# The math tutor I love. Or hate

In a moment of great math self-doubt and great faith in my ability to earn money, I called a very expensive math tutor in Washington DC to see if she could tutor my son online.

He is six and doing third-grade math, but I have no genes for math skills and neither does his dad, so I’m convinced that the only reason he’s doing third-grade math is that I inadvertently skipped things I can’t bear to teach. Like measurement. I hate that. I mean, look, I’ve gotten through my whole life not knowing metric conversions, so I don’t think we need to teach them since it’s clear that most people don’t know them and they still live happy, fulfilling lives. Or, really, even if they are not fulfilling, I have never heard anyone lament their inability to measure by the meter.

But I’m the only one who can’t measure metrically. This is what the consultant made me think. Because apparently, math is linear, and you learn step by step, and there are standards that kids need to meet before they go on.

I imagined the math corollary of putting a kid in front of a stack of Newbery Award Winners and telling him to read. But there is not that. I mean, there is no best-of for math problems.

So the tutor says my son needs to learn math according to math standards. And you know what? I’m really hopeful that maybe we do not really need rigid math standards and he could be a free-thinking math kid. But maybe the tutor couldn’t say this because she is certified to national standards.

I’m just not sure what to think, or what to do. Today, when my son asked what his math problems are, I gave him a painting by Miro and asked him to do a graph of triangles, squares and circles.

He thinks the assignment was BS. He likes multiplication drills, so I gave him a peppermint for each circle. Am I an unschooler if I use conventional bribery?

You need to buy a math curriculum. I recommend Saxon. Their website has placement tests so you can be sure that you get the right one. Pricy but worth every penny.

We don’t use a curriculum and my kids manage to learn math every day. If your son loves math drills then search for them online or buy him workbooks. Find real world problems for him to figure out. Read living math books. See if the video below resonates with you.

http://blog.wolfram.com/2010/11/23/conrad-wolframs-ted-talk-stop-teaching-calculating-start-teaching-math/

I’ve unschooled my son for 6th and 8th grade, and now I’m looking to get him into a local charter school for 9th grade. Some kids seriously benefit from unconventional schooling (I was going to say unconventional *learning*, but public schools are unconventional learning IMO), and anything we can do to broaden their horizons will help in the long run.

We haven’t touched math much in the past 3 years, but math is EVERYWHERE, all the time. Walk around your kitchen, the park, the mall; it’s there. Just acknowledge it gently and your son will absorb it easily. It’s when we are force-fed subjects that we regurgitate them so uncomfortably.

haha! this is great!

maybe you can get him used to the idea, slowly, that he’ll learn what he needs to be successful. And then just pull multiplication drills off the internet every time he gets a hankering for it!

I remember wanting to be the best in school and did my homework and extra readings and whatnot.

I wish my parents had taught me that even though it feels good to be the best in school it is better to invest your time in being better/best in social skills, public speaking, etc. Something that will translate into money, happiness, networking, etc. in my adulthood years.

Like sucking up.

I was too good for that when I was a kid.

No one is too good for sucking up. Ever.

Maybe you could let him play with the Khan Academy videos?

This article is interesting, on Jump Math, which really focuses on the process of learning: http://opinionator.blogs.nytimes.com/2011/04/18/a-better-way-to-teach-math/

I used to work as a tutor, though mostly for parents who wanted their kids to go from straight-As to being the valedictorian. Working with students who struggled felt more like doing triage.

I thought about those kids when I read Johann Hari’s post on his experience as someone who didn’t do well in school—he credits his later success to teachers who connected with him (http://johannhari.com/2011/03/22/what-i-had-in-common-with-jamie-olivers-dream-kids ). So maybe it’s both: start with the fundamentals and remember that not even the smartest tutor with the best qualifications will make as much of a difference as one who actually connects with the kid.

Thanks for the link about Jump Math. I have a sense that I need to learn a lot, fast, if I am going to be good at homeschooling the kids.I don’t need to learn the material, I need to learn ABOUT the material. And it’s so helpful for people to send over links.

There are pages and pages of links that people send to me. But I don’t like the pages of links. That feels like a google search. I love links sprinkled into comments. Links with context.

And now I’m thinking that maybe that’s how my kids might like to learn — new material sprinkled into stuff that’s fun and engaging to read.

PenelopeI don’t know about homeschooling. My main feeling against it is that I will limit my child to what I know and what I’m good at. (Well, and also the lack of random socializing available in schools and the fact that I’m comletely unexperienced in teaching a child). It seems to me that you want your child to learn from the best so I just want to tell you my own experience with math. When growing up, I was always great at school and great at math. (but not great at courses like history). And now I have a PhD in Electrical Engineering. I just want to tell you how deeply intellectually satisfying it is to understand math and physics deeply. I’m always applying math and logic to everything in my life. And that is after having labored through it for years and learning math systematically makes a lot of sense to me.

Just as a side note, I had never taken homeschooling in the current era seriously before you talked about it. But did you know that Marie Curie and their scientist friends took out their kids from public school and each of them thaught the kids the subject they knew best? If I had friends like that, willing to put the time, maybe I could do it too.

If he loves math, then math is play to him. If you reward him for Miro, then Miro can become work to him.

Try not “if you do this, you’ll get this reward,” but instead you can give a surprise reward from time to time.

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80 preschool 4-5 yr olds participated in a novel activity in individual sessions. In the expected reward conditions, Ss expected to win a chance to play with highly attractive toys by engaging in the activity; in the unexpected reward conditions, Ss had no prior knowledge of this reward. Orthogonally, Ss in the surveillance conditions were told that their performance would be monitored via a TV camera; Ss in the nonsurveillance conditions were not monitored. 2 wks later, unobtrusive measures of the Ss’ intrinsic interest in the activity were obtained in their classrooms. 2 significant main effects were obtained reproducing and expanding findings from earlier studies. Ss who had undertaken the activity expecting an extrinsic reward showed less subsequent interest in the activity than those who had not expected a reward, and Ss who had been placed under surveillance showed less subsequent interest than those not previously monitored.

Turning play into work: Effects of adult surveillance and extrinsic rewards on children’s intrinsic motivation.

Lepper, Mark R.; Greene, David

Journal of Personality and Social Psychology, Vol 31(3), Mar 1975, 479-486. doi: 10.1037/h0076484

———–

Conducted a field experiment with 3-5 yr old nursery school children to test the “overjustification” hypothesis suggested by self-perception theory (i.e., intrinsic interest in an activity may be decreased by inducing him to engage in that activity as an explicit means to some extrinsic goal). 51 Ss who showed intrinsic interest in a target activity during baseline observations were exposed to 1 of 3 conditions: in the expected-award condition, Ss agreed to engage in the target activity in order to obtain an extrinsic reward; in the unexpected-award condition, Ss had no knowledge of the reward until after they had finished with the activity; and in the no-award condition, Ss neither expected nor received the reward. Results support the prediction that Ss in the expected-award condition would show less subsequent intrinsic interest in the target activity than Ss in the other 2 conditions.

Undermining children’s intrinsic interest with extrinsic reward: A test of the “overjustification” hypothesis.

Lepper, Mark R.; Greene, David; Nisbett, Richard E.

Journal of Personality and Social Psychology, Vol 28(1), Oct 1973, 129-137. doi: 10.1037/h0035519

I think this might be my problem with bagels. I have rewarded myself so many times with bagels that I cannot get up the energy and focus to do anything hard without knowing I’m going to have a bagel.Not kidding, really. I mean, it’s so hard to learn for learning when learning is hard. I want to be intrinsically motivated, too. But I can’t really imagine, for example, writing all the freelance articles I write if I were not getting paid. Or posting on my blog as often if I didn’t have the good-as-bagels comments section to read.

PenelopeYour desire for bagels and comments actually makes it intrinsic again. You can be intrinsically motivated to earn rewards.

For a kid who wants drills, check out the math games for the Nintendo DS. Also there are free apps for your iPhone with math drills.

http://www.nintendo.com/games/detail/KgQB7Rh85a81xVsPrlD19IxrRFWJaSFu

Penelope, the conversion thing makes me wonder. If your consultant is trying to tell you that teaching measurement conversions is a foundational math concept, then what do you suppose countries that *only* have the metric system do for their kids? Are these kids somehow worse at math? I’d think not.

For help with your kids’ math day-to-day stuff, I suggest you get familiar with the http://www.khanacademy.org/ material – even though it’s no substitute for a good tutor. I don’t know at what grade level their lessons begin, but it seems like it will be useful to your kids soon, if not already.

My own personal experience through school — and later reflections — taught me that learning math (I mean really learning math, not just being able to fake it by passing tests to get grades) really IS linear, in the sense that you have to learn step by step, and it’s an insidious thing because you can cheat. You can learn how to solve a multiplication without really understanding why it’s just an extension of addition, by learning the mechanics of it(OK, simplistic example but you get the idea). And the more you cheat, the harder things become down the line and the more you have to keep cheating, and this difficulty builds only little by little, to the point where you will eventually lose interest in math and/or be bad at it.

So the consultant has a point – there is a linear progression that needs to be taught carefully if you want your kids to not hate math. So look into that.

If your child is 6 and already learning 3rd grade math let him learn what he wants and fill in the gaps when you get to them. So if measurement conversion is something 3rd grade students learn maybe by the time he is in third grade he will have selected this as something he wanted to learn and he will already know how to do it. As it is he already is surpassing where he should be at which is first grade standards.

Also remember that doing something you already know how to do is not learning. (completing a work sheet of multiplication problems would likely be busy work and not learning for him) There are many things that he can learn that will build on the skills he already has.

I was also thinking has this tutor spent enough time with your son to know what his deficits are? Once she does that she may have a better idea of where to start with him. For example a child may be able to easily calculate but has trouble with word problems even though the actual calculation is simple.

I’m not a math teacher but converting one thing to another and back is basic skill that your kid will need later on. For example to solve algebra-problems, to do basic physics or to calculate electric power conversion. Are you certain that you kid will never need any of these skills? ;) Maybe you can come up with an math exercise of your own that can teach your kid that one and the same thing can be described in very different mathematical forms? Like in language when the same thing can be described by different words in different languages (not synonyms).

Gustavo: I live in a country where we only use metric system. Nonetheless all the kids in school are taught to convert centimeters to inches and feet, liters to gallons and kilograms to pounds. It’s the skill of conversion that is taught in math class, not a specific measurement system.

Liobov, interesting. I don’t remember being taught this as a ‘skill’ at all when growing up – and I was also raised in a country where only metric is available. I do remember doing conversion-type problems in early science classes, before our math skills were advanced enough to do real physics problems (not math class, which was reserved for teaching mathematical concepts), but it wasn’t taught as a specific skill, just a typical, problem-solving, “find a solution that makes sense” approach.

Well, every country is different and the way subjects are taught varies dramatically among different schools as well. In Sweden, in my experience, there is no clear distinction between science and math at elementary school level. Textbook problems are tailored to mimic the situations a kid could encounter in their everyday life and aim to broader kids understanding of society and the world around them. Simple physics problems are often included. I assumed that the American elementary level math curriculum worked in a similar way.

One way to let the kid get a feel for what conversion really is about is take them to the kitchen and play around. Open a bottle of water and put it into a bowl. Ask how much bowl is a bottle of water? (Let’s say it’s half a bowl). Ask them then how many bottles is a whole bowl of water? Put eggs into a whine-glass, flower into frying pan etc. the wackier the better.Re-write an existing recipe for their favorite dish using the new measurements. If they ask why you are doing those crazy things tell them “what if you wanted make your favorite dish, but didn’t have any of your usual measuring tools, what would you do?” The goal is to make them understand that the same thing can be measured and mathematically described in different ways and still be the same thing. When you later get back to the books, they’ll have an easier way to understand the purpose of the conversion and have a better feel for numbers. Hopefully. ;) I did this with my younger cousin and it worked great for her, but every kid is different. (She is a real sweet tooth so the idea of not being able to make cake because of the lack of proper measuring tools was really disturbing to her).

Unschooling is really child-led learning. A curriculum like Saxon would help because the sequence is laid out for you so you won’t miss anything. YOU are supposed to present the lesson, though. That’s not what you want. When your child is older I bet he will be able to read the lesson himself without your help, but will need someone to talk with when he needs help.

For plain skills, I really like books from Key Curriculum Press: Key to Fractions, Key to Decimals, Key to Measurements, etc. There’s a simple introduction and practice problems, but they’re short so he doesn’t have to spend a lot of time practicing something that comes easily to him.

At age 6 he’s still so young! It would be nice for him if he could learn in natural, concrete ways, but if he’s into paper, then so be it! That’s unschooling.

Here is another link that I really like for math http://www.aleks.com/ Your son might not be ready for it but it is comprehensive.

think of math like a language. If you don’t learn the words, you will not master the language.

well, you might get away with not knowing conversions if you never leave the country. And they are only multiplications and divisions, which are kind of basic…..

We’ve done math in every conceivable way I think (Saxon, Miquon, internet worksheets, living books, etc.).

I’ve got one who loves drills (thrives in a traditional school environment), one who his highly kinesthetic and must. touch. everything (total unschooling material) and an ambitious 5yo who just wants to be like his older siblings and “do math.”

We use Math-U-See and it appeals to all. There’s a DVD to watch, worksheets to complete (not tons of drills) and blocks to manipulate.

Math has always been my favorite subject and I always did well, but when I started watching the Math-U-See DVD’s with the kiddos (I’m talking basic elementary concepts), I found myself saying things like, “Oh! That’s a clever way of doing it! That makes more sense!”

P.S. I’m not connected to MUS in any way other than being a paying customer. I do agree about the importance of sticking with some sort of curriculum for the “building block” factor. Last year I slacked off with my 3rd grader and now we’re paying for it because he doesn’t know his multiplication tables which makes everything we’re learning this year much more difficult. I’m thinking we’ll just scrap it all and go back for a while.

Just our experience.

Khan Academy is an awesome place to view videos/alternative teaching of math.

Our family loves and uses Singapore Math. http://www.singaporemath.com You can have your son take the online teat for placement. Books are inexpensive. Teacher guides are very helpful to me and my children.

Math is not taught in the same sequence all over the world. Singapore does it a little different than the USA.

Your son may have hit a developmental plateau as far as math goes. Let it go and learn some other things for a bit. :-) He will be ready for more math growth again soon.

Have you ever seen the TV show MythBusters? An episode or two of that could help show the real application value of measurement, whether they are measuring — force, sound, speed, or the relative hotness of peppers (Scovill units!). I think conversions are a relatively minor aspect of measurement, and the most important thing is knowing why we measure things.

Ms. Penelope, The most effective way to teach a child Math is to hire a tutor who can effectively communicate with him. That sounds obvious, however finding a communicator is very difficult, probably less than one percent of the cross section of classroom teachers and tutors can probe the minds of children.

I’m not intending to bolster my ego, but I’m one of the miracle workers and I have an online tutoring service. If you would like a sample lesson for yourself, my website contains, coincidentally, a teaching technique for converting units such as English measurements to the metric system! I’m sure after reading it, you and your child will understand the procedure as clearly as you know your own name. Please leave a message for me. Thanks.

Penelope

Penelope, the following is a continuation of my previous message. I’ve included an updated website so you can read my information more directly. As you can see, I accept students with extreme difficulties, even those who’ve tried other tutors before who’ve been unable to help them.

Regards,

David

You should order the Everyday Math student math journals for your kids to do. If you google Everyday Math and find the publisher, you can order the student math journals online. One of the great things about these math workbooks is that there are usually only about 6 problems on each page and every problem is different. So you aren’t staring at a page of a zillion problems and dealing with the tedious task of doing the same boring thing over and over again. Also, the problems don’t just teach kids the rules for computing math problems. It really gets kids to really understand math. I’ve gone through the first, second, third, fourth and part of the fifth grade student math journals with my kids and I am now better at elementary school math than I used to be and I even majored in math!