In Math Cram Sessions, Solving for Why • Hacker News Board

Re: In Math Cram Sessions, Solving for Why

#71

Post by learnstats2 » Tue, Sep 11, 2018, 1:12 AM UTC

ivansavz wrote: post #8

Yeah, private tutoring is the best. The custom, just-in-time curriculum that a tutor can prepare is the most efficient way to learn. I think equally important is the transmission of a relaxed, exploratory attitude towards the STEM subjects. When a learner sees their teacher take on positive attitudes towards complexity, they too develop this attitude and can go on to solve problems on their own. Unfortunately, this t…

I'm a private tutor so obviously I agree it's the best ;-) thanks

However, I wanted to pick up a couple of your examples - "parent touching math for the first time in 20 years" can also often be a great way for students to learn!

Adults are usually able to figure their way around a subject and this is a great learning point for kids - that you don't have to know everything, if you know how to find out about it.

Any parent has got through undergraduate education in any subject (and many who haven't) - who have learned how to learn - can find out what they need to know by looking it up and finding resources that help their comprehension. Being stressed about it is a different situation, and of course I agree with you there.

I also do sometimes say "This is stupid shit you have to know for the course" - because many courses contain bad content - but I will follow it up with "if we have time, it will be more practical to think about..." That also isn't a bad thing necessarily.

It's important for students' development to critically analyse why they are doing a particular course - if they're doing it to pass, then they should first pass.

Re: In Math Cram Sessions, Solving for Why

#72

Post by brianpgordon » Tue, Sep 11, 2018, 1:19 AM UTC

somethingroma wrote: post #56

Koshkin wrote: post #50

Earlier quoted context omitted.

> remembering the multiplication table is the antithesis of multiplying in ones head But it's not! Because in order to be able to multiply numbers in your head efficiently you must remember the multiplication table.

No. By definition remembering an answer is not the same as doing. Additionally my experience tells me otherwise.

I'm sorry but this seems patently wrong to me. There's only so much working stack space in your brain. If you're constantly having to think through multiple steps to multiply single digits then you're going to be at a serious disadvantage when you need to solve a bigger problem that involves more work than just single-digit multiplication.

Re: In Math Cram Sessions, Solving for Why

#73

Post by closeparen » Tue, Sep 11, 2018, 1:35 AM UTC

tesin wrote: post #53

saagarjha wrote: post #31

Earlier quoted context omitted.

No, I think you’re getting the relation backwards. Many parents who were well educated have the opportunities to send their children to good schools, regardless of whether they went to a good school themselves, because they realize that it makes it easier to be well educated there.

How would someone be well educated at a bad school? I feel like that loses any reasonable definition of good.

Aggregate test scores say more about the student/neighborhood population than the instruction. “Bad” schools become “good” as their neighborhoods gentrify, for example.

Re: In Math Cram Sessions, Solving for Why

#74

Post by tsumnia » Tue, Sep 11, 2018, 1:58 AM UTC

chrisweekly wrote: post #63

tsumnia wrote: post #60

Earlier quoted context omitted.

As Zeebrommer mentioned, I'd steer clear of this thinking. Carol Dweck's entire research has been on "fixed" and "growth" mindsets, and their impact on people's performance. Instructors that believe someone is or is not an "X person" have a negative impact on students. That is, if I believe in the idea that there are STEM-illiterate and STEM-literature people, why should I both helping someone who is STEM-illiterate?…

I think you've misunderstood me or conflated my comment with someone else's; mine said nothing about fixed vs growth mindset. The term "innumerate" -- just like "illiterate" -- indicates the current state of a person's abilities, not some fixed or inherent trait. The remedy is education.

My apologies, this my interpretation of your comment. Thanks for the clarification

Re: In Math Cram Sessions, Solving for Why

#75

Post by tsumnia » Tue, Sep 11, 2018, 2:00 AM UTC

jgamman wrote: post #66

tsumnia wrote: post #60

Earlier quoted context omitted.

As Zeebrommer mentioned, I'd steer clear of this thinking. Carol Dweck's entire research has been on "fixed" and "growth" mindsets, and their impact on people's performance. Instructors that believe someone is or is not an "X person" have a negative impact on students. That is, if I believe in the idea that there are STEM-illiterate and STEM-literature people, why should I both helping someone who is STEM-illiterate?…

aside: Sisk et al (To What Extent and Under Which Circumstances Are Growth Mind-Sets Important to Academic Achievement? Two Meta-Analyses DOI 10.1177/0956797617739704) looked at >450,000 students and found little or no effect size for this approach. standard primary literature caveats etc and where it is/is not applicable but this does put 'growth mindset' on the back foot.

Interesting find, I had no idea! I'll read through it, I'm curious if it discusses Dweck's "helpness" terminology as well.

Re: In Math Cram Sessions, Solving for Why

#76

Post by jordigh » Tue, Sep 11, 2018, 2:19 AM UTC

abdullahkhalids wrote: post #69

jordigh wrote: post #40

> A ball is thrown off a building at a speed of 15m/s and at 30 degrees to the horizontal. If the building is 100m tall, how far from the base of the building will the ball land? g=9.8m/s² 280.17 metres, right?

Nope. That's too far. I am too lazy to write out the equations, so we can use an app such as this http://www.walter-fendt.de/html5/phen/projectile_en.htm to find out that it falls 69.5 m from the base of the building.

It's not so difficult to fix.

-(9.8/2) t^2 + 7.5 t + 100 = 0

Positive root is 5.3472 seconds, multiply that by 15*sqrt(3)/2 to get 69.462

Re: In Math Cram Sessions, Solving for Why

#77

Post by credit_guy » Tue, Sep 11, 2018, 2:34 AM UTC

Koshkin wrote: post #6

somethingroma wrote: post #2

"This was the key. If you knew hhhhwwhy you didn’t have to memorize equations, or solve equations in the exact same way they did in the book..." I feel like this is a valuable lesson a lot of people could benefit from.

Knowing "why" is exteremely helpful in many cases. But let's not forget that, on the other hand, memorization plays a huge part in learning, and not only in mathematics. Learning "why" multiplication works will not help you to retain the multiplication table in your head. (Also, in many cases the answer to a question "why" you might get will be plain wrong - sometimes because the correct answer is too complicated, so…

May I add my support to your opinion? Or, to put it more bluntly, the "why" is overrated. The "modern" math education (in the US) comes courtesy of people like Jean Piaget or Seymour Papert. These guys were true geniuses, but made a grave error. They generalized from their own experience ("to understand is to invent") to everyone else. Unfortunately, for 99% of the people, the style of learning by discovery is extremely inefficient. So we ended up with a system that sounds great in theory, but in practice you have kids in the fourth of fifth grade still going over addition and multiplication.

Re: In Math Cram Sessions, Solving for Why

#78

Post by noobermin » Tue, Sep 11, 2018, 2:37 AM UTC

Koshkin wrote: post #45

jordigh wrote: post #40

> A ball is thrown off a building at a speed of 15m/s and at 30 degrees to the horizontal. If the building is 100m tall, how far from the base of the building will the ball land? g=9.8m/s² 280.17 metres, right?

Depends on whether the angle is above or below the horizontal. (The ball won't make it this far regardless.)

That's a good point. I'm not one for details and I just assumed it above the horizontal because it makes it a touch more interesting.

Re: In Math Cram Sessions, Solving for Why

#79

Post by noobermin » Tue, Sep 11, 2018, 2:38 AM UTC

sdenton4 wrote: post #25

unpythonic wrote: post #22

As much as the Common Core standards are criticized here in California, I have to say that the emphasis on the "why" behind every operation is really fantastic. It's usually in the last section of each homework, but it provides a good discussion point when going over the homework each night. Asking students to answer questions like the following are easy to zip through, but they provide a good place to pause and find…

I haven't worked in an american classroom, but as a math educator, thought the CommonCore looked great when it was first rolling out. Math education is (kind of strangely) a bit of a battlefield in the US (maybe not so strangely, when everything else seems to be, too)... I think a big part of it is prevalent math anxiety - perhaps embarrassment at seeing unfamiliar things on the kid's homework. Along with this, there…

I doubt the critics of CC know what "New Math" was.

Re: In Math Cram Sessions, Solving for Why

#80

Post by wodenokoto » Tue, Sep 11, 2018, 6:23 AM UTC

zodPod wrote: post #64

thomasfedb wrote: post #20

Earlier quoted context omitted.

Private maths tutor here — what I find most gratifying about tutoring is revealing to my students how much they already know. Often they'll know that they know the answer, but they don't realise that they also know why it's the answer!

How much are your services? I'm an out-of-school adult that never really grasped math but hate that I don't know more about it to this day. Just wondering what kind of range I'd be looking in to just get some explanations or something. I don't currently have any specific questions though.

Have you tried Khan Academy? It lacks all the person interaction and customization of a private tutor but they have (IMHO) really good explanations and quite good problems to solve for all math through high school.