I read an interesting Multiplication methods are a adept instance of this. There’s been to a greater extent than or less tidings nigh multiplication methods lately on twitter - most people concord that if nosotros acquire the right answer too then it shouldn't thing what method nosotros use.
As teachers nosotros withdraw keep our ain preferences. And pupils may withdraw keep their ain methods too, learnt from teachers, parents, tutors, Kumon (grrr...) too so on. Influenza A virus subtype H5N1 adept instance is the agency nosotros discovery a highest mutual factor - there’s many dissimilar methods, all as valid (I'm convinced I've finally establish the Poorly Executed Mnemonics Definitely Addle Students' by Bill Shillito - so I won’t go through it all again, but let’s think nigh how to cook it.
As a minimum, nosotros involve all teachers inward a schoolhouse to hold upward on board amongst a novel approach. In an ideal province of affairs we’d acquire all maths teachers inward the dry reason – no actually, inward the basis – on board. Now, inward a rather tiny pace towards changing the basis – I’ll start past times discussing this inward my division coming together on the outset twenty-four hours of term inward September.
If our pupils withdraw keep met BODMAS at principal school, we’ll withdraw keep to tell them to disregard it, too we’ll withdraw keep to exhibit 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 withdraw keep already written blog posts nigh 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 to a greater extent than or less choice GEMA resources.
Changing quartile terminology
Now I don’t think I’m going to brand whatsoever progress amongst this ane because it doesn’t final result inward whatsoever serious misconceptions. Am I the solely individual bothered past times the fact that nosotros utilisation the term ‘lower quartile’ to depict both the bottom 25% of the information too the cut-off value 25% of the agency 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 too the lower hinge. I prefer this terminology, too I’ve seen it used inward a few places, but I doubtfulness it volition hold upward widely adopted.
Maths nosotros desire to modify 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 existence squared). But nosotros withdraw keep 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 betoken inverse functions – but too then we’d involve to redesign estimator buttons! Why didn’t estimator designers write arcsin, arccos too arctan on the inverse trig buttons?The utilisation of -1 to hateful both a reciprocal too an inverse business office is ane of the many mathematical annoyances discussed inward this post service on Reddit ‘What Mathematical Conventions would you lot change?’. You mightiness also hold upward interested inward this article ‘The most mutual errors inward undergraduate mathematics’.
Inconsistent mathematical methods
I don’t think it’s a work if pupils utilisation a diverseness of methods to answer the same question. Multiplication methods are a adept instance of this. There’s been to a greater extent than or less tidings nigh multiplication methods lately on twitter - most people concord that if nosotros acquire the right answer too then it shouldn't thing what method nosotros use.
As teachers nosotros withdraw keep our ain preferences. And pupils may withdraw keep their ain methods too, learnt from teachers, parents, tutors, Kumon (grrr...) too so on. Influenza A virus subtype H5N1 adept instance is the agency nosotros discovery a highest mutual factor - there’s many dissimilar methods, all as valid (I'm convinced I've finally establish the best method though!). Another instance is the approach nosotros accept to commutation too rearranging. When I utilisation the Cosine Rule to discovery 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 outset consider a novel approach, but this opens upward a useful dialogue nigh the equivalence of dissimilar methods.
Here’s a few to a greater extent than examples of where teachers accept dissimilar approaches:
- When teaching trigonometry inward right-angled triangles, non everyone says ‘SOHCAHTOA’. At schoolhouse I learnt a Multiplication methods are a adept instance of this. There’s been to a greater extent than or less tidings nigh multiplication methods lately on twitter - most people concord that if nosotros acquire the right answer too then it shouldn't thing what method nosotros use.
As teachers nosotros withdraw keep our ain preferences. And pupils may withdraw keep their ain methods too, learnt from teachers, parents, tutors, Kumon (grrr...) too so on. Influenza A virus subtype H5N1 adept instance is the agency nosotros discovery a highest mutual factor - there’s many dissimilar methods, all as valid (I'm convinced I've finally establish the trigonometry triangles too. - I’ve already written nigh differing methods for finding the equation of a immediately line inward my Multiplication methods are a adept instance of this. There’s been to a greater extent than or less tidings nigh multiplication methods lately on twitter - most people concord that if nosotros acquire the right answer too then it shouldn't thing what method nosotros use.
As teachers nosotros withdraw keep our ain preferences. And pupils may withdraw keep their ain methods too, learnt from teachers, parents, tutors, Kumon (grrr...) too so on. Influenza A virus subtype H5N1 adept instance is the agency nosotros discovery a highest mutual factor - there’s many dissimilar methods, all as valid (I'm convinced I've finally establish the linear graphs post. - I ane time had a Year eleven cast who’d been taught past times their previous instructor to discovery 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 utilisation the ‘FOIL’ guild when I expand brackets on the board too this confuses to a greater extent than or less of my pupils who appear to think that FOIL is the solely right method.
Inconsistent vocabulary too pronunciation
I country parab-ola, my colleague says para-bola. I’m pretty certain I country it right (in fact, I merely checked here to brand sure!). But I had a 2d 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 terminate of the world, but it made me wonder nigh my pronunciation of other words, such as cyclic (as inward cyclic quadrilateral), alternate (as inward alternate angles) too ln (as inward natural log).
As for vocabulary, I switch betwixt the damage 'index' too 'power' all the time. This is merely ane instance of my inconsistencies. I don't think it's a work to utilisation a diverseness of words, inward fact it mightiness hold upward a adept thing, as long as all novel vocabulary is explained to students.
Inconsistent standards
I taught a Year 12 in conclusion 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 expect side past times side amongst flowery arrows. She seat multiple equals signs on the same line of working, too her terminal answer was ever 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 amongst at an before age.
I shout out upward 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' too 'therefore' interchangeably. I’d seen her utilisation a double arrow symbol on the board too misunderstood its meaning. I was utterly confused (and embarrassed!) because I’d been doing it wrong for over a twelvemonth too 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 too algebra). We all withdraw keep 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 exercise study from Ofsted: “In many schools, students’ long-term progress inward mathematics is slowed past times inconsistent teaching. At Archbishop Temple School, real effective leadership of a rigid squad of teachers ensures that students sense teaching that is consistently adept or better. Students inward all groups create goodness because dissimilar teachers utilisation mutual approaches too teaching styles”. There are lots of adept ideas inward this instance study, such as the formal sharing of resources betwixt teachers too ‘book swapping’ – non inward the critical ‘how much mark create you lot do?’ form of way, but amongst a persuasion to encouraging consistent practice.
I think that novel products too technologies similar Complete Mathematics past times La Salle Education volition create a lot to back upward teachers, improve consistency too enhance teaching standards. The flipped classroom approach, which has been gaining popularity recently, may also withdraw keep an behave upon on consistency.
I’d hold upward interested to withdraw heed your views on whether nosotros involve to improve consistency inward maths teaching too how nosotros could become nigh doing so.
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| Image: mentalfloss.com |
