We’ve all heard the saying, Don’t judge a book by its cover, but I did it anyway. Well, not by the cover, exactly — I also flipped through the table of contents and read the short introduction. And I said to myself, “I don’t talk like this. I don’t let my kids talk like this. Why should I want to read a book that talks like this? I’ll leave it to the public school kids, who are surely used to worse.”
Okay, I admit it: I’m a bit of a prude. And it caused me to miss out on a good book. But now Danica McKellar‘s second book is out, and the first one has been released in paperback. A friendly PR lady emailed to offer me a couple of review copies, so I gave Math Doesn’t Suck a second chance.
I’m so glad I did.
Overview
I was terrified of math.
I remember sitting in my seventh grade math class, staring at a quiz as if it were written in Chinese — it might as well have been a blank sheet of paper. Total brain freeze.
Nothing made sense. I felt sick to my stomach, and I could feel the blood draining from my face. I had studied so hard, but it didn’t seem to make any difference — I barely even recognized the math problems on the page.
When the bell rang and my quiz was still blank, I wanted to disappear into my chair. I just didn’t want to exist.
— Danica McKellar
Introduction to Math Doesn’t Suck
Like a compassionate older sister with an If I can do it, you can, too! attitude, McKellar aims to teach math-phobic middle school girls how to survive the toughest topics in arithmetic: factors, fractions, decimals, percents, ratios, word problems, and more. Step by step guides and example problems are interspersed with teen-magazine-style sidebars, testimonials, quick quotes, and personality quizzes. Each chapter ends with a short list of “Takeaway Tips,” summarizing the main concepts a student needs to master.
At the end of the book is a “Troubleshooting Guide,” giving practical tips for dealing with five common complaints:
- “Math bores me to death.”
- “When it’s time to do math, I get scared and try to avoid it.”
- “I get confused and lost during class.”
- “I think I understand something, but then I get the wrong answer in my homework.”
- “My homework is fine, but when it comes time for a test, I freeze up and can’t remember anything.”
What I Liked
The book is written in conversational English, a refreshing change for students whose only experience with math has been textbooks. McKellar doesn’t skip steps in the interest of concise prose, but clearly explains what she is doing as she works through the example problems.
I was glad to see that she doesn’t shy away from math terminology, but defines it clearly and uses it often enough for it to become familiar.
I liked the very short exercise sets that give students a chance to check whether they understand the topic just taught. Answers are in the back of the book, and fully worked out solutions can be found at the Math Doesn’t Suck website.
I enjoy word play, and I found some of the mnemonics delightful:
- Prime numbers are like monkeys (primates) hanging from the lowest branches of a factor tree.
- Re-FLIP-rocal. (Well, it was new to me.)
- Unit rates are “per-D” cool, when you speak with a Southern drawl.
That last one requires explanation: “Pretty” is pronounced “purty” in the South, and the unit that comes after the “per” names the Denominator of your fraction.
I liked the “Danica’s Diary” entries, which showcase math in interesting, real-life stories. They give the book a comfortable feeling, as if the reader were sitting down to chat with a friend.
What I Didn’t Like
Many of the lessons are step-by-step recipes for solving a certain type of problem. I would have liked to see more Why does it work that way? explanations, like the “Return of the Copycat” section in chapter 10 (which shows what is really happening when we move the decimal point before doing long division).
For example, I wish McKellar had taken the time to show why the shortcut of cross-multiplying works, that it is the same as finding the numerators of the common-denominator equivalent fractions. And I wish she had shown more clearly how “means and extremes” is the same as skipping a step when you simplify complex fractions, perhaps by working the same fraction both as a division problem and using means and extremes.
She comes very close to showing why these tricks work — an additional paragraph or two could have done it in each case. But instead, she presents them as mathematical magic for students to memorize.
Other Comments
Danica McKellar knows far more about math than I do. She majored in mathematics at UCLA and graduated summa cum laude in 1998. She and fellow student Brandy Winn coauthored a paper (pdf) with Lincoln Chayes, giving both students an Erdős number of 4. According to Wikipedia:
Because she also has a Bacon number of 2 through her acting career, she is one of the few individuals with a finite Erdős–Bacon number; in her case, 6.
McKellar took Terrence Tao‘s Introduction to Topology class “way back in 1997, and in fact was the second-best student there.” Tao writes about the Chayes-McKellar-Winn theorem here, and John Baez gives the short version here.
No, she doesn’t talk like a bratty kid demanding attention throughout the book. The semi-crude language is mostly limited to the title, contents pages, and a brief (but inspiring) introduction.
Buy, or Don’t Buy?
If you already understand and are good at math, then don’t buy this book. Instead, spend your money on more interesting enrichment or puzzle books, like Secrets of Mental Math or a book by Brian Bolt, Edward Zaccaro, or Raymond Smullyan. Or try one of the challenging books from Art of Problem Solving.
But if you identified with McKellar’s story about the 7th grade math test, or if you find yourself repeating any of those five common complaints, then Math Doesn’t Suck is for you. Buy it. Read it. Go over the example problems as many times as you need to, to be sure you’ve mastered them. Keep the book handy for reference. Whenever you have homework dealing with a tough arithmetic topic, review the relevant chapter — especially those “Takeaway Tips.”
I frequently meet homeschooling parents who are afraid of math and concerned about passing on their math phobia to their children. Starting now, this book and its sequel, Kiss My Math (review here), are my whole-hearted recommendations to any homeschool mom who tells me she “just doesn’t get math.”
As McKellar writes:
Working on math sharpens your brain, actually making you smarter in all areas. Intelligence is real, it’s lasting, and no one can take it away from you. Ever.
And take it from me, nothing can take the place of the confidence that comes from developing your intelligence — not beauty, or fame, or anything else “superficial.”
Math isn’t easy for anyone. It takes time and persistence to understand this stuff, so don’t give up on yourself just because you might feel frustrated. Everyone feels like that sometimes — everyone. It’s what you do about those feelings that makes you who you are.
It’s in those moments when you want to give up but you keep going anyway that you separate yourself from the crowd and build the skills of patience and fortitude that will allow you to excel throughout your entire life — no matter what you choose as a career.
Denise Gaskins' Let's Play Math 
Dear Denise,
“I don’t talk like this. I don’t let my kids talk like this. Why should I want to read a book that talks like this? I’ll leave it to the public school kids, who are surely used to worse.”
I saw this comment and was offended. Then I read the “About/Contact” page and found out that you homeschool your kids. Now I feel bad for them because they have to be suffocated with this attitude at home and at “school”.
As an ambassador from the world of public K-12 education, let me be the first to say that you suck. And your kids will undoubtedly suck if you keep them in your protective bubble.
Dear Chet,
You need to understand that parents have the right to decide what is right for their children. She decided she liked the book and recommended it, You we’re offended by her thought process.
What do you think of this book? Did you even look at it?
I figured out that publishers choose the covers and titles. “Don’t judge a book by it’s cover” definitely applies here.
I, too, don’t like the word “s***” . To my generation and I’m only 46(!), it has gross, s*xual connotations. Sorry, but that’s the root of the word. That’s why I don’t say it, nor let my children say it. We are judged by the words we use and I for one respect you *more* because you care about language.
Great review. Thanks for sharing it.
One very nice thing about the title is that I will not forget it when it comes time to recomend this book to the next math phobic I meet.
Thanks,
Kaz
This is funny, I had no idea you got review copies as well (just like I did). I managed to publish my review just one day ahead of you:
http://homeschoolmath.blogspot.com/2008/08/review-of-kiss-my-math-and-math-doesnt.html
“For example, I wish McKellar had taken the time to show why the shortcut of cross-multiplying works, that it is the same as finding the numerators of the common-denominator equivalent fractions. And I wish she had shown more clearly how “means and extremes” is the same as skipping a step when you simplify complex fractions, perhaps by working the same fraction both as a division problem and using means and extremes.”
I agree, I noticed the same “lack” with these two fraction “tricks”. It’d be good if she can add more proofy stuff.
The more I look over this book, the more I like it just the way it is. Please don’t forget to look at the website given in the book. The means and extremes shortcut is very helpful. Having the student work out the example themselves and getting the same answer as the short cut version will help show how it’s the same. She refers back to it. Also, we’re trying to make the complex fractions doable.
https://www.google.com/amp/s/www.biography.com/.amp/people/danica-mckellar-20970757
Hi Denise, The link above is a biography of Danica McKellar. She received a PhD in 2005 in mathematics from the U of Chicago(Wikipedia missed this!)
If you want to see her explanation of how the “trick” works for cross-multiplication in the answers on the website. I think it is necessary to do the exercises as they are part of the learning process, and although we might not read this book if we(parents) are good at math, we need to if our child is ready to learn it and can connect with this author. It would be good to follow along, or just ahead of them. I don’t know why “proofy stuff” would help, however, a parent or tutor following along would be able to share what they know with the student, right? I know my daughter likes talking to me about his she understands the math she is working on, and so I need to be ready to explain things, too. So, I say everyone should read this book and do the exercises.
We’ll, I guess this is really old! These are still good books!
Thank you for the link, Kim! Yes, these are old books, but they are the type of book that’s always useful to new readers. 🙂
As for the “proofy stuff,” I think it’s always good on principle to explain why a math trick works. Too many people think math is just about getting right answers, but it’s not. The real point of math is understanding why.
I will take another look at this book soon. I am going to read it and do the problems and see where the explanations are missing. Then, it might be clear to me what you are saying was left unexplained. I have to wait for the library hold to come.Thanks
We’ll, I took a good look at this book.
The cross multiplication short cut, on page 78, holds water, meaning there is a mathematical proof to back it up. Here’s a link to a video showing the proof:
If you say you need proof it’s not a trick, there it is.
Hi, Kim!
Yes, I agree there is a mathematical reason behind the method. My complaint was not about that.
Rather, my complaint is that McKellar (and many other teachers) present cross-multiplication as a technique without proof. And that many, many teachers let students use the method without requiring them to justify it.
If we let students get by with memorizing a trick they don’t understand, then we are no longer teaching them math. Math is ALL about the “why?” and the “how can we know for sure?” reasoning.
When my students use cross-multiplication (and yes, I do allow it), they have to explain to me why it works — how they know it is true for their problem. They have to give me a mini-proof. Every. Single. Time.
Or you can look it up on Wikipedia.
Look for cross multiplication. Note that it is not the same as cross product.
Never stop learning.☺
Okay.
I agree. The explanation for the methods you mentioned need to be in the book.
I am so excited to report back to you that I found some explanations for the “presenting without proof” in this book. In order to properly use this book, you need to go to the website http://www.mathdoesntsuck.com/extras/
On this extras page, you can see she has addressed at least one of these so-called tricks that do sometimes cause students trouble- PEDMAS. She writes it out, same style as the book, and tells the student how to use it. She must have updated the book, too. I’ve been looking closely at all this and hope to use it as a guide when my daughters do these topics she covers.
Also, she has written out the explanations of each exercise for all the chapters.
She has a way to contact her there also. She has a Phd in mathematics, however, she knows how to correct things that are unclear.
I urge you to contact her with your concerns about cross-multiplication if you don’t find it on the webpage.
I’m glad I investigated all of this. Thank you for your input.
You said, “When my students use cross-multiplication (and yes, I do allow it), they have to explain to me why it works — how they know it is true for their problem. They have to give me a mini-proof. Every. Single. Time”
How will they know how to do the proof? Would this be in a group that you are teaching or when you work one on one with them? My style, if you can call it teaching( seems more like research librarian/Mom) is tutoring. It kind of helps with the moving along in the materials, since there’s only one student.
Thank you for listening😃
When I am teaching, either at home or in a small group, we discuss the problems — similar to what I describe in my Buddy Math blog post. https://denisegaskins.com/2009/04/06/buddy-math/ The student who is explaining his work needs to justify every step.
Our justifications are short proofs. For instance, to use cross-multiplication in comparing fractions, a student might say, “This gives both fractions a common denominator, so all I have to do is compare the numerators to see which is greatest.” And if I ask what the common denominator of his fractions would be, the student has to know how to find it.
If the student’s explanation is something like, “Because the book (or last year’s teacher, or Dad) said to do it that way,” that won’t fly in my class.
https://www.theatlantic.com/national/archive/2012/11/a-new-kind-of-problem-the-common-core-math-standards/265444/
Quoting from Wikipedia Cross I multiplication page, “Each step in these procedures is based on a single, fundamental property of equations. Cross-multiplication is a shortcut, an easily understandable procedure that can be taught to students.”
So, what is the fundamental property of equations? I think students need to know them by the time they do fractions, before they get to equations.
Here’s a chart i found http://www.sparknotes.com/math/algebra1/expressionsandequations/section5/ I think I would read through all these properties with them and see if they have questions and/ or a discussion.
I’m glad I started thinking about this.
I think I will have my daughter choose which method she wants to use. I don’t have a group, just 2 daughters who I help one on one.
On mathsisfun.com they also divide the fractions and compare their values.
I am going to show them the proofs and go from there. Proofs are introduced in geometry. That’s my plan.😃
I like Buddy Math.😺 Thanks for the link.
If the student has successfully worked through the materials in this book, up to the place where she has you comparing the value of 2 fractions with different denominators, then I think it would be logical to expect the student to have the understanding of equivalent fractions being multiplied correctly to get the least common denominator. If you don’t know if they can compare the fractions that way, you can ask them what they know and have them show you.
Then, being confident that you and your student both know what the denominator is, you shouldn’t have to multiply it out. You should be able to say this short cut, called cross multiplication is only for comparing the value. Danica did write that on the page .She said it was on!y for comparing. So,that means these butterfly methods someone made up for adding, not comparing, will not be found in this book. That’s why I wouldn’t make them prove it. But I’ve been wrong many times before. All I know is that if I do these fraction lessons ahead of my DD, I will know if and when she is ready for this short cut and it will be NBD(no big deal).
Does this make sense?
Sorry, I just had to get this out of my head.Thanks.
By the way, it is completely realistic to expect your children to learn basic math without a teacher, if you homeschool. 🙂
I’m probably working with older kids than you. Also, I HAD to do proofs as a math major in college. So I see maybe proving it once. The reason you prove it is so you can use the cross multiply and Not have to multiply to get the new denominator. I would be willing to do a proof for cross cross applesauce if you want proof for that, too.☺
The amount of justification (the word “proof” probably implies too much formality) you expect from a student varies with the context. When a mom who is comfortable with math is working one-on-one with a student whose background she knows well, you get to the point where you understand each other.
But in my co-op classes, I see too many students whose parents really don’t like or understand math, and the kids have an uneven background. They’ve often been trying to get through solely on memorized procedures. Some of them can fake it very well for a while. But the procedures don’t mean anything to them, and the rules start to get jumbled together if they don’t review constantly.
I’m thinking of the junior high students who tell me that you have to always flip a fraction before you can multiply.
And that two negatives make a positive so -3 + -5 = 8.
And the kids who can solve a word problem flawlessly (as long as it’s just like the one they saw in class) but can’t explain what the numbers mean.
That is a problem for another place and time. If they can’t add, what would they be doing in a class working out complex numbers? Peer and parent/sibling tutoring are my suggestion for these students. Someone who can show them what the procedures mean. Maybe they could correspond with the author if they like this book. There are so many resources for remedial work, (for lack of a better word.
In my humble opinion, the students who do not understand need to be given help with arithmetic, including rational numbers, to include fractions. Keep the visual models and find a way to help them see where the techniques for fraction arithmetic originate, why they are the logical conclusions. These are the properties of arithmetic. Please look it up.
These are the properties of arithmetic:
https://www.khanacademy.org/math/pre-algebra/pre-algebra-arith-prop
Properties of real numbers ( including fractions because they are in the set of real numbers)
This needs to be understood because it is the sound reasoning of how to do arithmetic.