Math is one of those subjects that many people think is beyond their capacity to teach. As a child my math skills were less than stellar, so the knowledge that I was going to be teaching my children math was a little overwhelming. I ended up choosing a curriculum that required very little involvement on my part because the lectures were on DVD. All I had to to was check the answers in the back of the text book and if they had questions they could ask their father.
Over the last few years I have learned a few things that have helped me gain confidence in my ability as a math teacher.
- Math is important – It’s not always fun but math is very important. You need to be able to do it without a calculator. Don’t be afraid to pull out your child’s math book and read a chapter.
- You ARE good at math. Math is a not a mystery. As a parent it takes VERY little time to relearn the things that you may have forgotten. I can’t tell you how many times I would sit down to read the lesson before I taught it to Lucy only to discover that the very same concepts that eluded me as a teenager came easily to me. I hadn’t touched fractions in any measure beyond cooking in over a decade and yet I have been able to teach fractions with ease.
- Be wary of fuzzy math. This revelation came only recently. Lucy is the kind of girl who makes up her own math problems for fun (she takes after her dad in that respect). Being somewhat ahead of her peer level in math she was quickly going to pass my comfort level so I needed to brush up on my own skills if I wanted to be of any use to her. As I sat down to read the lessons I was becoming increasingly discouraged. I grew up at the time when the intellectual elites were changing the way math was taught based on their “theories”. Do you remember when public schools ditched phonics in favor of sight reading and then all of a sudden kids couldn’t read? Yeah, kind of like that but for math. Anyway, I grew up thinking that I was missing something and that if I just knew the “secret” of math then I would be home free. I now know that the “secret” of math is that there is no secret. Math is logical and to paraphrase Euclid, “There is no royal road to math.” I realized that the biggest problem I was having was that I was trying to refresh my knowledge with a “new method” of solving the same old problems. Once I realized what was happening I called my sister in despair. What was I to do? I had seven years worth of math curriculum and I didn’t want to switch… again! She gave me a few tips that I will share in a little bit, but I want to stress the point that fuzzy math is still alive and well and has taken steroids. Once I went back to basics and stopped trying all of the silly “short cuts” I realized I wasn’t nearly as helpless as I thought.
- Literature can help with math – Oh yeah, baby :)
First of all, if your state allows you some leniency, then don’t push it. You would be surprised at how far a child can get without any formal math instruction. Like with reading, don’t worry about pushing math unless it is interfering with their quality of life. Just like with potty training, mastering a math concept can take your child a day or a year. Don’t push it until they are ready.
Using story books you can help little kids understand mathematical concepts before you start formal teaching or if your child is struggling with a specific concept.
The Sir Cumference series is wonderful for little kids. There are seven or so in the series and they are wonderful for explaining concepts in story format. There is so much mathematical literature for children that I can’t even begin to count them all.
Mathematicians Are People, Too contain short stories about famous mathematicians.
You may remember my review of One Minute Mysteries: 65 Short Mysteries You Solve With Science. Well, there is also one for math. I haven’t read it but if it is anything like the science book it is well worth a read.
And there are some excellent works of fiction that can teach kids (and adults) about math. Toby Gold and the Secret Fortune is an excellent book that teaches kids about economics.
How Math Works by Reader’s Digest has a lot of valuable historical and background information. It is by no means a comprehensive mathematical book, but it has some fun projects and history that my kids have enjoyed.
Problems with text books/Fuzzy Math
These are excellent resources but you can only go so far with them. Eventually you will have to get yourself some instructional books that will actually teach your child math. My suggestion is to do your research and find the best curriculum that will work for your family. There is no RIGHT math curriculum. We started off with Saxon but ended up switching to Math-U-See because Emma needed a different approach. I was also able to review TouchMath with Spencer and in my opinion it is the best of the three. TouchMath only goes up to 2nd grade though and it can be a little pricey (though it comes with a license for multiple printing for family use so that may factor in to the cost.) The most important thing for you to remember when selecting a math curriculum is that YOU (mom/dad/teacher) need to be knee deep in it. You can’t just hand them the text book and call it a day. I did that for a while and it came back to bite me.
One of the reasons why Math-U-See appealed to me so much was being able to have the lectures on DVD. I wasn’t a “math person” so it was best to leave it to the mathematicians and I would teach the fun subjects. Lucy and Emma could watch their lessons and all I would have to to is check their homework. Simple, right? Not so much. It went pretty smoothly unless one of the girls couldn’t understand the lesson. They would come to me and I would try… and fail…. to help them. I was getting discouraged and frustrated. Why couldn’t they GET it? Remember the fuzzy math? They were learning math one way and when they were confused they would come to me and I would teach them a different way (seriously it’s like these companies are setting us up to fail). I didn’t want to switch curriculums again (soooo many other things I would rather spend money on) but I wanted the good old fashioned math book (you know, “carry the one” kind of math). As far as I could see EVERY current math text is PACKED with fuzzy math! Eventually I called my sister to rage about the failure of US math curriculum. Her answer was simple, “so teach them the right way.”
So I went through every math lesson searching for fuzzy math. When I found it I would stick a post-it on that page. The post-its would say things like “this is stupid, ask mom” and “this is REALLY stupid, skip entirely”.
Another thing I discovered while having these texts under a microscope is that there is SO much busywork! I hate busywork. I know that math is a skill and you need to practice but some of these problems are absolutely ridiculous. Does Emma know how to estimate? Yes. Therefore I am not going to make her estimate EVERY SINGLE PROBLEM before she solves it. So not only do I adjust the lessons but I also adjust the homework. My children are never required to do more work than necessary to master the skill. I’m not a fan of wasting my time and I am not going to waste theirs. And to be brutally honest, I hate the Math-U-See fraction manipulatives (though I do like the Primer ones). I guess I can see why they might come in handy for a few children who can’t grasp what a fraction is but for a child who doesn’t struggle with it they just get in the way. I’m not going to waste four days and 24 pages of worksheets for a concept that Lucy understood after five minutes of mom’s instruction (by the way, when I checked her homework she got every problem correct… so I know I’m teaching it right ;))
One of the other things that bothers me about fuzzy math is the idea that you need to teach children several different ways to answer a problem. I can see how that might come in handy in high school, but teaching young children several different methods to do double digit addition will ONLY confuse them. Emma is a perfect example of this. When you teach a child two or three different ways to add numbers together they will confuse the steps and end up mixing the methods together. I believe that teaching a fixed formula for addition that works every single time is preferable to what they call “inquiry-based philosophy“; which essentially teaches children the “theory” behind math and then makes them use a calculator. In my experience inquiry-based philosophy regarding mathematics will come NATURALLY as a person gains skill in math: But, if you spend all of your time teaching “deep conceptual understanding” rather than the tried and true algorithms, then your child will not be able to do math. Just look at this example of traditional vs. inquiry-based:
This is a SERIOUS problem! They are adding unnecessary steps and developmentally inappropriate concepts that make it so that our children aren’t mastering basic arithmetic until MUCH later than they should be. My view? Teach the formulas and HOW to do math and let them figure out the WHY on their own. A seven year old does not need to be dealing with the philosophy of mathematics, they are just trying to make sure she gets the same number of cookies as her brother. You cannot put a roof on a house before you have built the foundation and the walls.
Anyway, that was my very long way of saying that I tell my kids to ignore the directions of their worksheets telling them to find the answer using different methods. I want them to find the answer using the traditional algorithm. I also discourage “mental math”. Before you yell at me you need to know that by “mental math” I do NOT mean mental calculations. They don’t need to write down 2+2=4… but, I also don’t want to put such an emphasis on doing it in their head that they feel like they are cheating if they write it down. Yes. It happens… in MY house! I have to TELL Emma to WRITE IT DOWN because if she doesn’t she will get the wrong answer yet she me fights about it every time. I’m telling you, this mental math stuff is bad news! Also, don’t teach them “tricks” until AFTER they have nailed the formula. Introducing “find the 10’s” in multiple digit addition to a kid who still doesn’t really know what they are doing will mess them up.
I can’t tell you how much I wish I had more math confidence back when we first started. I switched to Math-U-See so I could basically wash my hands of the math instruction because I didn’t think I was good enough to teach it. In the end we decided to switch back to Saxon. Here are a few pointers for those of you who are still shopping for math:
- Saxon K – Don’t bother. You will cover everything in Saxon 1.
- Saxon 1 – Saxon 3 – Expect to cover years 1-3 quickly, especially if you wait until your child is 7 or 8 to begin math formally. There is a LOT of overlap with these three levels. There is also a good amount of unnecessary busywork. I don’t bother with the morning meeting, flash cards, number cards, etc. My approach is very simple. I sit down next to my child at the table with the workbook and the teacher’s manual. I open up the teacher’s manual and give it a quick skim. I always skip the “morning meeting” and everything else up to the new lesson. I may or may not follow the script of the lesson, it entirely depends on the level of the child and the concept being taught. I will usually follow the script with Spencer, not with Emma. I spend as much time as is needed for them to understand, but if they don’t “get” it in 10 or 15 minutes (depending on their age) we put it away and come back to it another day. We will go through the practice problems and one of the two worksheets together. Then I have them do selected portions of the second worksheet on their own. In Spencer’s case I continue to sit next to him and explain the problems since he’s not independently reading yet. Emma was able to skip Saxon 3 entirely and transition seamlessly to Saxon 54.You can buy the teacher’s manual new or used from Ebay or the Saxon Homeschool website. You can get the worksheets new from those same places.
- Saxon 54 – Calculus and Physics- Now is where it gets a little tricky. At one point before John Saxon died (I don’t know the exact year) Saxon Math switched from Saxon Publishers to Houghton Mifflin Harcourt. Shortly after this change, they stopped selling the hardcover copies of the books to homeschoolers. This did two things; first, it allowed for significant changes in the curriculum itself, and two, it increased the financial burden on homeschooling families. All of a sudden text books that could have been used year after year and for multiple children could only be found in flimsy softcover manuals and consumable workbooks. The excellent Saxon Math that earned an incredible reputation was gone and homeschoolers were exploited. Thank you Houghton Mifflin Harcourt. So here are a few tips when purchasing your Saxon Math books.
- It is VERY important that you buy anything above Saxon 3 USED. The phrase “they just don’t make them like they used to” REALLY applies to Saxon Math. For more information on which editions you should be looking for, go here, but in general you are pretty safe with a 2nd edition for everything but calculus (you want 1st).
- Buy the SET. When you are shopping look for the Saxon SET. This will include a text book, a test booklet, and a homeschool/home study booklet. You want to buy them at the same time because there are slight variations in the printings and you want the answers in the home study booklet to match the questions in the text and test booklet. This is the best way to ensure that happens.
- You do NOT need a teacher’s edition.
- Once you get into algebra and up the set will have FOUR components instead of three. Just something to keep an eye on. If you are buying calculus and the Ebay listing only has three things, there is something missing.
- When I teach Lucy and Emma (who are both using hardcover books) we still keep it very simple. Just like with the younger grades, I sit next to them at the table, skim the lesson, and teach them the lesson. I will read it out loud to them and have them work through the practice problems and help them when needed. Depending on the lesson and how quickly they catch on, I will either assign them selections from the problem set or move on to the next lesson. Saxon 54 and up does not have workbooks, so my girls will copy the problems and tests into a notebook. Emma usually gets through one lesson in each sitting (she skipped 3rd grade math so we are taking it slow) while Lucy can get through three or four. Occasionally we will skip a lesson if I think it’s stupid, but I can honestly say I haven’t found the Saxon to have NEARLY the amount of fuzzy math in it as there was in Math-U-See.
- Unless your child needs extra help, don’t bother with Saxon 4 or Saxon 87. They aren’t necessary.
I promise that yes, you ARE good at math. If you are still nervous however, Kahn Academy has been great in reminding me about certain mathematical algorithms.
Once you have decided how you are going to go about teaching your child arithmetic there are a lot of supplemental resources that can help reenforce the skill.
Life of Fred is EXCELLENT. It follows the story of five year old Fred, a professor at a local university. Life of Fred is not a replacement curriculum but works hand in hand with Saxon or whatever else you choose. The reason why it is so valuable is because it helps children think mathematically. Life of Fred helps children (and adults) fall in love with numbers and math. Saxon helps us learn the algorithms and formulas. I purchased Apples just to try it out and my children were just thrilled. They love it, I love it, and it is worth the extra cost. The day we started reading it I got such a good response that I got online and ordered four more (the next in the series and then three to help Lucy with reducing fractions and long division).
I have been mostly pleased with Math Doesn’t Suck (yes, that is Winnie Cooper). The only problem I have with it so far is that it makes a lot of cultural references that my children won’t understand and that I don’t love (aka. horoscope, etc.). This serves the same purpose as Life of Fred. It helps kids see the real world application of math.
A Beginner’s Guide to Constructing the Universe is another book that helps us fall in love with numbers and think mathematically. I can’t wait to get my hands on it but I promised Matt I wouldn’t open it until my birthday. Once I do get a chance to read it I will tell you what I think :)
I love, love, LOVE Dragon Box. It is an app that you can buy for your apple products or android. You can also get it for your Mac desktop. This app incrementally teaches children the logic behind algebraic formulations in a super fun (and slightly addicting) game. The first several levels use pictures instead of numbers and they try and isolate the “box” on just one side of the screen. Every few levels they get a new “power” which is really just another step in algebraic formulas. After a few hours of playing this game they are completing complex algebra problems perfectly. There are two versions, a 5+ and a 12+. I suggest just getting the 12+ because it’s basically the same thing and my three year old can play it just fine.
Here is a video showing how it works.
Math Rider is a program that helps them master the addition, subtraction, multiplication, and division tables. There are also a lot of books out there that can help your kids understand mathematical concepts. For more suggestions on math classics go to TJED.com.
Math is just one of those subjects that requires you to get out of your comfort zone. That’s ok. Pushing that comfort zone is the only way to get improve in life.
And remember that you never stop learning… even math. Ancora Imparo!
**This post has been updated**