Welcome to my 14th weekly gems post - this is where I feature five of the best teaching ideas I've seen on Twitter each week.

You may or may not know that I've been writing these posts while I've been at home on maternity leave. My baby keeps me busy during the day, but my evenings are blissfully free from marking and lesson planning so I have a rare opportunity to reflect on my teaching and gather new ideas. It's a shame that all teachers can't take a mini-sabbatical every five years to do the same. When I go back to work in January I'll have 100 maths teaching gems in my toolkit - it will be hard to know where to start!

You may or may not know that I've been writing these posts while I've been at home on maternity leave. My baby keeps me busy during the day, but my evenings are blissfully free from marking and lesson planning so I have a rare opportunity to reflect on my teaching and gather new ideas. It's a shame that all teachers can't take a mini-sabbatical every five years to do the same. When I go back to work in January I'll have 100 maths teaching gems in my toolkit - it will be hard to know where to start!

**1. Two Truths and a Lie**

Two Truths and a Lie is traditionally an icebreaker game - someone tells you three facts about themselves and you guess which one is the lie. For example my brother might tell you that he was once bitten by a donkey, he was once bitten by a snake and he was once bitten by a monkey. Bizarrely, only one of those statements is a lie. So let's take this game and turn it into an activity that prompts mathematical discussion.

This idea came from a tweet by @TCM_at_NCTM:

This tweet made me realise that I'm guilty of lazily telling my students that polygon is 'just another word for shape' when in fact I should be more specific - a polygon is a 2D figure with at least three straight sides and angles (the word derives from the Greek 'many-angled'), so a circle is not a polygon.

The two truths about quadrilaterals ('a square is a rectangle' and 'a rectangle is a parallelogram') will also prompt interesting discussions about definitions. The quadrilateral family tree might help clarify things. The Euler diagram below is also helpful.

Polygons (source: mathsisfun.com) |

The two truths about quadrilaterals ('a square is a rectangle' and 'a rectangle is a parallelogram') will also prompt interesting discussions about definitions. The quadrilateral family tree might help clarify things. The Euler diagram below is also helpful.

Quadrilaterals (source: Wikipedia) |

A related idea, Maths Lies (where the teacher tells one deliberate lie per lesson - see my first gems post) is still one of my favourite teaching ideas ever.

Speaking of things that can't be visualised, I absolutely loved this post 'From 1 to 1,000,000' from @waitbutwhy (shared by @mathtans). The writer takes us through a series of visualisations from the number one up to one million (the post ends with a million dots!). I've talked before about ways to develop students' number sense (see Gems 7 about Estimation 180). Show your students the dotty pictures so they get a good sense of the magnitude of numbers.

The image above reminds me of the 'If the World Were a Village of 100 People' visuals I talked about in Gems 1 - this is a nice way of conceptualising data that might help students understand percentages.

**3. Creative Mathematicians**

Thanks to @gareth_metcalfe for sharing this brilliant video 'What is a mathematical proof?'. The video explains why mathematicians spend most of their time trying things that don't work. Students are often reluctant to try a different approach if their first attempt at answering a question is a dead end. Show this video at school to encourage your students to be creative in their mathematical thinking.

**4. Communicating Reasoning**

Continuing the theme of encouraging students to try various approaches to solving problems, brilliant NQT blogger @MrDraperMaths gives us the post 'Maths You Can Redraft'. His idea - which I'm definitely going to try with my Year 12s - is to give students one challenging problem for homework and make them focus on the written communication of their thought process. It's all about constructing reasoned arguments, a skill that A level students often lack. Mr Draper has created an excellent homework sheet for this purpose - see his post for full details. Ed Southall (@solvemymaths) provides a whole set of puzzles that you could use to build students' mathematical thinking and communication skills - the example below is one that I particularly enjoyed tackling - see solvemymaths.com for the full range.

Source: solvemymaths.com |

**5. Five Expectations**

Prize-winning mathematical cake-baking duo @danicquinn and @MsBWellbrook set out their 'five expectations for a beautiful maths book' using the graphic below. This is a really clear and effective way of communicating expectations (the Why? bit is particularly important). Thanks to @MrReddyMaths for sharing this idea. I've made my own version - click here - which you're very welcome to borrow and adapt.

**What I've been up to**

Last week's gems post (unlucky 13) was my most popular post ever, with almost 2,000 views in a week. I also wrote a post on circle theorems last week that I was particularly proud of. I love my gems posts and my resources library, but it's my topic specials that I think people will find the most helpful. I like to think that new or recently qualified teachers will really benefit from these posts when planning to teach a topic for the first time.

Finally, do you receive Chris Smith's (@aap03102) weekly newsletter? If you don't already subscribe then email him now to get on the mailing list. This week he featured Pret homeworks which you should take a look at if you haven't seen them before. Chris also featured the excellent puzzle below, which I'm looking forward to giving my students when I return to work in January.

Lying in class: I fondly recall the time we were playing a Guess My Number game and I souped it up by telling the pupils I was allowed to lie once when answering. On one run someone used the question "Have you lied yet?". I hadn't, so I answered "Yes". That certainly gave them something to think about!

ReplyDeleteAlan

Clever! Teaching them the art of logical thinking.

DeleteHere's my favourite lying-in-class anecdote: http://www.overcomingbias.com/2008/02/my-favorite-lia.html

ReplyDeleteI love that story! It's one of the reasons I started writing these gems posts! :)

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