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Discussion in 'Mathematics' started by paul_mc, Nov 30, 2011.
Do you teach 4 + -3 as 4 plus minus 3 or 4 plus negative 3?
Oh dear...through force of habit I still often say 'plus minus three', but then have to remember that makes me a dinosaur - slapped wrist - and 'negative 3' is maths PC nowadays.
But I'm not sure that children are finding negative numbers any easier using this parlance - seems to me they're finding it harder.
If you write a computer program to parse arithmetical expressions you'll also find that this is a little hitch. When you encounter a '-' you have to tag it as either a subtract or a unary minus.
However we use the same symbol for both. It's too entrenched now to change.
I introduce the words add, subtract, positive and negative.
With the tags verb or adjective accordingly.
I do find, that in the long run, this goes a long way to clearing up the misconceptions.
Even with lowest ability year 7, this approach works ...in time.
I too find the SMP style of positive as a superscript very helpful in explaining directed numbers.
I always "correct" my pupils if they say, for example, 4 minus 7 equals "minus 3" rather than "negaitve 3" (right from year 7 up to sixth form). I won't say that their answer is wrong, but I'll say something like "yep, negative 3 ... try to remember to say negative rather than minus though ... but well done".
As per another post, I normally distinguish between them by saying that minus is a verb and negative is an adjective ... interestingly, however, it turns out that minus is NOT a verb. It is a preposition; you technically can't say that you "minused" 7 from 10 and got 3. Didn't know that until an English teacher told me! Not checked in a real dictionary, but all the online ones agree.
I always thought the superscript method was universal, backed up by Canadian and Cameroonian teachers who were also brought up on the superscript notation. I must admit, though, that it's not the first thing I ask when I meet someone from overseas!
Pedantically, perhaps we should eliminate the word minus with its inherent confusions. "Subtract" is a verb and "negative" an adjective.
speaking as a secondary specialist perhaps we should be building bridges to the primary sector and ask these professionals why they do what they do. It is easy to be critical without knowing how or why others do what they do.
So you do feel the need for bridges between primary and secondary? Otherwise I do not see the point of your post juxtaposed to mine.
Absolutely afterdark - there is often implicit or even direct criticism of primary teachers on here. This does nothing to improve the situation. (I do accept that as non-specialists many peddle misconceptions - but who taught them??) Working together to improve subject knowledge and confidence is vital.
What happened to the precision?
How then do you suggest students should answer the question
"is a square a rectangle;
schemes such as MEP have questions such as
"a rectangle is a also a parallelogram- true or false".
My point is about these definitions of plane figures is that they are deliberately "loose". They allow us explore how definitions sort shapes. We can use this to touch upon Venn diagrams and shape sorting flow diagrams.
Super precise and exact is not always best, IMHO.
I would heartily agree with giving/using definitions that are 'precise enough' for the intellectual development of the children that are being taught.
The difficulty is getting it exact enough for the level of the children and not introducing misleading misconceptions.
Many thanks. I know what you mean about who taught the. I hear many horror stories, but I think there is a need to break the vicious circle of unsatisfactory mathematics teaching. The question is how to build the bridges? speaking from personal experience, going into a primary school once a week to teach the children there might be a good start.
I did this a few years ago and it was very fruitful for all concerned.
Now I work in a school for 3 - 18 year olds.
I believe that this vicious cycle will be very difficult to break. Co-operation across settings is a good idea on a local level (and indeed I have benefited from similar visits from a secondary PE specialist). However, teachers are prickly beings so such schemes have to be handled sensitively - and I have heard isolated horror stories of secondary colleagues patronising primary staff.
The Primary Maths specialist scheme was also a good start - funding for which is now ceasing.
Perhaps primary teacher trainees should have a higher than GCSE grade C qualification?
It must be so interesting to work in your setting - seeing the progress from EYFS to A level would be fascinating for many of us.
A minimum requirement of grade B in GCSE mathematics will be with us shortly. Obviously this is still inadequate (it just about compensates for grade inflation) but the aim is to work towards higher entry standards than this. There will be a financial incentive for new Primary teachers who have an A Level in mathematics soon.
Does anyone know why my paragraph breaks don't appear?
You can instert paragraphs in chrome (as I'm doing with this post.
Thing is, the editor the TES website provides doesn't recognise chrome and so doesn't put in the HTML tags needed to get paragraphs.
But you can type them in yourself. (As I just have.)
Both, but inform them that from the purists' viewpoint (-3) is said as "negative three", and "minus" is something that is done to the numbers (an operator). With practice though the terminology should get lost and they should develop a proficiency at the calculation, just by viewing the mathematical symbols - that is how I have developed my "Integer Trainer" resource (for the interactive whiteboard and as an app for download for iPod touch and iPhones). I am willing to accept "minus three" or "negative three" as long as they are able to show a proficiency in their mental calculations.
No. KS2 students minus synonamously with both subract and negative. To say minus is used just to mean subtract is not true.
In KS3 they should start learning the separate names subtract and negatives.