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 problem-based. No matter which type, though, there is often more information in a current-day 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 problem-based 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 classroom-tested ideas for helping students learn to read their mathematics textbook effectively. One idea is for a whole-class setting, the second is for small groups, and the third is for pairs of students.

Whole Class

In the whole-class 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: K-12 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 self-efficacy, mathematics history, mental mathematics, and children's mathematical literature. She can be contacted at kahle.9@osu.edu.

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