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