The reluctant math learner

[Savoir Faire]

Hello all. Long story short. Two kids, ages 6 and 8.  We recently stopped Singapore math because honestly, it was going at too fast a pace for us-- the kids were not getting enough time to master a concept before going on.

We're back to working on simple subtraction-- a skill my 8-year-old seemed to forget how to do during Singapore math. Every day, every single worksheet-- I hear how HARD it is. 8-2? Gah! How am I supposed to know? This is so HARRRRRRDDDDD, I can't do it. I can't use my fingers. I can't use my abacus.

I always sit patiently with her...even long after the 6-year-old is finished. Even with all the complaining and moaning, I'm guessing she gets at least 80% correct. (Usually.) Sometimes she does much worse...but we all have off days.

This hour long complain fest is really getting old. I'm not a natural at math, so I'm definitely sympathetic to the situation. I just can't decide if math is really that hard for her or if she's just using the drama as an excuse.

But....she has to learn it. Should I just deal with the whining and keep working at it? Use some kind of chart? Hire a high voodoo priestess?

[beansmama]

Ooooh. I hear you!

My year old has a really rough time with math, and I have a rough time understanding her rough time, because seriously...she says she "can't" count on her fingers either. She can't subtract or add simple numbers that most kids could just say without thinking. BUT...it's gotten a little better since I sucked it up and put her back into 1st grade math. I just figured it was better for us to start from scratch. Some of the concepts are too easy and she breezes through them (and that makes her feel smart, which is nice for a change...when it comes to MATH!!) but others are really hard for her. We use Time4Learning - it's online, but they have a worksheet or two available to print for most lessons. Anyway, works for my dd who loves to be online ;)

Good luck!

[Lillian J]

Is it the remembering of the arithmetic facts that she's finding so hard? Maybe she could learn them more easily with games of all kinds, either hands-on or computer, or maybe she'd at least find it less painful. You might browse through my page of links to articles and websites that offer ideas - Go Figure! I wouldn't click on any till you've browsed through all the titles, because you might find just what you need lower in the list.

Several math enthusiasts I've known over the years have been adamant that children learn math better and have a better appreciation of it if they learn it with hands-on activities and games outside of a program until they're in higher levels - and that proved quite true with their own. When my son, who hadn't used a program, was 9 or 10, I took him to a math tutoring center to get evaluated, and the head of the center said he understood real math in a way that children don't tend to arrive at through endless worksheets. She said she spends most of her time trying to undo the damage that's been done through all the worksheets children do in school. We did use the Keys To workbooks for a while, though - they're bone simple and don't have a lot of worksheets. 

Lillian

[heatherdeg]

Can you just leave math alone for a while?  I mean, yeah--they have to learn it... eventually.  There have been several studies showing that pushing it on them early can actually backfire in their math achievement long-term (although the study I'm thinking of was specifically looking at early elementary/Kindy).  There are several countries that kick our arses in math that don't even bother with academics until the kids are 8yo.

When she's ready, she will pick it up quicker and more fluently than trying to fight with her.  Can you, in the meantime, just work on the math that comes naturally through life?  Cooking, shopping, building stuff...?  Maybe it is the drama.  Maybe she truly has a hard time (I seriously cannot do subtraction with my fingers at 40yo and I'm a math geek--it just completely stumps me because I don't know if I count THIS finger or start with the NEXT finger...  GAH!!!)

If you're not okay with letting it go, have you tried Life of Fred?  We've been using them and they are light on practice but strong on teaching the concepts in a way that kids seem to grasp pretty well.  They just published the "under 5th grade" series last year.  We're about to finish it.  We have friend with an artistic daughter who only wants to learn Calculus to find out what becomes of Fred.  

[SweetSilver]

We just checked out Anno's Math Games books from the library.  The last time we had them was over a year ago, and this time dd1 could nearly get through everything, even though we hadn't done any real math work that entire time.  I think it's true that with young brains, time alone can make a huge difference.

One chapter in Anno's math Games II teaches addition and subtraction using the story of a magic box.  It also shows pictures of real things that get more and more abstract until finally they are just circles.  It also teaches place value (tens), all without using any math more sophisticated than counting (and many puzzles you don't even need to count.)

What I like about this set of books is that I've been able to gauge dd's readiness for moving forward with actual algorithms.  She does these a little and enjoys them, homemade math "tests" dh gives her now and then.  In the meantime, she keeps herself busy with the occasional Sudoku puzzles and other games.  

I am all for the games at this age.  Battleship teaches coordinates and graphing.  Monopoly teaches simple addition (di) and more complex addition as well.  I definitely count origami as math.  

Regular, weekly allowance is teaching them several math skills, not just counting and monetary value but fractions as well ("quarter" refers to it being 1/4th of a dollar, "dime" is 1/10, "cent" is 1/100, etc.)  They don't understand these concepts yet really, but they are being introduced to it in a meaningful way.  One of these years, telling them about sales tax offers them a chance to learn about percentages (for now, I let the sales tax slide on most things).

As they get older, then I'll start keeping well-written math books around and start exploring math more academically.  At these ages (my girls are nearly-8 and 6) there are so many places to teach math that doesn't induce stress the same way as worksheets.  (Also, my girls really do love worksheets, but they are rare in this house and no one ever has to actually complete them.  Recently I reproduced a secret code puzzle using a number/letter graph but I made up the answers myself, like "HORSES ARE MY FAVORITE FARM ANIMAL".  They did 3 of these homemade puzzles in one day, then they don't ask for anything for weeks.

I definitely am a learn-the-concepts-behind-the-math advocate.  What I dislike about formal math is not just the method, but that it is presented in a certain order, and in my brief experience as a parent and HSing parent I've discovered that this order is, at it's best, irrelevant and at its worst a real obstruction to progress.  I learned this very quickly when dd1 understood multiplication 3 days after she understood addition, but subtraction took at least another year to sink in.  Most math quickly introduces subtraction after addition (being opposites, that's understandable),  yet many kids would do better just to jump to multiplication.

heatherdeg, I would love to know some of the troubles that your friend had to work through and how to avoid them.

[moominmamma]

I completely agree with the importance of conceptual learning, the efficiency of learning through life and play, the necessity of quiescent periods in children's mathematical learning, the arbitrary nature of much of what passes for "scope and sequence" in many math programs, and the benefits of delaying or slowing down formal math instruction in the early years. My ds was introduced to Singapore Primary Math at about age 6, but he disliked it, despite having many of the concepts and skills well internalized for practical application in real life. On paper, though, it was intimidating and confusing. As an unschooling parent I was comfortable doing nothing other than continue to model math as a delightful part of real life. At age almost-10, he decided to dive into the very same program he had balked at 3 years earlier. He was ready for Primary Math 3A, despite having not done any of the earlier levels, and he finished 6B six months later. He went from being (apparently) two years "behind" to being three years "ahead" in the space of 6 months. Awaiting readiness and motivation was definitely the right approach for us.

Having said that, I don't think Savoir Faire is at all unschooly in style, so I'm guessing she won't be comfortable taking math off the table for a while. So my suggestion would be to look at RightStart Math, because my impression is that it presents math in a hands-on playful way, but is systematic and structured and gives one the satisfying sense of "doing math every day" and progressing through an organized course of study. It is built to allow much more repetition than Singapore's consumable workbooks, and caters to a different learning style than the basic Singapore Primary program.  

Miranda

[pek64]

I was pushed hard in math by my father when growing up. As a result, I came up with my own ways of remembering things. For substraction, I just count up to the higher number (silently, of course). And the tricks I came up with for multiplication! I dislike pushing math as a result of my childhood.

I also heard, many years ago, that the Japanese students use an abacus until they can use an imaginary one!

All that said, I struggle with getting my son to do math. He just doesn't see a need for all te memorization. He has the ability, but refuses to put in the effort. It started with the multiplication tables.

My only advise is keep calm, try not to worry. Using an abacus would not be a stumbling block for me. Many adults use a calculator, so why should it bw different for children. Good luck to you.

[heatherdeg]

Originally Posted by SweetSilver 

heatherdeg, I would love to know some of the troubles that your friend had to work through and how to avoid them.

I re-read my post but I didn't see where I noted a friend that had troubles to work through...?  Are you referring to my statement about my friend with the artistic daughter?  I just meant that she enjoys art and hates math, but is enthused to get to (and through) to the Calculus book in the Life of Fred series at some point because she's just THAT interested in the story line.  She doesn't actually need to learn calc and her mother wouldn't push her to do so, but it's quite a statement that a kid that doesn't love math finds a set of teaching storybooks on a subject she hates enough to want to go past what is required of her... kwim?

If you're referring to something else, lemme know!

[SweetSilver]

No, that was Lillian.  I wrote that long post and then some details slipped out the other end and I never went back to fix it.  Sorry.

[Lillian J]

SweetSilver clarified what she was asking about - it was what problems the tutor had been trying to work with. What the tutor was referring to was the deadening of all those kids to math - making them think that stuff is math, and making them think they hate math. What she was so excited about with my son was that he hadn't had that experience, or at least not since his last year of school in 1st grade. We played around with math thinking, and avoided anything that would give him the idea it was something to dread. In fact, I got him Hands On Equations, the pre-algebra program, when he was 8 - it's actually created for kids that age and up - so that he could get the idea that algebra was a fun thing to look forward to. He never came to love math, but he also never learned to hate or dread or fear it. When he needed to get ready for the SAT for college entrance, he took a sample test, got a lot of good books, and worked with a math tutor to fill in missing pieces, and he did well on the test. If math were going to play an important role in what he wanted to do with his life, he said he'd have to study it more formally, but that isn't going to be the case.  - Lillian

Edited by Lillian J - 10/4/12 at 8:00pm

[pek64]

Getting back to math-- any ideas for getting those who would rather do anything other than math to actually enjoy math? Or at least tolerate it?

[moominmamma]

Originally Posted by pek64 

Getting back to math-- any ideas for getting those who would rather do anything other than math to actually enjoy math? Or at least tolerate it?

Play games with it: dominoes, chess, snakes & ladders, poker, cribbage, monopoly, yahtzee, UNO.

Build things with it: K'nex, Lego, wooden blocks, buckyballs, pattern blocks.

Craft things with it: weaving looms, knitting, crocheting, woodworking, origami, hand- and machine-sewing.

Cut and glue things with it: Kirigami, snowflakes, hexaflexagons, fortune-tellers, scrapbooking.

Cook and bake things with it: Muffins, cookies, squares, bread-baking, supper-cooking.

Make art with it: Mandalas, golden ratios, tesselations, geometric doodles, fractals.

Buy stuff with it: Give your child control over a small part of the family budget ($10 in groceries each week?), consider granting an allowance, make a loan on Kiva and watch the returns trickle in until you can re-loan. 

Marvel at it: Play with RGB and CMYK codes for colours in a computer paint program, watch Vi Hart videos, explore compound interest using a computer app.

Read about it: "The Number Devil," "Anno's Mysterious Multiplying Jar," "The Man Who Counted," "Penrose the Mathematical Cat," "G is for Googol," "How Much is a Million." 

Puzzle over it: Sudoku puzzles, number guessing games, imagine infinity, talk about whether "half of infinity" has any meaning.

Measure with it: Keep track of the height of a bean plant day by day, the temperature outside, your child's weight, how much electricity your family uses. Record, tabulate and graph the results. Get to now some spreadsheet software. See how you can manipulate your data.

If these sorts of math-y things are part of a child's life, very little formal study of math is needed to bring a child up to a high school level.

Miranda

[SweetSilver]

Originally Posted by moominmamma 

Make art with it: Mandalas, golden ratios, tesselations, geometric doodles, fractals.

Spirograph!  Found an old set.... still trying to find pens to use with it.

Bicycles can also teach some basics about ratios (and work, but then that's onto science--not that that's a bad thing).

[elizawill]

i'm using teaching textbooks with both of my kids this year (after years of using only CLE). my 8 year old son is using the 3rd grade level and it definitely starts at the beginning reviewing the basics. it was pricey imo, so i would recommend buying it used if you can find it. they have sample lesson on their website. my kids did the sample lessons before i bought it.  anyway. it has been a godsend this year for us.  to fill in any state standard gaps (as TT is written for homeschoolers), we play games online for the FCAT test preparation. anyway i felt it was worth mentioning. i've been very pleased with it.

ETA - oh...life of fred is good too.  i was fortunate to borrow the books, and the apples book and other elementary series go nicely with TT3 (or as a stand alone or supplement to any math curricula).

Edited by elizawill - 10/4/12 at 8:01pm

[Lillian J]

Originally Posted by pek64 

Getting back to math-- any ideas for getting those who would rather do anything other than math to actually enjoy math? Or at least tolerate it?

Here's some good reading on that:

From Boring to Board Games: Math Really Can Be Fun!

Crazy for Calculating - Making Math Fun

Home Education Magazine - Taking a Closer Look at Math

Lillian

Edited by Lillian J - 10/5/12 at 9:50pm

[pek64]

Thanks for the ideas! I'll try to let everyone know as the year progresses which work well for us.

[filteragainstfolly]

Originally Posted by moominmamma 

If these sorts of math-y things are part of a child's life, very little formal study of math is needed to bring a child up to a high school level.

This has absolutely been our experience as well.

DS informally explored much of the stuff mentioned in previous posts (with the addition of music-reading, which I believe was really useful to him in learning how to add and subtract fractions, but again this was an informal side-effect of learning to play a musical instrument, and not something he did "to learn fractions").

Math, integrated naturally as a useful and relevant aspect of DS' everyday life, gave him by age 10 the equivalent of what the average adult uses on a day-to-day basis. Because he'd been able to reflect, on his own terms, about numbers and how they worked, he'd acquired a much more profound understanding of fundamental math concepts, with none of the accompanying math-phobia that so many adults seem to have as a result of their early math drills and work-sheets (which encourage memorization/procedure rather than understanding).

If DS' math exploration had stopped there, he'd have had enough math to function smoothly through most of life's transactions, and I was okay with that. Honestly, there are many, many worthy paths in life that don't require algebra, let alone calculus.

However, six months ago, at age 13, DS decided he wanted to do high school math (he loves chemistry, and we'd discussed what the university requirements are for that). He plunged into Teaching Textbooks Algebra I without trouble, having done basically no formal math up to that point. The only gap he needed to fill was the multiplication and division of fractions, which he proceeded to learn in a day of worksheets we found online for free. He'd learned everything else he needed for algebra through everyday living math.

He's been acing the Algebra I program and will soon be moving onto Algebra II. Though he finds it easy, he does it out of necessity, not love for the material. But he continues to be self-motivated probably because, in addition to not having any of that math-phobia, he's now old enough to view math as a personal means to an end (chemistry).

I know it's become a tired cliché about homeschoolers being able to learn what they need through "living math", but our experience at the pre-algebra level has completely supported that. In our case, I think the key was to have DS view math as a meaningful and non-threatening part of his everyday life in the younger years, and then, once he was old enough, to engage him through an age-appropriate dialogue about what math he might need in his future. 

Here's a link to a thought-provoking essay on the current state of math education: Lockhart's Lament

[aderyn]

ETA a disclaimer really. First my computer is playing up a bit and I think I might only have read the first page of replies. Second, I am absolutely not trying to over-ride the unschooling approach, I'm just explaining what has worked for us, which has been a more structured approach. For all I know, the unschooling approach would have been as effective, its just that my personal hang ups don't allow me to leave math in the slightest to chance!

Just to add, we are a family where math is important, as parents we are a mathematician and a scientist-in-training and I do feel rather strongly about the importance of teaching math-to my kids. My experience was that despite coming from a mathsy family, despite going to a free-range school, I never really understood math and developed a strong self image of myself as someone who could not do it. I was actually borderline phobic about math for a long time, and self-identified as a non-math, arty/languages person. I've sorted this out now and am midway through a part time science degree but my god it is HARD to do it this way. I needed, when i was eight, for someone to sit me down and say, don't be silly, of course you can do this stuff, now what is actually the problem, lets sort it out. So I'm coming at this one as someone who strongly believes in the importance of early, good, inspired math teaching, especially for any kid who self-identifies as bad at math. I have to say, I'm especially on the look out for this with my girls because I'm aware of society telling them constantly that math, like heavy lifting, is something you get a man to do. I'm also married to a mathematician who is also (despite it not being his job) a really, really good teacher of maths and science. 

I'm not pushing this approach, but if, as I understand it, you are, like us, reasonably structured, you might find our experience helpful. Or not! 

Soooo what I have learnt so far (my kids are 9, 7 and 4, I'm aware I have an awful lot more to learn!).

First, I really do believe in the importance of play til around age 7. Both my older kids went straight from an early childhood of play to being slightly ahead in math (we use a computer program which happens to track them according to grade level-not my favourite feature).

Second, I believe in using manipulatives for absolutely as long as they need them. My just 9 year old is doing decimal and fraction work right now, and we absolutely still use manipulatives to explain the concepts, for him to use as long as he needs. We also use things like number boards, hundreds charts and so on. To be honest, even with the university level math courses I now do, if need be I use manipulatives for complex ideas. We have a good range of manipulatives, including coins for decimal/place value work. My rule is to ALWAYS start out visual then move to abstract only when kids can certainly cope. 

In terms of textbooks, my absolute favourite program is Miquon. Miquon is wonderful, the epitomy of a the hands on approach. We have never used it as a textbook though, sometimes we just used it as a a jumping off point for work. There is a teacher's manual with lots of great further activities, although for many of them you can easily work out how to supplement. When they had thoroughly finished Miquon we reluctantly moved to Singapore. But we did Miquon very thoroughly first, plus loads of maths games, real life maths, etc. I think if I had a math-reluctant child I'd actually just work with Miquon for a while, even if parts are too easy. I actually think you could probably go on til around 9 or 10 with Miquon, though mine moved on before than. It would certainly be my curriculum of choice if, say, I were teaching a math-phobic older learner.

There are other good books with a more structured approach, but I think what a math-reluctant child probably needs is a boost to their self-confidence in math (and every child is a mathematician, IMO) and Miquon is wonderful for that.

oh eta2. Don't use fingers, they are no good. You need something that can be put in one place to mean its already counted, IYSWIM. Even just coins are fine and better than fingers. Marks on paper. Anything.

[Tithonia]

The ideas people have posted are fantastic, but if you're still wanting another outside resource, I highly recommend Life of Fred. Here's the website: http://www.stanleyschmidt.com/FredGauss/index2.html

It's a great combination of a real approach to math and just plain fun.
 

[SweetSilver]

Originally Posted by aderyn 
 For all I know, the unschooling approach would have been as effective, its just that my personal hang ups don't allow me to leave math in the slightest to chance!

Just to add, we are a family where math is important, as parents we are a mathematician and a scientist-in-training and I do feel rather strongly about the importance of teaching math-to my kids. My experience was that despite coming from a mathsy family, despite going to a free-range school, I never really understood math and developed a strong self image of myself as someone who could not do it. I was actually borderline phobic about math for a long time, and self-identified as a non-math, arty/languages person. I've sorted this out now and am midway through a part time science degree but my god it is HARD to do it this way. I needed, when i was eight, for someone to sit me down and say, don't be silly, of course you can do this stuff, now what is actually the problem, lets sort it out. So I'm coming at this one as someone who strongly believes in the importance of early, good, inspired math teaching, especially for any kid who self-identifies as bad at math. I have to say, I'm especially on the look out for this with my girls because I'm aware of society telling them constantly that math, like heavy lifting, is something you get a man to do. I'm also married to a mathematician who is also (despite it not being his job) a really, really good teacher of maths and science. 

I know this thread is not about unschooling, so my comment here is a bit OT, but I have to agree with you that even unschooling parents would be wise, if children this age seem to be actively avoiding anything "mathsy", to look deeper into why so that they won't inadvertently mistake lack of readiness and meaningfulness for avoidance for just the reasons you are describing.

Sometimes I think my daughter pushes things aside from perfectionism when she sees others do it so much better, or "getting it" so much faster than her.  I made the mistake of making some tangram-style shapes by folding paper to get a precise square and triangle, etc while she was just cutting the shapes in her own way.  I was blissfully charging along, explaining how to get just the right shapes, completely ignoring her own efforts and I could see her deflate.  Too late to stop myself.  PHLBBBTTT!!  Just like that.  She had so much enthusiasm at first.  I should have waited and watched and let her have her not-so-perfect shapes and had *fun*.  Sigh!  I get so caught up I forget to let her have her own discoveries and get through her struggles without someone peering over her shoulder.  (And let her enjoy something despite its lack of geometric perfection.  Was that even necessary?  I don't think so!)