One student had seen the weather and knew there was a 90% chance of rain the other had not seen the weather and though the probability was 50% since it would either rain or not. They compromised and picked the middle but that’s not the part I cared about, I cared that they had a reasonable discussion about their thoughts.
The idea that all outcomes are equally likely is definitely wrong and I wouldn’t want any teacher who didn’t correct that teaching my kids Maths.
I’ll throw another support behind Maggie on this. I’ve had severe ADHD my entire life, and I’ve been lucky that I’ve been in environments that supported this. I am a scientific person by nature, but I worked in the creative arts for more than half of it. Got a degree in psychology, because it was the closest I could get to the hard sciences without having to concentrate the way I was. And it allowed me to open myself up to CBT and otherwise. Patterns of behavior go a LONG way. Writing myself notes all day long as to what to concentrate on. Without my sticky notes, I’m lost. But CBT helped me find the tools I needed to do this.
Ironically, getting on Adderall was the kick in the ass to do the hard sciences. Went back to school at 30 and picked up a BioChem degree to try to get into med school (I decided to go back and finish the psych phd instead because it was my real love). The math was soooooooooooo much simpler when I could spend an hour or two a week and just focus. ‘Hard’ math isn’t that hard. It just requires repetition until something sticks. A great professor also helps as they can give multiple paths to the right solution. And a great professor can also explain why there are sometimes no correct answers. I mean, estimation is a skill few people have. Simple things like being able to convert between lb and kg when you need a rough estimate. It literally takes 3 seconds to do this, and I know nurses that have to get out calculators for something that is well within tolerance range I.e., knowing someone is 500lb how much is that in kg? About 225…halve and subtract 10%. Is it the right answer? No, but close enough.
Math is so much more interesting when you can focus and find what is important.
Maggie, thanks! Your stories are nerdy, written with heart, and you answer back frequently, sorry for going a bit OT. Are you an ADHD too or in the family? Everyone here is ADHD but the wife is only ADD, that poor poor frazzled woman.
Here I can get good socialized care and just need to wait a bit to see a neurologist for a long term prescription because at the top of the system they consider it a neuro issue, therapist they are not so good on for ADD because I suppose they think it is a neurological issue best treated with (approved)meds in adults. I think I would need to hire a private psychologist or therapist for behavioral therapy, I should make an appointment to ask though. A neuro can write an Adderall script but they AFAIK only do the expensive name brand stuff and not generic dextroamphetamine or whatever molecule you like to join that amphetamine with so it is not subsidized if it is not an approved med for an approved diagnosis.
I am now struggling through flight school in a language I did not grow up with, I don’t need the meds to do the flying, that and navigating are easy and fun, the studying for tests in another language but already translated once from American texts is nearly insane.
On the balance, I am not suggesting we stop teaching math as a subject. In my perfect world, general math and basic numeracy would be worked into other curricula, especially during the younger schooling years. The problem as I see it is that by the time students get to the interesting stuff, they are already phenomenally bored, which probably carries over into their general opinion of school in general.
Bottom line: most people do not need anything much above basic algebra. Same thing for music theory, Japanese, or niche histories. That does not mean that these subjects are not interesting or enriching; but when people study these things, it is because they want to. That intentionality is what makes-or-breaks the educational experience.
Work basic math skills into other subjects, get rid of the 50 minute slogs through worksheets, and leave higher math for the students that actually want to study it. hopefully by the time they are faced with a choice, they won’t have any of their earlier enthusiasm burned out of their soul.
This puts me in mind of why I find the iPad algebra-game “Dragon Box” so brilliant. It doesn’t give points for the one right answer and zero points for everything else; rather, it scores according to both the right answer and the number of steps it takes the player to get there. So it’s really looking for the optimal answer. In so doing, it encourages the player to focus on procedure, which I think is way closer to the point than a fixation on right or wrong answers.
It was invented when politicians decided there should be high stakes testing. To a scantron, only one answer can be correct.
Why is it that all our internet and mobile technology remains hostile to communicating mathematical concepts? When kids can compose and txt equations to each other using their thumbs, math education will begin to benefit from technology. When internet comment boards can do the same, adult math-dummies can do the same.
So far, the “problem” with math education is that the most advanced tools are either closed-source exploitation scams (TI calculators) or pre-computer fallbacks (whiteboards). Educators are overthinking this, and tech/textbook/education companies cannot be trusted to move things forward.
I think I would have done much better this way and not have developed a fear of numbers. Math was the only subject I ever struggled with in school (with the exception of geometry, trigonometry and statistics, where I breezed through). Several of my teachers said they couldn’t figure how I was scoring mid-80’s to 90’s in physics and chemistry- and, in college, was the top in my year in Autocad- while doing so extremely poorly in math. I needed to count something, or at least visualize what the application was. It bugs me that nobody could teach me using a different method. As an adult, I now understand what my issues were and try to repair the damage, but I can’t help feeling all those years I spend ‘not getting math’ were wasted potential, if only from missing out on the sheer pleasure of understanding that vital language.
But, math is about getting the right answer. The whole point of math is that every one who uses it is going to get the same right answer. It doesn’t matter what path you take or who you are or what minority group you are a member of or even if you are an actual human being. If you follow the boring, tedious rules and pay attention to the details, you will get the right answer, and that gives you real world power, because the real world has no choice but to give the right answer. If you toss a pebble into the air, you can use math to figure out where it will land, and you will get the same answer as the pebble. Philosophers have marveled at this for ages, but it is this power that makes the real world comprehensible.
I understand that some people don’t care how much they get paid or what things cost or whether their car starts or they have fresh tap water or whether their legs are long enough to reach the ground. Those people don’t have to worry about getting the right answer. The rest of us are stuck.
CBT is a great practical extension of the concepts of “Set and Setting” from my point of view.
More like invented when urban industrial jobs placed kids without adult supervision and child labour laws were enforced to avoid killing kids in factories… so modern education was brought inline. The adult male population went to work in one factory, the adult female population went to work in another, if circumstances allowed, and the kids were left the trusting hands of The State. This has basically continued with vested interests (including textbook makers, test creators, politicians who champion one set of standards over another from a fiscal point of view) ever since. Then we added more layers of educational apparatus, in theory, for improve the mental capabilities of subsequent generations. This has happened. We have a solid three generations of reasonably well educated (in developed countries) individuals. One of which was able to leverage that into longstanding careers. Two of which of looking for opportunities to use that education to its full benefit in a workforce. This is where we have the biggest breakdown in that system… people want to be useful. Useful in ways that they have trained for for. We’ve seen what happens when masses of people, who lack opportunity, get frustrated with their circumstances.
(sorry for the rambling, I just thought the topic required more perspective than just one company)
Once, when I was teaching physics, the administration demanded that all tests be converted to multiple choice. The reason for this was to remove the subjective nature of grading problem sets; they felt a multiple choice answer was either right or wrong, period.
But I didn’t want to grade simply on getting the answer. I wanted to be able to test concepts. So I designed some questions that did not provide enough information to plug numbers into a calculator and get an answer. However, if you knew the concepts, you could make a ball-park estimate from the information given, and only one of the multiple-choice answers was reasonable. I thought it was a good solution.
However, some students challenged the test on the basis that I had not provided enough information to solve the equation (by plugging numbers in to their calculators), and I ended up having to not count those questions towards their grade. This was especially frustrating because a number of students who really did understand the concepts behind the equations were able to select the intended answer.
Are you aware that the American usage is “math”, but the British usage is “maths”?
Try Concerta. It’s a time release system that uses Ritalin but gives a steady dose for about 8-10 hours, instead of the lumpiness you find in time release Adderall, and the big spike in ritalin IR.
I’ve also heard that ampakine narcolepsy drugs are being prescribed off-label for ADHD, and have been successful. I’d assume there’s a lower chance for addiction and abuse with an ampakine like provigil.
Note: I am not a doctor, and my above statements should not be construed as medical advice.
That works to a point, but at some level, those worksheets are necessary to beat the math into our brains. Even at a much higher level, the way people (including me) who are not natural mathematical geniuses learn it is by doing a whole lot of problems, and getting explanations and feedback from the ones you got wrong. I’d say, in addition to algebra, geometry and trig are definitely important for anyone who wants to build anything (even the construction trades) or do any computer programming or computer graphics, which potentially includes a wide enough swath of the population that its worth putting in a standard curriculum. Calculus is not useful for anyone not involved in science or engineering, but I think basic stats would be a great thing for more people to know, so that we don’t have to be subject to so many people who can’t think quantitatively voting on what are fundamentally quantitative issues. (The problem, of course, being that I suspect that in most of those cases, it’s not that they can’t think quantitatively, but that they won’t, because then they’d have to accept some things that would make them feel bad.)
I took calculus with two housemates, and we always did our homework together. It helped a lot, to be able to talk though concepts, and check each others work. The prof was great, but practice made a huge difference for me.
As a first approximation when you know the alternatives are all plausible, and given no other information? Perfectly fine, and I wonder what you’d suggest instead.
In the example given? A forecast? Yesterday’s weather?
If I roll a die, I can either roll a six or not a six. Is saying there’s a 50:50 of me doing so ‘perfectly fine’?
What if I buy a lottery ticket? I can either win or not win, so I have a 50:50 chance?
While I also loved Godel, Escher, Bach: An Eternal Golden Braid, for beginners I prefer to recommend Innumeracy, by John Allen Paulos.
Agreed. If “either it will rain or it will not” meant the chance was 50%, then the rain chance is ALWAYS 50%.
