Book Critique

Overall Statement

My critique covers the 5^th grade level mathematics book by Scott Foresman. The book cover is bright and catches your eye. A beginning section tells children how they will be using this book to learn. The topics include

1. Build math power

1. problem solve
2. critical thinking
3. number sense, using data
4. calculators and computers

1. Do your best

1. expect to succeed
2. build your understanding
3. independent study

1. Active learning

1. math activities
2. reading, writing, talking, listening
3. working in groups
4. exploration

1. Enjoying math

1. at school
2. at home

At this point I was expecting a good book. This is actually a "sell" to teachers and administrators, and parents. If you were to stop here, this publisher seems to fulfill many of the goals set up by the NCTM Standards. But upon further review, I see this book as a "regular" math text, spruced up a bit to make you feel as though schools that are using this text, are changing with the times.

Each chapter is set up with the same format: topic, activity, not necessarily related to the chapter topic, followed by problems, then building understanding. This is one or two "stories" used to set up the topic. A section called "check understanding" which is gone over by the teacher, practice problems, problem solving, which contains story problems using the technique just described, then ending with "critical thinking" which basically is just another problem.

The following is a categorization of the chapters as they pertain to the IL Learning Standards:

1. Number Sense — chapters 1,2,4,5,7,8,10,11,12,15. This is the main topic of the book, as it probably should be for fifth grade.
2. Estimation and measurement — chapters 3, 6
3. Algebra and Analytical Methods — were not covered as a chapter
4. Geometry - chapter 14
5. Data Analysis and Probability — chapter 9(graphing) & 13

The instructional approach is teacher oriented. The activities have been added to make it appear more child-centered; however, my feelings are that those are often overlooked and not done. "Anyone" could teach from this book and get through the day, maybe even the year. It seems to be the "regular" way of teaching with a few additi0ons to make the appearance of being updated, and coinciding with "reform".

As for a priority on skills or concepts, the skills are definitely covered well. Some concepts are covered. An example topic would be the coverage of volume. There was a "reading connection" made to the topic, but it was more a discussion of the definition of volume.

There is very little use of technology. Some problems showed a picture of a calculator. For these problems the calculator could be used. I found on page 250, the section on calculators, that the book showed what the calculator looks like, some functions, and how to interpret how to read the numbers shown. In this entire section, it was not suggested for the children to get out calculators and use them!

Often the book attempted to relate topics, discussions the children’s interests, including problems that related to shopping lists, video games, and computers. Many estimations

were included throughout the book.

Overall, the book has the appearance of being updated. The first section was a "sell" to the public to show how up to date the series is. However, upon further review, it does not quite deliver all that is promised. This is not to say that this book could not be used. With other resources, and careful attention to including many of the "investigations", a worthwhile mathematics curriculum could be generated with the use of this book.

The textbook I critiqued is entitled Heath Mathematics Connections. I used the teacher’s manual for grade six. After browsing the textbook, I found that it is both teacher and student friendly. This partly could be because it was the teacher’s manual, but there were easy step by step instructions for the instructor. There were also alternative problems for every section, a "problem of the day," reasons why these concepts are important for students to learn, and connections to other real life subjects. There were an abundance of examples and problems for teachers to use in order to help students really grasp each subject. The activities were fun and interesting for students as well as teachers. The textbook also was very student oriented. Each page had diagrams or pictures for students to use while visualizing a problem. The pages also were not cluttered. I think this is a very important thing for students. When a student looks at a textbook page filled with nothing but numbers and problems, they may tend to feel intimidated and overwhelmed by the concepts being taught. However, when the page is partly filled by pictures and fun activities, the student is more likely to be relaxed and not as worried about whether or not they will understand the concepts.

The textbook is both teacher and student centered. The problems, worksheets, and activities are definitely aimed towards students. They are interesting and valuable lessons that kids need to learn. However, in the teacher’s edition, the side notes and extra activities are aimed towards teachers. They give instructors numerous ideas on what and how to teach to their students. This is a great resource for teachers to have because when worse comes to worse, the textbook will give you ideas on what to do when the lesson just is not working. Overall, I think that the textbook is centered around students’ needs as learners. It is easy to follow and when it can be, it is fun for the students to learn.

The content in the book not only follows the Illinois Learning Standards, but it also has a good balance of skills and concepts. Students have a large amount of practice when learning the skill, and they also are urged to figure out the underlying concepts of the subjects. This is what the Illinois Learning Standards are all about. It’s not only the skills that are needed in order to learn mathematics, but the concepts behind the skills. This way the students can learn why things work and not just memorize them for the test. I think this is a great way to teach students. When I was growing up, I never learned the concepts behind the skills. I understood all the formulas and equations, but I never grasped why they worked. It just was not taught. I always thought that when I was up at the front of the classroom, I would take extra time to ensure my students understood what they were doing and not just memorizing it for the test.

The only thing this book is really lacking is the use of technology within the lessons. There are a few calculator problems dealing with decimals and scientific notation. There are also a few optional resources listed where computer programs can be used. Other than these few examples, technology is not represented enough in this textbook. I think that a variety of computer programs can be used for many of these lessons. As a teacher, if I were using this book, I would have to look up other resources in order to tie technology into my lesson.

I would definitely consider using this book in my classroom. It follows the Illinois Standards very closely. It encompasses nearly all of the concepts listed in the standards, and also gives other ideas that I might not have thought of. On every page is an entire list of other resources that I could go to and collect information or new lessons for my students. I think the authors of this book do an excellent job of making sure the students are interested in what they are learning. They also give fun problems that can be used every day. This keeps kids on the edge of their seats at all times. There are some really great ideas in this textbook that can liven up a classroom. With just a little extra help, it could be a great guide in a middle school math class.

Textbook Critique

Addison Wesley, Addison Wesley Mathematics, 1995. 8^th grade.

If teachers use all the supplements, Addison Wesley Mathematics can be a very efficient textbook for an eighth grade mathematics classroom. When viewing a textbook for the first time, teachers and students are likely to notice its overall appearance. AW Mathematics has a very colorful cover and many interesting pictures throughout the book. Pictures sometimes help to make the material more exciting. Upon flipping through the teacher’s edition, I got the feeling the book was very teacher-friendly. There are many charts and explanations to guide teachers through the chapters. In order to figure out if the textbook was student friendly, I needed to look a little more closely at the content and approaches to material.

While looking at the content, I tried to notice how each chapter tied into the Illinois Learning Standards. I came up with a rating for how well the content overlapped with the Standards.

State Goal Rating (0=very little TO 4=very good)

1: Number Sense 4

2:Measurements 3

3: Algebra 2

4: Geometry 3

5: Statistics/Data 4

Basically, I rated the textbook as to the extent it covered each of the 5 Illinois Learning

Standards. This does not imply anything about the value of the instructional techniques. I will talk about the techniques next. Rating the textbook on content coverage seemed very difficult to me. I leafed through the chapters, but I do not think I really know the extent of each topic. The chart in the beginning of the teacher’s edition, which explained the particular pages in the book to cover each topic, helped guide me. I think I might be biased towards the topics I had in eighth grade. My eighth grade math class revolved around algebra, so I was surprised this textbook did not cover algebra more in depth. The algebra in the textbook appears very basic. I think there is a good amount of information on basic number sense and data. Number sense appears in each chapter. Overall, I do not think the authors of the textbook focused on the Illinois Learning Standards; however, they claimed to follow the NCTM Standards.

While the content may be somewhat in accord with modern standards, the textbook itself is very teacher-centered, even traditional. The book is set up for students to be able to learn a lesson and then do the homework problems and worksheets based on the lesson. There are many word problems using modern ideas such as computers and recent history events. Some of the problems even use multicultural topics, such as the percentages of African-Americans in the United States. The word problems help students apply the mathematics to some real world events, but these are still problems rather than activities. The textbook authors obviously intended students to sit at their desk and complete these worksheets and problems or use them as homework.

The ironic thing is the teacher manual suggests using many more student-based activities leading me to believe the textbook authors believe math classrooms need to be teacher-guided at all times. I really liked the group activities and classroom project suggestions in the teacher’s edition. Even if teachers used all the suggested activities, I do not think the students would learn as much as if they were allowed to do their own investigations. I am not sure why the authors could not include some investigative activities in the student textbook.

In addition to being teacher-centered, the textbook is very skill-oriented. There does not seem to be many connection among math topics. I can tell the focus is skills just by looking at the table of contents. The chapters are divided into geometry, algebra, data, etc. To concentrate on concepts, the chapters could focus on a concept such as conversions in geometry, algebra, measurements, and other topics. Once the student masters algebra, he or she leaves it behind to learn the next skill of geometry. A conceptual approach would build on students’ previous knowledge and challenge them to further their understanding. Then, AW Mathematics includes cumulative reviews after every few chapters. These reviews suggest it is the student’s responsibility to remember all the different skills separately.

Technology is becoming an integral part of our society. Students can learn various math concepts through technology devices such as computers and calculators. AW Mathematics incorporates few lessons involving technology. Using calculators is obviously not integral to the understanding of certain lessons. The textbook uses calculators to make skills such as estimating easier. There is no plan to help students learn about calculators. By eighth grade, students need to have a working knowledge of calculator functions and computers. Teachers can find ways to incorporate these devices consistently to help students learn math while learning about technology.

Although the textbook requires teachers to extend their lessons such as with calculators, the teacher’s edition of Addison Wesley Mathematics is quite extensive. The charts in the beginning of the teacher’s edition show teachers the location of various topics in the textbook. There is also a chart showing how the textbook incorporates the NCTM standards. There is a note on the top of these introduction phrases stating the textbook incorporates the NCTM standards. For every students’ textbook page, there are a variety of activities and teaching tips for teachers. If I used this textbook, I would definitely use some of these suggestions. I was overall very impressed by the teacher’s edition and the suggestions.

If I had looked over this textbook one year ago, this would have been close to my image of an appropriate math textbook. Now, I am more aware of the different ways of teaching. Just because I learned mostly through teacher-directed classrooms does not mean this technique is the best way to teach students presently. I have learned about making the classroom more student-centered and I would really like to use these ideas in my classroom. Therefore, I do not think I would like to teach from Addison Wesley Mathematics. The textbook is too traditional; it does not help students tie all the skills together into general concepts. Students get bored with the same textbook problems and homework. They need to work in groups on challenging activities. They need to have the opportunity to investigate areas of interest in math. I want my students to be able to understand the importance of math in the real world rather than know how to solve problems in a textbook.

Textbook critique

Addison-Wesley Mathematics Teacher’s Edition Grade 7

1. This is a seventh grade text that is quite appealing to the eye. The colors are bright and draw attention to the eye. Also, the teacher’s edition is quite sturdy in order to prevent tearing. This text can be carried around quite easily without any damage.

2. I would say that all of the state goals in the Illinois Learning Standards are covered quite extensively in this text. I would rate them a four. Solving problems, communicating, and making connections are also covered thoroughly and could be rated a four. However, the use of calculators would probably be rated a three because they are used for calculating some of the exercises but not much else. Also, working in teams cannot be rated because that is up to the teacher. If the teacher wants her students to do group work, then he/she would support these ideas in the standards. This is how I see that this text represents the standards.

3. The approach in this text is both teacher centered and student centered. There are some worksheets with many exercises. I do not think these would be beneficial to students. However, there are suggested activities for students to explore and investigate before a concept is introduced. These would be beneficial for students to make their own inquiries and conclusions.

4. Concepts are reinforced through the introduction and follow up activities of exploration and investigation. On the other hand, skills are emphasized if the worksheets or exercises in the book are used frequently.

5. The calculator activities seem to be added to the end of a lesson just so that some technology is involved. However, the computer activities allow students to better understand a concept. For instance, one computer activity is called "Escape", and students have to trap a thief by following his path on a graph. They can explore on their own for a while and come to some realizations about math concepts that they may never have understood before.

6. Support materials are quite extensive. This edition tells how to make connections to other subjects, how to increase communication and how to develop investigative situations. It also offers ideas for pacing and use of manipulatives. Also, this edition explains how to read each section of the book, which is extremely important. Teachers could use most of the information found in this edition.

7. I would like this textbook for my classroom for several reasons. First, it covers material that seventh graders need to know. Also, I like the suggestions of manipulatives and computer activities. However, I would not use all of the worksheets or exercises because I feel they are tedious and not helpful for students’ comprehension. This book is a great resource for me as a teacher, though. If used correctly, students would enjoy many of the activities from it, too. Therefore, I would consider using this as the textbook for my classroom.

1. Laidlaw: Series 2000.

Chapters 17-32

Grade 8

I thought this book seemed both teacher and student friendly. The index was very well organized and made it easy to find different topics and activities. I was very impressed by the number of colorful pictures used to explain concepts, the opening activities of each chapter, and the challenge activities that close out each section. They consisted of hands-on activities that would force the children to realize the need for math in real world problems or apply the concept they had just learned. It also provides the teacher with many good hands-on lesson ideas. The disappointing aspect of this textbook series is that there were no extra support materials for teachers, such as worksheets, manipulatives, or game boards, to accompany this book. Since the book does seem to require a bit more teacher work to pull off the hands-on activities, the text may be considered a little more student friendly than teacher friendly.

2.

1. This textbook contains a combination of both teacher centered and student-centered activities. Each chapter began with a story of a student investigation (which could be easily carried out in the classroom). These activities were mostly student-centered-giving them a chance to make connections between real world problems and mathematics concepts. Also the students would have a chance to practice communicating about mathematics and problem solving. Once a need has been created for a particular math idea, the book moves into more teacher-centered activities. The students will be taught a concept by the teacher, which will be followed by students doing problems from the book. At the conclusion of each section, a challenge problem will once again lead students in a hands-on activity. Overall, I think that the book tries to follow the same format for each chapter, but in some cases there could easily be more student-centered activities. I think it would be up to the teacher to add in these activities. As long as the book is only used as an outline for teaching math and not as a step-by-step guideline, I feel this would be a good book to use in the classroom.
2. I felt that this book focused on students learning concepts. That was the goal behind including the hands-on activity that forced students to apply what they had learned. This book was conceptually based, hoping to teach students how to use the math knowledge they learned by solving real world problems or exploring real world questions, rather than plug and chug through math problems that they are unlikely to encounter in the real world.
3. The book did include some technology activities, but they were based on using a computer to write programs, which could then be used to calculate. I did not think this book explored the best uses of technology in mathematics. For example, why did the text lack calculator-based labs? Why did it only use computers to calculate, rather than including playing some math games on the computer or using the computer to see patterns that are difficult and time consuming to recreate? I thought the use of technology in the text was very poor.
4. There were no teacher support materials in the library for this book. This included no supplemental book or workbook. There were no worksheets in the book or any to accompany the book. As I stated earlier, I think the lack of supplemental material is the major weakness of this series.
5. In conclusion, I would teach from the textbook Laidlaw: Series 2000. I think it provides a teacher with a number of good hands-on activity ideas, and I think it is very easy for students to use. Yet, I do think that there may be other textbooks out there that handle the use of technology better and come with supplemental materials for the teacher. This would also be very helpful! Therefore, although I would teach with the Laidlaw series, if I had a choice in the matter, I think it would be worthwhile for me to check out some other textbooks and what they have to offer before settling on this book.

The book that was picked for me to critique was Series 2000 by Laidlaw. The grade level in which the book was for was fifth. Overall, I enjoyed this textbook and felt that it is a great guide for the teacher and the students. However, there are so man activities/projects that can be done in the classroom that go above and beyond what is stressed in the book. I feel that the book has good basic concepts, but that there could be many more things in it to enhance the concepts being taught. For example, in the book there were a lot of pictures of measured objects. If I were teaching out of this book, I would have the students actually measure their own objects and then go on from there to answer the problem. The appearance of the book was good, but not great. It showed many different types of manipulatives, but lacked in bright, uplifting colors.

Regarding the five Illinois Standards, the extent of coverage on each was as follows: Number Sense=2

Measurement=4

Geometry=4

Algebra=1

Data and Chance=3

I felt that the instructional approach in this textbook was more teacher centered. There were a lot of practice problems and "mixed practice" problems. There were only a few pages with application projects on them. For example, working in small groups to make a plan and then solve a particular problem. There was also more focus on basic skills. Chapters 3,4,5 and 6 all focus on addition, subtraction, multiplication, and division. There is little emphasis on concepts. The main focus seems to be on basic facts and equations.

The use of technology is very sparse throughout the textbook. It is definitely an add-on to the rest of the chapters. The one activity (of three) that I found was called "Computer Bugs." This had the students look at a computer program and find the syntax errors in the program. Using their math/computer skills they were to figure out why the program did not work. In addition to few technology activities, I did not really find many teacher supported materials either. The ones that were there were useful and helped clarify the concepts that the students were learning.

In summary, I felt that this book is a good basis for the concepts taught, but there are so many projects and activities that the teacher could do to engage the students in the excitement of mathematics. I would definitely use this book as a guide to teach math, but would go above and beyond what the book has to offer. For example, I really love the fact that this book integrates math with many different subjects such as geography, art, music, science, social studies, and consumer education. For instance, it used mathematics to calculate the nutritional content in foods such as proteins, carbohydrates, fat, and calories. Relating math to real life situations makes it more interesting for the students. I would absolutely take each of the subjects and integrate it with math and have the students spend a solid amount of time on each project. (i.e. giving each student a sheet of music and having them determine how many beats to a measure and which notes get how many beats).

<Publisher: Laidlaw, Title Series 2000, Grade: 7>

1. Over all statement:

*Grade Level: 7^th.

*Appearance: There are lots of geometric figures on the front cover which has blue background. I thought it gave a clear image of rigid, boring math textbook which is not that attractive to 7^th graders.

*Accessibility: It’s more student friendly.

2. Content coverage:

1. Number Sense: 4
2. Estimation & Measurement: 2 - There is hardly any measurement activities, any discussion of length, capacity, weight, etc.
3. Algebra & analytical methods: 3 - There is no inequalities mentioned.
4. Geometry: 4
5. Data analysis & probability: 4

1. Instructional approach:

*It is a student centered textbook. Technically, there is no teacher needed for students to learn from this book. Students can read and initiate learning the skills and concept on their own.

*There are no projects.

*There are lots of seat work. Almost all the work are seat work. There are no worksheet that come along with the textbook. I don’t see any necessity for the worksheet since there are enough practice problems in the book.

2. Skills vs. concepts:

Definitely, skills are more emphasized. Only two sections out of seven sections in one chapter deal with concepts. However, I see that concepts are explained pretty well in depth, using real life examples as well as relating math in different content area.

3. Use of technology (give examples):

There are some lessons using graphing calculators (i.e. programming to find out squares and square roots, etc.). However, the use of technology is not integral to the book, but an add-on. There are not many lessons that use calculators and there are none that use computers.

4. Teacher support materials:

There is no separate support material for teachers.

5. Summary statement:

1. Solving Problems: Recognize and investigate problems; formulate and propose solutions supported by reason and evidence. (4)
2. Communication: Express and interpret information and ideas. (4)
3. Using Technology: Use appropriate instruments, electronic equipment, computers and networks to access information, process ideas and communicate results. (2)
4. Working on Teams: Learn and contribute productively as individuals and as members of groups. (4)
5. Making Connections: Recognize and apply connections of important information and ideas within and among learning areas. (4)

I was very surprised when I opened the book and read the goals listed on the first page. The goals the authors seek to accomplish are very similar to the goals set by the NCTM and Illinois Learning Standards. The goals listed at the beginning of the book include:

1. Students who are actively involved in learning mathematics.
2. Students who think and communicate mathematically.
3. Students who feel confident in their mathematical ability.
4. Students who think critically and construct their own problem solving plans.
5. Students who use technology while solving problems.
6. Students who experience mathematics that is realistic, fun, and connected to their own lives.
7. Teachers who have the appropriate tools for teaching and assessing understanding — and for creating an inviting mathematics environment.

1. Heath Mathematics: Connections. Level 5, Volume 2: Chapters 7-13.

This textbook seemed both teacher and student friendly. From just skimming the pages at first, I was pretty impressed with the structure of the book as well as the activities and worksheets that accompanied the chapters. I also noticed that this textbook works to outline the goals of the NCTM standards — this also impressed me.

2. State goal 6: 3

State goal 7: 3

State goal 8: 4

State goal 9: 3

State goal 10: 3

3. This textbook has both teacher and student centered activities. As I looked through the different chapters I did notice a lot of hands on, open-ended activities. Because of the integration and attention to the NCTM standards, I also noticed that the activities and worksheets in this book concentrate on mathematics as a relationship to the outside world, as connections, problem-solving and reasoning. These four aspects are ones that the NCTM standards deem important. I concluded from my investigation of the activities that the children have an opportunity to explore the problems and devise their own solutions. I was pleased by this observation because open-ended discovery by students is something that we talk a lot about in class and the familiarity gave me confidence that what we are learning in class is something that I will be able to enforce in my classroom.
4. I found that the activities and work sheets in this book were very conceptual based. Especially since this textbook tries to outline the NCTM standards, it made sense that these activities would be conceptually based. There were some work sheets that just did focus on skills but the textbook itself gave plenty alternative ideas and plans to integrate a conceptually based lesson with these worksheets.
5. This textbook did include a technology section. The technology section did fall at the end of each chapter. Despite its placement in the chapters, I would not say that the technology lessons were just "add-ons". The sections complemented the concepts in the chapter well. Once again, I found the technology aspects to be ones that we had discussed in class. Some examples from the textbook include using calculators to compare fractions to decimals (something we’ve done in class), using computer programs to find the area of a rectangles and using a computer to find probability. Once again, it was good to see things that we have talked about in class reinforced in a textbook.
6. I found this book to have great teacher supported materials. The teacher’s manual had great ideas for the teacher to use when teaching each specific lesson and concept. There is a teacher’s activity bank that guides teachers towards adequate manipulatives to use for each lesson. The teacher’s manual also provides excellent assessment ideas for each lesson. I particularly liked this because proper assessment is a must when teaching and it is comforting to have more than one idea in terms of this area.
7. Summary: I was very impressed by the Heath: Connections textbook. I really liked the way the book was outlined according to the NCTM standards. I think that it gives me a level of comfort because the textbook focuses on the ideas and concepts that I am currently learning about. After looking over this textbook, I am also anxious to learn about the other textbooks. I want to compare them to this one so that I can see if the others pay as much attention to the things we have been discussing in class as the Heath textbook does. To reiterate what I have said before I would like to comment on how good it is to see the things that we have been discussing in class come alive through a textbook. This provides security for me as I look to my future as a teacher. This textbook used technology and also had an introduction that talked about the importance of the future in terms of mathematics and how this applies to our future as well as the future of the students. I would definitely consider this textbook for my curriculum as a future teacher.

Mathematics Unlimited

10987, 1+504. Textbook. ISBN 003006452X. Holt, Rinehart and Winston Publishers, NewYork.

Review

Mathematics Unlimited is a series of textbooks, this particular one is for the eighth grade level. The cover is appealing to the eye- it has a lot of bright colors with numbers that show "art work". It is very simple to use; it has definitions, examples and problems for students. It is pretty straightforward; the material laid out in a very uniform manner.

This book is very teacher centered- it is most likely formatted to teach in the traditional style. There are some projects; for each chapter, there is a group project that somehow relates to the chapter. They include story problems that have a series of questions. It would benefit the student because it goes more in depth about the particular topic than the practice problems in the book. The majority of the book consists of worksheet type material; practice problems that would normally be used after the lesson, and for homework. Concepts seem to be emphasized during the group work but not necessarily for in the practice problem. There is an imbalance of skills and concepts. Skills are definitely more emphasized than concepts. Things are spelled out for the students and there isn’t much encouragement for students to explore and discover mathematical concepts on an individual basis. The teacher can easily just follow along the book and teach his/her lesson from it, but there should be a better way for students to get skills and concepts. There is a lack in the use of technology with the BASIC program and calculators. There is a specific technology section, but seems just added on. Every process is pretty much told step by step, that does not give the student ample opportunity to develop their critical thinking.

Though there are a lot of good and things about this book, for the intended purposes of students to receive skills and concepts this book could be used but with reservations. I would definitely not use it as the main source of learning; it would be used with other textbooks or workbooks that have a more investigative approach. I could certainly use the material in the text, but not necessarily in the exact manner that it is suggested.

Scott Foresman — Exploring Mathematics

I reviewed only a portion of the set of Exploring Mathematics books. The books I reviewed are the "Enrichment Workbook," "Practice Workbook," "Reteaching Workbook," and "Problem Solving and Critical Thinking Sourcebook." These are all supplemental materials for the textbook. These books are for grade level eight and are extremely teacher friendly. The majority of these books are composed of worksheets to be copied by the teacher and then given to the students. In the "Problem Solving and Critical Thinking Sourcebook" along with each lesson is a section of "Teacher Notes." These are helpful in guiding the teacher’s instruction of the material. Included in this section are areas such as: Focus, Materials Needed, Overview of the Lesson, Teaching suggestions, and Extension work. Sections such as these would be extremely helpful for a teacher to use in her instruction. It gives a better idea of what students are supposed to be learning and how to teach it in an appropriate fashion.

Concerning the Illinois Standards for Mathematics, this book does a fairly decent job of covering what is recommended. Goal 6 (Number Sense), Goal 7 (Estimation and Measurement) and Goal 8 (Algebra and Analytical Methods) deserve a rating of three — a good rating. These areas are discussed pretty well and there seem to be quite a few lessons covering this material. Goal 9 (Geometry) and Goal 10 (Data Analysis & Probability) deserve a rating of two — they are only moderately well covered in these books. There exist a few lessons on each of these topics, but nothing in depth or substantial.

The Practice, Reteaching, and Enrichment workbooks are student centered. These books only consist of worksheets to be copied by the teacher to hand out to the students. They don’t really give much responsibility to the teacher; the students just need to do the work on the worksheet. There are no projects within these books, only some of the enrichment activities could be expanded into projects by the teacher. It is then up to the teacher as to whether or not to expand the lessons. The Problem Solving book is more teacher centered. It includes the "Teacher Notes" section I referred too earlier. It also appears to be more project based. There are extensions of certain concepts that go into more depth. A teacher can facilitate better understanding with this book than by only using the worksheets from the other books.

Once again, there is a discrepancy between the four books I reviewed. The Practice, Reteaching and Enrichment workbooks have more emphasis on skills than on concepts. There are many formulas and pages full of exercises for students to practice the skills they have learned. It seems to focus on more rote memorization than understanding of the material. In the Problem Solving Sourcebook, the activities are more concept based. There are more projects and therefore more emphasis on in-depth understanding of the concepts presented. The meaning behind the computations and formulas is discussed and focused on. This book doesn’t necessarily come right out with the formula — it uses other ways of guiding children towards discovering those skills on their own. This book facilitates a greater understanding of the material to be learned.

The use of technology in these books is practically non-existent. They do not speak of any technology to go along with any of the lessons. It would totally be up to the teacher to incorporate the use of technology into the lessons presented. All of these books in general are considered teacher support materials. Extra worksheets and practice for the students, as well as extension problems are what are included in the books I reviewed. As I mentioned earlier, the "Problem Solving and Critical Thinking Sourcebook" is the only book with a section of "Teacher Notes" to be used as a guiding tool.

I think these books would be a good basis for teaching mathematics to eighth graders. I do not think I would want to only rely on this source of information though. Too many worksheets will get dry and boring for the students. I want to include more activities and projects in my classroom to make learning math fun and exciting for them. As far as presenting appropriate topics and material for the age level, I think the book does an excellent job. I would use this as a guideline, but create ways of my own to get the students to discover the skills and concepts on their own, instead of just handing them to them. Overall, I think the books are decent and would be a good starting point on which teacher could build a lesson.

Exploring Mathematics

1994, 635 pp., ISBN 0-673-45528-9. ScottForesman, HarperCollins Publishers, Glenview, Illinois.

Review

Exploring Mathematics is an attractive text with many pictures. The pages are packed with curriculum to learn. It is a student-friendly text, including a variety of activities involving group work, exploration ideas, and problems to provide students practice and to help them assess their understanding. There is an abundance of review questions, summations, and independent studies with the answers provided in the back. Interspersed in the practice problems are many projects, but not nearly in the same quantity as the problems. The precise index also makes the text easy to use.

Many of the Illinois Learning Standards are met and exceeded but there are a few areas where the coverage could be more extensive.

Goal 6: Number Sense - The book begins with an extensive section on number sense covering many concepts and presenting many thought-provoking problems. Fractions, decimals, and percentages are explained and connections are made. There are also problems that require students to choose the appropriate method for solving using mental math, estimation, and some technology. Score: 5

Goal 7: Estimation and Measurement — Explanations of different measurements systems and methods of estimation are given. Concepts are explained and problems are provided to sharpen skills. While the text supplies a variety of problems involving estimation and measurement, the amount of problems that require the use of rulers, protractors, and other tools is limited. The problems presented often give students the values, not requiring them to do the work themselves. Score: 4

Goal 8: Algebra and Analytical Methods — Extensive problems are provided about these topics but application is limited. More applications of algebra to economics and business are needed. Score: 4

Goal 9: Geometry — Insightful projects and computer applications are given on this topic. Only a few topics are not covered in adequate detail. There is little discussion of symmetry and perspective is not discussed with much detail. Formulas for finding areas, perimeters, volumes and other aspects of both two-dimensional and three-dimensional figures, but more explanation of how they are derived is needed. This section includes a strong focus on skills but concepts are not adequately enforced. Score: 4

Goal 10: Data Analysis and Probability - Calculators are directly integrated into the textbook. Pictures of calculators appear throughout the text signaling students to use them to compute circumferences, multiply decimals, and perform other simple procedures. There are also computer applications for a graphing, probability, and constructing tables. Unfortunately, there are few with interesting real-world applications. Score: 4.5

Many of the shortcomings of this text are common. It is challenging to incorporate real-world applications and projects that can be used in every classroom. I would like to use this text in my classroom and create some of my own projects to supplement it. I would create projects that work across the curriculum, relate to current events, or apply to situations that are specific to my students’ lives. A text can not be expected to supply projects that meet these high standards.

Martin, Mary Jane. Laidlaw Mathematics. Laidlaw Brothers Publishers: River Forest,

IL, 1987.

I reviewed the Laidlaw Series 2000 book for eighth grade. I reviewed chapters one through sixteen. The book itself has a bright and colorful cover and the inside is full of explanatory pictures and diagrams that help to clarify the concepts explained in the book. This book is accessible to both teachers and students. It is teacher friendly because it is well organized, each chapter is divided into small sections that each explain one idea and then provide problems to practice the new concepts. The book also offers special sections that deal with integration of math with different subjects such as music, art, science, social studies and technology. It is student friendly because they offer short explanatory sections of one idea so that students don’t feel overwhelmed by trying to deal with too many concepts at one time. It also has excellent diagrams and pictures to help explain the concepts they teach in the sections.

This book also does a good job of covering all the concepts suggested by the Illinois Learning Standards for math.

The instructional approach used in this text was a balance of teacher centered and student centered. I felt it was teacher centered because each chapter was well organized into small sections that each focused on one concept. It helps the teacher focus on one idea and make sure the students understand it before moving on to the next concept. There are also varied sets of practice problems which go from very easy to very hard which helps the teacher to see whether students really understand the concept behind the formula or equation. Another reason it is teacher centered is because at the beginning of each chapter there is a real life application of the concepts taught in that particular chapter. The chapters also present ideas for whole class projects. For example, one chapter gives an idea for the students to collect magazines and then in groups make charts of facts about their magazines such as price, date, pages, etc. Then in groups write word problems that can be solved using the facts in the charts. Then the groups can switch and solve each others problems. The chapters all have integration sections that integrate math with music, art, social studies, science, and technology. The book also provides sections at the end of each chapter that give teachers problems that cover past chapters and a section that shares the main ideas of the next chapter so the teacher knows how to prepare her students for the next chapter.

I feel this book is also student centered because of the short explanatory sections. They cover one concept at a time so students don’t feel overwhelmed by too many ideas and formulas. It also provides for students with short attention spans and lets them fully understand one idea before moving onto the next concept. The book also provides great diagrams, pictures and graphs to help students visualize concepts that appear more abstract. The real life applications help the students to see that people out in the world do use math in their everyday lives and careers. The integration sections allows students to see how math is used in every subject and doesn’t just have isolated uses.

I think the book has a relative emphasis on both skills and concepts. The book devotes a section to each new idea introduced and explains it fully. Then it gives a variety of practice problems. Some problems directly practice the skill by just plugging in the formula. Other problems require a more indirect use of the concept in the section and students also have to rely on previous knowledge to help solve the problem. They also give application problems that offer real life situations and can use the skill they learned to solve the problem.

I was disappointed in the lack of technology presented in this book. They had three applications of math in technology through using computer programs to solve word problems, area problems and number sentences. They only had two calculator applications, one for scientific notation and finding decimal equivalents of fractions. It seemed that the book was not too concerned with students linking technology with math. I also feel that writing computer programs to solve math problems might be above some of the students heads. The two calculator applications do address two important abilities on the calculator but they could have had much more applications with the calculator such as graphing and using it to help estimate. I feel it was an add on to the book because of the lack of technology presented.

I don’t think that the book had any teacher support materials because there was no teacher’s edition in the library. In the textbook itself, the really only teacher support materials were the integration ideas and the class project ideas which weren’t very detailed. This requirement was hard to judge because there was no teacher edition to look through.

I would like to teach from this book because I feel it addresses all the important concepts that students this age should know. It addresses these concepts in very thorough and clear way with plenty of practice problems. It also offers great applications and integration ideas. I feel that students don’t like math sometimes because they feel it has no uses outside the classroom and this book shows that this isn’t true. I also feel that this book provides great diagrams for more abstract ideas that would be harder for kids to understand. Overall, I feel that this book helps teachers to present a positive picture of math to students and makes math more interesting so students will want to learn.

Textbook Critique

1. Overall Statement

I critiqued the seventh grade book for Mathematics Unlimited (Holt). The cover of the book is definitely an attention-getter. It is a picture of a city and the buildings deal with numbers in a variety of ways. Numbers are turned into roofs, bridges, and buildings themselves. This shows how math can be related and seen in everyday life. This series is also very accessible. There is a textbook, workbook, and a resource book for the teacher. There is a list of teaching suggestions in the front of the teacher’s edition. Over 1,000 teachers helped to create the teacher’s edition so it is a teacher-friendly, flexible, and functional resource that helps to organize math lessons for the students. Some of the main areas that the book focuses on are problem solving experiences, building number sense to gain a conceptual base, step-by-step- skill developing, and activities. There is also software available to deal with interactive situations.

2. Content Coverage

*Number Sense — 5 — Number sense is seen throughout each of the 12 chapters of

the book, especially in seven of the chapters. They deal with operations on whole numbers, decimals, and fractions.

*Estimation and Measurement — 4 — One chapter is dedicated to measurement.

Almost every chapter has an activity that deals with estimation so it is covered, but not in as much detail as other topics.

*Algebra and Analytical Methods — 5 — Most of the chapters that dealt with

number sense also deal with algebra.

*Geometry — 4 — There is one chapter dedicated to geometry.

*Data Analysis and Probability — 4 — There is one chapter that teaches statistics

and probability.

3. Instructional Approach

There is a workbook and many of the sheets deal with life situations. So worksheets that the students could work on would not have to just deal with rote problems. Although, the book is more of practice problems and definitions. In the teacher’s edition, group and individual work is encouraged. There are many activities listed to work on so that the math lessons are not always coming from the book. There are puzzles, games, mental math, and challenges that tie into life experiences. It is up to the teacher whether these activities are used or not.

4. Skills vs. Concepts

There is a balance between skills and concepts being taught in the seventh grade book. Skills can worked on by completing worksheets and concepts can be reviewed by working on projects. For example, the students can bring in ads from a newspaper on car payments to work with numbers in a variety of ways. They can compute the total cost of the car, monthly payments, and which cars are better deals. They also list lessons to incorporate science and library skills.

5. Technology

The use of technology in the book is an add-on. Although, they have many activities listed throughout the book so it would be difficult not to use any of them as a teacher. There are calculator and computer activities on almost every other page of the teacher’s edition. For computers, the students can write programs. With calculators they can answer word problems. An activity that is suggested is to research the population of your state at the library. Look at the last five reports and calculate the increase or decrease from one report to the next. They can also find the total increase or decrease throughout the years.

6. Teacher Support Material

The teacher materials offer many suggestions so I would say they are very beneficial. They concentrate on making math work, practicing, reteaching, enriching, skills inventory, pretests, posttests, and management forms. Some of these areas deal with rote learning but I think they can be altered to change that. The enrichment section relates to the children’s lives by using word problems, so it does not all consist of rote learning. The teacher’s edition of the book is more helpful than the resource book because it involves activities that students can relate to and that use technology.

7. I would like to have the opportunity to teach from this book because I think it has