Back to: Module: Helping Students Do Math
Slide 1: Hello, and welcome to this webinar on learning from a math textbook with Daniel Showalter.
Slide 2: Helping students learn from textbooks took on a whole new meaning for me a couple years ago when I joined a team that published our own textbook. In some ways, a textbook author is like a teacher, because both want to help the students learn as much as possible. The main difference is that the teacher has ongoing interaction with the student, whereas the textbook author has to prepare all of the communication to the student in advance.
Slide 3: Because the textbook author is unable to adapt to the questions and needs of each student, it is quite possible for the student to disregard the textbook, seeing it as “too difficult” or “unhelpful.” As a paraprofessional, you can play a role in improving the relationship between the student and the textbook by helping the student figure out how he or she can benefit from a particular textbook.
Slide 4: It is useful to know how a typical math textbook is designed. Most math books are divided into chapters or units. Math textbook authors sequence these chapters carefully because math lessons usually depend on students knowing certain concepts already before moving onto new concepts.
Slide 5: Each chapter is then divided into smaller sections or lessons that may take a day or two to cover. Typically, a section comprises an instructional part and a practice part. The instructional part may include activities, discussion topics, graphs, charts, examples, or links to outside resources. The practice part is usually a series of exercises.
Slide 6: Each portion of the book—whether it is a chapter or a section—will probably start with learning objectives or main ideas describing the central topics considered in that portion of the book. By knowing what the main ideas are in advance, the student (and you) can know what portions of the textbook are crucial to understanding the topic and which ones are more optional.
Slide 7: There is one important thing that sets all math textbooks apart from some other types of textbooks: With math textbooks, students are expected to be active readers in order to learn the material.
Slide 8: What are active readers? Active readers interact in explicit ways with the books they are reading. For example, when students sit down to read a math textbook, they might have a notebook ready to work out problems and write down questions. They should read important parts slowly. They should reread important parts several times. They should use their notebook to trace the steps in example problems and to work out any practice problems.
Slide 9: Reading a math textbook straight through like one would read a novel is rarely effective and usually just results in confusion and frustration. The next few slides will explain some ways that a paraprofessional can help students read math textbooks more effectively.
Slide 10: The building blocks used to present ideas in math textbooks are the new concepts and terms. Terms may be defined within the instructional text within the chapters, in a glossary at the back of the book, or both. Because math is a language of precision, students should first make sure they understand the definition of each new word. One method students can use involves the Frayer Model.
Slide 11: The Frayer Model was created by Dorothy Frayer at the University of Wisconsin. It can be a useful tool to help people understand concepts in any subject. In the Frayer Model, the learner completes a template in which a new term is written in the center oval. The student then fills out the other four areas of the template. These areas relate to the term and, in turn, ask for definitions, facts, examples, and non-examples. A paraprofessional or teacher then can then look over the completed template and identify any sources of misunderstanding. Often, in math, the most helpful area of the Frayer Model is the non-example section. You will complete an activity with the Frayer Model in this module to get more practice in using it.
Slide 12: Look for how a textbook showcases important concepts and then focus on these. Many math books put important information in special boxes as shown on this slide. Other books have a special symbol that they use whenever there is an important concept or formula.
Slide 13: After reading about the important terms and concepts, the student should work through some examples. Students who jump straight to the exercises before attempting to understand the material will often get overwhelmed and give up. An excellent approach after reading the narrative is to work step-by-step through the examples presented in the section. These examples provide a careful explanation of how to put the concepts into practice. After working through the examples, the student will be more confident when approaching the exercises at the end of the section.
Slide 14: Research on learning math has shown the importance of immediate feedback. Oftentimes, a textbook will include solutions to some of the problems in the back of the book. Encourage students to check each solution, when provided, before moving onto the next problem. There’s nothing more discouraging than doing a set of 20 problems only to find out at the end you were doing them all wrong! In a later module, we will look more closely at what to do when a student’s answer is not correct.
Slide 15: As a paraprofessional, you may have access to the teacher’s manual that accompanies the textbook. One advantage of a teacher’s manual is that it often includes solutions to all of the problems. However, most teacher’s manuals offer much more. Look for margin notes that might include additional resources, tips for teaching the content, and ways to identify and handle common misconceptions that students may have. Teacher notes can be particularly helpful when there is a topic that you are unfamiliar with or when students are having an especially hard time understanding a concept.
Slide 16: With technology playing a growing role in education, most textbook publishers now offer online resources. In many cases, these resources are available for free, although you might need a teacher with whom you work to register for access to certain ones. When available, online resources are usually detailed in the first few pages of the teachers’ manual. It is well worth taking a look, because these resources can be very helpful for student learning, and many teachers are not even aware that they exist!
Slide 17: These days, math textbook publishers realize that students need to see where math is used in the world in order to stay motivated. Most textbook authors make an effort to include applications of the material the student is learning, both in the instructional text and in the exercises. Whenever you notice an application that may be of interest to a student, point it out to the student with enthusiasm. Math tends to be one of the hardest subjects for students, but it is also one of the most useful. When students realize that math is connected to the things they care about, they are much more likely to invest effort into learning the math.
Slide 18: As you help students work through a textbook, keep in mind that textbooks are written by human authors. I remember the first time I emailed the author of one of my textbooks, because I thought I had found an error. I was surprised, and delighted, when he emailed me back the following day! Not only did he explain the problem in a way that allowed me to understand it, but he also shared a story about what had inspired him to write that problem. From then on, I enjoyed reading that textbook more because I felt connected to the author. Encourage your students to write questions or comments to the authors. There’s no guarantee of a response, but unlike famous actors or athletes, math textbook authors like me are usually nerds who enjoy discussing anything related to math!
Slide 19: Math textbooks are rarely used to their full potential to assist with student learning. By understanding how a textbook is designed and how to help a student read it, you can contribute both to their learning and enjoyment of math!