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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.
(Score: 3, Insightful) by ikanreed on Tuesday March 28 2017, @05:19PM (12 children)
Which is why I think the quadratic formula should be banned from education until college math.
We're incorrectly teaching kids that math is boring, rote, be-the-calculator work. I think that math of that sort has no value to anyone in society.
You aren't going to make any scientists or engineers out of making math boring. You aren't going to keep the boring, rote rules in anyone's heads past their final exam, just in case they need to solve a quadratic equation or determine the third side of a right triangle 10 years later.
(Score: 0) by Anonymous Coward on Tuesday March 28 2017, @05:41PM (4 children)
Banning the quadratic formula does nothing helpful. It requires you to either go through the painful process of completing the square, you have to either engage in some rather exotic math or you have to restrict the quadratics given to ones that don't require irrational or imaginary numbers for roots.
Good math students turn as much of what they learn into memorized results as possible and having a surefire way of doing the problem changes the focus from being able to do the work to being able to do the work with the least amount of actual time and energy. The biggest difference between me now and when I was younger is that I've learn so many little tricks and such that I don't spend anywhere near as much time trying to reinvent the wheel or struggling as I know where to look a lot of this stuff up and how to use similar questions to work my way through the one I'm working on.
(Score: 0) by Anonymous Coward on Wednesday March 29 2017, @01:18AM (3 children)
Good math students turn as much of what they learn into memorized results as possible
People who are good at math actually understand the material on a very deep, intuitive level and don't just memorize facts, although memorizing facts is still an option. Don't confuse being 'good at math' with being a human calculator or someone who can quickly solve problems; they are not necessarily the same at all, and the vast majority of the time are not the same. Most A+ students of math understand next to nothing but have memorized much.
(Score: 0) by Anonymous Coward on Wednesday March 29 2017, @03:53AM (2 children)
Not really, I've been doing math professionally for the better part of a decade. And the more math I do, the more I've come to understand that the real difference between the people who struggle and the people who flourish is the sheer size of the memorized library of functions and results as well as the willingness to push for a solution.
And no, I'm very familiar with the difference between being a human calculator and being good at math. I wouldn't be able to improvise and solve problems of types I'd never been presented with if I hadn't developed a great deal of mathematical thinking.
It's just like any other skill, if you aren't relying upon a great deal of stored knowledge, you're not going to be fast or efficient. If you're constantly having to re-invent the wheel you're just not going to get anywhere.
(Score: 1) by shrewdsheep on Wednesday March 29 2017, @08:39AM (1 child)
I've been doing math professionally for the better part of a decade.
Care to elaborate? This smacks of self-declared superiority. What I suspect is that you lack in reflective capabilities. As a matter of fact, intuition is key for mathematics. A deep intuition makes it much easier to master and memorize the wider field of mathematics. If it is easy for someone to reproduce a mathematical fact from other such facts mentally, it becomes much easier to memorize. You may or may not be better in mathematics than people around you. If it is the case and you indeed know more mathematical facts, you fail to see that the underlying reason would be a better intuition.
(Score: 0) by Anonymous Coward on Wednesday March 29 2017, @03:56PM
You've got that completely backwards. The basis for intuition is a large amount of memorized patterns. There's a process here. If you haven't already matched the equation against a list of things you already know how to do, and things that look similar to what you're wanting to do, then you're wasting a ton of energy and leaving yourself open to edge cases which only come up occasionally.
But really, intuition is the result of having a lot of these facts memorized and being able to apply them in ways that aren't immediately obvious. Adding 0 and multiplying by 1 are particularly common examples.
(Score: 4, Insightful) by DannyB on Tuesday March 28 2017, @06:08PM (3 children)
In high school I found the quadratic formula and other "turn the crank" problems to be interesting. Programmable calculators were then quite new. And microcomputers programmed in BASIC. I developed a brief interest in types of problems that had a systematic solution. Adaptable to either calculators or microcomputers. I quickly moved on. But one problem that I continued to have an interest in through college and into the 1980's was simultaneous linear equations. Partly because they had a lot of practical application. Example: like in DC and AC Circuits with all the Thevenizing and Nortonizing. Naturally this led to extended study on my own time of playing with matrix addition, scalar multiplication, matrix multiplication, and matrix inversion. Building software that would allow expressing a matrix as a variable, and write matrix multiplication as A = B * C, seemed like quite a leap in the early 1980's. But at that time I hadn't gotten my hands on Lisp yet. :-)
My point is there's nothing wrong with problems like the quadratic formula, as long as you don't obsess on it. Like this one history teacher that was obsessively obsessed with the civil war and gave it a disproportionate amount of coverage while I wrote BASIC code in my notebook.
To transfer files: right-click on file, pick Copy. Unplug mouse, plug mouse into other computer. Right-click, paste.
(Score: 2) by ikanreed on Tuesday March 28 2017, @06:16PM
If they're anything like the history teacher I had who was similarly obsessed with the civil war:
1. It was very important to them to establish that there were good guys and bad guys in the war.
2. The slave owners weren't the bad guys.
3. It was an international history course and the US was supposed to be just a tiny sliver of the curriculum.
4. Reenactment society stories in place of actual history.
5. Incredibly creepy towards 15 year old girls.
(Score: 0) by Anonymous Coward on Wednesday March 29 2017, @04:37AM (1 child)
> But at that time I hadn't gotten my hands on Lisp yet.
The BEST moment in programming is when you realize an obstacle can melt before a good tool and careful expression.
(Score: 2) by DannyB on Wednesday March 29 2017, @02:00PM
In Lisp, many problems are solved in two steps:
1. Build a new language in which the problem is easily expressed.
2. Easily solve the problem in that language.
Example: I want to find a solution to some type of puzzle / game. Let's say, Sudoku. Or Unblock Me. Or some other game. Build a board type, and game pieces. Build proper operators that allow manipulating a board and pieces. Use a search, like breadth first search, to seek a solution. Or select different search algorithm to explore the graph of legal moves to find solution. Fine tune your search with rules specific to the type of problem. Extra credit: don't stop when a solution is found; structure your code such that it returns a lazy list of solutions. Pulling the next solution from the lazy list continues the search. Use a newer lisp like Clojure to make a lot of this easier so you don't have to build basic parts like lazy lists, immutable and persistent data structures, etc.
To transfer files: right-click on file, pick Copy. Unplug mouse, plug mouse into other computer. Right-click, paste.
(Score: 1, Interesting) by Anonymous Coward on Tuesday March 28 2017, @07:17PM (1 child)
They need to find a better way to teach them. If it's a matter of matching patterns to known rules, then find a way to encode the patterns and explain how to "read" the patterns to find out what to plug into what. If it's truly "mechanical", then find a way to mentally automate the mechanical processing in step-by-step algorithm that a student can "run" in their head. Look at the equation, convert it into the pattern language, look up the "from" matching pattern in the (memorized) pattern mapping table, then get the "to" that maps to the "from" pattern, and apply the "to" pattern.
The problem is that you'd have to introduce a pattern language, sort of like reg-ex's for math, and that would probably confuse most students even more. I kind of created such meta languages myself to help me memorize and process math rules, but I suspect a meta language that works best for me won't necessarily work on others. People think differently such that it's hard to make one-size-fits-all pattern language. (These roll-your-own pattern languages got me through school, by the way.)
Learning how to learn is one of the trickiest tasks of education because people think so differently. A technique that favors one group will slow another.
(Score: 0) by Anonymous Coward on Wednesday March 29 2017, @03:58AM
If you really want to understand math, a great exercise is to write you're own generator programs to generate classes of equation. Even just writing a program to take two random points and create linear equations for all three standard forms of equation will do wonders for your understanding of how the equations work.
I dare anybody here to do that and come back claiming they don't understand how the equation works or what the pieces do.
(Score: 0) by Anonymous Coward on Wednesday March 29 2017, @01:15AM
We're incorrectly teaching kids that math is boring, rote, be-the-calculator work.
Then we would have to ban everything but basic math, because schools aren't teaching any kind of math properly.