Consistent Mathematics

‘But Miss, that’s non what our lastly instructor said’

I read an interesting Multiplication methods are a practiced representative of this. There’s been roughly tidings almost multiplication methods lately on twitter - most people concord that if nosotros acquire the right respond in addition to so it shouldn't affair what method nosotros use.

As teachers nosotros take away maintain our ain preferences. And pupils may take away maintain their ain methods too, learnt from teachers, parents, tutors, Kumon (grrr...) in addition to so on. Influenza A virus subtype H5N1 practiced representative is the means nosotros notice a highest mutual factor - there’s many dissimilar methods, all as valid (I'm convinced I've finally flora the Poorly Executed Mnemonics Definitely Addle Students' by Bill Shillito - so I won’t go through it all again, but let’s think almost how to develop it.

As a minimum, nosotros postulate all teachers inward a schoolhouse to live on board alongside a novel approach. In an ideal province of affairs we’d acquire all maths teachers inward the province – no actually, inward the footing – on board. Now, inward a rather tiny pace towards changing the footing – I’ll start past times discussing this inward my division coming together on the commencement solar daytime of term inward September.

If our pupils take away maintain met BODMAS at master copy school, we’ll take away maintain to tell them to disregard it, in addition to we’ll take away maintain to demonstrate them why past times demonstrating the misconceptions it may Pb to. Like many others, I’m an advocate of teaching GEMA or GEMS instead. Some American maths teachers take away maintain already written blog posts almost this approach. It’s a hurting that most of my lovely resources reference the term BODMAS though. If I acquire fourth dimension over summertime I’ll brand roughly choice GEMA resources.

Changing quartile terminology
Now I don’t think I’m going to brand whatever progress alongside this i because it doesn’t termination inward whatever serious misconceptions. Am I the alone someone bothered past times the fact that nosotros work the term ‘lower quartile’ to depict both the bottom 25% of the information in addition to the cut-off value 25% of the means through the data? John Tukey, inventor of the box plot, used the tidings ‘hinge’ instead ie the lower quartile consists of the values betwixt the minimum value in addition to the lower hinge. I prefer this terminology, in addition to I’ve seen it used inward a few places, but I doubtfulness it volition live widely adopted.

Maths nosotros desire to alter but can’t
When nosotros innovate the thought of squaring sinx at Influenza A virus subtype H5N1 level, nosotros tell pupils to write sin²x instead of sinx² (to clarify that it’s non the x that’s beingness squared). But nosotros take away maintain to carefully explicate that sin^-1x doesn't hateful the reciprocal of sinx, but truly the inverse ie arcsin. The obvious solution to this confusing annotation is to halt using -1 to dot inverse functions – but in addition to so we’d postulate to redesign estimator buttons! Why didn’t estimator designers write arcsin, arccos in addition to arctan on the inverse trig buttons?

The work of -1 to hateful both a reciprocal in addition to an inverse business office is i of the many mathematical annoyances discussed inward this ship on Reddit ‘What Mathematical Conventions would yous change?’. You mightiness also live interested inward this article ‘The most mutual errors inward undergraduate mathematics’.

Inconsistent mathematical methods
I don’t think it’s a job if pupils work a diversity of methods to respond the same question. Multiplication methods are a practiced representative of this. There’s been roughly tidings almost multiplication methods lately on twitter - most people concord that if nosotros acquire the right respond in addition to so it shouldn't affair what method nosotros use.

As teachers nosotros take away maintain our ain preferences. And pupils may take away maintain their ain methods too, learnt from teachers, parents, tutors, Kumon (grrr...) in addition to so on. Influenza A virus subtype H5N1 practiced representative is the means nosotros notice a highest mutual factor - there’s many dissimilar methods, all as valid (I'm convinced I've finally flora the best method though!). Another representative is the approach nosotros take away maintain to exchange in addition to rearranging. When I work the Cosine Rule to notice an angle, I substitute the numbers into the formula a² = b² + c² - 2bcCosA then I rearrange. But I’ve noticed that most of my colleagues tell students to rearrange the algebra before they substitute. It mightiness confuse students when they commencement catch a novel approach, but this opens upward a useful dialogue almost the equivalence of dissimilar methods.

Here’s a few to a greater extent than examples of where teachers take away maintain dissimilar approaches:

• When teaching trigonometry inward right-angled triangles, non everyone says ‘SOHCAHTOA’. At schoolhouse I learnt a Multiplication methods are a practiced representative of this. There’s been roughly tidings almost multiplication methods lately on twitter - most people concord that if nosotros acquire the right respond in addition to so it shouldn't affair what method nosotros use.
  
  As teachers nosotros take away maintain our ain preferences. And pupils may take away maintain their ain methods too, learnt from teachers, parents, tutors, Kumon (grrr...) in addition to so on. Influenza A virus subtype H5N1 practiced representative is the means nosotros notice a highest mutual factor - there’s many dissimilar methods, all as valid (I'm convinced I've finally flora the trigonometry triangles too.
• I’ve already written almost differing methods for finding the equation of a at i time draw inward my Multiplication methods are a practiced representative of this. There’s been roughly tidings almost multiplication methods lately on twitter - most people concord that if nosotros acquire the right respond in addition to so it shouldn't affair what method nosotros use.
  
  As teachers nosotros take away maintain our ain preferences. And pupils may take away maintain their ain methods too, learnt from teachers, parents, tutors, Kumon (grrr...) in addition to so on. Influenza A virus subtype H5N1 practiced representative is the means nosotros notice a highest mutual factor - there’s many dissimilar methods, all as valid (I'm convinced I've finally flora the linear graphs post.
• I i time had a Year eleven degree who’d been taught past times their previous instructor to notice the nth term of a sequence using the a + (n-1)d formula that nosotros usually learn at Influenza A virus subtype H5N1 level. It worked well.
• I don’t work the ‘FOIL’ social club when I expand brackets on the board in addition to this confuses roughly of my pupils who appear to think that FOIL is the alone right method.

Inconsistent vocabulary in addition to pronunciation
I state parab-ola, my colleague says para-bola. I’m pretty certain I state it right (in fact, I only checked here to brand sure!). But I had a minute of doubtfulness when my pupils all laughed at my pronunciation because they’d heard it pronounced differently the previous year. Now this truly isn’t the destination of the world, but it made me wonder almost my pronunciation of other words, such as cyclic (as inward cyclic quadrilateral), alternate (as inward alternate angles) in addition to ln (as inward natural log).

As for vocabulary, I switch betwixt the price 'index' in addition to 'power' all the time. This is only i representative of my inconsistencies. I don't think it's a job to work a diversity of words, inward fact it mightiness live a practiced thing, as long as all novel vocabulary is explained to students.

Inconsistent standards
I taught a Year 12 lastly twelvemonth whose piece of work was laid out so badly it was almost impossible to follow. She scattered her workings all over the page, sometimes showing me where to hold off adjacent alongside flowery arrows. She set multiple equals signs on the same draw of working, in addition to her lastly respond was e'er hidden away somewhere. Her piece of work was also mathematically incorrect. Although I commented - many times - on the province of her workings, I decided it was to a greater extent than of import to focus our express fourth dimension together on fixing her mathematical misconceptions. I felt frustrated that her appalling approach to setting out her piece of work hadn’t been dealt alongside at an before age.

I recollect when I was a pupil inward the Upper Sixth Form, my maths instructor wrote on a homework that I’d used the symbols for 'equals' in addition to 'therefore' interchangeably. I’d seen her work a double arrow symbol on the board in addition to misunderstood its meaning. I was utterly confused (and embarrassed!) because I’d been doing it wrong for over a twelvemonth in addition to she’d never mentioned it before!

I also think nosotros could create a lot to a greater extent than to encourage clearer mathematical handwriting (both numbers in addition to algebra). We all take away maintain our ain styles though. I’m guilty of writing diagonal lines inward fractions on the board fifty-fifty though I know I shouldn’t.

A instance study
It’s worth reading this good practise written report from Ofsted: “In many schools, students’ long-term progress inward mathematics is slowed past times inconsistent teaching. At Archbishop Temple School, really effective leadership of a potent squad of teachers ensures that students sense teaching that is consistently practiced or better. Students inward all groups create goodness because dissimilar teachers work mutual approaches in addition to teaching styles”. There are lots of practiced ideas inward this instance study, such as the formal sharing of resources betwixt teachers in addition to ‘book swapping’ – non inward the critical ‘how much marker create yous do?’ form of way, but alongside a stance to encouraging consistent practice.

I think that novel products in addition to technologies similar Complete Mathematics past times La Salle Education volition create a lot to back upward teachers, improve consistency in addition to heighten teaching standards. The flipped classroom approach, which has been gaining popularity recently, may also take away maintain an touching on on consistency.

I’d live interested to take away heed your views on whether nosotros postulate to improve consistency inward maths teaching in addition to how nosotros could become almost doing so.

Image: mentalfloss.com

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