If you've ever had to help your child with math homework, you really appreciate their teachers, who do it every day. "Math anxiety" isn't something only kids experience.
Maybe you haven't seen an algebra formula in years, and weren't that comfortable with them when you were a student. Maybe you're a skilled mathematician, but don't know how to explain what you're doing to a child. Whatever the case, math homework can leave parents feeling every bit as frustrated as their children. Homework doesn't have to lead to unpleasantness, though.
What I've learned through my own experience—as a teacher, a researcher, from helping my own children, and now watching my daughter work as an elementary school mathematics teacher—is that communication is (excuse the pun) the common denominator when it comes to making math homework a positive experience.
The National Science Foundation (NSF), where I work, is dedicated to research. We support scientists across the country who study learning and education systems. But we're also teachers at heart. On lunch breaks in the past, a group of us gathered to help our NSF peers with their own questions about how to help their kids learn math.
Do Soylentils have better tips, things that have really helped their own kids learn math?
(Score: 0, Offtopic) by Anonymous Coward on Saturday May 13 2017, @05:08AM (1 child)
Since the homework is almost certainly going to require only rote memorization to solve, the kid shouldn't need help to be able to find the correct answers. Maybe they will need help in actually understanding the material, but at that point, you really should just homeschool them if possible; it would probably be more effective than the disaster that is our education system, and would be more helpful than just occasionally helping with homework.
(Score: 0) by Anonymous Coward on Saturday May 13 2017, @09:50AM
but at that point, you really should just homeschool them if possible; it would probably be more effective than the disaster that is our education system,
Yeah, at your "homeschool", your precious future nabobs will not be brainwashed into conformity with things like "math", and "history", and "reading" and "riting" and "rithmatic". You can teach them whatever you want! Like how other races are inferior, how Mama likes being chained up in the basement, and why you should never trust cops, or tell them about all the bodies buried in the back forty. Yeah, homeschooling! Make Amerka Grate Agin!!!
(Score: 4, Insightful) by Anonymous Coward on Saturday May 13 2017, @05:21AM (23 children)
Stop teaching math. It just doesn't work.
For really gifted kids, math at school is incredibly boring. Endless repetition of things they already know. Their desires for more fulfilling mathematical knowledge are left unanswered -- not lust for more complicated mathematical formulae, but joy that comes from dabbling in something that can be as abstract as one wants. Math in schools is not leaving anything to the child to discover on its own... and that is how schools lose mathematical prodigies, instead of fostering their talents.
For the rest, math is just an obstacle to overcome, not a joy to be had, or a useful thing to learn. And as a result, they just don't learn it. If anything, they just memorize.
One of the examples given, was 1/3 + 1/4. I dare say that it is not a problem of lack of genuine understanding by the child, but a problem of lack of any interest in the problem. Mathematical prodigies will do the task without even realizing that there exists a problem, the rest will do the task by remembering an arbitrary rule without realizing what is the actual problem they are actually solving.
(Score: 3, Insightful) by kaszz on Saturday May 13 2017, @05:25AM (11 children)
Gifted kids ought to be smart enough to outsmart school and workaround it..
(Score: 0) by Anonymous Coward on Saturday May 13 2017, @05:41AM (9 children)
By quitting and furthering their education another way, you mean? I agree.
But if that's not what you meant, then they would have to waste their time completing useless assignments, and that's time they could be using to actually learn something. If something is a waste of time on a very fundamental level, then no amount of workarounds will give you your time back.
(Score: 2) by kaszz on Saturday May 13 2017, @06:23AM (8 children)
I'm thinking that all they need is to get the entrance exam to high school or possible college right. In the end it's about getting past employers screening or having enough skill to start a business by oneself. All this is just a big sign that the school-job-death treadmill has past the best before date.
(Score: -1, Flamebait) by Anonymous Coward on Saturday May 13 2017, @07:20AM
getting past employers screening or having enough skill to start a business by oneself
Bullshit a small number of people and get a job, or start a business and bullshit a large number of people. I see a fucking pattern here and it's BULLSHIT.
the school-job-death treadmill has past the best before date
When all you PRODUCE is BULLSHIT, your civilization is past the best before date.
(Score: 0, Insightful) by Anonymous Coward on Saturday May 13 2017, @09:03AM (6 children)
When I was a kid in school, I truly thought I was going to be valued according to my grades.
Now, that I have passed into retirement, and went through this, I know the grade thing was to teach us to be good subordinate minions, to those who knew how to play the game.
Playing the game has nothing to do with math. Why do all the big Ivy-League schools emphasize their sports teams so much? That is where one learns to "play the game".
Minions do math.
Good grades are only an indicator to the Player who is going to take subordination well.
(Score: 1, Interesting) by Anonymous Coward on Saturday May 13 2017, @09:54AM (5 children)
You are an idiot, trying to externalize your lack of success.
Schools emphasize sports because that is the main source of alumni support. Everyone knows that.
Generalized qualitative analysis scales, like grades, are admittedly superficial but necessary standards.
Let me guess: you're an artist.
(Score: 0) by Anonymous Coward on Saturday May 13 2017, @11:29AM (1 child)
Very perceptive! You are right! The word "artist" comes about as close as can be to describing me.
You may consider me an idiot, however I was just trying to discourage any beliefs that excellence in math was required for career success.
The most successful people I have known were not necessarily academic.
They knew how to play the game.
I did not. I did things the hard way. Maybe the word "idiot" is appropriate.
I am happy we can post AC here, just so we can be brutally honest.
(Score: 0) by Anonymous Coward on Saturday May 13 2017, @11:45AM
"Well, you're a good man, lieutenant. A good man always knows his limitations."
~ Inspector Callaghan
(Score: 1, Interesting) by Anonymous Coward on Saturday May 13 2017, @05:37PM (2 children)
You are an idiot, trying to externalize your lack of success.
Haha! Your inferiority complex and jealousy is bare naked on display! Straight A student here, 99% percentile on standardized tests, etc etc, who agrees with GP. Guess I'll need to fish out the login and correct GP's -1.
I wasted so much energy earning those straight As, and they were meaningless. I should have been learning about how to bullshit, as another AC noted, and working on trying to become a sociopath instead of wasting my time and energy on "accomplishments" that had absolutely NO value. None. Zip. Zero. Nana.
(Score: 0) by Anonymous Coward on Saturday May 13 2017, @05:40PM
99th percentile
Whoops! I guess an IQ of 160, which is probably average if not a bit low on this site, is no defense against not having had one's morning tea yet!
(Score: 2) by kaszz on Sunday May 14 2017, @10:21AM
Was that straight As in elementary, high school or university? and what major subject?
I'll guess it matters if you straight A major in say physics or English literature.
Grades are usually only good to impress employees (bypass HR) or get a pass to the next academic level.
(Score: 0) by Anonymous Coward on Saturday May 13 2017, @10:16PM
And gifted athletes ought to be able to subsist on double cheeseburger and fries diets. That doesn't mean their performance and healthy wouldn't suffer.
(Score: 5, Insightful) by bradley13 on Saturday May 13 2017, @05:54AM (10 children)
I have to disagree with you. Part of math - or indeed any subject - is rote memorization. Personally, I remember having to memorize the multiplication tables in 3rd grade: 6*7 = 42, 6*8=48, etc.. Boring, repetitive, but utterly essential if you want kids to be able to multiply arbitrarily large numbers. Part of what I see in "new-fangled" teaching methods are futile attempts to make the rote-learning parts magically disappear.
The second part of math is teaching systems, and systematic work. Being a math nut, I taught my kids a lot of their basic math before they got to it in school. When we made the transition from adding single-digit numbers to multiple digits: I emphasizes the system: If you carry from digit 1 to digit 2, then you've discovered the system that works for digit 3 and digit 4 and digit 5 and... Schools stop at 2-digit numbers, and the students in their class "didn't know how" to add three digit numbers. That's a huge error in presentation by the teachers.
Building on those foundations comes the problem solving. At each level, teachers need to find practical, interesting problems for the kids to solve. At the lowest level, these are the word problems: "Billy has 15 pieces of candy. He wants to share equally with his two friends. How many pieces of candy does each kid get?". The mistake I see made by teachers (and parents) at this level: They try to retreat back into rote learning,so kids memorize the answers to individual problems, instead of understanding how to solve entire classes of problems.
If you pull off all three steps correctly, kids see that math is a useful tool, something that does apply to their daily lives. The problem is: kids with math-allergic parents won't get the support they need. And far too many elementary school teachers are math-allergic themselves, and don't understand even basic math well-enough to pull of the steps described above. Not sure how to solve that problem, unless it's by having separate math instruction from the earliest ages.
Everyone is somebody else's weirdo.
(Score: 2, Insightful) by Ethanol-fueled on Saturday May 13 2017, @06:41AM (4 children)
Kids don't need math parents to do well in math, there are plenty of non-parental resources available for B̶l̶a̶c̶k̶ ̶s̶t̶u̶d̶e̶n̶t̶s̶ kids with busy parents, what they do need is a parent or guardian or two willing to kick their ass if the kids don't do what it takes to pass math.
Unfortunately, the threat of violence is no longer a deterrent because in America that can get your kid taken away and you charged with a felony. Which means the kid can scream and cry all night wanting to play X-Box instead of doing boring things like memorizing multiplication tables and parents literally have no choice between appeasing the kid and being ran through the courts.
(Score: 3, Insightful) by anubi on Saturday May 13 2017, @09:35AM (3 children)
Ethanol... your observation about physical parental discipline:
I was raised with physical discipline. I would say in retrospect that it was best that my Dad did it than to have a Law Enforcement Officer do it.
I would not consider a lack of interest in math a reason for discipline, no more than I would consider a lack of interest in sports ( guilty as charged ) a reason.
I was really good in math. That did not mean I was a success in the workforce. I believe STEM is really overhyped by those wanting cheap minions.
However, I will not tolerate things like bullying, shoplifting, vandalism, or other social nuisances which would be sure to make my kid end up in prisons.
So, today, its a felony if Dad has to resort to physical means... so why is it not a felony for our Law Enforcement Officers to do what Dad was supposed to have done?
Believe me, they will also resort to physical means if they have to.
Our Law Enforcement Officers do not need to be tasked with doing what Dads should have done.
You just nailed one of my biggest fears on being a dad.
The other main fear I have is divorce law.
I do not believe the modern guy stands a chance in today's legal environment when it comes to family things. I do not even know where to start. My reaction to all this law was to avoid this part of life.
Probably just as good for all concerned, anyhow, except for the lawyers.
"Prove all things; hold fast that which is good." [KJV: I Thessalonians 5:21]
(Score: 3, Insightful) by aristarchus on Saturday May 13 2017, @09:56AM (2 children)
The other main fear I have is
Quadratic equations?
Infinitesimals parading around as integers.
Irrational relations, Pi, Theta, and their kin.
Prime numbers, how do they work? Is it like magnets?
And you are afraid of divorce law? Wow, just wow.
(Score: 4, Touché) by maxwell demon on Saturday May 13 2017, @10:16AM
I never heard for someone whose private life failed because of the failure to solve a quadratic equation. On the other hand, the consequences of a a divorce can certainly lead to a failed life.
The Tao of math: The numbers you can count are not the real numbers.
(Score: 0) by Anonymous Coward on Saturday May 13 2017, @04:30PM
I'm affraid of The Donald. He's an irrational number.
(Score: 1, Interesting) by Anonymous Coward on Saturday May 13 2017, @06:49AM
You seem to misunderstand what I am trying to say. Every single part of human knowledge requires understanding of facts, and You cannot understand something without first remembering what it is -- I agree with that. And I'm not trying to push something that will magically make memorization disappear. The crux of the problem is in what You had said: teachers at some level retreat to rote learning. But that is just a symptom of a problem -- that educators have to teach people who have no interest nor ability in the subject. The only way for a teacher to do so to a class of X, where X is sufficiently large, is rote memorization -- which for mathematics looks like it works, because each year students show that they can solve progressively more complicated "problems". So that is the first thing that I'm trying to say: stop teaching it to everybody.
Maths is still required for some tasks, though -- but mostly to show precise relations between real world objects. But the problem I see with education, is that kids are shown the solution to a problem before they even know what the problem is.
The candy example is almost good: but make kids actually do things, and then show them a solution. Show them two heaps of candies and make them choose which one they want. Or show them two heaps of peas, and make them choose which one they prefer to eat. Which one is smaller, and why? After several attempts, on different objects, they will get it, although they will probably be unable to describe how they do it. That's the second thing: don't start by making students learn the solutions to problems they don't know about, but describe (or even better: help them describe) ways of solving problem they already know. This can show them that mathematical notation is useful for describing general solutions, which can be applied to various classes of problems. But, as You hopefully see, this is totally impossible without rote memorization (I have to remember the tasks that I have done). But mathematical notation actually requires less memorization and is more general to problem solving, than solving the same problem over and over again for different kinds of objects. Rote memorization of mathematical notation is also required, but this can be done eagerly by children only after they can understand that it actually helps them, and saves them effort.
Now for systematic work: again, children learn by doing, and not by me saying things to them. They have to be shown that systematic work pays off, right now. But that can only be understood by them iff they show interest in a solution -- and that is usually not so in the case of mathematical problems shown in class and at home. If anything, mathematical problems are reduced so much because they not only have to be described in one class, but usually a solution to them has to be describable within the duration of the same class. There simply is no time for systematic testing of hypotheses -- systematic work and systematic reasoning are two different things. When can a child have the leisure time to sit down and think for an arbitrary amount of time, to employ their minds to come up with different solutions to problems and allow them to test each one systematically? Certainly not at school, next period is biology, drop that maths, and after that is history, stop thinking about that biology. I think, the reason why You were able to teach Your children before they went to school is because they have had the time to understand the terms You tried to teach them in their own time.
(Score: 0) by Anonymous Coward on Saturday May 13 2017, @07:34AM (2 children)
I have to disagree with you. Part of math - or indeed any subject - is rote memorization.
Why are you doing this? You say that "part of path" is rote memorization, but schools concentrate almost entirely on rote memorization. Your comment is therefore irrelevant. Our school system is an utter abomination and it always has been.
Of course you need to retain information to some degree, because otherwise you'd never learn anything. I don't know a single person who says otherwise, which is why I get tired of the 'But some memorization is required!' responses.
Part of what I see in "new-fangled" teaching methods are futile attempts to make the rote-learning parts magically disappear.
No such thing is happening. Instead, they pretend they're not doing rote memorization, but in reality, they are heavily relying on it. What is missing is a true, deep understanding of the subject. We are not encouraging people to be real academics, but mindless drones.
(Score: 2, Interesting) by anubi on Saturday May 13 2017, @10:18AM (1 child)
When I help the neighbor's kids with math ( usually algebra ), I take over an old DOS laptop loaded with GWBasic, MathCad for DOS, Borland Eureka, and Borland C++ for DOS.
The kids always get hung up on word problems, and how to convert a word problem into equations - and what they even mean.
So, we start off talking about the word problem. What the unknowns are, and their relationship to each other.
Throwing all the arithmetic into the fray quickly derails the understanding I am trying to teach the kid... so I have the computer deal with it until I can get the kid seeing the larger picture of how to abstract some unknown number as a variable. In my experience, that has been the biggest hurdle of Algebra. Once I can get the kid knowing that "X" represents a number, but we don't know what that number is... I am pretty well on the way.
I start off pretty simple. Let X=10. Print X. Let X = X + 5. Print X. Then once the kid catches on, go from there.
When I get done, the kid can conceptualize the word problem into an equation.
I will use the MathCad for more intensive maths, such as calculus or linear algebra, just so we can concentrate on the math, not the arithmetic.
Otherwise, I fear the kid will get lost in the minutiae just as I got so lost in the minutiae of interpolation of logarithm and steam tables in my college thermodynamics classes that for years I did not see the big picture. Not until a computer shouldered the burden of all that arithmetic minutiae and let me focus on what was really going on.
There is no call for me to calculate square roots the long way. Just knowing what they are is what I need. Same with integration and differentiation. Knowing what and why I am doing this operation is what is important. I did analytic solutions in college to get a grade. I do calculus all the time, yet never have I had to resort to analytical methods anymore, as I never knew the exact equations to that which I was analyzing! It was streams of data. Knowing how to tell a computer what I wanted it to do with the streams of numbers I was feeding it was what was important. ( things like Simpson integration methods ).
Another thing - computers made it easier to show kids how statistics works and why we do things the way they are done. MathCad is really handy for that one, that I can show how discrete and continuous solutions both come up with the same answer. You know... the bell curve probability functions.
This new graphic apps stuff coming out is too good though. One can't peek under the cover to see whats going on behind the display. I much prefer the older stuff for trying to teach a kid. For the same reason I would teach using GWBasic instead of delving right into C++. I will fire up Borland C++ for DOS later just to show how one can write stuff for fitting into much larger stuff, but that's for way later when the kid is ready to tie the whole shebang together.
"Prove all things; hold fast that which is good." [KJV: I Thessalonians 5:21]
(Score: 0) by Anonymous Coward on Saturday May 13 2017, @06:03PM
In my failed quest to get cisfemale programmers to precipitate out of the æther, which I have given up out of sheer frustration with third-wave feminism and their sexually abusive, homophobic white knights (not to be confused with their blatant transphobia and blind, right-wing-authoritarian-follower's reverence of the gender dichotomy wrapped up in oppression Olympics), QBasic and GWBasic were two that I considered: QBasic for being one of the first IDEs that I used (also Turbo Pascal), GWBasic for resembling TI-Basic on the TI-99/4A (not to be confused with the Basic interpreter on TI's graphing calculators). One co-worker even suggested that it might not be a bad idea to load up a TI-99/4A emulator and use that.
I settled with Ruby because it supported both. Perhaps in hindsight I should have done Python, but I knew Ruby at the time and not Python. (Also significant whitespace is against my religion.) Vim became our IDE, and irb became the line-mode equivalent of GWBasic/TI-Basic. I felt it worked very well. We even tangented into a few side-quests having to do with basic algebra, and I was left with the impression that my mentorship had helped at least put a dent in her math anxiety.
Unfortunately, my last student became infested with evil and is now a Deadite. If it's not obvious, I write bombastic comments to cover up for my own pain at the betrayal and abuse I've experienced at the hands of feminists. I have been crying a lot lately....
(Score: 2) by AthanasiusKircher on Saturday May 13 2017, @02:05PM
Great comment. I agree that practical problems are the key, and primary teachers often don't find ways to integrate this stuff.
The problem is: kids with math-allergic parents won't get the support they need. And far too many elementary school teachers are math-allergic themselves, and don't understand even basic math well-enough to pull of the steps described above.
This is the really hard part. Math is a kind of language. Like actual speaking or reading, it takes TONS of practice to become fluent, particularly in terms of abstract reasoning or broad understanding. Lots of parents and unfortunately primary teachers never actually achieved that -- instead, they learned the "crutch" of symbolic manipulation and symbolic algorithms as a proxy for actual math intuition.
Then the teachers are faced with kids whose natural inclination is to explore the world and develop intuition about things, and inevitably kids figure out other methods of doing problems (sometimes good alternatives, sometimes things that are wrong). Teachers who are "math-allergic," as you put it, can't cope with this intuitive childhood exploration of math concepts, so they at best smile and nod when the kid comes up with the right answer through alternate means, and at worst shut down such exploration pre-emptively. They often aren't competent/intuitive enough with math to recognize whether the kid has happened upon a good way of doing things or whether the kid's method is actually something that will fail when applied generally. Instead, focus on symbolic algorithms that they KNOW work. (This, I think, is even a bigger problem than rote memorization.)
Kids rapidly pick up this "math-allergy," because (1) they learn it's NOT about exploration (which is fun), (2) symbolic algorithms are the most abstract representation, so kids often find them the hardest to understand, thus making the math seem harder than it is, and (3) abstract symbolic manipulation is BORING for most kids. They may even pick up the anxiety directly from the teacher.
It's a real problem.
(Score: 2) by kaszz on Saturday May 13 2017, @05:22AM (2 children)
Considering a recent soylentnews submission [soylentnews.org]. Has there been any evaluation on what teaching methods that are the most efficient ones? Currently it seems more like throwing dart arrows in the dark and see what sticks.
(Score: 5, Insightful) by fido_dogstoyevsky on Saturday May 13 2017, @05:57AM
Has there been any evaluation on what teaching methods that are the most efficient ones?
Yes.
Easy answer - it depends on each kid. When it comes to learning, they really are snowflakes. Teacher:student ratio high enough to allow personalised teaching OR save money and have a one size fits all teaching style; pick one.
Almost forgot: you need to have maths teachers teaching maths, not just some random warm body from the staff room.
It's NOT a conspiracy... it's a plot.
(Score: 3, Interesting) by bradley13 on Saturday May 13 2017, @06:13AM
Interesting ideas - I look forward to the discussion. Some initial thoughts:
- For pure transmission of information, yes, you can be more efficient by omitting pauses, time spent drawing, etc.. However, to some extent, these pauses are needed and used by viewers to digest information they have already received. I can skim written material at a couple thousand words a minute, but I cannot understand anything new or difficult at that speed. Compress the material, and people who want to actually understand what is going on will press the pause button a lot.
- Anyway, for most kinds of learning, video is a stupid format. Of course the cool kids watch videos at double-speed - it's because most presenters blather on about stuff irrelevant to the topic they're supposed to be presenting. And anyway, there's no information gain in seeing the presenter. If you're going to compress things down to the essential, you're going to remove the presenter, boil the words down into carefully edited sentences designed to be clear and easily understandable, and include only the finished diagrams, and you have... wait for it... you have reinvented the book.
Finally, there is this little aside: "Excluding assignments and practical experience". Those are the key to any university-level education. If a student isn't spending at least twice the lecture time working on assignments, they're not getting the most out of the education. That's where most of the time goes, or should go.
Everyone is somebody else's weirdo.
(Score: 3, Insightful) by Ethanol-fueled on Saturday May 13 2017, @06:04AM (3 children)
Your kid sucks at math. Deal with it. Learning math isn't supposed to be fun, it's supposed to be a life-lesson in that all the hard things are fought for with extreme tedium, and the only time people appreciate math is when they're not actually using it.
Though I will say this -- before Common Core homeschooling used to be the method of choice for religious nutbags. Now, homeschooling is the last resort you have to prevent your kid from becoming a retard.
Quantitative reasoning was the last bastion of a good honest foundation in logic and critical thinking, but with Common Core even math has now been subjectified-away into nebulous guesswork so that your smart White kid is now on equal-footing with one of Jamal's many illegitimate offspring, and it's now possible for your teacher to fail your kid even if they get correct answers to the problems.
(Score: 3, Insightful) by maxwell demon on Saturday May 13 2017, @07:22AM (2 children)
Well, in that case I seem to have missed that life-lesson. ;-)
Honestly, if I think of extreme tedium back in school, the first thing that comes into my mind is learning vocabulary. Long lists of words with translations to memorize. There cannot be anything more tedious than that.
The Tao of math: The numbers you can count are not the real numbers.
(Score: 2) by fido_dogstoyevsky on Saturday May 13 2017, @10:40AM (1 child)
Learning math isn't supposed to be fun, it's supposed to be a life-lesson in that all the hard things are fought for with extreme tedium
Well, in that case I seem to have missed that life-lesson. ;-)
Me too.
...Long lists of words with translations to memorize. There cannot be anything more tedious than that.
Except sport/phys ed classes.
It's NOT a conspiracy... it's a plot.
(Score: 1) by anubi on Saturday May 13 2017, @11:55AM
Math... any of the sciences... shop... fun!
No problems with spelling or grammar.
English Literature was my own personal hell.
Especially lengthy tomes by Charles Dickens, Shakespeare, or Chaucer.
I loved a good science fiction read.
The other stuff, like History, wasn't fun, but do-able. I much preferred the "why" part of it to the "who" or "when" part.
Geography was interesting.
PE was a welcome break from the tedium of sitting in the classroom. I was good at rope climbing in those days, but did not run worth a damm. Like a skinny little monkey. No good at it now, though.
"Prove all things; hold fast that which is good." [KJV: I Thessalonians 5:21]
(Score: 2, Insightful) by Anonymous Coward on Saturday May 13 2017, @07:35AM
Mathematics teachers today don't know mathematics. Teach them and the problem is solved.
You need to look at Jim Simons, who is a mathematician, hedge fund manager and a billionaire and he is spending actual money to teach mathematics to the teachers in the U.S.
http://www.pbs.org/wnet/need-to-know/culture/math-for-america%E2%80%99s-jim-simons-and-his-secret-to-improving-math-education/8682/ [pbs.org]
Website: http://www.mathforamerica.org/ [mathforamerica.org]
That is unlike Bill Gates, who likes to threaten the world with biological warfare.
I believe the difficulties in math education in the U.S are due to jews taking over the education system and ruining it so they can raise goy slaves.
(Score: 0) by Anonymous Coward on Saturday May 13 2017, @08:13AM
The tips are trivial obvious stuff.
Meanwhile, this year I'm homeschooling calculus and physics, aiming for the AP tests. The mid-year ages are going to be 18, 16, 14, 12, 12. (all together because I can't deal with them separately)
This... is terrifying.
(Score: 3, Insightful) by looorg on Saturday May 13 2017, @02:42PM (1 child)
If you've ever had to help your child with math homework, you really appreciate their teachers, who do it every day. "Math anxiety" isn't something only kids experience.
Shouldn't we blame them for doing a horrible job instead? Clearly they are doing something wrong if large sections of society live in constant fear of mathematics, generation after generation.
Somehow mathematics is the exception to every rule. Society seem to be able to accept or excuse it every time when people proclaim their fear of it ("math anxiety", do you need a safe space to get away from all the evil numbers?). Somehow we don't seem to be as accepting about other "hard" things, whatever they might be. Would you be as forgiving to someone that claimed they had PE anxiety, or History Anxiety or whatever other subject you can come up with? Somehow it always seem to be mathematics.
(Score: 2) by AthanasiusKircher on Saturday May 13 2017, @03:34PM
It's the teachers. Seriously -- many, many studies have shown it. As someone who taught secondary math and physics for a few years, I chatted with primary school teachers from time to time. I also encountered a lot of teachers for elementary and middle school math during certification, also at workshops and such. Many of them will just admit it openly -- even to another teacher they barely know. The fact that I taught high-school math and physics seemed to make them feel like they needed to "confess" they were "never good at it."
Primary teachers have math anxiety and pass it to students. As you point out, the very fact we have a term "math anxiety" is potentially a big part of the problem too. Why single out math that way? Now teachers "name" their own "disorder," and just accept it as if it's some sort of clinical condition. What's perhaps even worse is that they often propagate stereotypes: studies have shown that female teachers (as most primary school teachers are) who have high math anxiety tend to endorse attitudes with students that reinforce the stereotype that girls are worse at math. We often have debates about girls don't go into math-heavy STEM fields or whatever -- but to change that, we need to break the ridiculous cycle of "anxiety."
(Score: 4, Insightful) by AthanasiusKircher on Saturday May 13 2017, @02:47PM (1 child)
You know what one of the strongest predictors of math performance in school is? Early childhood math skills. Kids who are ahead in preschool generally stay ahead at least through primary school. A lot of struggling later can be helped with early intervention.
And, frankly, this starts at home. Math is a language, with its own rules. This of how much practice kids get with actual language to learn simple usage, grammar, etc. They try out utterances hundreds or thousands of times. Sometimes they are successful; sometimes they are corrected.
If you want a kid to be intuitive with math, they need the SAME reinforcement. It starts even before they are 1 year old. Ignore the "developmental milestones" or whatever. Ignore the psychologists who say "Kids below the age of X can't understand Y concept" -- a lot of that has been shown to be bogus in recent years as a lot of pre-K programs have been doing more advanced concepts with young kids. Obviously there are limits and steps, and your kid may have more difficulty with some of them than others, but find ones they are interested in -- and then reinforce them. Over and over.
Even before they turn 1, you can talk about shapes. Almost every kid seems to have a "shape sorter" toy. Do it with them. Over and over and over. Tell them what the shapes are. Show them other shapes in your house that are similar. If they master the shape sorter early, buy them a more advanced one with different shapes. Once they get that, introduce simple puzzles with different shapes. Spatial reasoning and manipulation starts THAT early. The more activities you do with your kid like that in the first couple years of life, the better they'll be later. And this isn't just for math: shape recognition means they learn the alphabet earlier, which means they can read earlier.
Count with them. ALL THE TIME. Do it over and over and over. Make games of counting. Make games of identifying "how many?" Teach them ordering through other games and songs and rhymes. Repeat the days of the week or the months of the year over and over -- make silly songs about them, or look some up. We used to have an entire cultural repertoire of songs/rhymes passed around in communities -- a lot of that has been lost as families have become more isolated and "nuclear." Show them numerical symbols and count.
Once kids master order and counting to at least 20, start doing simple addition and subtraction -- but through objects in the world, not though symbols. Any parent, regardless of math background, should be able to do activities like this. Yes it may seem tedious, but you're supporting your kid in developing the same intuition they develop by repeatedly experimenting with language every day... except you're also doing it with numbers. After enough experiments, start building toward abstract -- show fingers on each hand and add them. If this seems too abstract, forget it and try again next week with the kid. Eventually something will "click" and they'll start to figure it out.
Above all -- don't FORCE boring stuff. If the kid isn't paying attention, try a different activity. If they don't seem ready for a concept, don't force it. Just try again in a couple weeks. If they DO suddenly seem interested, explore that concept again and again. In that case in particular, don't pay attention to the "developmental milestones." If your 2-year-old is counting to 20, and the "books" say the average 5-year-old should be able to do that, well, count to 100 with your 2-year-old. Get books or puzzles or make up your own colorful flashcards and keep doing it. If your 2-year-old seems really good with shape recognition, get more advanced puzzles. For most kids, SOME "age ratings" will be appropriate for them, but in other areas where they are interested, buy them stuff that's a year or two "ahead," and just see what happens. As your kid masters the common toys available for particular tasks, consider finding better "manipulatives" used in hands-on work with young children. Montessori programs frequently have a lot of great stuff that's amazing for teaching math concepts with simple physical objects. Buying the "real" Montessori stuff is pricey, but you can often find something similar or make your own.
Recent research and programs in pre-K show that most preschool kids can develop pretty good addition and subtraction skills, as well as great intuition about it, BEFORE they start kindergarten. Traditionally, psychologists claimed this was only "normal" for kids in 1st grade. Again, no reason to force your kids if they don't get it or seem bored or frustrated. But keep introducing possibilities. Keep "modeling" math in everything you do with them. Count things aloud. Talk aloud as you perform measurements of anything around the house. Pre-K kids often love to "help" with adult tasks. Use this for math development. If you like being "handy," show them how to measure stuff. They won't get it -- maybe for months or years, but keep showing it and modeling it, and at some point it will "click." If you like cooking or working in the kitchen, get them to measure stuff with you there. Recite recipe ingredients aloud as you measure them. Patiently explain -- again and again and again -- how fractions relate to each other. It will be meaningless to most toddlers, but kids learn language through usage. Math concepts, like just about any other word or concept, will become more intuitive if they keep hearing about it. If you get bored with the repetition and reinforcement, find some good apps made for young kids that do the same thing. You may have to actually spend a few bucks on several until you find good ones -- and try different ones to see what your kid likes. It's amazing how a 3-year-old or 4-year-old can just sit and do an app that counts balloons up to 20 again and again for an hour. You may think that's useless, but that's teaching ordering and counting fluency.
Do stuff like this, and chances are your kid will show up to kindergarten already having a lot of math intuition. Chances are SIGNIFICANTLY better that they will at least sail through primary school math while never having a problem with math homework.
And if you really want your kid to succeed in math, keep doing it. Find ways to explore the world through math in everyday life. If your elementary school kid is building triangular towers of creamers at the diner where you're having breakfast, use the opportunity to get them to figure out how to determine the number of creamers necessary for a triangular tower of arbitrary height. And if the kid is interested, keep going. Flip over the paper placemat and instead of playing tic-tac-toe, start making a chart of numbers for different size towers of creamer. Collect data. Derive an algorithm. Show them how to generate Pascal's triangle, which sort of looks like what they're doing already, reinforces addition for young kids, AND shows the answers to the algorithm you just developed. Talk about triangular numbers, then arrange squares. Talk about square numbers. Segue into multiplication.
The possibilities are endless -- and all because your kid started playing with creamer at a diner. If they get bored, shrug it off and do something else. Play tic-tac-toe. (Then start discussing possible strategies, leading to discussions of combinatorics and game theory on a very basic level if you want....) If they're bored with math for a while, give it a break. Or buy some fun books that present math in a silly way. Lots of kids books out there.
Model interest in math with your kids, and they will often follow you. Find places in everyday life to explore, and they'll often go with it. Kids are curious. If you do keep this up through elementary school chances are they'll rarely need help with their math homework again, because by that point they'll have intuited the basics of math as a "language" and learned how to create their own new concepts and algorithms.
(Score: 2) by hendrikboom on Sunday May 14 2017, @01:23AM
You have more or less summed up the curriculum of the first few years of primary school here in Quebec. Then for some idiotic reason they switched to the older memorize-the-algorithms style in later years. At least that's the way it was when my children went through the English school system.
(Score: 3, Insightful) by srobert on Saturday May 13 2017, @07:21PM (1 child)
I don't have any kids (didn't learn to multiply:-) ). But when I was a kid my Dad helped me with math (that's maths for you Brits) by forcing me to spend enough time on it to master it. Don't let your kid get distracted by TV and video games. My dad never got his high school diploma, so I was on my own when it came to trigonometry and calculus, but he set the foundation for that by emphasizing how important arithmetic was when I was in grade school. Math is cumulative. Get a good enough grade in arithmetic and we put you in algebra and geometry. Do well enough in that and it's on to trig, and so on.
(Score: 5, Insightful) by hendrikboom on Sunday May 14 2017, @01:20AM
Math is cumulative.
That's of the hard things about math. Miss one thing and the rest becomes gibberish. And you won't even know which thing you missed. You won't even know that there *is* something straightforward that you missed.
So tutoring someone who has trouble with a particular problem can usefully start with simpler and simpler things -- kind of like ranging shots -- until the tutor figures out the simplest thing that the student doesn't know. That's what needs to get taught first. Start with anything else and you're wasting time and effort..
(Score: 0) by Anonymous Coward on Saturday May 13 2017, @11:57PM
Show students all of the amazing things you can do with math (build robots, make video games, design rockets etc...), then show them how to get there. Interested students are effective students and students need an end-game just as much as anyone.
(Score: 2) by mrpg on Sunday May 14 2017, @04:16AM
https://khanacademy.org/youcanlearnanything [khanacademy.org]