramp to the stair" seems incorrectly stated, and I suspect you mean something like "build a wheelchair ramp, having the same vertical height of the stair(s), that can be used in place of the stair(s)" (actually, even this doesn't completely describe it). (continued) – Dave L Renfro Jul 31 '14 at 13:51
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    (continuation) Also, you specify a maximum legal angle, but the answer is "how far out", which seems to assume that a specific angle is used rather than a range of angles. (Just because the maximum legal angle is a certain value doesn't mean the ramp has to be built using that value for its angle.) Also, "6 degrees from the ground" should probably be more specific, such as "the angle of inclination with the ground is 6 degrees". I think you should pay a lot of attention to wording, since they have neither the math nor the English to fall back on when something is unclear to them. – Dave L Renfro Jul 31 '14 at 13:58
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    I approximated the wording from the original; I am pretty sure I specified that the step was 6" tall. As for "angle of inclination," unless you advocate introducing 5+ new terms per day to a remedial class, that one got cut. (It's a 10 week course and 3/10 of them came in not knowing the word "pentagon".) 9/10 of the students drew the picture correctly, one student apparently either didn't know the word ramp or had a lot harder time decoding the problem than the rest. I don't even think the word "maximum" registered for most of them, but you're right, I should have omitted it. (continued) – Opal E Jul 31 '14 at 16:20
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    You're right that the phrasing of problems is an important aspect of helping students struggling with word problems, and if there are suggestions on how to word problems better without relying on unintroduced vocabulary, I'm all ears. I'm worried that making the problem too long would have the same effect as using too large of words; that is, defeat. It took me half of the course to get them to draw pictures when they didn't know the whole answer. – Opal E Jul 31 '14 at 16:24
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    For example, in colloquial English, although we could rephrase things as an "if...then" construct, this is very rarely done... except by mathematically-inclined people wanting to (I think spuriously) claim that mathematical language is not so much different from ordinary language. – paul garrett Dec 6 at 0:48
up vote 4 down vote accepted

You can't build on sand. If they don't have the reading skills, you need to teach that first.

(There is a strong temptation to go to the prior teacher of reading and beat them about the head and ears for their incompetence, along with the administrators of the school for passing kids that aren't ready, but this, while satisfying, seldom gets results, and can result in your search for a new job. This, may be a solution.)

I would suggest giving a short course in decoding word problems. One phrase at a time. Where possible illustrate the problem with an undimensioned example of what they are supposed to do.

Start with simple examples.

"The shadow of a 50 foot flagpole is 110 feet from the base of the pole. How many degrees above the horizon is the sun?

Or even simpler:

  • John has 6 times as many apples as Chris.

  • John has 6 more apples than Chris.

  • John has 6 fewer apples than Chris.

  • John has half as many apples as Chris does.

  • John's speed is 1/3 more than Chris's speed.

Also: Go the other way. Draw the picture on the board, and have them generate a word problem. (You may also find that your students do not understand drawings. That too is a learned skill.)

Concentrate on the phrases. There is a rather odd phrasing in word problems in math books, with passive case being used a lot, and far more complex sentence structure than commonly used in speech. Do easy ones first, then do ones taken from achievement tests and standardized tests to get them familiar with the (sometimes arcane) wording of those instruments.

You may find yourself skipping a lot of word problems while you make up their reading deficiencies. Do not worry about doing word problems at a couple years below the current nominal grade level. At this point, you are looking for the translation from words to math. Let them be easy math problems.

One step at a time.

I am unclear at what "grade level" you are dealing with, however, independent of grade level you may be interested in the relatively new series of books published by Princeton University Press - The Best Writing on Mathematics: Year X, where books for 2010, 2011, 2012, and 2013 have appeared so far. The Forewords of these books have been written by William Thurston (now deceased), Freeman Dyson, David Mumford, and Roger Penrose, respectively. While I may quibble with the presence of some individual articles that have appeared in these volumes, on the whole these are very varied and interesting materials, over a broad swath of different aspects of mathematics and mathematics education. The reading levels for the different articles also varies a fair amount but there is a lot to like in these books.

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    I had it tagged as "secondary-education," if that helps clarify :) – Opal E Jul 29 '14 at 20:43
  • There are lots of nice articles in these books at the secondary education level. Another source of nice materials at the secondary level are the NCTM year books. – Joseph Malkevitch Jul 30 '14 at 14:21

Whole language proponents may sing hosanna to the virtues of silent reading without boring kids with letters and their sounds, but their method does not work. Reading, at least when one just learns to read, is not silently recognizing funny squggles as distinct words, it is building words out of phonemes and pronouncing them. Reading is like playing back from magnetic tape. Books are like tape recorders. Only when played back and heard, words are recognized. After this is achieved, the task of basic reading instruction is done.

"Teaching reading in a content area" sounds like a lot of BS. When one can read, one can read. After that it is about comprehension, memorization, recollection, insight, making connections, drawing conclusions, etc, all that humans do pretty much subconciously unless they were brought up by a wolf pack. Actually, even if raised in the wild humans will still be able to do all of the above but reading, because this skill requires instruction.

I don't see this as a "reading" problem. If it is, then it is not "reading in a content area" problem, it is just a problem of basic literacy. A simple test: ask them to read a meaningless word like "gleromasticaloramic" or "befoodoristiclin". If they cannot, Buy "Why Johnny can't Read" book, it has twenty or so pages of reading instruction in the back. Use it. After that, just explain the terms of the subject area as you go, and basic logic for "if...then".

I agree with Dave L Renfro that the church problem is badly phrased. I would re-phrase it somewhat like this: "A satanist fun house has a step raised 6 inches above the parking lot. They want to build a wheelchair ramp from the parking lot level to the step level. The maximum legal angle of inclination for wheelchair ramps is 6 degrees. How far out horizontally from the stair will the ramp reach if the maximum allowed angle of inclination is used?" Nothing wrong with learning some new terms as you go.

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    I strongly disagree with a "reading is reading" notion, based on considerable observation of mathematics students at levels from undergrad through grad, at least. Mathematical language, and its implicit assumptions, even at an elementary level, is/are significantly different from the context of ordinary language (English, at least). Ordinary language does not include "reasoning", but mostly questions and assertions, and assertions need not be grounded in fact, etc. (I'm resisting political comments.) Ordinary language is just a narrative, including no book-keeping, unlike mathematics... – paul garrett Dec 6 at 0:56
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    1. This answer would be improved by backing it up with arguments, such as research or even personal experiences. 2. Link to or short explanation of "whole language" would improve the answer. Wikipedia has an article, but I do not know if it is current or good: en.wikipedia.org/wiki/Whole_language – Tommi Brander Dec 6 at 8:41
  • @paulgarrett Of course ordinary language includes reasoning: "If I don't behave, mom would not give me candy". Mathematics uses strict logic for proofs, but with geometry being the only subject where proofs are taught, and this happens in 10th grade, your students are left without logical scaffolding, you need to teach basic logic yourself. If a student can decode written words, but cannot have a mental image of a raised step with a ramp, it is the fault of the parents, who left their child with a screen in their hands instead of a crayon or play-doh or a hammer. They crippled their child. – Rusty Core Dec 6 at 16:54

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