Stories
Slash Boxes
Comments

SoylentNews is people

posted by n1 on Tuesday March 28 2017, @04:36PM   Printer-friendly
from the no-royal-road-to-understanding-students dept.

Oxford researchers are taking part in an international study to film the teaching of quadratic equations for secondary school pupils. The hope is that lessons will be learned on how to bring out the best in pupils learning about mathematics.

Over the next few months, video cameras will appear in secondary schools across England that have chosen to take part in an international study to observe maths lessons focused on quadratic equations. Researchers from the University of Oxford have joined forces with the Education Development Trust to undertake the study in England, which will involve up to 85 schools from different parts of the country. The research team has to enlist 85 teachers and around 1,200 pupils, so they can analyse video footage of different teaching practices and pupils' responses to assess what works best. Schools in Oxfordshire will be among those approached about taking part in the pilot.

The research project is led by Education Development Trust, working with Dr Jenni Ingram and Professor Pam Sammons from the Department of Education at the University of Oxford. They will analyse how pupils' attitudes toward quadratic equations are linked with their progress and results, and observe how teachers' attitudes and methods affect outcomes.

Dr Ingram said: "We believe this study will improve our understanding of the relationships between a range of teaching practices and various student outcomes, including their enjoyment of mathematics, mathematical knowledge and engagement with learning."

Or you could watch Khan Academy.


Original Submission

 
This discussion has been archived. No new comments can be posted.
Display Options Threshold/Breakthrough Mark All as Read Mark All as Unread
The Fine Print: The following comments are owned by whoever posted them. We are not responsible for them in any way.
  • (Score: 1, Informative) by Anonymous Coward on Tuesday March 28 2017, @05:38PM (5 children)

    by Anonymous Coward on Tuesday March 28 2017, @05:38PM (#485325)

    Students struggle with it when it's not being taught correctly. I struggled with it because the schools here were using guess and check. I had to discover why all the pieces work the way they do on my own, or not get it at all. But, it's not freaking complicated even if you're going to factor it out. ax^2 +bx +c where b can be split into two factors of ac which gives you something like this to factor ax^2 +bx +dx +c and you should always have the same ratio between b/a and c/d.

    Otherwise, you've got the quadratic formula or completing the square as backup. But, the quadratic formula is hardly difficult to understand. You can derive it by completing the square on the generic equation ax^2 + bx + c =0 and solving for X. Otherwise the -b/2a is the horizontal shift of the vertex from the base function and the square root of b^2 - 4ac is the distance from the axis of symmetry to the roots. Hence if it's zero yo have one repeated root and if it's negative you have only imaginary roots because it doesn't cross the X axis.

    Starting Score:    0  points
    Moderation   +1  
       Informative=1, Total=1
    Extra 'Informative' Modifier   0  

    Total Score:   1  
  • (Score: 3, Funny) by VLM on Tuesday March 28 2017, @06:45PM (1 child)

    by VLM (445) Subscriber Badge on Tuesday March 28 2017, @06:45PM (#485385)

    You can derive it by completing the square on the generic equation

    When I took algebra, admittedly decades ago, this was implied as the pinnacle of the class, the purpose for taking the class. And we got to write the whole proof down and took a fill in the blank test to make sure we really understood that the biggest accomplishment of algebra is applying about a page worth of rules can numerically solve an entire class of equations. Not solve one particular equation. Not solve some members of a class of equation. But every member of that class can be solved at the class level.

    Which is actually pretty amazing if you didn't already know.

    Where my algebra class fell down was in not extending the argument a wee bit to explain why there's no similar simple equation for, like, 9th degree polynomials. So trying to rush things and pack more work in resulted in the most interesting point being missed, that some classes of equations can be algebraically solved at the class level and some entire classes of equations cannot.

    Its a hell of an argument against sex education in schools. If the same people developed the sex ed curriculum as developed the algebra curriculum then somehow sex would be the most boring, tedious, and pointless experience that a human can have, and people would take great joy in telling each other proudly how incompetent they are at it "I donno I just push buttons randomly until it works" "without electronic/mechanical help I can't do anything" "One kid does all the work and the rest just watch" "I can't estimate I just plug and chug" "I do my homework by asking the 4chan anons for the answers" "My mom can't do it so she can't help with my homework" Well that's beginning to sound creepy. Hilarious but creepy. Anyway school can just suck the life right out of the whole topic or hobby. Likewise I'm glad there's no programming classes at my kid's K-12 school district, I can't imagine a better way to ruin programming for life for kids than to make it a topic of K12 education.

    • (Score: 2) by meustrus on Wednesday March 29 2017, @12:57PM

      by meustrus (4961) on Wednesday March 29 2017, @12:57PM (#485852)

      I dunno, that sounds like an argument for sex education in schools to me. Sex is not the pinnacle of human experience, after all, no matter what advertisers would rather you believe.

      --
      If there isn't at least one reference or primary source, it's not +1 Informative. Maybe the underused +1 Interesting?
  • (Score: 0) by Anonymous Coward on Tuesday March 28 2017, @11:12PM (2 children)

    by Anonymous Coward on Tuesday March 28 2017, @11:12PM (#485543)

    First, for context: I'm 3 to 4 standard deviations above the mean for intelligence, so perhaps an IQ of 145 to 164. (as of age 17)

    My algebra class started off with simple stuff. I guess you would call it "guess and check" these days. I was really good at that.

    We were then supposed to learn how to complete the square, but I never learned it. I was too good at guessing. I can guess with fractions, imaginary numbers, whatever. I still don't know how to complete the square. (Huh? Eh, I'll just put the answer.)

    There we got to the quadratic formula. I memorized it like you'd memorize a jingle or poem, or like the alphabet. I don't forget it. Even before I got around to programming it into my TI-62 calculator (with unreadable non-English instructions) I was flipping it around in my head to avoid excess keypresses. Why use parentheses if you don't need them?

    Having learned the formula, I never found a need for completing the square. The formula works fine... though I can still guess faster for typical school problems. I'm older now, with my mind resistant to new things, so I'll probably never learn to complete a square. Oh well.

    • (Score: 0) by Anonymous Coward on Wednesday March 29 2017, @12:32AM

      by Anonymous Coward on Wednesday March 29 2017, @12:32AM (#485582)

      The only time you ever have to use completing the square is if you're wanting to convert the standard quadratic equation to the vertex form of the equation. Otherwise, you'd be foolish to complete the square as the quadratic formula is just the completed result of the process.

      As far as guessing goes, that's your teachers' faults for not giving sufficiently difficult problems. If you've got a string of decimals like you commonly see come up in physics questions, you're not likely to be able to just guess the answer. Similarly, if you've got 3 or 4 digit coefficients that don't reduce, you're not likely to be able to just guess those either.

      The quadratic formula itself is great because it will give you an answer no matter what quadratic equation you're given. It's just not always the most efficient way of getting there.

      As for the parentheses, they're definitely not optional. The parentheses involved with completing the square are there for your protection. They save you from creating this thing that you then have to factor. They also exist as a way of handling nonstandard coefficients on the squared term.

    • (Score: 0) by Anonymous Coward on Wednesday March 29 2017, @01:23AM

      by Anonymous Coward on Wednesday March 29 2017, @01:23AM (#485602)

      I'm 3 to 4 standard deviations above the mean for intelligence, so perhaps an IQ of 145 to 164. (as of age 17)

      But apparently too ignorant to have realized that IQ comes from the social 'sciences' and has never been rigorously proven to be significantly related to one's intellect. IQ correlates with several things our mouth-breathing societies consider important, but again, there is no proof that those things are excellent indicators of one's intellect.