25 May 2024

AI Maths Resources

I've been sceptical about the potential of AI to produce high quality resources. I'd much rather have a set of carefully crafted tasks created a skilled maths teacher than a worksheet of random repetitive questions churned out by artificial intelligence.

However, a new collection of resources has come to my attention that may start to change my mind.

Maths teacher Duncan Grantham contacted me to explain how he's been using Chat GPT to write LaTeX code to generate maths resources. The underlying ideas behind these resources are atomisation and depth. Duncan's goal is to make resources that are hugely detailed that anyone could pick up and use with very limited editing. There are examples for teachers to work through, questions and worksheets, answers and so on.

The first resource Duncan sent me is about prime factor decomposition. It starts with a whole series of non examples and examples just getting students to think about what product of primes actually means:


Then a series of questions around getting students to just read off the prime factorisation:


Then a bit of working backwards:


Before actually just doing it for real:



The second resource is about about solving linear equations.

It starts by getting students familiar with the definitions e.g. 'what is an equation?':


Some nice tasks about the properties of equations:


Thinking about what solving actually means:


Then learning about manipulating equations:


Thinking about inverse operations:


And then getting students to solve equations where they have to show working out:


Before ultimately something a bit more standard:


ChatGPT made these resources so there may be mistakes or things that don't make sense. 

But isn't it interesting what AI can do?

I think there are loads of good ideas here.

Duncan has shared these two resources:

If teachers find these helpful, he will continue to produce them and will share a large collection on his own website.












18 May 2024

GCSE Paper 2 Resources

We are very fortunate in maths education to have so many hard working teachers and tutors preparing materials we can use between GCSE Papers 1 and 2, and later between Papers 2 and 3. 

My final timetabled lesson with my Year 11 class is a double on Friday 24th May, in which I plan to use the 1st Class Maths Practice Paper 2

We also have a 1.5 hour session over half term (optional for students, but I expect high turnout) in which I might use the Preparation Papers from Corbett Maths (before anyone asks - it's totally optional for my team to come in for this, and yes - we do get paid for it!).

I could write a blog post where I list all the various predicted topic lists and papers for all exam boards, but why replicate what's already done so well elsewhere? I highly recommend Colleen Young's post GCSE Maths Revision – Paper 2 and Adam Creen's Best Guess GCSE Dropbox. Colleen and Adam are very good at keeping track of everything that's published. Thank you both!




Assessing Year 10

We disagree about a lot of things in maths education but I think there’s one thing that makes total sense to everyone: we should never assess students on content they haven’t yet been taught. Doing so has absolutely no benefit to their learning.

Picture the scene:

A Year 10 student works hard and wants to do well. They enjoy maths and they always get good marks in end of topic tests. In the summer term they have been taught some challenging topics: probability, surface area and inequalities. They have a strong understanding of these topics.

As their end of year assessments approach, they put a lot of effort into their revision in all of their subjects. They diligently practise all the topics they’ve been taught in maths throughout Year 10, working particularly hard on surds and quadratics which they learnt back in September but feel a bit rusty on.

This student has been taught well and they have worked hard, so they feel confident and motivated. They look forward showing off what they've learnt in their end of year assessments. They want to make their parents and teachers proud.

The day of their end of year maths assessment arrives. They sit at their desk in the exam hall. Their stomach flips and their mind races as they look through the questions. It is a full GCSE paper. They haven’t been taught half of the content yet.

They leave the assessment with tears in their eyes. Not a single question came up on surface area and inequalities. All that work in the summer term and all that revision… and not a single question. And worse – there were big questions on vectors, iteration, circle theorems and functions. Five markers. But they’ve never been taught these topics so how could they possibly know how to do them?

This student is really upset. They worked so hard and they were not given the opportunity to show what they knew. What was the point in the questions on topics they'd not been taught? They don't understand. They ask their teacher who mumbles something about data. It makes no sense.

The child feels let down. They lose their confidence and their motivation.



***


To those schools who still do this, I would love to know what your rationale is. In the past I have heard teachers try to justify it but none of their reasons make any sense to me.

We wouldn't dream of giving A level students a full A level paper halfway through the course, so why on earth would we do it at GCSE? An English teacher wouldn't dream of giving an assessment on a book they hadn't yet taught.

It is not difficult to make a more suitable Year 10 assessment. The easiest approach is to take a past GCSE paper (choose one that specifically includes questions on topics you've recently taught) and remove the question on topics they haven't studied yet. Replace them with equivalent difficulty questions on topics that they have studied. Simple. It doesn't take long. If you're struggling to do this, feel free to email me for support and advice.




12 May 2024

Love Triangle Book Launch

Tickets are now on sale for the book launch of Love Triangle by Matt Parker.


If you fancy coming you'll need to move fast as these tickets will sell quickly!


A lot of my readers attended the launch of Matt Parker's book Humble Pi back in 2019 and had a fantastic time. They will be pleased to hear that Fox Dog Studios are making another appearance! 

Here are two videos filmed at Matt's last book launch. The first one was during Fox Dog's performance - it shows how much fun the audience was having! The second one is about superpermutations.





Who knows what will happen at this one.

I hope to see you there on 15th June. Book now!




8 April 2024

5 Maths Gems #179

Welcome to my 179th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Maths Advance
I blogged about Maths Advance in Gems 173 - it's a website full of excellent challenge questions, perfect for high attaining classes. I've now had the pleasure of meeting the author of the website, George Bowman, at two recent conferences. Here are a couple of examples of his problems:



The problems are available for free, but subscribing to the website gives access to answers plus full video solutions.


2. A Level Topic Frequency and Advice
Thank you to @the_chalkface for sharing his analysis of topics appearing in Edexcel's A Level Maths and Further Maths exams. 


And thanks to @JohnRubinstein1 for sharing his 'advice for A level maths'.


3. GCSE Revision 
@draustinmaths has added to her excellent collection of revision grids. New additions include More Quadratic Equations and Inequalities, Circle Theorems, and Sine and Cosine Rules.


@MrMorleyMaths has added a number of new resources to his website mrmorleymaths.co.uk including Suggested Revision Booklets for Higher and Foundation Edexcel Paper 1, plus around 70 new How To Sheets with worked examples and exam questions.

Ken Stafford's website mathslinks.co.uk has been updated with worksheets containing Edexcel Past Paper questions for every topic, with handwritten worked solutions.

Also, check out these lovely hand-drawn posters of the GCSE syllabus from @mindmapmaths. These were shared four years ago but somehow I missed them at the time!


For more revision resources check out my GCSE 9 - 1 Revision Resources page. Or if you're looking for some handpicked recommendations and guidance on how to structure your revision lessons, see my recent blog post about GCSE revision.

4. Algebraic Fractions
@andrewmaths1 sent me some great questions from his travels in Canada. Here's one of my favourites:


I also like this one, for reasoning about graphs:


5. 1st Class Maths
I'm a big fan of the high quality resources produced by @1stclassmaths. They come in the style of both AQA and Edexcel. Recent additions include kinematic graphs, capture recapture, enlargements, algebraic proof, equation of a circle, tangent to a circle, circle theorem proofs and vectors. These are linked through my resource libraries. 





Update
Here are some things you might have missed:
  • LUMEN launched their Key Stage 3 curriculum: learn about it here
  • Your students might be interested in this Polypad competition. The deadline for entries is 17th May. 
  • Designing your own maths resources? This geoboard from @StudyMaths makes very neat diagrams.

I've been busy since my last gems post. I had a great day at #mathsconf34:


And I enjoyed my visit to Stratford-Upon-Avon for #jointconf24, where I attended an excellent session on A Level by Rob Southern and Susan Whitehouse. Their book Teaching A Level Maths is out soon.



I recorded a podcast with Craig Barton which has had some lovely feedback.


I also recorded a video explaining the Factor Method for finding a HCF and LCM (this has also had some surprisingly nice feedback, but I don't think I see a career as a YouTuber in my future...).

And I enjoyed a great night out at Puttshack (highly recommended for a work social) with my fantastic team.


I have a vacancy to join my team - it closes on 15th April. If you're looking for a change, and you want to work somewhere where it's a pleasure to teach maths to students with excellent attitudes, apply now. I can offer majority A level teaching, or a range of classes from Years 7 - 13, or just Years 7 - 11 if preferred.



This month marks the tenth anniversary of resourceaholic.com. I've written 478 blog posts in the last decade! Check out the archive here.

I'll leave you with an idea to get some spare Casio 83GTXs for classroom and exam lending. Since Casio discontinued this model but we still have three year groups using it, it would be helpful to ask departing Year 11 students to donate their calculator after their last GCSE exam (provided they won't need it next year). As an incentive, we might stand outside the physics exam as students come out and offer a swap - chocolate for calculator!





31 March 2024

The Factor Method for HCF and LCM

I've blogged and presented about methods for finding a Highest Common Factor and Lowest Common Multiple numerous times, but I still think that The Factor Method* deserves a bit more love. 

[*also known as The Ladder Method, and various other names]

When I trained to be a teacher I was told that the Venn Method was THE way to find HCFs and LCMs. A few years later a colleague showed me a very different method that she'd learnt from a student, and this is what started my fascination with methods. I went on to write the book A Compendium of Mathematical Methods

Never trust anyone who says that a particular method is the best way of doing something because there is absolutely no research to back up their claim (it's a great shame that no one in maths education academia does large scale studies comparing methods - it seems like a big gap in our profession's pedagogical subject knowledge). However, I think it's reasonable to describe something as a favourite method. The Factor Method is definitely my favourite.

I've a made a 28 minute video explaining in detail how to find HCFs and LCMs using the Factor Method. This is a video for teachers, not for students. In it I model a number of examples, including those that might spark discussion. I also talk about how we can use this method to find an HCF and LCM of three numbers, and how we can easily use the Factor Method to work backwards.

I'm not a YouTuber so please forgive the ropey handwriting...




9 March 2024

5 Maths Gems #178

Welcome to my 178th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Inverse Proportion
I really like this tweet from @catrionateaches. When teaching inverse proportion I always talk about constant products but then I head straight into the formula y = k/x. Catriona suggests a subtle change in method. 



2. Graph Transformations
MathsPad has published another brilliant interactive tool for the Higher GCSE topic graph transformations. It shows how points on the original curves map on to those on the transformed curves. There is a separate section for quadratic graphs, which is particularly useful for relating completed square form to graph transformations. 


There is also a section for trigonometric graphs, where transformations of the graphs of y=sin(x) and y=cos(x) can be explored.


It's great to see a new resource published for teaching graph transformations - I always find that this is the GCSE topic for which it's trickiest to find suitable resources, because many tasks still include stretches (these were removed from the syllabus back in 2017 - GCSE now just covers reflections and translations).

Do check out MathsPad's full range of interactive tools - some of them are free to use even if you don't subscribe (you really should subscribe to MathsPad though!).

3. GeoGebra
It's worth following @geogebra to see ideas for interactive GeoGebra maths resources that can be used for demonstrations in lessons or student activities. Here are a few recent examples:




4. Pythagoras

@nathanday314 shared a clever set of questions on Pythagoras' Theorem. There's a lot of challenge here (check out Question 12). Question 3 is deliberately impossible, and note the subtle differences between Questions 3, 4 and 5.


5. Prime Factors
@StudyMaths shared a video showing how to use the interactive Prime Factor Tiles on MathsBot to find a lowest common multiple, and in response @MrCowardMaths shared this really lovely task.


Update
Here are some other things you might have missed:

My school is still seeking an A level teacher to start in September. I can offer 100% A level teaching, or alternatively I can offer a timetable with Year 11 - 13 (or similar) if that's more desirable. Our students are a delight to teach and my team is awesome. If you live in Surrey or South London, this is an amazing opportunity. Please get in touch (email resourceaholic@gmail.com) if you're interested - I'm very happy to arrange a tour or call.

I'm presenting at two maths conferences in the next four weeks. The first is #mathsconf34 which is near Bristol:


And in the Easter holidays I'm presenting at the Shape Up conference in Stratford-Upon-Avon:


Finally, it's been a while since I've hosted a social event so I'm excited about this... more information coming soon.





14 February 2024

5 Maths Gems #177

Welcome to my 177th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. MathsLinks
I discovered the website MathsLinks through TES. It's run by maths teacher Kenneth Stafford. He has collated lots of resources in one place. For example, on his GCSE Questions by Topics page he has included links to websites such as Corbett Maths and Maths Genie for every topic.


He has produced numerous other resources including Grade 1 GCSE Maths Questions where he has combined the first two pages of Foundation GCSE maths papers, and a set of questions on Reverse Mean


Check out Kenneth's TES page and website for more.

2. Oak National Academy
It's good to see the collection of maths resources at Oak National Academy has grown since I last blogged about them in Gems 175. Here are a few extracts.


3. OAT Maths
Thanks to @jemmaths for sharing some new algebra units published by OAT Maths: The Cartesian Grid, Introduction to Sequences and Linear Inequalities. Check out the carefully sequenced slides and booklets.


4. Etymology Update
One of my favourite resources of all time is @boss_maths' amazing vocabulary resource. It aims to relate mathematical terms to key words from other subjects that share the same etymology. It has recently had an update.



5. Tasks
Here are a few nice resources I've spotted on Twitter recently.

A prime puzzle from Sarah Farrell, suitable for Key Stage 2 or 3:




An area task from @brynspiration in which students have to find the area of the polygons, where no perpendicular lengths have been given:


@ChrisMcGrane84 shared a really nice logs task:


Update
I've not posted much on my blog recently but I've very been busy in the background. Thanks to maths teacher Alastair Mundy, who kindly offered to help out and has been an absolute legend, I've finally got my Key Stage 3/4 resource libraries in order. I've fixed broken links and added some new resources - everything is now in much better shape. I still have work to do: my next step is to fix my A level pages.

I also published a post on GCSE revision resources and one on A level resources

The start of 2024 saw a very well-deserved MBE for my brilliant friend Chris Smith (congratulations Chris!).

I'm looking forward to conference season. I will be at #mathsconf34 in Yate (near Bristol) on 16th March presenting on 'Ten Strategies for Good GCSE Results'.


Over the Easter holidays I'll be at the Joint Conference of the Mathematics Subject Associations in Stratford-Upon-Avon. I'm running a nice long session in Pythagoras so we'll have time to get stuck into some fun maths.


I have a couple of vacancies on my team, so if you're looking for a change of school in September then do come and join us. We're based in South London. Here's my fabulous team at the Christmas party:


One of our two vacancies is for a mechanics teacher. We currently have a thriving Year 12 cohort (we are by far the most popular subject in the school, with three A Level Maths classes and one A Level Further Maths class). Most of the A level teaching is done by me (statistics specialist) and my colleague (mechanics specialist). Sadly my colleague is relocating in September so I need to replace her, preferably with an experienced A level teacher. For the right candidate we'll be able offer a timetable where the vast majority of classes are A level (Year 12 and 13 Maths and Further Maths). The Year 13 Further Maths module they'll be teaching is Further Pure 1. I think this is a really appealing job - my school is lovely, and teaching A level is a delight. If you have any questions about the role, or you want to visit prior to interview, feel free to contact me (resourceaholic@gmail.com). The closing date for applications is 26th February 2024.

I'll leave you with these lovely magic squares from Chris Smith. Did you know that Don Steward had an entire blog of magic square activities? Check it out at medianmagicsquares.blogspot.com.