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How can I help my 12 year old daughter strengthen her math skills?

My strategy up until a year or so ago had been relaxed. I subscribe to the idea that the best motivation for learning is the intrinsic kind. Unfortunately it's become clear that my daughters intrinsic motivation to learn math is close to zero. Waiting and hoping that she'll fall in love with the subject seems like an irresponsible gamble.

My new strategy since a few months back is to force her to spend more time working on math examples, on her own and with me. So far it's hard to tell if this is helping. One definite result is more antagonism between the two of us. She's frustrated because she can't spend as much time on Netflix and I'm frustrated because she rushes through the examples getting half of them wrong (if I give her a set number of examples to solve) or drags her feet (if I tell her to work a fixed amount of time).

I made her play an iPad game that teaches basic algebra and that worked pretty well. This didn't made the work more enjoyable to her (she still hated it), but it took away the appeal of rushing it or dragging her feet.

Are there similar gamified approaches with examples to last her all the way through high school? Pointers to any iPad apps or websites like that are very welcome. Please note that English isn't her first language, so anything language-independent gets a bonus.

I'm also open to other, non-technical, approaches.

Some updates and further thoughts.

To answer your questions: I'm not homeschooling. Grade wise she's passing but not much more, which has me worried that she'll be in for a real uphill struggle in the coming years if she does not get a stronger foundation now.

When I was her age I loved math and I loved programming so much so that I ended up becoming a programmer. For the longest time I thought that any person could love any subject given the right impetus. First time I started doubting this was when I spoke to one of my instructors at University. He was involved in a project teaching philosophy to kids. Being a parent himself he tried to interest his own kids. One of his kids was totally fascinated by the subject and his other kid just found it boring.

Today, as a father of three, I find this very unsurprising. Children, even within the same family, with the same upbringing, are very different and have very different interests. My five year old is showing more interest in math than my 12 year old did at that age. My three year old is has an unfearing, adventurous side that is completely absent in her older siblings. People are different. Unfortunately the educational system doesn't really care about that. In three years my 12 year old will be forced to do equations and trigonometry, and failing to master those subjects will limit her choices for higher education, even if she decides to major in history or some other subject that doesn't actually require any math beyond basic addition.

"How would your daughter like to learn origami?" Opal E asks. Well a couple of years ago she asked me to show her how to fold a paper plane. So I took out a paper and started showing her: "You fold along the middle. Then you bring this edge down to the middle line." Right about there she stopped me and blurted out in frustration: "Why are you jabbering about lines? Just show me how to do the damned plane!" I don't think modular origami is going to be a hit with her.

jonsca suggests that I leverage her interest in Netflix by introducing her to the inner workings of recommendation engines. I'll give it a try but I'm not too hopeful about it.

A couple of answers suggest introducing an element of play. Right now talking about math with her is more like pulling teeth. Going from that to a state of playfulness is hard.

I feel that the answers given here fail to see that some kids are just not fascinated by math, no matter how many trippy fractals you show them. How do we, as parents or educators, help these kids attain the mathematical knowledge they need to function in society?

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I can't make my wife love the music I love, and I would never attempt to tell my daughter (15 now) what subjects to have passion about. You're not clear, in my opinion, about what her resistance is or where she stumbles. Teaching your own child is tough, but the first step is that understanding. –  JoeTaxpayer Jul 20 at 23:39
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Is your daughter doing okay in math in school? Or is she homeschooled? –  mweiss Jul 21 at 0:04
    
I share mweiss's question -- are you homeschooling, or supplementing what happens in school? –  PurpleVermont Jul 22 at 2:38
    
I feel that your extra thoughts may have unfocused rather than focused your question. Specifically, you ask how to help kids attain necessary mathematical knowledge, but earlier you say that a history major needs only master basic addition. I am guessing one of those is meant more as a dramatic expression than an accurate representation of the extent of essential mathematics knowledge. More importantly, you express dissatisfaction on the basis that the suggestions are hard. I will edit my question to address your changes. –  JPBurke Jul 23 at 1:06
    
I think you need to start from the other end: What is your daughter interested in learning about? –  mweiss Jul 23 at 1:50

6 Answers 6

The best thing you can do for your daughter is to talk to her and especially have her talk back to you. You noted that she doesn't like doing exercises. If you want her to like math, and she doesn't like doing exercises, more exercises are not going to help her like math. She is already intrinsically motivated to do certain things. People learn when they are faced with a problem they are motivated to solve; unfortunately, many problems of 12 year olds do not have mathematical solutions. So what you have to do is construct situations that are desirable to be in, in which mathematical thinking can be a part of them.

If you have a good relationship with her, her desire to interact with you (which may wane a little into teenagerhood) is an advantage you need to use. Instead of suggesting games on the iPad, or doing exercises in isolation, I'm going to suggest more interaction between the two of you in ways that show her other aspects of mathematics.

Games like the ones here involve mathematical thinking and involve some of the content areas that she is encountering in school at her age. And playing them with her has the advantage of you helping her to see mathematical patterns. Or, as she notices things, you can help her mathematize what she is seeing (by talking about ways to generalize, use the scholastic langauge out of the books she's using in her math classes, etc.). If you are working with her, that also solves the language problem.

Your question specifically was "How can I help my 12 year old daughter strengthen her math skills?" -- you didn't specify which skills, so I am focusing on thinking mathematically in general rather than any specific problems. Especially because your description of her reaction to working exercises does not suggest "more exercises" is the answer.

The answer is: spend a bunch of time with her regularly talking, but have that talk involve math. Play games that involve mathematical thinking. Also, listen for the things she likes to do and think of how any aspect of mathematical thinking can be a part of them. Instead of working more problems and worrying about whether she got them right or wrong, have her talk more (to you) about the few problems she is doing. Make sure she is doing most of the talking. Teach her to explain her reasoning in the problems. When she gets a problem wrong, focus on getting her to explain what she did and what she thought, and how she justified her thinking. This can help her to be more reflective as well.

It may not make her like working exercises any more. I can't say. But it may help her have a way you can show her that she and math can have a better relationship than what she may be starting to believe.

Addressing your further thoughts (which may or may not be worth anyone's time, since they address issues related to, but apart from, the original question. This reflects the addition's slightly wider focus extending to thoughts about people in general.):

You express dissatisfaction with the answers given on the basis that they will be hard to follow through on (specifically, that playfulness in math education with your daughter may be hard). It could be said that this sort of difficulty is at the heart of math education - that teaching can be a very difficult endeavor. Judging by most media reporting I see about teachers, this is a profound and uncommon realization you (may have) arrived at.

You also note that people are different. You're uncovering truths about education here that I think are very important. When you hear people refer to a past of education when traditional methods were dominant and everything just worked better, this difference you refer to is what is responsible. In other words, we had a system that catered to very specific types of learners (i.e. the ones who were likely to succeed almost no matter what). And so, we had a filtering function. And the students who succeeded believed that the education that resulted in their success was the best type. And that others who did not succeed just had some sort of failing.

When I referred to you talking to your daughter, and more importantly getting her to talk, I am mentioning precisely the only thing in the world that can address your observation that people are different. Even knowing that people are different we only learn how they are different by listening to them. Where you have generalized about the education system to be uncaring of student differences, I will grant you that this is a better description of more traditional approaches to mathematics instruction. Research has brought upon realizations that understanding student thinking is (or can be) an important key to improving teaching (Fennema et al., 1996).

Many people have taken this realization and tried to understand how this changes things like teacher preparation and instruction inside (and outside) the classroom. And that has often involved getting students' ideas to be a part of instruction more and more.

Perhaps it seems backwards. Why should students be talking more -- don't we want them to learn what we think is right? But, ignoring that misconception of learning as putting our ideas in kids' heads, if we want to address your concern about individuality of people, we need to understand those differences. We need to understand those students. And that means more listening and more interacting. How else do you respond to differences?

To narrow this down back to your case, none of us here can tell you what motivates your daughter or what is best for her in her specific situation. That she doesn't want to do exercises does not uniquely identify her. The responses given are not only notable for the playful aspects. They have also applauded and encouraged your own interaction with her in different activities. Bot parts of that are important: your involvement (talking and listening) and trying different activities.

Whereas "play" may indicate games to you, I find a more helpful (to your situation) use of the word in the writing of Bruner. Bruner (1976) noted that an important function of play in development is the combination of behaviors that might not otherwise be tried. Clearly, this can result in something being discovered. In your daughter's case, the hoped-for discovery is some activity that is unexpectedly engaging to her but also one you can help make mathematically meaningful by your presence. That last part is a special challenge of math teaching. But choosing the right activities can help with that (and you've gotten some suggestions in the responses here). Play, to Bruner, also served to provide a lower-stakes environment in which mistakes are acceptable. Since it is clear that your daughter becomes frustrated with exercises, some of the respondents here are probably thinking in line with this when they suggest playful engagement. It reduces frustration.

None of this changes my answer, and I think much of it is in line with he other responses you're getting. I hope it helps you understand a little better why you are getting these sorts of responses. And also to understand that nobody really thinks that helping your daughter suddenly becomes easy with any of these suggestions. Consider them part of a large bank of things to try because, as you noted, people are different. That makes your daughter uncharted territory. And you are the one there with the most motivation (and time, relatively speaking) to chart it.

Cited:

Bruner, J. S. (1976). Nature and uses of immaturity. In J. S. Bruner, A. Jolly, & K. Sylva (Eds.), Play: Its role in development and evolution (pp. 28–64). New York: Basic Books, Inc.

Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A Longitudinal Study of Learning to Use Children’s Thinking in Mathematics Instruction. Journal for Research in Mathematics Education, 27(4), 403–434.

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@Mathdad - I hope my updates help. Specifically, perhaps you can see these answers as a bank of related suggestions. –  JPBurke Jul 23 at 1:55

In all honesty, and I say this not to be harsh, but it sounds like what you are doing is going to avert her to mathematics completely, and this is not desirable for obvious reasons.

As the other answer touches on, numeracy, which is a skill that is most useful to students, regardless of their future vocations, is something that you should be emphasizing, if anything. It's helpful to have an intuition about "Exit polls indicate 54% of people (margin of error 3%) approved of the town referendum" and whether she'll buy enough paint/carpet to cover a room, etc., rather than being able to solve for "X". If she likes Netflix so much, discuss with her the process of movie recommendations, as this was a super-hot topic in machine learning a few years ago. This will give her an opportunity to apply mathematics reasoning to something she's seen and is important to her, and she's able to learn about correlation and regression in the process (I realize the process of recommendations requires a lot more than that, but it's a start).

Finally, she may end up gravitating towards "formal" math in the long run anyway if what she is truly interested in requires some mathematics. Many students (young and old) like to build things and get introduced into subjects like engineering through a "product design" sequence in high school. These students soon realize that to get anywhere with the engineering theory, they need to strengthen their mathematics skills, and the association becomes more natural, rather than the regimented approach that many instructors and parents are using.

I applaud your involvement in your daughter's education, and I think your philosophy is great, but it is my humble opinion that it may not serve her best interests in the long run.

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I will echo the sentiment of other commenters here and say that the way you are approaching seems like it will squelch, rather than foster, any interest in mathematics your daughter may have. I will share my personal experience with my father, an engineer, and his father, an engineering professor, in an attempt to help you find ways to help your daughter have better mathematical reasoning and possibly begin to enjoy math. At the same time, this may require you to rethink your opinion of what "math" is, and to divorce any opinion that calculation is math.

The answer is, in my opinion, in play. Not just forcing her to play, but playing yourself. I always saw my father messing around on his computer. I think he had a mandelbrot set generator when I was little. He'd show me how clicking in different places led only to more complexity, and say they used math to generate it. I spent an hour clicking different places, going back up to the top and starting over. Later on he showed me the snowflake fractal (Koch's snowflake). I learned how to draw it myself. One day he asked me how long the snowflake's edge was. We spent some time discussing its edge length and area. Discussing fractals can be beneficial if your daughter struggles with fractions and fraction addition. You don't have to go to limits, but just try to figure out how long the snowflake's edge is with iteration 1, 2, 3. My dad was not just asking me questions, but asking himself questions and sharing them with me, stuff like "I read somewhere that flower petals follow the fibonacci sequence, but I don't understand why. I'm curious. Want to join me counting flower petals?"

I'll make a plug here for geometric games and trinkets. My dad had little puzzle toys, you know the topological ones, where you had to get a ring off of the rod, or free the rope from the wooden shape. My grandfather had 3d puzzles where we tried to arrange the blocks into a cube. My grandfather had a illusion mirror (I'm not sure what they're called) that had two parabolic mirrors and formed an illusion of whatever was inside it at the top.

Tessellation blocks are fun to make patterns with, especially magnets. Give her some to decorate her wall with (but don't tell her they have anything to do with math), possibly get a magnet board on her wall. She might have some fun creating new patterns on her own, and it will give her geometric intuition. Any geometric game or puzzle can help--tangrams, tetris... There is evidence tetris can improve cognitive function and I would not be surprised if other geometric games can do so as well.

How would your daughter like to learn origami? It was a favorite pastime of mine. Make her some different origami figures, share them with her, particularly ones that move -- then find her a book and let her have at it. Preferably one that includes modular origami at the end. Kirigami is another good variant.

Lastly, build something with her. As a kid my grandfather built a trebuchet. Figure out something she'd like to make and have her design it. Help her out. If you are learning at the same time, that's fine -- she needs a role model for learning, not just one telling her the answers. She needs to see that it's okay to not know the answers, and see how you find them. She needs to see you asking questions and being curious. She may very well see math as ver prescriptive and oppressive, and I hope that if you do some of the things I've listed here, she might begin to find more joy in it.

Edit: In any sense, rote calculation will be miserable for her, and I'm merely aiming to suggest some things she can do, that might be fun/interesting, that would also enhance her math ability. Another option would be to try and find some authentic tasks at her level. People don't learn unless they're motivated to learn. Here are some examples for math.

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I'll reiterate the suggestion to play games with your daughter and give her games to play, rather than requiring her to do exercises. If your daughter has a limited amount of "screen time" (for Netflix, video games, TV, etc.) you might allow her to earn extra for any time she spends on one of these games (which would also not count against her limit, since they are "educational").

Some suggestions, in addition to the excellent games linked by JPBurke:

Sudoku -- you can find these all over the place, and many kids who don't like math do like solving these. If she likes Sudoku, expand her horizons to KenKen and Kakuro which require some arithmetic. A lot of my students who "don't like math" enjoy working on KenKen and Sudoku puzzles.

KenKen is similar to Sudoku, but requires numbers in certain outlined regions to add up to a certain sum (in the simplest version) or to adhere to other similar restrictions.
KenKen online: http://www.kenken.com/play_now
They have a mobile app too: http://www.kenken.com/store/mobile

Kakuro is another kind of Japanese number puzzle -- these are like crosswords but you have to make certain sums, using each digit only once per entry. Two places to download Kakuro for printing: http://akidsheart.com/math/prints/kakurop/index.html
http://krazydad.com/kakuro/
play online here: http://www.youplay.com/games/view/kakuro/ (among other places)

I don't have an iPod or iPad so I haven't tried this one but it looks excellent: https://itunes.apple.com/us/app/wuzzit-trouble/id600190128?ls=1&mt=8

This is a great game that will help with fractions: http://illuminations.nctm.org/ActivityDetail.aspx?ID=178

This one is good and quick for thinking about numbers in terms of their factors: http://illuminations.nctm.org/Activity.aspx?id=4134

The SET daily puzzle is great for finding patterns: http://www.setgame.com/set/daily_puzzle

Hope that helps.

One bonus game: The Logical Journey of the Zoombinis is an excellent game for developing logic and problem solving skills. Unfortunately, it's an old PC game that doesn't run well on modern computers. But apparently TERC is planning to put out a mobile version sometime this year. https://external-wiki.terc.edu/display/ZOOM/Home If that happens, it's definitely worth getting.

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First, I think it's great that you want to get your daughter to like math. However, this seems both ambitious and (based on your descriptions) possibly misguided. It seems like your main stated worry is her possible future struggles with mathematics, rather than her possible future love of it.

What would you do if your child were struggling with a subject such as English* or Science, or another subject where early struggles can indicate future struggles? You don't have to love Shakespeare to get an A in English, but you may have to work harder on your essays and your reading skills. Along these lines, your emphasis on "math" (and trying too hard to encourage a love of it) may actually be causing you and your daughter to lose track of a more general fact: If a struggle has to be overcome, sometimes you have to overcome it, whether you like it or whether you prefer Netflix. This is not a problem unique to math: Most students need to work hard to get good grades.

On the antagonism from your daughter: It's unfortunate that these kinds of conflicts can cause antagonism between parents and children, but it happens, and maybe someday she'll realize why you chose possible antagonism over letting her flounder in mathematics. That said, you can still try approaches that don't antagonize her too much. Even small changes like, when she wants to just "know the answer," telling her the answer might signal that you are willing to listen and work with her. (This is an imagined scenario raised as an example; I know you didn't mention such an interaction in your original post.) Different students gain confidence in different ways, so it'll be important for you and her to explore the ways in which she can gain this comfort with mathematics.

Finally, at 12, she may be socially in-tune enough to realize that the games you propose are simply attempts to get her to do math. Depending on her personality, a certain cynicism may turn her off from these games. If so, you may be better off telling her straight that she simply needs to do better at math in school. Or that you care about her future, and while you know she doesn't like it, she has to do it.

I'd like to say one more thing about teaching math, because I know a lot of mathematically inclined people become caught up in teaching the love of math rather than focusing on the real need for math. It is easy to hang onto the idea of the student who learns to love math under your tutelage, but the majority of students benefit simply from feeling confident or comfortable about math. While we should encourage enthusiasm, we shouldn't create the illusion that mathematics requires enthusiasm, nor the illusion that it is a realm for only those who love it. Mathematics is also a real necessity, and whether you like it or not, you need to do it. Many of us view math as play--but for most people, it isn't; especially when they begin to dislike it.

This brings me to your question: "How do we, as parents or educators, help these kids attain the mathematical knowledge they need to function in society?"

While I have no specific answers aside from what I've already said, I should say I was very much influenced by Lisa Delpit's "Other People's Children," where she talks about the same issue from the perspective of teaching English to underprivileged students. (She focuses also on students in cities, and in Native American Reservations, in the United States.) Her book influenced my educational philosophy greatly, and I recommend it for anybody interested in education in the United States.

*I apologize for using English as an example, but I don't know where your daughter is growing up, or what the equivalent "native language" class is in your schools. I also apologize if my answer seems to center on societal values that aren't helpful to you--I've worked mostly with inner city students in the United States, so my thought process is probably biased by that experience.

Also, in a completely different direction: Depending on your daughter's personality, a book by Danica McKellar may help.

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Entice, don't require.

Play around with things at the edges of math. Might she like programming in Scratch? Might she like the book The Number Devil? What about chess and go? Does she like you to read to her? Read her The Man Who Counted.

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