Nick: Reading and Specificity

A colleague of mine has been fond of saying that students will only go as far in math as their reading skills will take them. While I agree that students who don’t read won’t be able to progress, the more troubling aspect of this maxim is that students who do not read carefully for content, not just skimming, will not progress in math.

I’m writing about this now because this is the point in the semester when so many of my meta-goals are being met at once. In my geometry class, students have worked on a single problem for about an hour in one sitting (persistence). My linear algebra students are connecting ideas independently and we are having interesting, well-informed discussions in class (including what set could be a basis for the trivial vector space!). Although the notes for both of my classes sit at about 40 pages for the entire semester and students are usually working on problems and definitions on the same page, I have not been able to get students to read the little bit that is necessary in a meaningful way.

In my geometry class, we were developing the standard position form of an ellipse from the definition. The definition of an ellipse was literally right above the question the students were working on, and many good students stated that they had no idea where to go with the question. While it generally just takes a question like “What does the definition say?” from me to get the student unstuck, I have not seen my student progress in this area of reading  carefully and independently. This troubles me because in a traditional classroom setting there is no one to even ask “What does the definition say?”. Additionally, the same students who get stuck by not reading the preceding sentences will search for the problem on google as soon as they start their homework. This shows that they are looking to solve the problems and get some help but they are not using the resource that was built for this and is right in front of them.

My linear algebra students have completely differentiated themselves according to their attention to detail. The best students noticed the details when we first saw them and now that we are applying things to abstract vector spaces, they are able to do things very easily. When I ask some of the weaker students to read a definition they are trying to use, they skim the sentence and try to pull out what they are looking for. This is impossible in higher mathematics since the specificity of the language is so sharp. I have tried to tackle this problem in past semesters when we had a textbook by building an activity about how to read a mathematics textbook. This idea came out of a conversation with Christine Von Renesse with the intent to build something that I can share with others. Instead I learned that students were not able to differentiate the most vital pieces of information in a textbook from the other highlighted (often literally) ideas. This, in part, spurred me to not use a textbook in my current classes. While I think the use of my own notes has been good for the students and myself (despite the immense amount of work it has been), I don’t feel like I have furthered my students’ appreciation of the specific language of mathematics or their ability to independently process this language in a useful way.

I will be teaching these same classes again in the spring and I already have several changes that I think will help students make important improvements. However, I am unsure about how to build my students’ reading skills and I see this as being something that will inhibit their growth in mathematics and elsewhere. I would be especially interested to hear from other people who have focused on these ideas and any activities they have created.

Let me know if you have any ideas or questions in the comments. I’m always available at longne at sfasu dot edu.

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5 thoughts on “Nick: Reading and Specificity

  1. TJ says:

    I struggle with this one, too. My linear algebra course requires students to get their first look at the material through a fairly traditional textbook. I tried a “how do we read math” day. It sorta helped? Kinda?

    Next semester, I want to do something earlier and with better forethought.

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    • What kinds of activities did you do on your “how do we read math” day?
      When I have done such activities, I focus on the differences between reading a theorem or new notation (and all the unpacking that come with) versus reading examples or explanations.

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      • TJ says:

        I pick a few pages of text and model “proper reading behavior.”
        I take notes on the document camera, ask questions, make my own examples, pick apart hypotheses, etc.

        I just do what we call reading, but publicly and explicitly, with some commentary on why I I each thing.

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  2. The best strategy I have found to help in this area comes from Reading Apprenticeship strategies and is basically modeling behavior. I teach Basic Math and use this mostly for word problems. I read the whole thing aloud, then go back and read the first sentence stopping to note what I am thinking as I read. Having taught this course numerous times I know where students lose meaning so I stop at those points and act as if I am having what I know to be a typical struggle. For example: the problem mentions “area” so I say that I stop and try to remember which is area and which is perimeter; then it mentions dimensions and I am not sure what that means so I ask or look it up…. I am not sure how this might work with more advanced students but it seems to help my students develop reading strategies. They seem to connect better when I show them what to do rather than tell them.

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    • Thanks for the idea Barbara. Recently, after students present on a topic I give a five minute summary and a five minute intro to the next topic. I try the modeling ideas you talked about during these times. One of the biggest difficulties I have seen with student reading in the higher level classes comes from where the particulars of the language can change the meaning and emphasis of the statement. The commonality is that we are trying to get students to identify that they are doing a different kind of reading.

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