Although there are some pockets of collaboration throughout the UK, for example through regional TeachMeets, the fact is that the majority of UK maths teachers live in a bubble. Through no fault of their own, they know very little about approaches taken in other schools - including pedagogy, curriculum design and new technologies. Twitter is part of the solution, but it doesn't go far enough.

When Dr Vanessa Pittard from the Department for Education talked about Shanghai (am I the only one starting to get a bit bored with Shanghai?), she talked about their teachers having regular dedicated time to share expertise and ideas. That's what we need in the UK - dedicated thinking time. We're all too busy teaching. As @srcav says in this post, "in high performing countries teachers spend 30% of their time teaching, with the rest spent planning, preparing and assessing as well as working on improving their practice. Compared to the UK, where it’s 90%".

This weekend, 500 maths teachers gave up a precious Saturday to learn from each other. I'm very grateful to La Salle Education for providing that opportunity. To me it further highlighted the need for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing about our schools' latest marking policies, we should all be out having mini-conferences of our own. Let's hope that when our new Maths Hubs get back from their trips to Shanghai, improving collaboration is top of their list of priorities - and by that I mean collaboration with

*all*schools, not just the schools with tweeting teachers or a proactive Head of Maths.

Now for my weekly maths gems. For those who have just started reading my blog, this is where I share five great ideas that I've seen on Twitter each week. If you want to read any of my previous gems posts, they're all here.

**1. Paint! And my ideal classroom**

smartwallpaint.com |

This got me thinking about my ideal classroom. I'd have all the walls painted with whiteboard paint (student work would be proudly displayed in the corridors instead of in the classroom). I like the idea of students sitting in a horseshoe when I teach, like in the picture below. I think this would stop low-level disruption and would encourage better class discussion. They could also do independent practice in these chairs.

hyperspacellc.com |

The rooms I currently teach in are too small for me to easily reach every student while they're working, so even just a little more space would work wonders.

**2. Indices**

If you're looking for a new approach to teaching index laws, you might enjoy 'Number lines and indices' by @theshauncarter.

This post is about how he used a number line to explain concepts relating to index laws. It's a nice method and well worth a read if you're teaching indices. It could also be an interesting way into logarithms.

Once you've taught indices, try my index laws homework and fractional/negative indices homework.

**3. ThingLink**

I've just discovered ThingLink which allows you to create and share interactive images. Using this tool, teachers or students can add content inside any image - including photos, videos and web links. It's basically an interactive annotation tool. Although I think it may have more applications in humanities than in maths education, I've seen some great examples from @mathycathy that make me wonder whether students could use ThingLink to create revision material, or teachers could create linked pictures to point students in the direction of resources for support or extension. Have a play with this example 'Getting to Know Quadratic Functions' so you get the idea.

Here's some more examples of @mathycathy's work - hover over the images to see the links.

If you're looking to make some of your own material in ThingLink, a good starting point might be these fantastic crib sheets from @dotmaths. You could upload one of these crib sheets to ThingLink, annotate it with information, examples and a homework task, then share it with students using a class blog or VLE.

**4. Concept walls and revision walls**

@c0mplexnumber shared this brilliant concept wall. If you've not seen this idea before then do read the original post 'Mathematical Concepts Wall' by @mrprcollins and @srcav's subsequent post. This works by giving students a list of mathematical words and asking them to pick one or two words to write or draw about. Look at the impressive results!

Shared by @c0mplexnumber |

**5. Interesting graphs**

Statistical literacy is so very important. In 1951, Samuel S. Wilks said,"Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write!" (he was paraphrasing HG Wells). Although through our curriculum we teach students how to create and interpret a variety of graphs, I'm not convinced that 'the general public' are able to make sense of many of the graphs they see in the media. I think it's worth spending some time looking at both misleading graphs and interesting graphs.

Ridiculously misleading graph |

Source: 'How we believe' by Micheal Shermer |

Source: ONS |

Speaking of interesting graphs that spark discussion, you must read @heather_kohn's post 'Ambiguous Sports Graph'. Like the examples above, give this graph to your students and you may be surprised by what they come up with.

'Which Sport?' by Malcolm Swan |

**Final thoughts**

I want to end my gems post this week by recommending a few blog posts. First, @MathsWithMrHill wrote a great post about teaching place value. I love posts with lots of ideas and resource recommendations for a specific topic - they're very useful for lesson planning (I've written a few topic specific posts too).

Second, I want to mention @Jeremy_Denton's post about revision races. This is one of those posts that not only provides a fantastic resource but also clearly explains how to use it effectively.

Finally, I want to recommend @fmaths42's post about times tables starters which provides a set of progressively challenging practice grids, plus a suggestion to print these grids onto stickers. Times tables are rather helpful so I'd urge you to ignore Jo Boaler's advice about not ensuring that children learn their times tables - surely she must have said that in a moment of madness. Read @websofsubstance's post The Educators - Jo Boaler for some interesting (in my opinion - very sensible) views on this.

Finally, have a go at this question from Tony Gardiner's session at yesterday's conference, shared by @mrsdenyer. I'll be using this as a quick starter with both Year 11 and Year 12.

PS - I'm off to Center Parcs tomorrow (term-time holidays are a huge advantage of being on maternity leave!) so there won't be a gems post next Saturday. I'll be back the following week though.

Second, I want to mention @Jeremy_Denton's post about revision races. This is one of those posts that not only provides a fantastic resource but also clearly explains how to use it effectively.

Finally, I want to recommend @fmaths42's post about times tables starters which provides a set of progressively challenging practice grids, plus a suggestion to print these grids onto stickers. Times tables are rather helpful so I'd urge you to ignore Jo Boaler's advice about not ensuring that children learn their times tables - surely she must have said that in a moment of madness. Read @websofsubstance's post The Educators - Jo Boaler for some interesting (in my opinion - very sensible) views on this.

Finally, have a go at this question from Tony Gardiner's session at yesterday's conference, shared by @mrsdenyer. I'll be using this as a quick starter with both Year 11 and Year 12.

PS - I'm off to Center Parcs tomorrow (term-time holidays are a huge advantage of being on maternity leave!) so there won't be a gems post next Saturday. I'll be back the following week though.

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