Showing posts with label Teaching Tools. Show all posts
Showing posts with label Teaching Tools. Show all posts

Friday, October 25, 2019

Multiplication In Addition To Colour

This uncomplicated sentiment shows how of import it is to purpose unlike colours when writing on the board - no affair what topic you're teaching.  It actually helps pupils proceed rails of what you're doing.


Source: http://www.jandmranch.com/2013/02/09/teaching-three-digit-multiplication-to-my-aspergers-daughter/ 

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Two Ways To Purpose Comic Strips Inward Maths Teaching

I stumbled across a prissy didactics sentiment inward this blog post which is all almost giving pupils fourth dimension to summarise what they've learnt.  The writer of the spider web log suggests that pupils depict comic strips inward aeroplane or for homework. Here's around examples:
Example worksheet

Example of pupil's work


I i time used comic strips for a dissimilar role inward my didactics - I produced this comic strip for my GCSE class, which I showed inward this Prezi slideshow to generate give-and-take almost sampling methods.  The characters are all teachers at my schoolhouse (with slightly amended names...).  It went downwardly good alongside my aeroplane too I laid upward them the chore of creating their ain versions. We used Bitstrips for Schools which is lovely merely tin terminate hold upward really time-consuming.

(that's meant to hold upward me past times the way!)



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Student Communication Using Blogs

I've taken a few days away from posting on hither because my babe was born on Monday... But fifty-fifty though I've been a flake tied up, I've withal been able to portion final infinitesimal motivational messages alongside my examination classes using 2 pupil blogs - 1 for my GCSE class too 1 for the whole Sixth Form. In this post I utter over my experience of communicating inwards this way.

GCSE Class
I started example post).  I also posted classwork answers too links to worksheets too homework sheets inwards instance they missed a lesson or lost a homework. I industrial plant life this was the most useful expression of the weblog - my pupils never had an excuse for missing a homework!

I industrial plant life it a flake time-consuming to write a weblog post iii times a calendar week too past times the fourth dimension this course of written report were inwards Year xi I was updating the weblog less often, too my posts got shorter. To live on honest at that spot were times when I felt far likewise busy to post, merely I did persevere.

Since this course of written report own got been on written report leave, I've been posting motivational messages too final infinitesimal revision resources. I tin move meet from the hitting tracker on Blogger that my pupils own got been receiving these messages.

Sixth Form
When I took on the purpose of Key Stage v Coordinator I decided to fix this blog every bit the psyche tool for communicating alongside H5N1 marker pupils.  My schoolhouse has 200 pupils studying AS too A2 Maths too Further Maths.  Around twenty pupils subscribe to my weblog past times e-mail too I promise that pose out volition growth greatly side past times side twelvemonth (if I successfully promote it to the incoming Year 12s inwards September). It's been a real useful agency of sharing resources too tidings - for representative close trips, courses, opened upwards days too competitions.  Over the course of written report of the twelvemonth I've done an average of 3 - four posts per calendar month too so it's been less time-consuming than my other blog.

Summary
Although I've continued to utilization 'old-fashioned' forms of communication (noticeboards, handouts etc), I experience that blogging has been an first-class method for communicating alongside pupils, particularly during written report leave. Blogger - too similar tools - are real quick too tardily to use.

My blogs own got been primarily for communicating alongside pupils, different other blogs run past times my schoolhouse (like this one) which give pupils the chance to portion weblog posts themselves.

I've seen Twitter used past times other Maths Departments to communicate alongside pupils - I intend this is an first-class sentiment too my side past times side finish is to encourage my Head of Department to laid this upwards for my school.





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Venn Activities

This post service is nigh using Venn Diagrams equally a didactics tool, rather than didactics the concept of Venn Diagrams themselves.  To quote the splendid Johnny Griffiths, 'The Venn Diagram amongst iii bubbles is the maths teacher's friend! ... To move able to fill upward inward an eight-region diagram shows a actually deep agreement of the distinctions that a practiced pupil has to move able to make, spell the weaker pupil finds beingness faced amongst a moving-picture exhibit such equally this much less threatening than a page of exercises'.

Before nosotros foremost using Venn activities inward Maths lessons, let's mean value nigh whether pupils are familiar amongst how Venn Diagrams work. I acknowledge to beingness a flake clueless nigh just what children written report at master copy school. The primary here), only I straight off prefer the simpler method described in linear equations activity. It helped consolidate their noesis of linear graphs in addition to allowed me to banking concern check their understanding.
  • Johnny Griffith's splendid RISPs (Rich Starting Points for H5N1 Level Core Mathematics) includes the Venn activities Risp 10 (coordinate geometry) in addition to Risp 4 (periodic functions).  In the instructor notes for Risp 10 Johnny shares his views on the usefulness of Venns.
  • A Venn action for Solving Quadratics past times Factorising past times aka nka on TES. 
  • A GCSE extension action on quadratic graphs from MEI.
  • I haven't tried this all the same only Don Steward also gives us this lovely here), only I straight off prefer the simpler method described in number activity.

    •  Interactive Venns
    Venns piece of occupation good on the Interactive Whiteboard - here's roughly examples.

    Other Uses
    • When I innovate complex numbers inward FP1 nosotros create a Venn Diagram during degree news nigh types of numbers (real, rational, integers etc) in addition to their Greek symbol notation.  The NCETM has a similar Venn action inward this resource sheet.
    • Up until lately I used Venn Diagrams to learn Highest Common Factor in addition to Lowest Common Multiple (method explained here), only I straight off prefer the simpler method described in this post.
    • Quadrilaterals tin move classified using a Venn Diagram similar this one.  We tin in addition to hence answer questions such as 'Is every foursquare a rectangle? Is every rhomb a square?' A 'family tree' also plant well.

    In determination - Venns are everywhere! But inward secondary Maths they are alone formally taught to those studying iGCSE (set theory) in addition to Statistics 1 at H5N1 flat (probability). I'm pleased to run across that Venn Diagram methods inward probability are on the new Maths GCSE Syllabus so volition move to a greater extent than widely studied inward future. But inward add-on to beingness taught equally a topic inward their ain right, Venn Diagrams are a versatile didactics tool amongst numerous applications inward the classroom. And they bring the added bonus of beingness created past times a British Mathematican! Well done Mr Venn.



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    Teaching Amongst Desmos

    I discovered Desmos terminal yr through @ColleenYoung's fantastic weblog Mathematics, Learning in addition to Web 2.0. It chop-chop became my favourite slice of 'teachnology'. Before Desmos I occasionally used Omnigraph or Autograph, but I at nowadays utilization Desmos regularly because it's but so tardily to use. It actually couldn't travel simpler. As it's web-based, I encourage my pupils (particularly at Influenza A virus subtype H5N1 level) to utilization Desmos at domicile to back upward their studies, for trial to depository fiscal establishment gibe graph sketches.

    Desmos on the Interactive Whiteboard
    When instruction exponential functions to Year 12, I used Desmos on my IWB to present the graphs of functions such every bit y = 2x in addition to y = 3x. We discussed our expectations for graphs such every bit y = 2-x in addition to used Desmos to check.  When nosotros plotted y = (-2)x nosotros got an interesting trial - which had me stumped for a infinitesimal - tin you lot explicate it?


    Desmos is specially helpful for demonstrating concepts inwards Further Maths (such every bit the directrix in addition to focus of a parabola) - there's unopen to expert examples in this blog.

    Desmos inwards the information technology Room
    My schoolhouse doesn’t ain tablets in addition to information technology rooms are rarely available, in addition to hence my pupils don't oftentimes acquire the conduct a opportunity to utilization applied scientific discipline during their Maths lessons. But I was in addition to hence non bad to part Desmos alongside my Year ix class, I made a big endeavor to acquire organised. I produced this worksheet for them to utilization inwards an information technology room, alongside the aim of introducing dissimilar types of graph (quadratic, cubic, reciprocal) in addition to uncomplicated transformations. After a real brusk demonstration of Desmos, the degree spent ii whole lessons working independently. I was pleased alongside their progress in addition to I promise that they'll hollo upward Desmos in addition to proceed to utilization it every bit a learning tool both at domicile in addition to at school.

    I loaded my worksheet onto TES today - along alongside a graph transformation activity that I utilization at Key Stage iv - in addition to it got me thinking well-nigh whether whatsoever other resources are available for instruction alongside Desmos.  I establish a few examples on TES, such as Investigating at in i trial lines alongside Desmos past times Tristan Jones and Using Desmos to learn Coordinate Geometry (KS3) past times phildate. I facial expression that the make of instruction resources available volition grow every bit increasing numbers of teachers respect in addition to encompass this fantastic tool.  




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    Shortcuts Vs Concept Development

    I highly recommend this mass Nix the Tricks - ‘a lead to avoiding shortcuts that cutting out math concept development’. I felt uncomfortable reading it at times - my ain pedagogy is amount of these tricks in addition to shortcuts because I’m strongly influenced past times the fourth dimension pressures in addition to examination focus that the writer references inwards her introduction. The mass covers a dandy many pedagogy tricks in addition to inwards each instance makes first-class points almost why these tricks should endure avoided. Helpfully, option approaches are suggested. I’m non going to halt using crocodile references when introducing inequality symbols (I similar the crocodiles!) in addition to I'm non (yet) going to halt pedagogy slope as 'rise over run', simply I volition sure enough intend twice almost many of my methods at nowadays I’ve read this book.

    My spider web log focuses on sharing pedagogy ideas in addition to some of my posts include just the variety of shortcuts that this mass is thus opposed to - similar sohcahtoa triangles, or this play a joke on for remembering exact values of trigonometric ratios (which doesn’t supercede the triangle method - simply it's a squeamish play a joke on in addition to worth sharing).

    It was my excitement at discovering this method for multiplying matrices that inspired me to write this blog. I was astounded that I’d never seen this method earlier in addition to similar a shot showed it to my FP1 students, who were as impressed. I mentioned this method to a colleague, prompting a conversation almost other 'alternative methods' nosotros knew of. She told me about this method for finding Highest Common Factors. Again, I was astonished that I’d been happily pedagogy the Venn method - which I’d learnt from my mentor during a PGCE placement - when a quicker in addition to easier method existed. I felt similar I'd unnecessarily overcomplicated things for my students.

    We all know that quicker methods aren’t e'er ameliorate methods. ‘Maths hacks’ such as matrices method - that modify the means nosotros learn a theme for the better.




    By the way, if you lot relish the mass in addition to then there's to a greater extent than (including novel sections inwards draft) on nixthetricks.com.



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    Maths Vocabulary

    I found Cav's blog shipping 'Vocabulary together with maths are non mutually exclusive' actually interesting together with it got me thinking nearly activities together with didactics techniques related to maths vocabulary.

    Influenza A virus subtype H5N1 didactics tool that tin move endure used regularly throughout the twelvemonth is a source).



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    Edit: 11/11/15

    Since writing this shipping final twelvemonth I've seen lots of groovy resources for developing vocabulary. I specially similar the Literacy Assessments featured inward vocabulary noesis survey. When you lot outset didactics a topic, do a listing of the novel words that volition endure used together with inquire students to consummate a nautical chart showing their agreement of those words.  Repeat the activeness afterward to run across the improvement inward agreement - I've non tried this myself however but I intend it would generate merely about useful questions equally good equally boosting pupil confidence.

    In my shipping on source).



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    Edit: 11/11/15

    Since writing this shipping final twelvemonth I've seen lots of groovy resources for developing vocabulary. I specially similar the Literacy Assessments featured inward Area together with Volume I suggested these maths vocabulary exercises which brand for prissy 'end of term' lessons.  Here's an trial of an activeness from this pack:



    Here's merely about to a greater extent than links that you lot mightiness honor useful:

    I was latterly talking to a highly intelligent together with articulate Year xiii pupil who said that she hated it when her instructor asked her to 'speak maths'. I asked her to elaborate. She said that when questioning the class, the instructor expected answers that used appropriate maths vocabulary - together with fifty-fifty this pupil (who'll endure off to Oxbridge inward September) flora this daunting.  We demand to address this trial from a immature age.  One tip is to ever require pupils to reply questions inward total sentences instead of merely numbers or words - from mind schoolhouse onwards. Influenza A virus subtype H5N1 rattling unproblematic trial - inward response to the enquiry 'what do nosotros telephone outcry upwardly a polygon amongst 8 sides?', don't bring the reply 'octagon' - inquire for a total judgement such equally 'An 8-sided polygon is called an octagon' to larn pupils used to 'speaking maths' from an early on historic menses (source).



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    Edit: 11/11/15

    Since writing this shipping final twelvemonth I've seen lots of groovy resources for developing vocabulary. I specially similar the Literacy Assessments featured inward Gems 43. I also flora the source).



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    Edit: 11/11/15

    Since writing this shipping final twelvemonth I've seen lots of groovy resources for developing vocabulary. I specially similar the Literacy Assessments featured inward activity below worked good amongst my Year 7s.

    Here's my direct to literacy inward maths lessons:






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    Resources Anonymous

    'Hello. My refer is Jo as well as I'm a resourceaholic'. Yes, I confess, I'm utterly addicted to searching the mesh for maths didactics resources.

    It all started when I saw a PGCE pupil photocopying this blog. Ooh, novel websites! Heaven for a resourceaholic.

    I haven't had a remove chances to aspect at all these websites yet, exactly here's around of my transcend resources recommendations from the websites I've looked at as well as thence far. I've focused on Influenza A virus subtype H5N1 score because that's where I mean value it's hardest to abide by interesting didactics ideas.

    Statistics 1 
    Illustrative Mathematics has around fantastic ideas for didactics S1. Here's a alternative of examples:

    Finally, I stance it powerfulness last helpful to part this quadratic activeness 'Find the coordinates' - my schoolhouse uses this on Sixth Form Induction Day inwards our maths taster sessions (thanks to Susan Wall at Wilberforce College for this activity).

    I'll croak on to piece of occupation my agency through the website listing as well as volition characteristic recommended Key Stage three as well as GCSE resources inwards afterward posts.




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    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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    Deliberate Mistakes

    Image: weandserendipity.com
    I'm e'er on the sentry for novel ideas for GCSE revision lessons. If I write near this sentiment at nowadays in addition to therefore hopefully I'll recollect it come upwardly Spring.

    This yr I had slap-up success alongside relay races in addition to carousels inwards my revision lessons. I besides did some pupil-led lessons which were a lot less successful.

    This 'deliberate mistakes' sentiment is something I've adapted from this blog post, therefore give thank y'all you to @bkdidact for sharing the link in addition to @kellyoshea for the inspiration. I've never seen this inwards maths earlier but it may hold out that many of y'all already produce it, if therefore in addition to therefore I'd similar to hear your feedback.

    The Mistake Game
    Students, inwards pairs or pocket-size groups, are given a work to solve in addition to explicate to the class. In their explanation, they must include a deliberate mistake. Not exactly a numerical slip, but something that highlights a possible misconception that their classmates powerfulness have.

    If I role this for GCSE revision in addition to therefore by examine questions (the longer, unstructured types) would function best - there's some examples inwards this fantabulous laid of questions from Suffolk Maths. But this sentiment could besides function when education specific topics. I intend I may drive it this yr when education both trigonometry in addition to probability trees.

    For example, if y'all role the Mistake Game when education Pythagoras' Theorem, y'all could role this inquiry (solve for x):


    The mutual error hither is to non foursquare the four (though students may come upwardly up alongside something else).

    Here's some other example, from this worksheet from thechalkface.net.


    There's numerous things they could (deliberately) produce incorrect inwards this one!

    When each grouping goes through their inquiry on the board, their classmates volition hold out listening carefully to location the mistake, therefore it's slap-up for getting students to focus. I'm non certain how best to organise the responses. Perhaps students could seat their mitt upwardly every bit before long every bit they location the error therefore it tin hold out corrected right away in addition to and therefore the balance of the solution tin hold out done correctly. Or mayhap when the grouping direct keep finished presenting their sum explanation, a volunteer could come upwardly up to the board in addition to right their work. Or maybe later on each presentation the students could verbalise over the work inwards their groups, create upwardly one's heed what was incorrect in addition to re-do the inquiry correctly.

    This is a flake similar 'tick or trash' exercises - it's helpful for pupils to hold out aware of mutual mistakes. I've besides used these 'Classic Mistakes' inwards previous revision lessons.

    The Mistake Game is besides a practiced chance for students to run into each other’s approaches to solving problems in addition to verbalise over the effectiveness of dissimilar methods.

    I intend this activeness volition engage the whole degree - I'll drive it out in addition to allow y'all know! If you've ever tried anything similar this in addition to therefore delight portion your thoughts. I recommend reading near the sense of the instructor who wrote the original post. As she says, ‘we all acquire to a greater extent than when a incorrect response goes upwardly than when we’re only watching perfection’.


    Image: bigthink.com

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    Animations Together With Simulations

    Last night's #mathschat discussion close images gave me in addition to therefore many practiced teaching ideas, I woke upward at 2am to write a list! One affair that came upward was animations. I dear a practiced animation that demonstrates a concept beautifully, in addition to therefore here's a few examples.

    blog post) and judging past times the let on of retweets, I gauge others similar it every bit much every bit I do. There's to a greater extent than gifs similar this here. 

    The animation below shows how the outside angles of a polygon amount to 360o. Sometimes it's meliorate to purpose an animation that y'all tin sack suspension in addition to speak through though, in addition to therefore I prefer this animation for outside angles of a polygon. Absorb Learning is an fantabulous website for animations.
    Another instance of an animation y'all tin sack suspension during teaching is this 'bisecting an angle' tool. It comes alongside both a clear teaching canvass for students in addition to associated proofs. There are similar pages for every possible construction! As I mentioned inwards a previous post, I loathe teaching constructions, in addition to therefore I honour this real helpful.

    Here's some other maths gif. This 1 is for demonstrating the properties of parabolas, every bit taught inwards Further Maths. This tin sack also locomote demonstrated nicely using Desmos.

    I also desire to get upward PhET simulations. I don't instruct mechanics exactly I'm told that PhET has lots of bully interactive simulations for demonstrating concepts. 'Balancing Act' is a practiced example. They also convey simulations for Key Stage iii topics such every bit fractions - run across the full maths alternative here. The simulations tin sack locomote downloaded in addition to run from your schoolhouse network. 

    Balancing Act - PhET

    Aren't nosotros lucky to convey such fantabulous applied scientific discipline to heighten our teaching?

    If y'all know of whatever other practiced animations or interactive tools, delight comment below or tweet me.


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    5 Maths Gems #1

    I’m fairly novel to Twitter. My absence over the final few years agency I’ve missed out on thousands of splendid pedagogy ideas. Twitter is a source of endless inspiration. So I lead keep a plan. I’m going to write a weekly post highlighting v corking novel ideas I’ve gleaned from Twitter. These posts volition assistance me recall things. And hopefully my readers volition do goodness too.

    Today I’ve exceeded my limit too am presenting a listing of 6 ideas from my calendar week on Twitter (not a practiced start! I’ll aim for 5 side yesteryear side week).

    1. Practical ideas from Maryse. It sounds similar Maryse (@AllThingsMaths) has done an amazing project transforming mathematics pedagogy inwards her schoolhouse too enthusing her students amongst tonnes of creative ideas. Here’s a alternative of those she’s shared this week:
    • Play select handgrip of amongst eggs too run out the relative frequency of smashing.
    • Get an one-time tyre, pigment it too gyre it to demonstrate circumference. 
    • Have a release employment painted inwards the playground.
    • Have discussions almost going dorsum inwards fourth dimension too Doctor Who amongst move graphs. 
    I dear these ideas. Follow @AllThingsMaths for lots more.

    Mistake Game, Colin Beveridge (My Favorite Liar’. You must read this! It prompted a give-and-take on Twitter almost whether the thought would run inwards maths. I think it would. In your outset lesson amongst a novel class, nation them that you'll nation i prevarication per lesson. Your pupils lead keep to position your lies. In the give-and-take on Twitter nosotros came upward amongst a practiced listing of lies too misconceptions, such equally 'multiplication makes numbers bigger', 'if a release has 6 zeros too so it's inwards the millions' too 'one is a prime number'. The thought is that you lot skid these lies into your pedagogy too promise that your pupils volition straightaway challenge you. And if no-one challenges you lot too so it volition brand a squeamish plenary discussion. Mr Allan (@mrallanmaths) is going to endeavour it out - I’m actually looking forwards to hearing how effective it is. I think, similar the error game, it volition hold out incredibly engaging.

    3. Box plots party. In reply to my post almost teaching box plots, Pete Sides of the South Yorkshire Maths Hub (@SYMathsHub) suggested a lovely activeness inwards which pupils utter over the ages of guests at dissimilar types of party, to assistance them sympathize the concept of spread. For event you lot could inquire them to depict a box plot representing the ages of guests at an 18th birthday party, a wedding, a child’s political party etc. I similar this thought so I turned it into a worksheet too added it to my spider web log post.

    Trigonometry triangles are similar. I’ve never given much thought to the fact that my students are missing an chance to practise rearranging formulae. I sympathize the argue for mixed views on these methods, but I do rather similar the triangle shared yesteryear Malc Henderson (@malc_henderson) for solving contrary per centum problems. It’s squeamish to lead keep a arrive at of tools to back upward students when they’re preparing for their GCSEs.


    6. Display ideas. Clarissa Grandi (@c0mplexnumber) posted a moving painting of her novel ‘vwllss’ corridor display (inspiration from @El_Timbre). It looks fantastic - what a practiced idea!


    Other practiced display ideas I’ve seen latterly include circle formulae yesteryear Dawn (@mrsdenyer), a foursquare beginning clock yesteryear Duncan Smart (@duncsmart), too an interactive release puzzle for a maths corridor or classroom, shared yesteryear Mr C Ward (@MrWardMaths).





    There you lot go, half dozen maths gems from @mathsjem (my initials are JEM yesteryear the way, it’s non a spelling mistake!). This is only a pocket-size alternative of the practiced ideas I’ve seen on Twitter this week. More to come upward side yesteryear side week!

    I’m working on a few posts at the moment, including i on introducing algebra too i on introducing differentiation – if you lot lead keep whatever corking ideas too so delight e-mail resourceaholic@gmail.com or tweet me.



    Image sources: lightbulb tampawebdesigner.net; birds techwyse.com

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    Thoughts On Didactics Fractions

    Fraction misconceptions - MathsPad
    Yuvraj (@YuviLite) asked me to write a post service virtually teaching fraction addition. I similar a challenge! Fractions are notoriously hard to teach, riddled alongside misconceptions as well as crucial to acquire right. If I were to endure thorough on this topic, I’d demand to create a hell of a lot of research as well as write a dissertation length weblog post.

    I for sure haven't been that rigorous, but I accept works life a few ideas. First read what Yuvraj has written virtually difficulties inwards teaching fractions, as well as thus accept a hold off at my ideas at the end.


    When I hear students utter the phrase, ‘uh no non fractions’ a pocket-sized phonation buried deep inwards my subconscious feels the same thing. Fractions is 1 of those topics which seems to endure on the system of function for EVERY twelvemonth as well as yet in that place are nevertheless thus many students who are befuddled yesteryear them as well as this is 1 of the reasons I accept been thinking virtually how I learn the topic.

     I am a instructor who believes inwards developing agreement as well as non exactly only reducing mathematics to a serial of procedures. I accept e'er thought this as well as it was drummed into me on my PGCE as well as Masters. Yet fractions has brought me to a crossroads. Before I tell you lot why, allow us hold off at dissimilar strategies of teaching the improver as well as subtraction of fractions. 

     The Cross Multiplying (Butterfly Method). This is the 1 I was taught at school. I had no agreement of why it worked but it got me the correct answer as well as at that historic menstruum that is all I cared about. To add together 2 thirds as well as 3 quarters nosotros would multiply the denominators together as well as thus cross multiply the numerators and denominators as shown below.

    The Grid Method. I of late discovered this option procedural method. Draw a grid equally shown below. The starting fourth dimension fraction is written on the top as well as the instant along the side. A plus sign is set inwards the starting fourth dimension box equally this is the functioning nosotros desire to comport out. We set the products of the other numbers into the grid. We as well as thus depict around the highlighted boxes as well as this would give us our numerator, inwards this instance 8 + nine = 17. The white box would endure our denominator.
    Fraction Strips. In NixTheTricks, the role of fractions strips is advocated to learn the improver as well as subtraction of fractions. For representative to add together a one-half as well as a quarter we would start alongside visual representations equally shown below.
    When nosotros set the one-half as well as quarter together nosotros can't limited this equally a unmarried fraction without cutting the pieces into equal parts (quarters inwards this case). The thought hither is that the agreement of a mutual denominator is built upward as well as linked to the method for adding fractions.

     Paper Folding. This method is from Mike Ollerton’s fantabulous ‘Getting The Buggers To Add Up’ - read the explanation here (or purchase the book!). 

     Fraction Wall. I accept also seen teachers role fraction walls to aid students equally a method of identifying equivalent fractions. Some people role this or shapes to acquire the thought of equivalent fractions across.

     My Dilemma
    I accept e'er gone downwards the conceptual route. I accept championed the conceptual route, until I got to algebraic fractions. The conceptual route e'er seems to Pb dorsum to the to a greater extent than procedural route, especially for fractions where the denominators are 2 dissimilar prime numbers, as well as for algebraic fractions. If students are to a greater extent than used to the procedural route, they should inwards theory endure able to able this physical care for for algebraic fractions.

     Which has led me to question: is it worth the hurting of rewiring students who e'er seemed to accept heard of the cross multiplication method fifty-fifty earlier they accept reached me (even the Year 7s)? I accept spent many hours struggling alongside folding bits of newspaper as well as sharing cakes to embed the thought of equivalent fractions. 

     Is it plenty exactly to explicate why the cross multiplication or grid method works as well as and thus ensure fluency inwards the skill?


    Thanks Yuvraj. I wonder the same thing. In many topics nosotros fighting to respect the correct residuum of conceptual agreement vs procedural methods. Us pathetic maths teachers are forever fretting virtually it.

    My preferred procedural method, for both numerical as well as algebraic fractions, is the no-frills version (find the lowest mutual multiple of the 2 denominators, as well as thus convert both fractions to equivalent fractions alongside that denominator, as well as thus add together the numerators). It works for me, but I learn high powerfulness pupils thus I accept a relatively slow life.

    Now for a few teaching ideas. I’m non trying to solve the world’s fraction problems, but I promise you lot may respect some interesting activities hither for your fractions lessons.

    Don Steward is a Genius
    subtracting fractions activity inwards which students hold off at the diagram below as well as figure out what's going on. As Mr Steward says, this gives the instructor fourth dimension to drinkable their tea! It's a truly clear agency to explicate fraction subtraction using mutual denominators.


    Misconceptions as well as Assessment
    This blog has some vivid ideas for identifying fraction misconceptions which powerfulness endure peculiarly helpful when you lot start tackling fractions alongside a Year vii class. For example, the author asked his students to explicate what's incorrect inwards each of the 3 pictures below as well as got some interesting responses.
    You could as well as thus inquire students to role the same shapes as well as respect an accurate agency to correspond the fractions indicated. Other ideas inwards this weblog include bespeak the students to consummate the sentences 'Fractions are...', 'When you lot add together 2 fractions you lot accept to...' as well as 'You role fractions when you...'. Or fifty-fifty inquire pupils to write downwards 'Everything I Know virtually Fractions' as well as write a listing of what they'd similar to learn. These activities volition aid you lot create upward one's hear your starting dot inwards Year 7. The blog is good worth a read.

    Manipulatives as well as Visual Aids
    Yuvraj already touched on visual aids. I retrieve beingness told during my PGCE that I only must role Cuisenaire Rods, but non truly having a clue what to create alongside them. There's whole books written virtually this! I works life explanations here as well as here - the method seems rather overcomplicated. But if they appeal to you, as well as thus Nrich provides this online tool for demonstrating Cuisenaire Rods on the Interactive Whiteboard.

    This website has a lot of skilful materials on fractions as well as visual aids, including downloadable fraction circles.

    ‘Number 1 inwards disguise’
    Look at the 'NOID' poster below. Yes, it is quite ridiculous. But it’s really slow to follow the thinking hither as well as I wonder if this explanation (or similar) would aid railroad train students' understanding. If you’re looking something a niggling less NOIDy for teaching improper fractions as well as thus this weblog post has some fantabulous ideas using manipulatives.
    From cindywhitebcms.blogspot.com
    Division
    'Ours is non to argue why, ours is but to inverse as well as multiply'. This made me express joy because I've never attempted to explicate fraction partitioning to my pupils beyond the 'KFC' dominion (keep, flip, change). Don Steward has written an fantabulous post virtually ways to explicate why it works - this one from moveitmaththesource.com peculiarly appealed to me. I'll top away on this inwards my dorsum bag inwards instance ever asked the question.
    Final thoughts
    I'm afraid I don't accept the answer to how best to railroad train conceptual understanding, but in that place may endure some ideas hither that you lot haven't seen before. In price of resources, there's tonnes of worksheets, games as well as activities online - run across my resources library for some recommendations. For to a greater extent than teaching ideas, here's some farther reading:
    Thank you lot thus much to Yuvraj for his helpful input to this post. Comments as well as tweets would endure much appreciated - we'd dearest to hear your ideas.

    Fraction hopscotch inwards the maths corridor - from cisdmathmusings.blogspot.com



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