algorithm - does anyone know what this is?

www.dictionary.com/browse/algorithm

I don't know if the definitions really help all those of us who are not mathematicians!

You might need a degree in Maths to understand it! I've given up!

It's a way of getting a sum total so far as I can understand. In maths anyway.

In its simplest terms, an algorithm is a series of processes. It starts with data, processes it, and produces a result. An algorithm is value-neutral.

So:
Think of a number
Add three
Multiply the total by six
Result = a number

...is an algorithm.

So is a recipe.
Take an amount of flour
Add half the same amount of fat
Add a pinch of salt
Rub fat into flour and salt
Add an eighth the amount of cold water
Mix all together and roll out
Line a flan dish with the rolled mixture
Bake in a hot oven for 10 minutes.
Result = pastry case

I am no mathematician, but below is what I think defines and algorhythm.

It is using a set pattern to fit together a number of different facts and/or numbers and/or operations to reach a conclusion. The same pattern is applied automatically to a whole load of similar examples, so as to give answers that can be compared fairly with one another, without involving human bias.

Different algorhythms can be designed for different purposes.

Exactly what geekesse said; a set of mathematical instructions or rules that, especially if given to a computer, will help to calculate an answer to a problem.

Nothing to do with logarithms.

geekesse That is more understandable than my definition.

I like the recipe example. A very similar recipe with a few changes in ingredients and method would give you either sweet pastry or a crumble topping.

The skill is in designing the recipe or the algorhythm to suit what you want to end up with.

The current exam hoo-ha is because many think that the recipe for grades should have had different quantities of some ingredients, or they should have been combined differently.

In its simplest form, an algorithm is just a formula or a series of formulae.

They're very useful for handling millions of pieces of data and showing trends and giving averages. However, they're counterproductive when used for individuals.

These kind of algorithms have been used in schools for about 15 years to calculated what grades pupils should achieve based on prior achievement and other information such as date of birth, postcode, etc. The government even uses them to judge whether a school is good or failing.

Managers/inspectors can see whether a school is improving over time. However, I've argued for years that they're not very helpful for calculating what individual pupils will achieve or how much progress they will make. One problem is that managers (headteachers) don't always understand the maths themselves. They think you can input a load of figures (even if they're flawed) and the computer will churn out a load of smart looking graphs and charts.

Algorithms are used all the time to calculate things like life expectancy, given a number of variables. That's useful for comparing different areas or genders over time. However, they still can't tell when an individual will die.

If you go to your GP, you might be told what chance you have of having a heart attack or stroke within 10 years. An algorithm will have been used to calculate the chance, based on your medical history, weight, blood pressure, cholesterol etc. Your GP will probably decide to prescribe preventative medication based on your risk.

In terms of the exam grades, it’s about how the statistics are used.

It works like this example:

Over the last three years, a class with 10 children each year has produced the following results for A Level basket-weaving:
One student got A* two years ago (about 3%)
One student each year got A (10%)
Two students each year got B (20%)
Three years ago, four got C. Two years ago two got C. Last year three got C (30%)
Two students each year got D (20%)
Two students last year got E (about 7%)
Two years ago, three students got U (about 10%). There were good reasons - all three had got involved in something unsavoury out of school.

Therefore, if this years grades have to match the last three years, this year’s 10 students therefore are statistically likely to get the following grades;
1 x A
2 x B
3 x C
2 x D
1 x E
1 x U

All this year’s students have been taught better by a new hot-shot specialist teacher. Based on mocks and timed work, They are all likely to do better than previous cohorts. The school has predicted an A* for a really bright student who worked really hard. Two others are working at A grade, and three at B grade. All four others have a good record of C grade work. So the school predicts
1 x A*
2 x A
3 x B
4 x C

Using Ofqual’s algorithm, these will be adjusted to match the percentage from the last three years:
A* will be downgraded to A
Both predicted As will be downgraded to B
All three predicted Bs will be downgraded to C
Two C grades will be downgraded to D
One C grade will be downgraded to E
One C grade will be downgraded to U.

Thank you for having the patience to type that all out geekesse.

Apparently, there was something else ...

Ofqual were aware of the "overestimation", so they had to reduce grades slightly, because centre assessed grades had already been awarded to small school and subject entries. The totals had to fit the curve.

Therefore, an A* was only awarded in the case of a class of 20 if at least 5% of the previous three years' cohorts had been given an A*. If it was only 4.9%, nobody was awarded an A*.

However, at the other end if even a fraction a percent had been given a U in the past, then one entrant this year had to be given a U.

Well done geekesse

It's a set of instructions given by a human to a computer to work out an answer.

Unfortunately, as computers are entirely logical, they can only work on the instructions provided and any human aberration such as a couple of extremely bright pupils in a school which has had consistently low results for years are disregarded.

is disregarded, sorry.

You’re right, growstuff - there were other factors. Students in an entry of five or fewer were awarded centre-assessed grades. Groups of between of between 6 and 15 pupils were weighted slightly in favour of centre-assessed grades. If there were more than 15 pupils for one subject, the grades were awarded based on the algorithm alone, including an adjustment so that across the country, there was only a very small increase from previous years. Selective and independent schools often have small numbers per subject. This means that kids in a large school or sixth-form centre were effectively penalised because pupils in small schools did better than previous years.

The trouble is, statistics work well for populations and probabilities. They don’t predict well for individuals. Say you have a class of ten, all working at B grade. There’s a good chance that one will bomb the exam by misreading a question, so to say ‘one of these ten students will get an E’ is likely to be an accurate prediction. But unless they actually sit the exam, you can’t say in advance which one will misread the question. So it’s horribly unfair to give one of the an E just because statistics show that one of the ten is likely to get E.

I've just realised you can't have 4.9% of 20, so change that to a class of 33 - I'm sure you know what I meant.

Growstuff You could have a fraction of a pupil, you'd just have to take a large saw into class with you and choose where to divide them. Would you remove an arm, a leg or a head?

I really like your contributions on this thread Elegran. Your definition was concise and understandable. Your solution for fractions most practical. 😄

They could have given everyone N grades right across the board, no arguments then.

Actually, I still don't see why they couldn't have taken examinations and had a combination of those results and teacher assessments over two years..

Callistemon, that is quite similar to what the French have done. They have taken an average of each student's grades over the previous two terms and used those as their results. They have also opened up 10,000 more university places.

That seems sensible.

One would be medical student on our local news could not understand why they couldn't take their exams as self-distancing is a requirement anyway.
She was downgraded but has had her grades re-assessed and is off to medical school now.

I first came across the word algorithm when I was teaching catch-up maths. You probably don't know it but you've been using one for years when you add large numbers for example. (And I didn't know either). If you want an explanation watch this-https://www.youtube.com/watch?v=NNj1OYwPDKc

link again. www.youtube.com/watch?v=NNj1OYwPDKc

annodomini

*Callistemon*, that is quite similar to what the French have done. They have taken an average of each student's grades over the previous two terms and used those as their results. They have also opened up 10,000 more university places.

The reason the UK couldn't do that is because coursework was scrapped. There is no standardisation of any internal work. In France and Germany, there are interim assessments, which are overseen in France by the government and in Germany by each individual "Land".

Once the decision to abandon exams was taken, there never was going to be an easy solution. Any solution would have been the "least worst".

It would have caused less heartache (and have been easier for universities to manage) if Centre Assessed Grades had been accepted from the start. Yes, there would have been some slight grade inflation. Yes, it would have involved admitting more students on to higher education courses - but that would, at least, have kept the unemployment figures for 18 year olds down.

Ofqual and the government deliberately chose a solution which was flawed. They didn't care less about the sixth formers in inner cities. They didn't reckon on the backlash from grammar schools and the highly academic sixth forms, some of which are in the private sector. They thought they could ride the storm and they probably would have done if it had "only" been the pupils from deprived areas who had suffered. They could easily have got the compliant media to blame teachers for overinflating the estimated grades of deprived pupils, but it didn't work out like that.

Elegran

Growstuff You could have a fraction of a pupil, you'd just have to take a large saw into class with you and choose where to divide them. Would you remove an arm, a leg or a head?

Hmm ... headless chickens, legless politicians, 'armful advisers! Now why does this sound like a familiar scenario?