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MAA Reviews and Basic Library List

The maa reviews and basic library list (bll) editorial board manages the content for maa reviews, which features book reviews and maintains the basic library list, a collection of essential mathematics resources for community college, college, and university libraries..

MAA Reviews serves as a comprehensive resource for information on mathematics books, providing details on recent publications, top recommendations, and suggested acquisitions for libraries.

Publishing eight reviews of mathematics-related books bi-monthly, MAA Reviews now hosts several thousand reviews along with listings of thousands of other books. This extensive database offers a wealth of information for those interested in mathematics literature.

Each book entry includes publication details, a cover image, and, when available, the table of contents, ensuring that users have access to thorough and useful information.

Review Copies

Publishers should send review copies to the following address.

MAA Service Center ATTN: Gazzet Byrd 9050 Junction Drive Annapolis Junction, MD 20701

Contact the Editor

MAA Reviews  belongs to the members of MAA, and so we hope you will be willing to help out! Please send the following items to the attention of the Editor.

• Point out mistakes. As we enter data and reviews for thousands of books, we're bound to get some things wrong. If so, please let us know! If it's a matter of opinion (e.g., is it a textbook or a monograph?), we'll talk it over. We particularly want you to point out books with inappropriate topics, broken links other html errors, and spelling errors.
• Become a reviewer. Contact the associate editors for your area(s) of interest.  Our shelf is always full of books waiting for reviewers.
• Suggest books. We can only review the books we get. If there's something we've missed, let us know. Or even better, contact the publisher and tell them to send us a copy!

MAA Reviews  wants to serve you all. Feel free to pitch in. Most of all, we hope you'll visit the site, read and enjoy the reviews, and spread the word.

Book Categories

We started with only two of these: “textbooks” and everything else. But then it became clear that we should have a few more. So here is a rough guide to the types of books we review.

• Anthology: a collection of papers by several different authors. See also “Festschrift” and “Proceedings”.
• Collection: a collection of papers by one author.
• Dictionary: anything that has entries and definitions.
• Festschrift: an anthology put together in honor of someone.
• General: anything that doesn’t fit anywhere else, but especially “trade books” aimed at the general public.
• Handbook: an overview of some topic intended as a “ready reference.”
• Manual: in our usage, restricted to a software manual.
• Monograph: a book whose main goal is to explain a specific subject.
• Problem Book: a collection of problems.
• Proceedings: an anthology connected to a conference or meeting.
• Report: an official report from some entity.
• Sourcebook: a collection of (usually historical) source material.
• Student Helps: a book meant to supplement textbooks.
• Textbook: a book intended for course adoption.

At the graduate level, the difference between a textbook and a monograph becomes very tenuous. Our decisions there have been somewhat arbitrary.

Basic Library List (BLL)

The site also hosts the MAA’s recommendations for library acquisition. Whenever you open the page for a book that has been recommended for libraries to purchase by the MAA Reviews and Basic Library List editorial board, you will see a note telling you that and indicating the strength of their recommendation, from BLL to BLL***.

Editorial Board

Tricia Brown , Georgia Southern University ( [email protected] )  Combinatorics, Graph Theory, Discrete Mathematics, Game Theory, Math for the General Public, Recreational Math, Fiction, and Generally Hard to Classify

Dan Curtin , Northern Kentucky University ( [email protected] ) History of Mathematics, History of Science, Biography, Memoir, Collected Papers

John Ross , Southwestern University ( [email protected] ) Analysis

Bill Satzer , retired from 3M ( [email protected] )   Differential Equations, Calculus of Variations, Dynamical Systems, Ergodic Theory, Control Theory, Numerical Analysis

Contact the Editor at [email protected] .

For all other areas, contact MAA Publications ( [email protected] ). 

We need associate editors to cover probability, statistics, and mathematical physics. If you are interested in becoming an associate editor, contact Carol Baxter ( [email protected] ).   

Materials Matter

We provide free reports that help you evaluate instructional materials because high-quality content matters to teachers, to kids, and to our collective future.

Select a subject to browse reports

Adoption Steps

What you select and how you select matters. Explore these best practices to ensure your next adoption delivers meaningful results for students and teachers.

State of the Market

Learn about the availability of programs aligned to college and career-ready standards and how regularly they’re being used in classrooms.

Dive into our vast collection of how-to resources, case studies, educator voice blogs, webinars, videos, and much more highlighting why materials matter for students and teachers.

Recent Reports

Explore our latest reviews of K-12 math, English language arts, and science instructional materials.

Issues and Science, Third Edition Revised

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New Visions High School Biology

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How reports are developed.

About EdReports

Our mission is to increase the capacity of teachers, administrators, and leaders to seek, identify, and demand the highest quality instructional materials. See how our reviews can lead to better materials for students.

Review Criteria and Evidence Guides

Our educator-developed review tools identify criteria for high-quality instructional materials. Dive into our review tools for details on what we look for in our substantive review process.

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Learn more about our educator reviewers which consist of outstanding classroom educators, district coaches, and state content leaders who understand the importance of high-quality materials.

The Review Process

At the heart of EdReports is a commitment to a by educator, for educator instructional materials review process. See how educators are leading the way to support teachers with the tools and resources they need to support students.

Why We Care

At EdReports, we know materials matter for kids. Our mission is to increase the capacity of teachers, administrators, and leaders to seek, identify, and demand high-quality instructional materials to ensure students at all levels receive an excellent education.

Student Learning

Rigorous college and career-ready standards can improve and deepen student learning. What is taught matters.

High Expectations for All

Not all students have the same access to high-quality instructional materials and this perpetuates the opportunity gap.

When teachers are provided with high-quality materials and aligned professional learning, this increases the opportunity for all students to learn and grow.

Related Resources

Data Dive: The Curriculum Support Teachers Need

Evan Stone, co-founder of Educators for Excellence, and Eric Hirsch, executive director of EdReports, discuss the importance of centering and supporting educators in the selection and implementation of high quality instructional materials.

Why Math Curriculum Must Have Quality Language Supports

Quality math curriculum requires quality language supports and curriculum-based professional learning so teachers can help every student thrive in math.

EdReports’ New Advisory Board for Pre-K Curriculum Reviews

The board will guide development of EdReports' first-ever pre-K curriculum reviews, supporting quality in early childhood education and instructional materials.

“When you’re adopting instructional materials, it’s easy to think that receiving the textbooks you’ve chosen is the end of the process. But really it’s only the beginning. These tools from EdReports guide us in assessing the strengths and weaknesses of our academic programs so that we can offer teachers targeted, strategic supports and ensure the materials we have will help students thrive.“ Geoff Dean, Instructional Math Coach, Clovis Unified School District

Copyright 2024. EdReports.org, Inc. All Rights Reserved.

All The Math Books You’ll Ever Need (Updated 2024)

Countless math books are published each year, however, only a tiny percentage of these titles are destined to become the kind of classics that are loved the world over by students and mathematicians.

Within this page, you’ll find an extensive list of math books that have sincerely earned the reputation that precedes them.

For many of the most important branches of mathematics, we’ve provided what we consider to be the best math books for the subject at hand. We aimed for a list of titles that were either introductory in nature or that fall into the category of “must-have” math reference books.

Naturally, a universal consensus doesn’t exist but the books below are as close as it gets to a wish list for any aspiring mathematician or person who’s interested in mathematics. We highly recommend each and every one of these titles and hope that you’ll enjoy them, too.

Please note, this list will constantly be updated so as to keep it current.

MATH BOOKS MENU

Abstract Algebra

• Calculus Helpers
• Calculus II
• Coffee Table
• Combinatorics
• Differential Equations
• Encyclopedias of Mathematics
• Foundations of Mathematics
• History of Mathematics
• Information Theory
• Linear Algebra and Geometry
• Mathematical Methods
• Numerical Analysis
• Number Theory
• Precalculus
• Probability

Real and Complex Analysis

Abstract algebra books, contemporary abstract algebra.

by Joseph Gallian

by David S. Dummit and Richard M. Foote

Algorithms Books

Introduction to algorithms, third edition.

by Thomas H. Cormen, Charles E. Leiserson and Ronald L. Rivest

The Art of Computer Programming, Volumes 1-3 Boxed Set

by Donald E. Knuth

Calculus Helpers Books

The calculus lifesaver: all the tools you need to excel at calculus.

by Adrian Banner

Calculus Made Easy

by Silvanus P. Thompson

Calculus I Books

Calculus, vol. 1.

by Tom M. Apostol

by Michael Spivak

Calculus II/III Books

Calculus, vol. 2, calculus on manifolds, coffee table math books, mathematicians: an outer view of the inner world.

by Mariana Cook

Sacred Mathematics: Japanese Temple Geometry

by Fukagawa Hidetoshi and Tony Rothman

Combinatorics Books

Principles and techniques in combinatorics.

by Chen Chuan-Chong and Koh Khee-Meng

Combinatorics and Graph Theory (2nd edition)

by John Harris, Jeffry L. Hirst, and Michael Mossinghoff

Differential Equations Books

Differential equations and their applications.

by Martin Braun

Encyclopedias of Mathematics Books

The princeton companion to mathematics.

by Timothy Gowers, June Barrow-Green and Imre Leader (Editors)

Encyclopedia of Mathematics

by James Stuart Tanton

Foundations of Mathematics Books

A mathematical introduction to logic, second edition.

by Herbert Enderton

Classic Set Theory for Guided Independent Study

by Derek C. Goldrei

Categories for the Working Mathematician

by Saunders Mac Lane

History of Mathematics Books

Mathematics: from the birth of numbers.

by Jan Gullberg

What Is Mathematics? An Elementary Approach to Ideas and Methods

by Richard Courant and Herbert Robbins

Mathematics and its History

by John Stillwell

Information Theory Books

Computational science and engineering.

by Gilbert Strang

Information Science

by David G. Luenberger

Introduction to Coding and Information Theory

by Steve Roman

Linear Algebra and Geometry Books

Linear algebra done right.

by Sheldon Axler

The Four Pillars of Geometry

Mathematical methods books, mathematical methods: for students of physics and related fields.

by Sadri Hassani

Mathematical Methods in the Physical Sciences

by Mary L. Boas

Number Theory Books

Elementary number theory.

by Gareth A. Jones and Josephine M. Jones

An Invitation to Modern Number Theory

by Steven J. Miller and Ramin Takloo-Bighash

An Introduction to the Theory of Numbers

by G. H. Hardy, Edward M. Wright and Andrew Wiles

Numerical Analysis Books

Numerical analysis with cd-rom.

by Timothy Sauer

Numerical Recipes 3rd Edition: The Art of Scientific Computing

by William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery

Precalculus Books

Precalculus mathematics in a nutshell: geometry, algebra, trigonometry.

by George F. Simmons

Basic Mathematics

by Serge Lang

Probability Books

Introduction to probability models, tenth edition.

by Sheldon M. Ross

An Introduction to Probability Theory and Its Applications

by William Feller

Probability Theory: The Logic of Science

by E.T Jaynes

Fifty Challenging Problems in Probability with Solutions

by Frederick Monsteller

Real and Complex Analysis Books

Principles of mathematical analysis, third edition.

by Walter Rudin

Real Analysis

by N.L Carothers

A First Course in Complex Analysis With Applications

by Dennis Zill and Patrick Shanahan

Visual Complex Analysis

by Tristan Needham

Statistics Books

Statistics in plain english, third edition.

by Timothy C. Urdan

Review : Just as the title implies, the author has submitted an unequivocal and palpable exposition on statistics. Statistics in Plain English is regarded by many as the most appropriate statistics primer for undergraduates. Urdan has managed to compress everything one needs to know about statistics into a compact 250 page book that doesn’t feel hurried or unfulfilling. The text is general enough to be used in a variety of mathematical areas yet retains its comprehensiveness and accuracy. Urdan masterfully moves through essential concepts without losing the reader the way many professors would. Students harboring apprehension towards statistics will tremendously enjoy this book. More info .

Introductory Statistics

by Neil A. Weiss

Statistics, 4th Edition

by David Freedman, Robert Pisani and Roger Purves

Topology Books

Introduction to topology and modern analysis, introduction to topology: third edition.

by Bert Mendelson

Feel free to get in touch if you think the list is really missing out by not listing a specific book. If you are a publisher and feel that we’re missing a great book of yours, drop us a line. Please understand that we recommend only what we consider to be the best books on the market today. No exceptions.

Disclaimer : Here at MathBlog.com we believe in full disclosure. The links to Amazon.com have our referral id which earns us a tiny commission every time you buy from these links. Think of it as a tip that won’t cost you a cent, to reward us for our time investment. We appreciate your support.

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7 Honest Homeschool Math Curriculum Reviews

July 11, 2016 by Susan 9 Comments

This post may contain affiliate links.  See my disclosure for more information.

The ultimate review collection.  Reviews of all of the math curriculum we’ve tried over 10 years of homeschooling.  What worked & what we really wanted to work but just didn’t…pros, cons, hits, misses.

When we started homeschooling, the one thing my kids asked was that we not use Saxon Math curriculum.  The charter school they had attended used it and it was not their favorite.

Let me say clearly…I know lots of homeschool families that use and LOVE Saxon.  It’s just not a good fit for us.

One of the very best things about homeschooling is that you can pick and choose what will work for your family.  And if something doesn’t work… you can try something else!

Math Curriculum

With math, we have used a number of different curriculums (I know “curricula” is the correct plural, but it sounds funny, so I don’t say it).

When I was looking for things to try, I loved reading about other people’s experiences.  So today, I thought I’d share ours.  Each one of these had pros and cons , things we liked and things we didn’t.  You can click on the images to read more about each curriculum.

Teaching Textbooks

There is a lot to like about Teaching Textbooks.  It is engaging and the fact that it is self-grading is so convenient!  It was our experience, like others I’ve read, that the levels seem to be about one grade level behind other programs.  For example, Math 6 we found to be more appropriate for a 4 th or 5 th grader.  The website has placement tests , though, so there’s not too much guesswork in knowing which level to order.

(My buying tip is to check used curriculum sales, craigslist, and ebay first.  When you get a used copy , you need to contact the company and they will give you a new user code.  Easy peasy, and way cheaper!  Just make sure you check if what you’re buying is self-grading.  The first versions of the upper level courses are not, but they’ve come out with “2.0” versions that are.)

Teaching Textbooks was my younger son’s math curriculum of choice up through Algebra .  He completed Algebra 1, though not terribly successfully .

It was a difficult math year for us.

Teaching Textbooks teaches Algebra in a way that is different from the way I learned it, and the way many other curriculums present it.  This made it difficult for me to come alongside and help him with his work when he struggled.  I made the decision to switch to a new math curriculum the following year.  We had several good years with this, and I would definitely recommend it up through Pre-Algebra without hesitation.

Life of Fred

Because I always felt that Teaching Textbooks was a little on the easy side, I instituted “Second Math” for my son that was using it.

“Second Math” was Life of Fred.  We used Fractions, Decimals & Percents, and Pre-Algebra (with Biology).  We loved them!

I won’t argue with anyone who chooses to use Life of Fred as your sole math curriculum.  But for us, it was a perfect supplement .

Note:  When we were doing Geometry a couple of years ago I picked up Life of Fred Geometry as a supplement, thinking it would be a nice help.  Not so much.  Much like Teaching Textbooks presented Algebra in a different way, Life of Fred teaches Geometry in a very different way than our core curriculum, so we didn’t end up using it much.

While I haven’t used the newer, elementary books , I know several people who use them and love them.  What I’ve seen in flipping through them is impressive.  If you have a child that likes to read, thinks ‘outside the box’, or just wants to try math in a different way, I would definitely give these a try.

“Key To…” Series

Later, we used Key to Algebra  as our Pre-Algebra/ introduction to Algebra.

I love the format of these booklets.  For kids that may get overwhelmed by a giant math textbook, they are easily digestible .

There are so many problems, that it’s a great resource to pick and choose what you want to do.  I would often review a topic with him, and then tell him to choose 3 problems from the page to do.  If he got them right, I knew he understood the concept and we moved on.  Feeling like he was getting to “skip” a bunch of math was encouraging and made for less stressful math sessions.

My biggest piece of advice with these is to not write in the booklets.  Use a notebook.  I use these frequently when I tutor kids that struggle with math.  These are such a great resource !

RightStart Geometry

My eldest is very hands on and so, when looking at math curriculum, I was drawn to RightStart Geometry.  It’s a middle school curriculum that is very concrete .

Much of the work is done with a drawing board.  Instead of just looking at figures and doing problems, students are creating the figures.

This was a low-pressure math year for us, which was great!  I’d recommend it for middle-school for sure, especially for students who don’t love math.  I wouldn’t say it’s especially rigorous.  But for a middle school curriculum, after students have mastered basic arithmetic but maybe aren’t quite ready for Algebra 1, this was a great filler year.  And it was by no means fluff.  Thumbs up!

No-Nonsense Algebra

It is small for a textbook, which I liked.  It presents each topic in a very straightforward manner on just a page or two.  Each lesson presents a single topic, gives examples, plenty of practice problems, and a few problems for review.

And the best thing is…you get a code to log in and watch a video lesson for each lesson in the book!  It’s an amazing value!

I really love this curriculum.

Ask Dr. Callahan & Jacobs Geometry

My boys both used this and I would definitely recommend it for someone looking for a textbook-based course.

The Ask Dr. Callahan video series teaches with short lessons , which the boys liked ok.  And I liked that the program didn’t have them working all of the problems in the textbook.

I also really appreciated the time that the publisher takes in answering questions via email.  After a difficult year with Algebra 1 with my youngest, I was unsure about diving right in to Geometry.  I sent an email asking if we should consider purchasing their Algebra 1 course before going on to Geometry.  I received a quick reply suggesting that we go ahead with Geometry, as the course has quite a bit of Algebra review in it.  I found this impressive, as they could’ve told me to order the other course just to make more profit off of me.  (And he was right, the review in the course was sufficient.)

The only complaint I would have is that the tests, although taken from the book, are not always representative of what students have covered in the chapters.

After a few poor test grades, and my kids complaining that they weren’t being tested on what they’d studied, I ended up going through and previewing the test questions and changing them up a bit.  I still pulled questions from the chapters, but chose different problems to substitute.

Time 4 Learning Algebra 2

I wish I could say that this was a smashing success as well, but I can’t.  And I so wanted it to be.  We used the Time 4 Learning platform for my youngest’s math this past year for Algebra 2 . We had several issues that made it something I can’t recommend.

First, my son repeatedly scored poorly on the assessments .  When we’d talk about it, here’s how he described what he felt was going on:   “It’s like they teach you to spell c-a-t …and then test you on how to spell ‘encyclopedia’.”   He got very frustrated after thinking he understood a lesson, only to go to the assessment problems and not have a clue what they expected.  After running this by our math tutor , she agreed.

Another thing that gave me pause was that our tutor found errors in the answer key on at least 3 occasions.  I get human error, but I don’t think we’ve experienced this much error in any other math curriculum we’ve used.  The final element that was difficult was the over the top corniness of many of the lessons.  A little corny is cute… a lot is wearying and a real turn off.

I will say that the customer service is fantastic.  They were always quick and helpful in responding to any questions I had.  Like I said, I really wanted this to work.  It just wasn’t a good fit for us.

My eldest had a statistics class through his dual enrollment at a local community college this year and was thrilled that, barring any changes in his plans, he is done with math classes forever.  (That was a real motivation when trudging through the course!)

My plans for my younger son for this upcoming year include working to prepare for the College Mathematics CLEP test.  I’m using the REA Study Guide as a foundation for planning.  My niece will tutor him again.

I’ll let you know how it goes.

Update:  We found THE BEST math curriculum for Algebra 2 and ended up doing that CLEP test instead.  Oh how I wish we’d have found this curriculum sooner!

I think if we’d have discovered Mr. D Math to begin with, this post would have been a lot shorter!  You can read my full review or go straight to the Mr. D site to check it out for yourself.

You know, I knew this before, but have really become firm in my belief that everyone will have different experiences with curriculum.  That’s probably why I like to read so many reviews before deciding on something.

Another thing that I firmly hold to is that one of the best things about homeschooling is the ability to find what works for your child…even if that means some hits and misses along the way.

Check out our path to finding the best history curriculum here (thankfully we found our fave with less misses this time!)

Click here to read more homeschool curriculum reviews.

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August 4, 2016 at 3:01 pm

Great insight into those 7 math curriculums.

August 4, 2016 at 3:11 pm

Thanks, Erin. I know I relied heavily on others’ reviews when looking at curriculum, just trying to pay it forward.

August 5, 2019 at 10:19 am

I was wondering, since you love No Nonsense Math for Algebra 1 so much, did you go on to use No Nonsense Math for Algebra 2 or Geometry or beyond? We have used Teaching Textbooks 3rd grade – Algebra 1, but I have been hearing more and more about how it is below par for HS math and have been researching other options.

August 6, 2019 at 8:56 am

Unfortunately, No Nonsense Algebra 1 is a stand alone book, not part of a larger curriculum. If it was…yes, we’d have used it! (You got me excited there for a second to think that they had come out with books of No Nonsense Math for those upper courses, and I hopped over to Amazon to look for them 🙂 ) And my issue with Teaching Textbooks wasn’t so much that it was below par but that they taught the skills in such a different and confusing way that not only did my son not understand them, but I was unable to help him much because I didn’t understand their methods. I’m telling you…if I were doing it again, I’d use Mr. D math from Pre-Algebra on. Hands down.

March 26, 2020 at 9:18 am

My son has been using Mr D this year for Algebra 1 and it’s been a nightmare! Will not use it again. Very disappointed especially with the cost! Ridiculous!

March 31, 2020 at 10:32 am

I’m so sad it isn’t working for you. I’d love to know what you guys don’t like about it.

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Textbooks: Do we know which ones are effective?

Ze’ev Wurman

September 28, 2022, 10 comments.

Wouldn’t it be nice if all teachers had verifiably excellent instructional materials at their disposal and if every school and school district had a reliable guide as to which instructional materials are effective, before adopting — and paying for — such?

Clearly, it would be nice. And it might actually help improve children’s education — were such labeling true and based on evidence. Yet the people who brought you the mediocre Common Core are now engaged in convincing everyone that textbooks, simply by virtue of being aligned with Common Core, are necessarily also “high quality” and “effective.” They do it without any empirical evidence of them actually being of high quality or effective, while disparaging the quality and effectiveness of textbooks that were proven as truly effective by successful widespread use.

Before 2010, when every state had its own educational standards, some states attempted to provide such guidance by reviewing and creating a list of approved textbooks from which schools and school districts were encouraged — and sometimes forced — to select. Other states left such decisions to schools and school districts. Neither system worked very well. Textbook publishers had significant financial sway over state and local selections, too often overriding the textbooks’ academic merit. Further, the review committees, particularly local ones, often lacked competent content reviewers and input from parents. Publishers added to the confusion by having multiple versions of essentially identical textbooks customized in a minor way for different states. All in all, not a very good situation, even though some highly effective, even if not fashionable, textbooks such as Saxon Math ,  Singapore Math , or Open Court Reading managed to survive.

The situation has changed since the adoption in 2010 of Common Core standards by almost all of the country. Now most states have kind-of the same standards so, suddenly, rather than competing with each other over each of the 50 states, textbook publishers could focus on competing at a single national level.

In theory this could have been a boon for improving the quality of textbooks and other instructional material. After all, there are only so many textbooks on the market addressing essentially the same educational standards — Common Core — so seriously reviewing them all should have been doable.

And, indeed, an organization called EdReports was established in 2014 to do precisely that: review textbooks. EdReports is a nonprofit, a major chunk of whose support comes from key promoters of the original Common Core. EdReports is dedicated to reviewing the alignment of textbooks with Common Core, yet its ratings are based only on “paper review,” not on any studies of the textbooks’ actual effectiveness.

Then, in 2017, the Council of Chief State School Officers ( CCSSO ), the originator of Common Core, established the High-Quality Instructional Materials and Professional Development ( IMPD ) Network dedicated to promoting materials rated well by EdReports as “High Quality” to member states. The key financing of this effort has been by the Bill and Melinda Gates Foundation, which funded its creation, and promoters that lend it credibility, such as the Fordham Institute.

All this would be fine if the Common Core standards were actually improving American education. But the standards are mediocre at best , and they have caused a clear deterioration of American student achievement in math and reading as visible on the 2017 and 2019 National Assessment of Educational Progress, or NAEP — the first declines in more than two decades. Here is what Education Department’s National Center for Education Statistics (NCES) had to say about the 2020 Long-Term Trend (LTT) NAEP, taken just weeks before the pandemic :

“The reading and mathematics scores of 13-year-old students fell between 2012 and 2020—the first time in the almost 50-year history of the National Assessment of Educational Progress (NAEP) long-term trend (LTT) assessment. …  The mathematics scores for the lower-performing students (students at the 10th and 25th percentile) declined among students from both [9 & 13] age groups from the previous assessment in 2012. Scores also declined in mathematics for 13-year-olds at the 50th percentile. Scores for higher-performing students (at the 75th and 90th percentiles) did not change. … Mathematics scores at age 9 declined for females but did not change significantly for males since 2012.”

If it was not bad enough that EdReports rates textbooks on how well they are aligned with mediocre academic standards, it also verifies that textbooks do not stray from the Common Core standards’ scope and sequence (e.g., move standards to different grades) or spend a significant amount of time on additional standards. In other words, much of EdReports “quality” is embodied in checking whether textbooks closely follow Common Core rather than whether they present meaningful math or effectively teach it.

Then the Instructional Materials Network elevates those evaluations and promotes them as “High Quality” to states without any research to back it up.

You can see this with Singapore Math, which gained its fame because of its proven efficacy as demonstrated in Singapore’s high achievement on international mathematics tests. Yet, of the five textbooks based on Singapore Math, four of them receive EdReports’ lowest possible score, and one gets the second worst . And sure enough, the effectiveness of the texts in teaching math is not even checked by EdReports, which prefers a narrow and formalistic evaluation of effectiveness rather than actual empirical evidence. Similarly, Open Court Reading, which was responsible for improving the reading skills for millions of early grade students in California is deemed not worthy of evaluating its usability by EdReports as it doesn’t align with Common Core standards.

Perhaps in the future when parents are given a significant voice in their children’s choice of schools, such maverick textbooks will have a chance. Meanwhile, the Council of Chief State School Officers peddles untested textbooks hewing to mediocre standards on our teachers, giving them fake “High Quality” seals of approval and eliminating the chance to penetrate the wall of mediocrity.

Ze’ev Wurman  is a research fellow at the Independent Institute , chief software architect with MonolithIC 3D, and former senior policy adviser with the Office of Planning, Evaluation and Policy Development at the U.S. Department of Education.

The opinions in this commentary are those of the author. If you would like to submit a commentary, please review our guidelines  and contact us.

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Phil Brubaker 11 months ago 11 months ago

I'm a retired Mathematical Engineer that has been attempting to Train Educators on Modeling, Simulations & (Mathematical) Optimizations. Optimizations require an Objective (function). Today's Engineers & Scientists solve problems with a “Find X” mind-set. With some Operational Research training they could expand their thinking to a “Find X to Optimize Y” mind-set. “Find X to Optimize Y” thinking among professors will cause most Engineering & Science textbooks to be rewritten with optimization examples … Read More

I’m a retired Mathematical Engineer that has been attempting to Train Educators on Modeling, Simulations & (Mathematical) Optimizations. Optimizations require an Objective (function). Today’s Engineers & Scientists solve problems with a “Find X” mind-set. With some Operational Research training they could expand their thinking to a “Find X to Optimize Y” mind-set.

“Find X to Optimize Y” thinking among professors will cause most Engineering & Science textbooks to be rewritten with optimization examples and discussions. This will be great stuff for industries and government; applied engineering and/or science; not just theories.

Today’s Math textbooks need to be replaced with 1950s or 60s textbooks that taught MATH that is used in industries today. Not some ‘new math’ concepts as done today; just old math concepts, terms, & logic.

How to get future authors and evaluation studies to realize that math understanding for future jobs is the main reason for math education, correct?

Phil Brubaker Oregon State University ’67 (Applied) Mathematician | Electrical Engineering | Author

Barry Garelick 2 years ago 2 years ago

Excellent points. Many people think that a high rating from Ed Reports means the textbook is effective. Alignment with the Common Core standards is not a measure of effectiveness. In terms of Singapore Math, they got dinged because the standard algorithm for multidigit addition and subtraction was "assessed" in the textbook prior to 4th grade in which the standard appears. CC does not prohibit teaching the standard algorithms earlier than the grade in which they appear, … Read More

Excellent points. Many people think that a high rating from Ed Reports means the textbook is effective. Alignment with the Common Core standards is not a measure of effectiveness.

In terms of Singapore Math, they got dinged because the standard algorithm for multidigit addition and subtraction was “assessed” in the textbook prior to 4th grade in which the standard appears. CC does not prohibit teaching the standard algorithms earlier than the grade in which they appear, but the publishing guidelines prohibit the testing (i.e. “assessment”) of same in grades prior to when the std algorithm appears in CC. Note, it’s the publishing guidelines, not the CC standards themselves.

Dave G. 2 years ago 2 years ago

Let the teacher decide!

Cathy Kessel 2 years ago 2 years ago

The reference for “mediocre” is a report dated December 2017. Here are some examples of what it has to say about the Common Core standards for mathematics. Standard 1.OA.6 is criticized for its “long list of different ways of doing the operations.” In 2013, I examined a similar criticism from the same author, noting that the "different ways" appear as headings and objectives in Singapore Primary Mathematics 1A, Teacher’s Guide for the first half of grade … Read More

The reference for “mediocre” is a report dated December 2017. Here are some examples of what it has to say about the Common Core standards for mathematics.

Standard 1.OA.6 is criticized for its “long list of different ways of doing the operations.” In 2013, I examined a similar criticism from the same author, noting that the “different ways” appear as headings and objectives in Singapore Primary Mathematics 1A, Teacher’s Guide for the first half of grade 1. See comments-on-milgrams-review-of-final-draft-core-standards.

Other criticisms mention two poorly written problems which were not part of the CCSS.

The report also claims that “[4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm] is fully two to three years behind what is expected from students in high-achieving countries” and gives addition and subtraction examples that include 4- and 5-digit whole numbers from a translation of a grade 3 Russian textbook originally published in 1978 by Pcholko, Bantova, Moro, and Pyshkalo.

In contrast, the 2007 Singapore Syllabus says for grade 2 “Include: addition and subtraction of numbers up to 3 digits.” For grade 3, it says “Include: addition and subtraction of numbers up to 4 digits.” It doesn’t say anything further about whole-number addition and subtraction in grade 4, but it does include “addition and subtraction of decimals (up to 2 decimal places).” The 2012 Singapore Syllabus has similar expectations, see pp. 37, 42, 50 of the syllabus, which is here: https://www.moe.gov.sg/primary/curriculum/syllabus . (There is a new syllabus for the 2021 cohort but it doesn’t have entries beyond grade 2.)

The reference for “mediocre at best” is a report dated February 2010. The CCSS were released in June 2010: http://www.corestandards.org/about-the-standards/development-process/

Ze'ev Wurman 2 years ago 2 years ago

Cathy Kessel is correct in that one of the references for the mediocrity of Common Core I quoted is from February of 2010, while the final version of Common Core was released only in June of 2010. So here is a report with similar finding on the final Common Core version, published in July 2010. https://pioneerinstitute.org/download/national-standards-still-dont-make-the-grade/ Kessel also finds an issue with the other paper I quoted, which argues Common Core "is fully two to three years … Read More

Cathy Kessel is correct in that one of the references for the mediocrity of Common Core I quoted is from February of 2010, while the final version of Common Core was released only in June of 2010. So here is a report with similar finding on the final Common Core version, published in July 2010.

https://pioneerinstitute.org/download/national-standards-still-dont-make-the-grade/

Kessel also finds an issue with the other paper I quoted, which argues Common Core “is fully two to three years behind what is expected from students in high-achieving countries” and demonstrates that when it comes to integer addition, it is “only” one year behind. There are other standards and expectations where Common Core is more behind but, eventually, all this is now moot, when we have actual empirical evidence of Common Core mediocrity.

On PISA international comparison, US declined between 2009 and 2018 by 9 points (from 487 to 478). On long-term NAEP our age 9 student declined 9 points (almost a grade level) between 2008 and 2019. And the C-SAIL report is the clincher, where the researchers embarked to find Common Core superiority and instead found that:

“Our study revealed that the adoption of the new college- and career-ready standards had significant negative effects in grade 4 reading. Specifically, our analysis suggests that had the “treatment” states stuck with their prior standards, their grade 4 NAEP reading scores would have been 2.3 to 3.8 points higher on the 0-500 NAEP scale during the seven years after the adoption of the new standards. We also found a significant negative seven-year impact on grade 8 mathematics. While most of our results were statistically non-significant, they tended to be in the negative direction.”

https://www.the74million.org/article/song-did-common-core-standards-work-new-study-finds-small-but-disturbing-negative-impacts-on-students-academic-achievement/

Re "demonstrates that when it comes to integer addition, it is “only” one year behind”: Does “Include: addition and subtraction of numbers up to 4 digits” mean “fluency with addition and subtraction of numbers up to 4 digits using a standard algorithm”? I don’t see anything in the Singapore teacher’s guides that says so. Also, note that grade 3 addition and subtraction expectations for Russia (then USSR) and for Singapore differ: one includes 5-digit numbers, … Read More

Re “demonstrates that when it comes to integer addition, it is “only” one year behind”: Does “Include: addition and subtraction of numbers up to 4 digits” mean “fluency with addition and subtraction of numbers up to 4 digits using a standard algorithm”? I don’t see anything in the Singapore teacher’s guides that says so. Also, note that grade 3 addition and subtraction expectations for Russia (then USSR) and for Singapore differ: one includes 5-digit numbers, the other does not. I believe this discrepancy may be due to an error in the 2017 “mediocrity” report’s account of Russian mathematics education history, and will link an account of details here: https://mathedck.wordpress.com/2013/08/04/comments-on-milgrams-review-of-final-draft-core-standards/ .

On the page about the C-SAIL “report” (“Effects of states’ adoption of college- and career-ready standards on student achievement”), the reader is told that it was a working paper (that is, not peer reviewed). I write “was” because the link for the paper is dead. There is a more recent peer-reviewed article with a somewhat similar name (“Did States’ Adoption of More Rigorous Standards Lead to Improved Student Achievement? Evidence From a Comparative Interrupted Time Series Study of Standards-Based Reform”), somewhat different conclusions, and two of the same authors. Its abstract says:

“This study was designed to assess the effects of states’ adoption of more rigorous standards as part of the current wave of standards-based reform on student achievement using comparative interrupted time series analyses based on state-level NAEP data from 1990 to 2017. Results show that the effects of adopting more rigorous standards on students’ mathematics achievement were generally small and not significant. The effects on students’ reading achievement were also generally small, but negative and statistically significant for Grade 4. The study also revealed that the effects of states’ adoption of more rigorous standards varied across NAEP subscales and student subgroups.” https://journals.sagepub.com/doi/abs/10.3102/00028312211058460

Similarly, there were mixed results when, years ago, the Singapore books were used at four US sites. Here is an excerpt from the report (which was published in 2005 by AIR, the American Institutes for Research):

“The Montgomery County [Maryland] outcomes were positively correlated with the amount of professional training the staff received. Two Singapore pilot schools availed themselves of extensive professional development and outperformed the controls; two other pilot schools had low staff commitment coupled with low exposure to professional training and were actually outperformed by the controls. Professional training is important in helping teachers understand and explain the nonroutine, multistep problems in the Singapore textbooks. Teachers also need preparation to explain solutions to Singapore problems, which often require students to draw on previously taught mathematics topics, which the Singapore textbook, in contrast to U.S. textbooks, does not reteach.” https://www.air.org/resource/report/what-united-states-can-learn-singapores-world-class-mathematics-system-exploratory

After noting the variability in test site outcomes, the AIR report says: “our study shifted from merely assessing the results from the U.S. textbook pilots to developing a broad comparison of the coherence and quality of the Singapore and U.S. systems for delivering mathematics instruction.” For example, it notes “Singapore’s teachers must take a stringent examination before being accepted to education school, and while they are students, they are paid a teacher’s salary.”

Also, “Singapore’s professional development program offers sustained learning opportunities through a modularized approach that adjusts to teachers’ learning needs and is integrated into a continual learning process that includes experiential training experiences in nonschool settings. In contrast, professional training in U.S. school systems focuses on short-term workshops that fit into teachers’ released time. Evaluations suggest that these experiences are not likely to improve teachers’ performance in mathematics; the teachers themselves agree and do not seem to value this training very much.”

A recent PD example from Singapore: https://www.science.edu.sg/for-schools/teacher-professional-development/teacher-work-attachment . A recent PD example from the US: https://edsource.org/2022/we-need-to-fix-professional-development-for-teachers/678632

As with the AIR study, the mixed results of the C-SAIL study may have prompted more focus on the US educational system, rather than a single component of the system. The Center on Standards, Alignment, Instruction, and Learning (C-SAIL) conference in 2020 was on “What’s next for standards-based reform? With the release of the 2019 National Assessment of Educational Progress results in math and reading, it became clear that standards-based reform has not moved the needle on student achievement. This may be due, in part, to how districts, schools, and teachers are making sense of and implementing college- and career-readiness standards.” https://www.c-sail.org/videos

Transforming expectations (such as standards) into instruction is no easy matter—as shown by three decades of standard-based reform. “We failed to prioritize the hard work of translating standards into rigorous curriculum materials, instructional strategies and teacher training,” says a recent essay ( https://www.future-ed.org/unfinished-agenda-the-future-of-standards-based-school-reform/ ).

Cathy Kessel and I could continue this back-and-forth for a long time, yet a few facts are indisputable: The key ones are that the regular (Main) NAEP results started to level off and drop since the 2017 NAEP, after decades where they consistently grew. Similarly, the results for Long-Term (LTT) NAEP dropped for the first time between 2008 and 2019. PISA results, particularly in math, did the same for US students. US TIMSS achievement increased by 22 (!) points … Read More

Cathy Kessel and I could continue this back-and-forth for a long time, yet a few facts are indisputable:

The key ones are that the regular (Main) NAEP results started to level off and drop since the 2017 NAEP, after decades where they consistently grew.

Similarly, the results for Long-Term (LTT) NAEP dropped for the first time between 2008 and 2019.

PISA results, particularly in math, did the same for US students.

US TIMSS achievement increased by 22 (!) points between 1995 and 2015, yet *dropped* by by 4 points between 2015 and 2019.

All this occurred *before* the pandemic but after Common Core adoption.

Kessel is correct when she quotes “Transforming expectations (such as standards) into instruction is no easy matter – as shown by three decades of standard-based reform,” particularly in systems similar to ours where teachers are often encouraged not to follow recommendations based on robust research “invent” curricula and pedagogies on-the-fly behind their closed doors. Yet such consistent *national* (as opposed to local and regional) results across multiple national and international tests, of actual *decreases* in achievement since Common Core entered the mainstream of our classrooms, cannot be “explained” away as just “complexities of implementation,” as Kessel attempts.

There are many other issues with Kessel’s attempts to show that standards like Singapore’s or other high achieving countries are “similar” to Common Core, but this is inside baseball to most so I will not engage in it here.

People concerned about children’s education might appreciate clarification of claims about high-achieving countries. The 2017 “mediocrity” report Wurman cites says “[Common Core 4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm] is fully two to three years behind what is expected from students in high-achieving countries” (page 16, https://pioneerinstitute.org/pioneer-research/academic-standards-pioneer-research/mediocrity-2-0-massachusetts-rebrands-common-core-ela-and-math/). In contrast, Wurman is a co-author of a 2020 report that says “MA.3.NSO.2.1 Add and subtract multi-digit whole numbers including using a standard … Read More

People concerned about children’s education might appreciate clarification of claims about high-achieving countries.

The 2017 “mediocrity” report Wurman cites says “[Common Core 4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm] is fully two to three years behind what is expected from students in high-achieving countries” (page 16, https://pioneerinstitute.org/pioneer-research/academic-standards-pioneer-research/mediocrity-2-0-massachusetts-rebrands-common-core-ela-and-math/ ).

In contrast, Wurman is a co-author of a 2020 report that says “MA.3.NSO.2.1 Add and subtract multi-digit whole numbers including using a standard algorithm with procedural fluency” is “exemplary” (page 2, Better Than Common Core, https://www.independent.org/publications/article.asp?id=13176 ).

Perhaps a future Independent Institute report will explain this apparent contradiction.

NAEP results: As a commenter has pointed out, Minnesota did not adopt Common Core. Its grade 8 NAEP scores follow the national pattern.

https://nces.ed.gov/nationsreportcard/subject/publications/stt2019/pdf/2020013MN8.pdf

Despite the predictions of the “mediocrity” report (full title is Mediocrity 2.0: Massachusetts rebrands Common Core ELA & Math), grade 8 NAEP scores in Massachusetts were higher than Minnesota’s:

https://nces.ed.gov/nationsreportcard/subject/publications/stt2019/pdf/2020013MA8.pdf

One author has suggested that state investment in teachers is an important part of the explanation:

“Even more relevant for us is the experience of Massachusetts, which in the early 1990s had mathematics achievement that was fairly typical of the US, but which decided that that was not good enough, and embarked on a long-term effort to improve. The Massachusetts Education Reform Act of 1993 provided for increased funding to make opportunities to learn more equitable, substantial professional development, and higher mathematics requirements for teacher certification (thus impacting teacher preparation programs) [6]. It worked. Massachusetts now, considered as a separate country, has test scores significantly above the US average [20], [16], [11], [7]. Massachusetts also comes out at the top in the National Assessment of Educational Progress (NAEP), the US’s own instrument for assessing student achievement. For example, in the 2019 edition of NAEP, Massachusetts eighth-graders had the highest overall average of any state, and perhaps more significantly, 48% of them scored at the proficient or advanced level [12]. Only two other states had over 40% at these levels. The rest of the country should take some lessons.”

For references and the rest of the article, see https://www.ams.org/notices/202006/rnoti-p842.pdf .

Bruce William Smith 2 years ago 2 years ago

Minnesota was wise to reject the Common Core mathematical standards while accepting those for English; One World Education Centre has long done the same. We use the Singapore mathematics textbooks in use in Singapore, rather than those being marketed as such in the United States, and our students consistently score in the 99th percentile on American math tests like the SAT and ACT, and on the exams for AP Calculus.

Linda Diamond 2 years ago 2 years ago

This article is spot on. Ze'ev got it right. Not only is the Common Core dated, it's relationship to what we know from evidence is necessary to learn to read is tenuous at best. In fact, many excellent proven ELA programs and foundational skills curricula do not even bother submitting because although they have proven results, they know they will not fit the Common Core criteria. As Louisa Moats pointed out, the CCSS was weak … Read More

This article is spot on. Ze’ev got it right. Not only is the Common Core dated, it’s relationship to what we know from evidence is necessary to learn to read is tenuous at best. In fact, many excellent proven ELA programs and foundational skills curricula do not even bother submitting because although they have proven results, they know they will not fit the Common Core criteria. As Louisa Moats pointed out, the CCSS was weak from the start on word recognition and writing and spelling. Thank you Ze’ev!

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Textbook recommendations for self-studying high school math?

I'm a high school student who is trying to figure out a complete course of self-study for each year of high school. How can I self-learn grades of math without devoting too much time? This is a complex issue for me, as other students at my competitive high school have tutors and the like. Please recommend textbooks that have detailed explanations and progressive practice problems, for self-study for each area such as:

Trigonometry and Analytic Algebra

Pre-calculus

BC Calculus

Other people have skipped grades of math due to help from tutors and parents. Can I cover all of geometry and trigonometry in 8 months without going insane and be able to skip a grade?

• reference-request
• soft-question
• book-recommendation

• 2 $\begingroup$ Tutor teach nothing other than what's stated in books. But the way of teaching may be different. But i have seen people excelling classes without instructor especially at maths unlike any other subject. $\endgroup$ –  BigSack Commented Aug 25, 2012 at 6:30
• $\begingroup$ Check this question out! math.stackexchange.com/questions/69060/… $\endgroup$ –  Aditya M P Commented Sep 30, 2013 at 9:10
• 2 $\begingroup$ Possible duplicate of Recommend books for learning math from elementary school? $\endgroup$ –  user53259 Commented May 28, 2018 at 4:24

7 Answers 7

If you master pre-algebra, then you can figure out almost any other branch of mathematics using the appropriate study material. Geometric formulas will be second nature to you. Trigonometry and Calculus are not required to graduate from every high school. If you are strong in Algebra, then your college placements scores will exempt you from college preparatory courses.

College preparatory courses are great if you want to master the fundamentals. I suggest you take all the college preparatory courses in your field if you are going to specialize. For Mathematics, you should take discrete mathematics.

Because of the way the brain works, you will gain better dominion of subject matter by studying for a few hours everyday rather than cramming. Yet, you seem to have found out how some high school experiences are less adequate than independent studies.

You might want to go for the General Education Development test, then transfer to a college or university. A community college offers more advantages for students. You can get an associates in arts degree and transfer to a university from there to get a four-year college degree and postgraduate degrees. (You will need to pass college algebra and another college level mathematics course to get your associate in arts degree.)

Have you ever skimmed or read from a GED preparation workbook? You should go a college library and take it out. It's similar to the SAT workbooks. These books will give you detailed explanations. Yet, what do you mean by progressive practice problems? The word progressive can have many meanings; do you mean updated versions? That's up to the student to send in suggestions and report errors to the publishing company.

Remember, it's what you learn that counts. Most things we believe to be requisites are psychological exaggerations. Remember, being a student is a profession.

You probably won't find one book that covers everything, but in all honesty if you're a good math student you could probably skip through trigonometry with ease. I'd recommend Algebra Demystified and Trigonometry Demystified . They have a good amount of practice questions, and go through the motivations of the topics involved (especially in trigonometry). You could also find more than enough around the internet, say through Khan Academy which has plenty of videos and more importantly a decent practice section.

While I'm not sure what the curriculum is where you are, in my high school we did:

Grade 9: Cartesian coordinates and linear equations

Grade 10: Quadratic Equations (factoring, expanding, completing the square and the quadratic formula) and basic trigonometry (working with definitions of $\sin$, $\cos$ and $\tan$).

Grade 11: Functions, factoring higher-degree polynomials, proving trigonometric identities, shifting/stretching functions, graphs of trig functions.

Grade 12: More functions, inverses, exponentials and logarithms, inverse trig functions, secant,cosecant and cotangent functions, how to divide polynomials the long way and with synthetic division, the remainder theorem and rational root theorem.

I don't think that's quite everything, but it's more than enough. Stroll through google books (you can see quite a bit of the books on there, including whole sections and practice problems) and the internet at large if you want more. Also see this wonderful list of legitimately free textbooks and/or course notes .

I have created some autocorrected online exercises in Mathematics that you could use as supplemental material.

I have also started an online index to the fourth edition of James Stewart’s Calculus textbook, as a subset of “ Mike’s Ready Reference ”. My online index is much more detailed than that of the textbook itself.

• $\begingroup$ Your first link is dead. The second has nothing to do with math? $\endgroup$ –  user851668 Commented Jul 2, 2021 at 6:41

The books Stewart's pre-calculus, mathematical Ideas and Stewart's calculus contain all of the material that is assumed to be needed to enter college and more. I used all of those during elementary and high school.

However I also recommend that you go to practice contest type questions because they are good for learning some problem solving and they can be very fun.

Have a go at the book Mathematical omnibus. Thirty lectures on classic mathematics by Dmitry Fuchs and Sergei Tabachnikov. This book will engage your mind and point you to very interesting mathematics.

Another good book to try out is this one: Vladimir Arnold: Problems for children from 5 to 15 .

Algebra: 1. Algebra for Beginners. 2. Elementary Algebra. 3. Higher Algebra. All three by by Hall and Knight.

You can check out the following books for "detailed explanations and progressive practice problems":

Schaum's Outline of Review of Elementary Mathematics

Schaum's Outline of Elementary Algebra

Schaum's Outline of Intermediate Algebra

Schaum's Outline of Geometry

Schaum's Outline of Trigonometry

Schaum's Outline of Precalculus

Do note that these books from the Schaum's Outline Series are not intended to replace traditional textbooks on the subject matter, but are meant as supplements. Personally, I have obtained the best-possible benefits from these books by reading some other introductory textbooks on the subject matter, supplementing my readings with further material from the Schaum's Outline Series books, and then trying to solve the practice problems afterwards.

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Basic Algebra with Applications - 6th Edition

Ivan G. Zaigralin, Arden-Arcade, California

Copyright Year: 2018

Publisher: Ivan G. Zaigralin

Language: English

Formats Available

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Learn more about reviews.

Reviewed by Perla Salazar, Associate Professor, Garden City Community College on 12/6/22

The textbook covers all concepts expected in a basic algebra textbook. The index/glossary is well organized and finding what you are looking for is very easy. All concepts are well explained and give good examples as well as homework problems. ... read more

Comprehensiveness rating: 4 see less

The textbook covers all concepts expected in a basic algebra textbook. The index/glossary is well organized and finding what you are looking for is very easy. All concepts are well explained and give good examples as well as homework problems. I would have liked that more methods for factoring quadratic trinomials were included. The only method explained in the textbook about factoring quadratic trinomials is the trial and error method.

Content Accuracy rating: 5

The content presented is accurate and well explained. The examples, definitions, and solutions are accurate.

Relevance/Longevity rating: 5

The content is relevant to the topics being covered. The examples and solutions are well chosen. Topics expected for an introduction to algebra are covered. This would be a good book for an intermediate algebra class or a review for college algebra class. I plan on using this book with my companion section for college algebra. The organization of the book makes it easy for instructors to update examples if needed.

Clarity rating: 5

The book is very clear. The definitions are followed with illustrative examples. Multiple examples and their solutions are provided for most topics.

Consistency rating: 5

The book is very consistent in its terminology and framework. The organization is easy to follow, topics are easy to find. Terminology is well defined and well illustrated by examples following the definitions.

Modularity rating: 5

The textbook is organized in chapters with smaller sections within each chapter. This textbook can be easily divided into small reading assignments.

Organization/Structure/Flow rating: 5

The content organization of the textbook is very good. There is a logical sequence of topics and ideas are grouped in a reasonable manner.

Interface rating: 5

I didn't encounter any interface issues. All images and charts were displayed well. The textbook navigation was easy and I could find what I needed fast.

Grammatical Errors rating: 5

I found no grammatical errors.

Cultural Relevance rating: 4

I didn't come across any words or examples that would be considered offensive. However, it could be a more inclusive textbook if people's names from multiple cultural backgrounds are added to the examples. All names currently used in examples can be perceived as being from one single cultural background.

This textbook does a good job at breaking down algebraic concepts to its basic parts. This textbook would be good for an intermediate algebra class or for a review class before college algebra. I plan on using this textbook to help my companion college algebra class review and fill in gaps of knowledge so they can be successful in college algebra. I wish the textbook covered more factoring methods, such as the ac method or the box method, but overall it has everything I was looking for in a college algebra review book.

Table of Contents

• Chapter 1. Concepts
• Chapter 2. Linear Equations
• Chapter 3. Graphing
• Chapter 4. Linear Systems
• Chapter 5. Polynomial Equations
• Chapter 6. Factoring Polynomials
• Chapter 7. Rational Expressions
• Chapter 8. Radicals
• Chapter 9. Quadratic Equations
• Appendix A. To Instructors
• Appendix B. To Developers

Ancillary Material

• Ivan G. Zaigralin

About the Book

Basic Algebra with Applications

About the Contributors

Ivan G. Zaigralin, Los Rios Community College District

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Teaching Textbooks: Math 3 through Pre-Calculus

When I first looked at Teaching Textbooks, I knew right away that this series was going to be popular among homeschoolers. These fantastic courses were designed specifically for homeschoolers in order to solve some of the issues that make math challenging for them. The courses are great for independent study since they are easy for students to use on their own, they require no work on the part of parents, and they are relatively inexpensive for sophisticated, computerized courses.

The Teaching Textbooks series is a college-prep curriculum even though it is not as rigorous as some other courses. The courses for the elementary grades move at a gentler pace than most others. Teaching Textbooks math levels are roughly equivalent to grade levels, but many find their students, especially more advanced ones, need one level higher than their grade level. Teaching Textbooks is self-paced, so students are able to move as quickly or as slowly as needed. Placement tests on the publisher’s website will help you select the correct level, and tables of content are available for each level on the website. Teaching Textbooks should be a good choice for the student who has struggled with other math programs and needs a less pressured pace and style of delivery.

Students should aim to complete approximately one lesson per day, and the courses each have about 120 lessons. That should leave you many days in the school year for extra work on troublesome concepts, “mathless” school days, or getting a head start on the next level.

The Teaching Textbooks courses have evolved over the years since they were first created, in keeping with technological advances. The courses are sold as apps rather than as physical products. While an internet connection is required, students can download up to six lessons at a time which can then be completed offline. This will make the courses usable even when good internet connections are lacking. The completed lessons sync up with the gradebook when students get back online.

The apps can be loaded onto desktops, laptops, tablets, and phones, although phones are probably not a good choice because of the screen size. Whatever device students use, they need headphones or a speaker to hear the lessons.

Only one student can use a course, and they have access for one year. Courses cannot be used by another student even if it is within the year. Large-family discounts are available.

All of the courses have a free trial that includes the first 15 lessons. There is no time limit on using the free trial, and you can try out multiple courses. If a student has started working in a trial course, if you purchase that course, the student’s data will be transferred into the complete course.

How It Works

Parents create a student account, then students can log in with their own password. The apps present lessons directly to the student with audio instruction, animated lessons, and frequent interaction. Parents do not need to do anything but keep tabs on student progress.

Explanations are clear and complete, with plenty of practical examples and word problems. Students are frequently asked to identify items, enter answers, solve puzzles, or otherwise respond to the lesson material during the instructional component of the lessons. They are given immediate feedback and opportunities to correct their responses. For incorrect answers on problems, students can view the readily available solutions.

The courses have a scratchpad feature so that students can work out problems on their device. But Teaching Textbooks recommends that most problems and solutions be written out with paper and pencil.

All answers are entered into the program, and it automatically maintains a running course average. So you can always tell how well students are doing. Daily emails are sent to parents to let them know what students have accomplished that day.

Students take a quiz approximately every seventh lesson, and the frequent quizzes continually review previously learned concepts.

A lighthearted touch gives the courses a user-friendly feeling. This is evident in everything from the program’s dashboard and the layout of the lesson screens to the cartoon animations and even the wording of the lessons. The basic screen designs are colorful, and students can add an animated buddy and a wallpaper background to personalize the display screen for the program. Students should have no problem figuring out what to do since the program is simple to navigate.

The courses have the complete textbook for that level built into the program as a searchable ebook. The ebooks include all of the instructional material and problems that are in the program, and you can print pages if you wish. (An answer key is also available within the program.) The ebook might be very useful for at least two reasons. First, parents can quickly scan the ebook to see what their child is learning or to get an idea of which topics are covered when. Secondly, printed pages can provide students with an easier format to work out the solutions to longer problems on paper. (Answers still need to be entered into the program to track student scores.)

The program’s built-in grade-book feature shows parents detailed information. You can see scores on lessons as well as information on how students handled individual problems, including whether or not the student viewed a hint or solution or tried to answer a second time. Parents can manage student accounts from any device.

Individual Course Details

Math 3 covers addition, subtraction, multiplication, division, fractions, money, time, geometry, and measurement, plus a final lesson that introduces percentages. Much of the addition and subtraction instruction reviews concepts that should have been learned at earlier levels since it begins with simple addition and very gradually builds toward carrying and borrowing (regrouping). Instruction on other topics also reteaches the basics before moving on to more advanced concepts. Multiplication covers up through single-digit multipliers, and division teaches through single-digit divisors. Fractions are taught up through adding and subtracting fractions with common denominators. Numerous word problems help students with mathematical thinking and practical applications.

Math 4 reviews concepts taught in Math 3 such as addition, subtraction, place value, carrying, and borrowing. It teaches new concepts such as rounding and estimating, multiplication, division, geometry, money, fractions, and Roman numerals. Reflecting the slower pace of Teaching Textbooks, concepts that generally appear earlier in other courses don’t show up till near the end of Math 4. Some examples would be multiplication by two-digit multipliers, long division, division with a remainder, and changing improper fractions to mixed numbers.

Math 5 again reviews the basics, with the early lessons heavily focused on addition, subtraction, and multiplication. Both fractions and decimals are covered extensively at this level.

Math 6 reviews the four basic arithmetic operations, place value, and time. It spends a great deal of time reviewing and teaching new concepts with fractions, decimals, and percents. It also covers geometry (points, lines, line segments, angles, area and perimeter for polygons, circumference for circles, and an introduction to geometric solids), units of measure (including the metric system), graphing concepts (e.g., thermometers, bar graphs, circle graphs), the order of operations, decimal remainders, equations, and probability. A remedial student with weak math skills might be able to pick up what he or she is missing since this course is fairly comprehensive on arithmetic basics. It might be too repetitive for a student who already has developed strong skills in basic operations. I mentioned earlier that the Teaching Textbooks series moves more slowly than many other programs, and it becomes more noticeable at this level.

Topics taught in Math 6 are briefly reviewed. Then each topic is tackled at a distinctly more challenging level. For example, fraction instruction moves on to ratios. Percents include work with fractions and decimals plus real-life applications like commissions and sales tax. And geometry gets into computing the volume of solids. Also taught this year are statistics, probability, graphing, equations, inequalities, exponents, square roots, the Pythagorean theorem, and negative numbers.

Pre-Algebra

Pre-Algebra begins by revisiting whole-number operations, fractions, decimals, percents, and measurements. The rest of the course covers beginning algebra, negative numbers, exponents, roots, plane and solid geometry, functions, relations, graphing, statistics, probability, formulas (e.g., rate x time = distance), solving equations using the distributive property, and absolute value.

Algebra 1 has more review of basic operations and pre-algebra concepts at the beginning than do some other first-year algebra courses, but it also has lessons covering functions, relations, statistics, probability, graphing with a calculator, the quadratic formula, absolute value, two-variable inequalities, and other more-challenging topics. Overall, topic coverage is similar to that of many other first-year algebra courses, but the explanations are more thorough. However, it is not as advanced as either  Saxon's Algebra 1   or Shormann Interactive Math's Algebra 1 .

Algebra 2 covers topics such as second- and third-degree equations, systems of equations, roots, exponents, irrational numbers, logarithms, matrices, determinants, statistics, and probability. The course also includes practical applications in areas such as banking and physics plus word problems that help students understand how they might use algebra in the real world.

Geometry uses a traditional Euclidean approach, beginning with a chapter on logic and reasoning, then moving on to definitions, postulates, and theorems. Formal proofs are introduced very early. Analytical geometry using the coordinate plane is reserved for the end of the course. As with the algebra courses, practical applications and occasional word problems help students understand how they might make use of geometry. 

Pre-Calculus

The Pre-Calculus course includes problems modeled after those on the pre-calculus CLEP ® exam which should help students prepare for that exam. This is a challenging course that begins with functions and moves on from there. It covers various types of functions, such as polynomial, radical, and trigonometric. It also teaches triangle trigonometry, trigonometric identities, vectors and polar coordinates, systems, matrices, determinants, advanced analytic geometry, sequences, probability, and statistics. Special topics taught in the course include Pascal’s Triangle, The Binomial Theorem, Synthetic Division, More Sines and Cosines, Complex Numbers, De Moivre’s Theorem, and Fitting a Graph to Data.

Pricing Information

When prices appear, please keep in mind that they are subject to change. Click on links where available to verify price accuracy.

version 4.0 online:

Math 3 - Math 5: $45.95 per student per course Math 6 - Math 7: $58.95 per student per course Pre-Algebra through Pre-Calculus - $72.95 - $74.95 per student per course subscription for 4-8 students - $216.95

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Math Smart, 3rd Edition: The Savvy Student's Guide to Mastering Basic Math (Smart Guides) 3rd Edition

• ISBN-10 152471058X
• ISBN-13 978-1524710583
• Edition 3rd
• Publisher Princeton Review
• Publication date November 7, 2017
• Part of series Smart Guides
• Language English
• Dimensions 5.5 x 0.73 x 8.18 inches
• Print length 352 pages
• See all details

From the Publisher

Get Smart! These books help you master the essentials of math and English, so you can excel in class and on tests.

Editorial Reviews

About the author, product details.

• Publisher ‏ : ‎ Princeton Review; 3rd edition (November 7, 2017)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 352 pages
• ISBN-10 ‏ : ‎ 152471058X
• ISBN-13 ‏ : ‎ 978-1524710583
• Item Weight ‏ : ‎ 13.8 ounces
• Dimensions ‏ : ‎ 5.5 x 0.73 x 8.18 inches
• #1,190 in Math Teaching Materials
• #5,088 in Study Guides (Books)
• #7,497 in Education Workbooks (Books)

About the author

The princeton review.

The experts at The Princeton Review (www.princetonreview.com) have been helping students and professionals boost their exam scores and get into their dream schools since 1981. We provide the tools needed for success in high school, college, graduate school, and beyond, and help our students become well-rounded applicants with guidance tailored to today’s academic challenges.

Our proven methodology of test-taking strategies helps students achieve better scores. With a wide array of test prep books addressing every major standardized exam—from all-in-one guidebooks to flashcards to subject-specific practice books—The Princeton Review has a solution for every study need.

We also offer private tutoring, semi-private and traditional classes, and online prep to fit any schedule and learning style. With our on-demand Homework Help and Admission Counseling for college and grad school, we help our students become more than their test score by providing resources for better grades and a stronger application.

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This is a great workbook for the basics of math!

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Florida Releases Reviews That Led to Rejection of Math Textbooks

To explain its puzzling rejection of dozens of textbooks, the state released 6,000 pages of comments, revealing an often confusing and divisive process.

By Dana Goldstein and Stephanie Saul

It was the equivalent of: “Show your work.” To help explain its puzzling rejection of dozens of math textbooks, the state of Florida released nearly 6,000 pages of reviewer comments this week and revealed an often confusing, contradictory and divisive process.

A conservative activist turned textbook reviewer was on the lookout for mentions of race. Another reviewer didn’t seem to know that social-emotional learning concepts, like developing grit, should be banned, according to the state. A third flagged a word problem comparing salaries for male and female soccer players.

As part of the official review process, the state assigned educators, parents and other residents to review textbooks, in part to determine whether they adhered to Florida’s teaching standards for math — from simple addition in kindergarten to interpretation of graphs in high school statistics.

But Gov. Ron DeSantis, a Republican, and allies in the state legislature have also fought against what he calls “ woke indoctrination ” in public schools and advanced a series of regulations and laws intended to limit how race, gender and social-emotional subjects are taught.

So reviewers were asked to flag “critical race theory,” “culturally responsive teaching,” “social justice as it relates to CRT” and “social-emotional learning,” according to the documents.

In an illustration of how politicized and subjective those terms have become, the various reviewers seldom agreed on whether those concepts were present — and, if they were, whether the books should be accepted or rejected for including them.

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Findings from Florida's math textbook review undermine DeSantis' claims

By Ja'han Jones

Last month, the Florida Department of Education completed a review of math textbooks submitted for use in K-12 public schools. The analysis was part of Gov. Ron DeSantis' crusade to block teachings on racism, social inequality and other issues Republicans have willfully mislabeled as “critical race theory.” 

The department initially rejected 54 of 132 math textbooks up for review, nonsensically alleging they included the "divisive concepts" of critical race theory and "other unsolicited strategies of indoctrination." The department later said it was reintroducing 19 of those rejected books after publishers made changes that included "removing woke content."

Last week, the department shared partial results of the textbook review, and — surprise, surprise — the findings undercut conservatives’ claims.

As the Florida textbook review seems to indicate, most Americans don’t back the conservative movement’s assault on school lesson plans.

The trove of documents released included nearly 6,000 pages of responses from reviewers asked to determine whether content in Florida math textbooks aligned with a statewide rule banning “critical race theory.” (It's worth noting once again: Critical race theory is a college-level field of study that isn't being taught in public grade schools in the United States.)

The documents showed reviewers’ responses to the content — but not the content being reviewed. Nonetheless, reviewers overwhelmingly said the textbooks they read were either in “good” or “very good” alignment with Florida law. And a significant portion of reviewers specifically indicated the books contained no references to critical race theory.

A few responses clearly echoed right-wing talking points about education. For example, one reviewer — conservative activist Chris Allen — bemoaned a high school textbook referencing topics she claimed were “inappropriate for school aged children.” Those topics, Allen wrote, include things like divorce and vaccinations.

“The lesson on vaccination does not mention natural immunity, medical inability to get it, or religious exemption to the vaccine,” Allen wrote in her review. “Vaccination in general should not be discussed in a school setting as it’s a parent’s choice whether their minor child get it or not.”

Allen also claimed a diagram in that same book “implies that people who consider themselves conservative are more likely to have racial prejudice,” which she said would deter students from becoming or acknowledging themselves as conservatives (as if students need more reasons to reject conservatism).

Still, in spite of reviews like that, it’s hard to overstate just how sparse they are, and how inconsistent Florida Republicans’ claims of indoctrination are with the actual facts about Florida’s education system. In fact, the majority of people who took issue with the textbooks weren’t right-wing revisionists trying to whitewash school lessons. They were people who thought lesson plans ought to promote more collaboration among students or be more accessible to students with disabilities or use more contemporary references to relate to today’s students. 

Those findings align with recent polling data that showed Americans with school-age children overwhelmingly support their school’s curriculum, but many believe schools can provide better services to help kids.

As the Florida textbook review seems to indicate, most Americans don’t back the conservative movement’s assault on school lesson plans. Unfortunately, the conservative movement is largely unconcerned with the issues Americans do care about.

Ja'han Jones is The ReidOut Blog writer. He's a futurist and multimedia producer focused on culture and politics. His previous projects include "Black Hair Defined" and the "Black Obituary Project."