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# Maths Café

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# What is algebra?

petegriffin 25 October 2007 13:17 - Last edited by petegriffin on 25 October 2007 13:18
Assistant Director (Secondary)
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The bold statement that "Algebra in Key Stage 3 is generalised arithmetic" is made in the Secondary Strategy's Key Stage 3 Framework for teaching mathematics.

What does this actually mean in practice with our students?

Are the problems and exercises that we have at our disposal (mainly from text books) useful in promoting this view of algebra?

I would be really grateful if we could share any views and practice around this issue.

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Chris1974 28 October 2007 07:41
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I did some work a few years ago on teaching Algebra to Y7, and we worked around 4 aspects of what Algebra is. 1. Transformational - i.e. rearranging/ solving 2. Generallising (sp?) - ie the nth term type stuff 3. I don't remember! 4. Structural Maths. As I recall (and it was 7 yrs ago) this was the important bit, with us looking at developing a real need for Algebra, rather than it being a bolt on extra. We looked at how we could use algebra to improve students understanding of all topics, from geometry to data handling. Part of the project was to remove the innate fear students have of algebra, by making using it easier than not. If Alf or Laurinda or any of the others read this, and I have it horribly wrong, I wouldn't be upset by a correction!
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petegriffin 31 October 2007 20:26 - Last edited by petegriffin on 02 November 2007 15:57
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Does this animation provide a fruitful algebra activity? Which of Chris's aspects does it fit with?

Has anyone else got any good activities or, indeed other ideas or thoughts?

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Mathemagician 03 December 2007 16:57 - Last edited by Mathemagician on 03 December 2007 17:02
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I like to think that algebra is pattern. So, I guess this fits best with Chris's nth term idea. Again, I think we overcomplicate it sometimes for students with our laws of this and our laws of that...algebra is pattern, and much of it is just shorthand for simple concepts.

Not all algebra, I grant you, but I think if we are not careful we can paint a picture of unncessary mystique around this important branch of language...when I visit primary schools, I introduce Year 5 children to it and they have no problem understanding the concept. Mind you, I don't refer to it as 'algebra' as I think the word itself, like 'fractions' or ;'calculus' has emotional attachments in many people's minds.

Does anyone agree/disagree?

Andrew

Maths is Magic!

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petegriffin 03 December 2007 21:02
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I remember having my attention drawn to the difference between spotting pattern and spotting structure and I found that quite useful.

In the classic type of task where pupils are asked to find the number of matchsticks, say, in the nth term of a growing pattern many will be able to spot a pattern in numbers in a table but fail to get a sense of the structure which is where the generality lies. That's why it is useful to ask learners to attend to the structure of a complex example (i.e. the 15th term) rather than build up the pattern one by one.

In Dave Hewitt's article in MT163 (the ATM journal) called "Approaching Arithmetic Algebraically" he makes what I found a very thought provoking comment concerning the algebraic statement 3x + 1:

"But let us not confuse the two words involved - algebraic and statement. The algebra is the work you do in order to get yourself in a position where could make a statement (such as the example given above where there is a way of seeing the matches so that the formula is just a way of expressing what is 'seen'). '3x + 1' is the statement part, and only hints at the algebra which may have taken place to make such a statement".

Do our learners do this kind of work when they are doing school algebra?

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kathrynp 03 December 2007 21:54
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There's a lengthy discussion on Sequences - finding the nth term on the Secondary forum which links in well with this discussion.

I'm currently preparing a GCSE resit class for the (final!) algebra coursework task. I'm having great difficulties with a number of learners who can 'find the rule' or make an algebraic statement, based on a number pattern, but who steadfastly refuse to engage with the structure/algebra, perhaps because following an algorithm to find a rule is less taxing than actually thinking about maths and making connections. And I did start by using Derek Robinson's ideas from the above forum!

Perhaps the problem is actually that KS 3 statement "Algebra in Key Stage 3 is generalised arithmetic." That paragraph ends  "This insight releases in due course the full power of algebra." Or do some students get trapped by the generalised arithmetic, unable or unwilling to progress beyond it? Students do seem to feel most comfortable with techniques and rules they have learnt in earlier years - it has taken a long while to wean my AS students off using y=mx+c all the time, when it would be much better to use other forms of equations of straight lines.

Just pondering...

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petegriffin 31 October 2011 17:43
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While browsing, I found this lovely article by Alf Coles and Laurinda Brown in the "Research Gateway" entitled "Developing algebra - a case study of the first lesson from the beginning of year 7".
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mary_pardoe 01 November 2011 19:28
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I think that this short illustration by Doug Williams may be helpful when thinking about prompting students who are trying to express what they have seen.
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