Fundamentals of Mathematics
Denny Burzynski, College of Southern Nevada
Wade Ellis, West Valley Community College
Copyright Year: 2008
Publisher: OpenStax CNX
Conditions of Use
The text is mostly comprehensive with the exceptions that the text provides only one method for computing an answer and that there are very few applications. The text has a good table of contents and no glossary. read more
The text is mostly comprehensive with the exceptions that the text provides only one method for computing an answer and that there are very few applications. The text has a good table of contents and no glossary.
I did not find any mistakes.
With the text being set up to primarily show computational methods and examples worked out, the text is not obsolete. Current applications would need to supplemented by the instructor to add relevance to the skills in the text.
The math vocabulary is explained at the beginning of a section which is helpful when using the words in that section. However, a glossary of vocabulary referenced would be easier to use than searching through different sections to find the word again. The exercises include some vocabulary questions to assess understanding of the new math words. The problems are not numbered so referencing them in class would be difficult.
The text uses language and terms consistently throughout. The sections follow a recognizable pattern from one section to another.
The text is able to be broken into smaller reading sections. The sections flow in order and the order can be changed in most cases. The Applications Involving Fractions section, though, uses algebraic methods which is not introduced until later in the text.
The text is easy to navigate. Other than introducing solving an algebraic equation with fractions, the order was logical and clear.
I liked the links in the Proficiency exam sections back to the section where that material was covered. Sometimes, this required scrolling through the whole section to find the topic of challenge within the section.
I saw no grammatical errors.
Language is neutral other than references to men and women without another option. Word problems are mostly academic oriented as opposed to real world problems so there is little cultural bias. There are not multicultural examples.
I found the textbook layout and organization was easy to follow. With the examples and exercises being included along with the text, the skills were easy to follow. The links within the book directed to topics already covered were useful for refreshing previous content. Since the textbook is primarily for computational problems, the instructor would need to supplement with real world examples for word problems and graphs.
Fundamentals of Mathematics covers all topics taught in MDE 010 and BSK1-MTE1-4. The contents address each topic by chapter and objectives within that topic are in the chapter subsets. It is clear where to go for an objective. Objectives are... read more
Fundamentals of Mathematics covers all topics taught in MDE 010 and BSK1-MTE1-4. The contents address each topic by chapter and objectives within that topic are in the chapter subsets. It is clear where to go for an objective. Objectives are listed in the first subset for each chapter and each chapter ends with a proficiency exam.
In all of the examples I checked, I found one typo in the cluster estimation. The accuracy of the answers seems very good. It is difficult to have bias in a basic math text and find this to be bias free
There are a few word problems ending each chapter. They are generic and hard to date, but there is one question referencing a VHS tape. This is an easy update.
Terminology is introduced at the beginning of each chapter. Terms are reinforced in the directions for the sample sets. In the summary for each chapter, terms are again reviewed. Newly introduced terms are repeated in subsequent chapters. Topics build in as each chapter is introduced and topics within are reinforced throughout. Students need to be introduced to mathematical language and I see use of correct terminology throughout.
I found the text consistent in its breakdown of objectives, attention to each and amount of practice for each chapter.
The division of chapters is logical. It builds from the basics and utilizes information in subsequent chapters. The contents clearly allows the user to zero in on the needed topic
As stated before, the topics are well organized in progressive order and topics build with each subsequent chapter. My only area of frustration is the numbering system. Chapters are numbered 1-13 and objectives within are 1.1, 1.2, etc. This is clear. Then it breaks down to sample set, practice set and exercises. These contain as many as 30 examples and there is no numbering. I find this unnecessarily confusing. The exercises have solutions for only half of the problems. If these were assigned, it would be confusing to identify or go over in class.
The text is easy to navigate. There are few charts and no images in the book.
I detected no grammatical errors.
There is no mention of cultural issues so it is free from offense of any kind.
The overall content is thorough and easy to follow. There could be more examples, but this is a good start and the instructor would want to supplement. My only dislike is the lack of numbering of problem sets. That would make following along much easier. I would recommend this text for a Developmental Mathematics course.
The text covers all topics in the course outline of Math 010, and more. It covers a wide range of topics and applications. read more
The text covers all topics in the course outline of Math 010, and more. It covers a wide range of topics and applications.
Content is accurate down to every detail I could perceive. There are no signs of bias and all essential information is given.
Content is universal and will always be relevant from a mathematical standpoint. There is no content that refers to particular technology processes or platforms: it is strictly math.
The text is extremely clear. All terms are defined precisely and in more detail than I have seen in any other math textbook. There are no assumptions that the reader already knows a piece of content, and every explanation is very clear and easy to understand.
The text is internally consistent in terms of terminology and framework. Each lesson is presented in the same clear format. At the beginning of each lesson is a list of objectives. All objectives are consistently fulfilled. All content is consistent, as far as I could tell, with the definitions and rules that are initially laid out.
The text is divided clearly into units and sections. Each section is bite-sized and very specific. It is clear to see how the categories and topics are divided.
The text is clear from the beginning on what to expect in the structure of each lesson, as well as each lesson’s objectives. Each lesson is presented with uniform structure in clear categories, and all content is organized in a way that makes sense.
The text has an interface that is usable, but does not stand out as exceptionally user-friendly. There are subheaders in bold, and bullet points to organize text content.
There are no apparent interface issues, but the visual alignment of graphics and text is very ordinary, sometimes a little awkward - there has been no special effort made to improve the visual appeal or readability of the interface.
The text is very grammatically clear and precise, with no errors perceived.
For a math book, this book is excellent in terms of cultural relevance. It draws in lessons and content from diverse cultural backgrounds, explaining them clearly and without bias.
The content and teaching of this book is very thorough. There are no mysteries; everything is clearly defined and explained in depth.
I really enjoyed the way the authors explain every concept. For each topic, they start off with the very basics, assuming no previous notions other than what they have covered earlier in the text. The language is clear and the examples are clear... read more
I really enjoyed the way the authors explain every concept. For each topic, they start off with the very basics, assuming no previous notions other than what they have covered earlier in the text. The language is clear and the examples are clear and detailed. Each chapter has a summary of concepts to review terms and general procedures.
There are a few typos, but the information in the book appears to be accurate.
The content of the book is not generally such that would become outdated. New methods of performing the arithmetic could possibly arise, but the logic and procedures presented here definitely have longevity.
I found the book very easy to read. As is the case with a lot of situations involving many steps in a process, there were a few situations where the explanation might be difficult to follow, but they were immediately demonstrated with appropriate examples that clarified any confusion or possible misinterpretations.
I appreciated the consistency of the book since I have not seen that in some of the recent textbooks I have used. The processes taught early in the book were consistently used in later concepts, reinforcing the logic behind the method and building foundations for potential use in later applications and classes.
The sections of the text were presented in such a way that they could be integrated into other classes as appropriate without relying on the entire book. Three recent classes I have taught included some of the topics from the text - some topics in more than one of the classes, and some in only one of the classes. The explanations, examples, practice problems and homework problems from each of the appropriate sections could be integrated into the appropriate class without having to rely on the entire text. Some of them would benefit from the processes described in earlier sections, but that could easily be done using only the necessary concepts of the earlier sections.
I liked the order in which the material was presented. Some of it was a little different from what I have seen in the past - for example operations on fractions and working with decimal numbers - but this flow seemed like it would allow for the concepts (for example of multiplication and division of fractions) to be ingrained before introducing more complicated problems (for example addition and subtraction of fractions, especially of those with unlike denominators).
Also, each chapter began with the objectives, followed by the concepts (overview, any necessary terminology, explanations, examples, practice problems), a chapter summary, additional exercises, and chapter exam.
There are some issues with the interface. Several of the links, that are supposedly intended to bring the reader to a specific part of the text to review a concept, actually bring the reader back to the text's preface. This seemed to be more of an issue in the later chapters.
Also, I'm not sure if this is an interface issue, but some of the review questions, practice problems and exercises clearly should have a blank space or line to be filled in, yet there is none. For example: "A comparison, by division, of two unlike denominate numbers is called a ." and "Complete the following statements. 7-5= since +5=7."
The grammar seemed fine to me. The phrasing of some of the percent application problems were a little poor, but that's not really a grammar issue. This wasn't a large issue, either. I found only a few examples of this.
From section 9.7:
"On an 80 question exam, a student got 72 correct answers. What percent did the student get on the exam?" This question might be better phrased as "What percent of the questions did the student get correct?"
"A bottle contains 45 milliliters of sugar and 67 milliliters of water. What fraction of sugar does the bottle contain? Round the result to two decimal places (then express as a percent)." The question is about fractions, and poorly worded, then instructions say to round to two decimal places.
The book is culturally relative to most everybody who would potentially be taking a class using this text. Applications and example problems refer to various occupations and situations that could apply to all races, ethnicities and backgrounds.
I think this book is fantastic. It might be a little too much material for one "one quarter" class, but pieces of it could be used in a variety of math fundamentals classes and introductory algebra.
This text covers all the areas that I expected to find in a fundamentals text. It begins with addition and subtraction of whole numbers and progresses in a logical order to multiplication/division, exponents, fractions, decimals, ratios,... read more
This text covers all the areas that I expected to find in a fundamentals text. It begins with addition and subtraction of whole numbers and progresses in a logical order to multiplication/division, exponents, fractions, decimals, ratios, measurement/geometry and into beginning algebra. I will find this useful for the math class I am teaching, which is a multi level group of students who are preparing for the GED Math test. There is no glossary of terms but the index is thorough enough so it probably is not a problem. However, it would be nice to see a whole page with all formulas listed. Would also like to see a section on the coordinate plane.
I can't say that it is error free because I have not read every single word of the text. However, in most of what I have studied, I have not seen anything inaccurate enough that would cause confusion for students. There is one place where there is text on top of text, making it difficult to read, in the tables on page 548, 549.
I would suggest updating for a number of reasons; 1. The font is difficult to read. It looks like a photocopy of old typewriter pages. 2. One of the benefits of a digital format is that you can have lots of color without the high cost of color printing. This text has no color! So boring! The content is still relevant, so I can't imagine that it would need to be updated much. The suggestions above should be easy to implement.
It is written clearly, but is lacking in interesting or imaginative ways to demonstrate the real life applications of the concepts.
The book is extremely consistent making it easy to become comfortable with. The user can quickly predict where and how to locate a particular concept and its related components such as exercises and solutions.
The text is very modular and this is very useful especially in a multi level classroom. The sections can be isolated and then used in combination with other texts and materials as needed. Because the text is very consistent in its terminology and framework, it can be used as a reliable core structure for the scope and sequence of a math course.
The text is presented in the same logical order that I would have designed it and the same order in which I prefer to present my material.
The pages of the PDF do not align with the text pages. It would make it more "friendly" if they were consistent. The font is not nice. They should have used something like Cambria, Times New Roman or Century rather than the old typewriter style.
The text is grammatically accurate.
There is not really anything to comment on. In looking at the real life applications of the math concepts in every section, I do not find anything to be culturally offensive. The examples seem quite simplistic and neutral to me. Perhaps if the author could add more interesting or imaginative ways to demonstrate the real life applications of the concepts, this would be the way to add more cultural diversity.
Would like to have a section on the Coordinate Plane
This text covers most of the areas that I teach. It has a good table of contents and index, but no glossary. read more
This text covers most of the areas that I teach. It has a good table of contents and index, but no glossary.
I did not see any inaccuracies or biases. The material is accurate.
Most of the word problems and graphs used situations from the late 1970's and early 1980's. The problems were still of interest, but 35 years old. It would be relatively easy to correct this problem.
The book is well written, however it lacks pictorial instruction on many mathematical concepts that can be illustrated in a simple visual manner. It would be easy to visually explain squares, square roots, prime numbers and factors, decimals and areas of polygons. The authors did, however, did a good job explaining place value in addition and subtraction of whole numbers. I like how they tied in calculator use with many of the concepts.
I like how they introduced algebra in the first chapter of addition and subtraction of whole numbers. However they put in some problems of probability and determining the mean of a number without any explanation of these concepts.
The book is divisible into many subsets of the skills needed to master a certain mathematical skill.
The book is well organized, arranging the skills in a logical manner that enables the student to be ready for each new concept.
The book does not have any simple navigational tools to go from one part of the book to another without scrolling through the pages.
I found no grammatical errors.
I did not find the book to be culturally insensitive or offensive, but I did not find any examples of multicultural word problems.
The book gives straightforward explanations of the topics covered in the book. I seek out books with more visual explanations. It provides many exercises for students to practice their skills.
Book was very comprehensive and covered most topics for basic mathematics. Book title could have included a one line or two liner about who the book is for and what it covers. The book lacks glossary and effective index which is helpful for... read more
Book was very comprehensive and covered most topics for basic mathematics. Book title could have included a one line or two liner about who the book is for and what it covers. The book lacks glossary and effective index which is helpful for learners/users.
Drills/Exercises presented were accurate and showed step-by step process which is advantageous for students/readers.
Examples presented in the book need to be updated to be more relevant to users. Need more real life applications of where and how to use the different concepts of mathematics. Some of the materials can be presented using online/interactive way to keep up with how math and other subjects are taught currently.
The presentation of the materials is very clear to the point of being very tedious. Jargon used is appropriate, sufficient, concise and accurate. Language used is at par with what users can learn from. Words used are easily comprehensible.
Language used is unified and in line with what is being explained/discussed. Framework presented in an orderly and organized way for students/readers to follow in symmetry.
The book can be divided in different modules so that it is not overwhelming to leaners. This way students can work at their own pace and print materials that they need more focus on. Presenting materials by chunks is more discernible,
The book can still use some organization of topics. Presenting the topics in modular form will be more beneficial to students and other users of the book.
The book lacks graphics which will be to the advantage of most visual learners. Modeling of some of the exercise/drills can help detangle some concepts which may be confusing to students/readers.
There was no significant grammar errors in the book. It is written in accurate use of the English language.
Mathematics is a universal language and easily comprehended by native speakers and non-native speakers alike. Though examples relied heavily on American culture, there were some examples that related to other cultures. There were no glaring offensive reference to different cultures.
Overall, the book is very helpful as a fundamental learning material for mathematics. Although, it can still benefit with some revisions such as collapsing the pages (700+ pages can be overwhelming). Practice makes perfect but too much drills/exercises can be counterproductive.The book can also utilize some graphics to deviate from too much words. Majority of learners rely on visuals and it helps in remembering easily. An update of the book using more real life applications and digital version is recommended.
This text does not contain a glossary of terms. The index system is composed of two parts. One part operates as an index would. The other refers to keywords and the section that the word is associated with. What I found challenging to understand... read more
This text does not contain a glossary of terms. The index system is composed of two parts. One part operates as an index would. The other refers to keywords and the section that the word is associated with. What I found challenging to understand is why a keyword like Burnzynski had 85 citations throughout the text. I then read the Attributions section and saw the various modules and the name Burnzynski repeatedly and it started to make sense. That information could have been better organized. There were other keywords that didn’t seem necessary like ‘fundamentals’, or ‘mathematics’ that also had a large number of associated sections. I think a student of this level could quickly become lost looking for the information they need and as an instructor I would have to use class time to explain how to use the index. Finally the text doesn’t present multiple methods for operations. For example, in the discussion of multiplying and dividing rational numbers it was never mentioned that the GCF and the LCM could be useful tools for doing the same problems. Also I never saw the fundamental theorem of arithmetic mentioned. I am going to give the comprehensiveness a 3. While there is room for improvement I think that there is something good worth noting and that is the double decimal system that organizes the information within each section would allow me as an instructor to make easy reference to material in the book.
I found no statement that was biased or inaccurate.
The content needs to be updated with hyperlinking through the text and the page of the pdf needs to correspond to the page in the table of contents and the page numbering. Some images would be help break up the drudgery of black pixel on white pixel text. I am going to evaluate this category to a 3 because I think it might be real easy to link this to lecture whit the double decimal indexing through each section.
I found that the descriptions were as void of extraneous content as possible. Some might find that inadequate. I am going to evaluate this at a 3 because I have read math books that are enjoying to read. This is not one of those.
I found no inconsistencies within the use of terminology or framework.
I found the units to be independent enough to allow some reorganization of material however some of the initial chapters will need to be covered because they lay the foundational work for the rest of the material. I give it a 5 since they present the material in the same progression that as an instructor I would present it.
I find that the dependence of symbolic representation reduce the clarity of the topics. I find that the organization of topics under each chapter to be logical in their ordering and build on concepts throughout the chapter. I am going to evaluate this category at a 4 because I feel that a little embellishment would improve the flow and readability of the material.
There are no hyperlinks from the table of contents and the page number in the table of contents don’t line up with the page number of the pdf. The text doesn’t work in an electronic format. I am going to award a 3 to this category because I feel there is a good link to a lecture and I can’t give it a 2.5.
I found no grammatical errors.
It makes no use of examples that include race, ethnicities or backgrounds and is sterile of cultural insensitivity and offense. I am going to evaluate this as a 1 because I feel that mathematics gains huge relevance as a vehicle of discussing current events.
The number of problems are excessive resulting in repetitive work that doesn’t help the student understand the concepts. Better written questions would also reduce the high page number. As a student that was placed in a class that was using this as its textbook, I would feel greatly intimidated. For me this reads like graduate level mathematics.
Table of Contents
- 1 Addition and Subtraction of Whole Numbers
- 2 Multiplication and Division of Whole Numbers
- 3 Exponents, Roots, and Factorization of Whole Numbers
- 4 Introduction to Fractions and Multiplication and Division of Fractions
- 5 Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions
- 6 Decimals
- 7 Ratios and Rates
- 8 Techniques of Estimation
- 9 Measurement and Geometry
- 10 Signed Numbers
- 11 Algebraic Expressions and Equations
About the Book
Fundamentals of Mathematics is a work text that covers the traditional study in a modern prealgebra course, as well as the topics of estimation, elementary analytic geometry, and introductory algebra. It is intended for students who:
- have had previous courses in prealgebra
- wish to meet the prerequisites of higher level courses such as elementary algebra
- need to review fundamental mathematical concenpts and techniques
This text will help the student devlop the insight and intuition necessary to master arithmetic techniques and manipulative skills. It was written with the following main objectives:
- to provide the student with an understandable and usable source of information
to provide the student with the maximum oppurtinity to see that arithmetic concepts and techniques are logically based
to instill in the student the understanding and intuitive skills necessary to know how and when to use particular arithmetic concepts in subsequent material cources and nonclassroom situations
to give the students the ability to correctly interpret arithmetically obtained results
We have tried to meet these objects by presenting material dynamically much the way an instructure might present the material visually in a classroom. (See the development of the concept of addition and subtraction of fractions in section 5.3 for examples) Intuition and understanding are some of the keys to creative thinking, we belive that the material presented in this text will help students realize that mathematics is a creative subject.
About the Contributors
Denny Burzynski is a mathematics professor at College of Southern Nevada located in Las Vegas, Nevada.
Wade Ellis, Jr., has been a mathematics instructor at West Valley Community College in Saratoga, California for 20 years. Wade is currently Second Vice President of the Mathematical Association of America. He is a past president of the California Mathematics Council, Community College and has served as a member of the Mathematical Sciences Education Board. He is the coauthor of numerous books on the use of computers in teaching and learning mathematics. Among his many honors are the AMATYC Mathematics Excellence Award, the Outstanding Civilian Service Medal of the United States Army, the Hayward Award for Excellence in Education from the California Academic Senate, and the Distinguished Service Award from the California Mathematics Council, Community College.