HOW TO READ A MATHEMATICS TEXT
|Summary Any text (except example ) between
two heading should
receive a one -to-three sentence summary . One should be able to read
the summary and have a clear picture of the substance of the text.
Prose text is a portion of text that lies between pairs of
named concepts and/or examples.
Sometimes a definition or other named concept is embedded in the midst of prose text and
should be entered in the Named Concepts box. Sometimes, particularly with advanced texts,
examples or theorem proofs are presented in the guise of prose text.
Otherwise, the text usually serves to explain, amplify,
motivate, or otherwise discuss the ideas
presented in the named concepts or examples. These sections typically cover no more that two or
three paragraphs before an new named concept or example is formally presented.
It is important that the reader have an opportunity to ponder this information so as to assimilate
the ideas as fully as possible. As such, the graphic organizer provides blocks for summarizing a
block of prose text. The student will benefit most when the summary is in his or her own words.
However, the beginning student may find this exercise too difficult; I recommend that a student
who is having difficulty paraphrasing the main ideas of the text be content with identifying and
copying the topic sentences of the paragraphs. The reader may also wish to annotate the entry
with a page number so that the text and graphic organizer may be compared at a later date.
Theorems and Proofs
Except for geometry classes, theorems and proofs are somewhat rare in secondary and lower - division
texts. As my version of the graphic organizer was developed for a secondary
environment almost devoid of proofs, no accommodation has been made for them.
A reader wishing to use this method with a text that devotes a significant amount of resources to
proofs must find a way to adapt the existing graphic organizer. On way is to redesign the
organizer from scratch (see the next full section). One easy way of doing this is to design a third
page that is devoted to proofs.
Another way is to notice that a proof has much in common with an example . Both are logical
sequences that need to be understood, both are presented for some reason that transcends the
individual example/proof, both link new concepts to prior learning, and the reader has an
opportunity to express in his or her own words some aspect of a learning experience. Thus, the
reader can, in a pinch, use the existing graphic organizer without modification when confronting
a rare proof.
|Reflection – Complete after reading all
the text and examples. Describe the section in four or five sentences.
What would you like to have explained differently? What more would you like to know about this subject?
The reflection is a period of contemplation that occurs
after the section has been read with the
use the graphic organizer. The student may wish to take a few moments to allow the mind to
“organize” the material. When ready, the student then uses the Reflection portion of the organizer
to summarize, in his or her own words, the main ideas of the section. This is not a quiz; there are
no right or wrong answers here. The act of articulation helps with the process of understanding
In addition to the summary , the reader is asked to respond to two higher-level questions.
What would you like to have explained differently ? Not everything the student reads will be
crystal clear, even after a second or third reading. This is why it is critical that a student read the
text before the material is presented in lecture. A student is prepared to pay closer attention to a
lecture when he or she recognizes what is about to be discussed next and also recognizes that
their understanding of the material is weak. The student has, so to speak, paid their dues. If the
student still does not understand a concept after the instructor’s presentation, that student should
be very motivated to ask a clarifying question at that moment.
In short, reading the text before a lecture transforms a student from being a passive
participant in a lecture to being an active participant. A student can anticipate what is
coming next and be continuously checking those expectations against what actually transpires.
Correct anticipations will reinforce the learning process; deviations from the expected
information will stimulate discussion or further investigation.
What more would you like to know about this subject? Of course, the stock answer for most
students most of the time is likely to be very little or nothing at all. However, there is always the
opportunity to recognize a connection between the section material and something of interest the
student has encountered elsewhere. Answering this question is a precursor to self-motivated
research. It becomes a type of post-it note the student can read at a later time and motivate the
student to pursue the extended learning process.
Modifying the Graphic Organizer
The Structured Reading Guide for Mathematics Texts has its current appearance for one very
simple reason : I constructed it to look that way and it has worked fairly well for my applications.
This does not mean it will work as well for you. It may be that modifying the form will make the
reading experience more effective. For example, there is no reason the form could not be used,
either as is or with simple modifications , to other technical texts such as physics, chemistry, or
engineering. Second, you may simply need more space for your examples than what is provided
for you on my version of the form.
There is nothing sacrosanct about this organizer; you are invited to modify it to fit your needs. In
fact, I would be thrilled if you modified the form, found success with your version, and sent me
1) an electronic copy of your modified form, and 2) a description of what you made different,
why you did so, and how it has enabled you (or your students) to be more effective readers of
I will be happy to post revised versions of the organizer on this web site along with your
description as to how it works. This will encourage other readers to experiment with your forms.
Soon, we may have fourth or tenth generation graphic organizers that are highly effective
reading tools and are available for everyone’s benefit.