Classroom Vignette
Getting to Know Your Middle Grades Mathematics Textbook
by Diane K. Kahle
A student could likely go through his or her entire middle school career without
using the mathematics textbook for more than gathering homework problems and looking
at sample problems. A century ago, textbooks did not contain much more than that.
In the last couple of decades, however, traditional middle grades mathematics textbooks
have become a great resource.
From the introduction of the NCTM standards in 1989 and 2000 and the Ohio Academic
Content Standards for Mathematics in 2002, mathematics educational practices have
been rattled. The standards call for students to do more than computation―they require
students to engage in problem solving, do mental mathematics, write about their
thinking, and use technology in the mathematics classroom.
Textbook companies have responded by developing two types of textbooks: traditional
textbooks and textbooks that are theme and problembased. No matter which type,
though, there is often more information in a currentday textbook than a teacher
can possibly include in one school year. That is why it is important for teachers
and students to get to know their textbook early in the school year.
For some students, middle school may be their first experience with their own mathematics
textbook. Some elementary classes may have instead used workbooks, handouts, or
problembased instruction. These students, especially, will need to get to know
what is in the textbook before they can fully utilize its resources. Additionally,
students need to understand how to read mathematics technically to get the most
out of their textbook. This article addresses both sets of needs. To do this, first
the article describes a scavenger hunt for students to show what resources are available
in the book, and then it presents ideas for helping students technically read the
text.
Scavenger Hunt
During the first week of the school year, I like to send my students on a scavenger
hunt through their textbook to help them understand how it can be more useful to
them. This activity takes ten to fifteen minutes. Students will find that their
book contains practical applications of mathematics, terms identified, and perhaps
even answers in the back of the book!
To send your students on a scavenger hunt, simply pose the following questions and
allow students time to find the information individually in their textbook. My experience
is that students will find more than you request. Students may look at the pictures,
the special features, and mathematical concepts.
Reading Mathematics
Once students know what is in their mathematics textbook, it is time to learn how
to best read the book. Many students never read their
mathematics textbook. Instead they find the specific examples or problems they need
and pull out the desired information. I remember using my mathematics textbooks
that way. Sometimes, however, reading the mathematics textbook is the only way to
get important information―for example, when a student needs to catch up after an
absence, when a parent wants to read with a student to find out how to help his
or her child with a lesson, or when a student is reviewing and looking for some
specific facts.
The truth is that mathematics students rarely read the textbook and do not get much
from it when they do try to read it. As a mathematics teacher, I want to help my
students learn to read mathematics, which is very different from reading science,
social studies, and language arts. Students have learned in those classes to read
at their regular pace and pull out key information. Reading the mathematics textbook
is also significantly different from reading a novel for pleasure where you often
read quickly. The mathematics textbook contains far fewer sentences than those other
books, but those few sentences are loaded with information and symbols, and so students
need to read slowly.
I encourage my students to learn how to read their mathematics textbook by practicing
in class. First I help them understand the need for learning to read in a different
way by asking all students to open their book to any instructional page where words
appear. I allow them to read for one minute and then ask them to look at the page
number and close the book. Next, I ask them to make a quick list of all the facts
and information they remember, then open the book and compare. My students are typically
amazed at how much more is in the book than they remember.
Another way to motivate students to learn to read differently is to ask them to
open the book to any page and count the words on the page with which they are unfamiliar.
A final motivation is to ask students to open to any instructional page and count
the lines of text with mostly words and compare the count with the number of lines
that are mostly numbers or symbols. There are numerous mathematical techniques for
analyzing these results. My students like to find individual results and a total
class average of each of these statistics compared with the total lines of text.
Now that they understand that reading mathematics will be different from other kinds
of reading, it is time to practice. Following are three classroomtested ideas for
helping students learn to read their mathematics textbook effectively. One idea
is for a wholeclass setting, the second is for small groups, and the third is for
pairs of students.
Whole Class
In the wholeclass setting, first tell students your goals of learning the lesson
and learning to read technically. I explain to my students that they will take turns
reading from their textbook. When it is not their turn, they should be listening
for important ideas or new vocabulary. Encourage students to signal their recognition
of an important idea or new word by raising their hands. Additionally, when they
think of a question or notice a prerequisite skill, they should raise their hands
to share it with the class.
When someone raises a hand, ask the student to report what he or she is thinking.
Welcome all ideas that are accurate. The teacher's job in this activity is to be
the recorder of information. Record ideas, and have students copy them down as notes.
I have found by doing this activity that students want to pull out more information
than I typically might have. They can also develop a community of discourse about
how to phrase statements or decide their importance. Students usually welcome this
method of reading as an alternative to just taking notes or listening to a teacher.
Small Groups
To practice technical reading with small groups of students in my mathematics class,
I start by dividing the students into groups of three or four. All students should
have their own textbook, paper for taking notes, and a pencil. Ask students to take
turns reading the material by changing readers after each paragraph. Students should
listen to their reader and ask him or her to stop and reread anytime they do not
understand. After time has been allowed to read the selection completely, the teacher
then can ask the groups to reread the passage and take notes on any important ideas,
new terminology, prerequisite skills, or questions they have. One
word of caution: If the two sets of instructions by the teacher are given
at once (reading the passage and taking notes), the students likely will try to
take the notes without completing the reading. So I have found it more effective
to ask the groups just to do the reading first, and then I give them the instructions
for noting important facts after the reading is complete.
After a sufficient amount of time, the whole class has a discussion. During this
discussion, each group is to report on one idea, term, etc. After each group has
shared, additional ideas may be shared by any group.
Partners
A third method to practice technical reading is the partner reading method. In this
method, pairs of students work together. One student reads a sentence, and then
the partner reads a sentence. The partners continue taking turns, sentence by sentence,
until the passage is completed. After each sentence, the partners should make sure
that both understand what has been read, and both should take notes on key ideas.
This method works best if they first jot down notes such as "What is a trapezoid?"
or "How do I find an angle's complement?" They can go back to fill in the details
after the whole passage is completed.
General Tips
I have found that expecting students to read their mathematics textbook in class
for about ten minutes is plenty of reading time. More than that in one sitting tends
to decrease the effectiveness and to lessen interest. If the students need to do
a longer reading, I try to include some other activity or a class discussion to
break up the reading session, which seems to encourage them to stay on task.
Consider how you approach a new textbook. Experienced teachers usually have a method
for looking at the book and a high interest level in learning about how this tool
will help them in the classroom. Students do not just open up their textbook with
the same expertise and interest as an experienced teacher does. Rather, middle school
students likely are just waiting for your direction. Mathematics textbooks can be
quite an effective student resource. Why not help them get to know their mathematics
textbook?
References
National Council of Teachers of Mathematics. (1989). Curriculum
and evaluation standards for school mathematics. Author: Reston, VA.
National Council of Teachers of Mathematics. (2000). Principles
and standards for school mathematics. Author: Reston, VA.
Ohio Department of Education. (2002). Academic content standards:
K12 mathematics. Columbus: State Board of Education.
Diane Kahle is pursuing her Ph.D. in mathematics education at Ohio State University.
She has fifteen years of teaching experience in middle school mathematics. Her interests
include improving mathematics selfefficacy, mathematics history, mental mathematics,
and children's mathematical literature. She can be contacted at kahle.9@osu.edu.
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