I read with interest, this post from The Learning Scientists, “Learning Math from Errors” on a paper by Deanne Adams and colleagues that demonstrates learning from errors.
What I think is neat about this paper is the researchers gave students erroneous math examples (specifically, decimals, which can be hard for middle schoolers) rather than waiting for them to make the errors themselves. The researchers also required the students to identify explanations for the errors (like elaboration through self-explanation) and correct the errors themselves. They compared this learning condition to what appears to be the standard in math: solving practice problems.
Megan Sumeracki – The Learning Scientists
The results whilst showing no differences between the two groups on the immediate post-test did show a better performance by the students in the erroneous examples condition than the students in the problem-solving condition on the one-week delayed post-test.
I have always found it valuable to use resources where students identify and discuss errors, and have checked and updated this collection of resources – Spot the Mistake.
Recently added to the page, published in 2023, Mathematics Curriculum Reforms Around the World, the 24th ICMI study is an Open Access publication which can be downloaded for free.
For puzzle fans perhaps try Henry Ernest Dudeney’s puzzle collection.
Looking at the free Kindle offerings, these include Mind Hurdles: Mystery Number – a set of ‘number mysteries’, one or more of which would make a good lesson starter and Henry Ernest Dudeney’s – Amusements in Mathematics a puzzle collection (with solutions). The first set of puzzles will offer a trip down memory lane for those who remember money – pre-decimal! There are several categories of puzzles available.
And do make sure you have Colin Foster’s KS3 books in your collection.
Colin Foster – Instant Maths Ideas
Remember that Colin Foster’s KS3 Instant Maths Ideas (3 books) are freely available online; these contain a wealth of ideas to try in the classroom. Colin Foster is a Reader in Mathematics Education at the Mathematics Education Centre at Loughborough University. Read Colin’s blog here.
On Webmaths, new for A Level Maths, “3 a day” for Year 12 Maths; these resources look excellent; solutions will follow. You can also find Year 13 3 a day.
Still with A Level, remember that AMSP’s Mathematics Topic Plans cover the whole of the AS/A level Mathematics specifications. These comprehensive documents include links to easy-to-use resources, including technology-based teaching files and student tasks, suggested questions and prompts to promote mathematical thinking and reasoning. and identification of common student errors
There are many excellent resources chosen in these topic plans, for example, we have Ab-surd! from Underground Mathematics.
From the Calculator Guide, another very helpful video for the new Casio fx-991CW Classwiz Calculator on Calculating & Solving Functions. See Casio ClassWiz 2023 for further information on the new Casio calculators.
From ATM, see the Summer Solvers series, For Twitter users these are tagged #summersolvers. Each day in August, at 10 am, ATM are posting a problem from their archives for a range of age groups, we have problems to work on for KS2 to KS5 (UK ages 6 – 18).
For August 4th we have Number Spirals, from 30 Years On, a collection of classic mathematical ideas and activities. Note that you can look inside the book and the pdf includes 2 problems, Fractional Triangle and Number Spirals.
Nrich are again publishing a challenge a day throughout the UK summer break. Every weekday from 10 July to 1 September, a new challenge will appear on this Primary page (for under 11s) and this Secondary page (for over 11s). Once students have tried the day’s challenge, they will be able to compare their approach to previously published students’ solutions.
Perhaps try some curve stitching on Transum. Also, on Transum, you will find School Holiday Maths Activities; this collection has many activities to encourage students to continue their learning during the holidays. These are categorised, and we have a lovely mixture of learning, puzzles, and games to make students think. There is a great deal of choice here. See also the full list of all fun maths activities.
To highlight just a few resources from this large collection, Algebra includes the lovely SolveMe mobiles puzzles.
Or, for a rather different approach, try Shuttle Mission Workshop from Math Playground, here students build and solve their own visual math puzzles. Play Shuttle Mission Pro first to practise.
Nrich features on many pages, including reading; Nrich has many excellent articles on the use of games in the classroom; hence a Reading page.
Geometry includes a collection of puzzles from Catriona Agg, who has made a collection of screenshots (Google Drive link) freely available.
Catriona Agg
Given three squares and a rectangle. What’s the shaded area?
In response to this puzzle, Rob Smith created an Autograph file. Rob has set this up to change both squares, and you can also move a point on the smaller square.
The collection includes from Cambridge PhD student Omar Wagih, ‘Guess the Correlation‘, a rather addictive game with a purpose – Omar Wagih is collecting the data on the guesses collected and using it to analyse how we perceive correlations in scatter plots. Select About to read the rules and further details.
The Underground Maths page includes several resources on puzzles and games.
One of my favourite maths resources! Maths comprehensions on 12 different topics (such as mountains, rivers, etc.) which then challenge children to retrieve and use mathematical information from the text and graphs to answer questions. https://t.co/n4nPs68qL9#edutwitterpic.twitter.com/pQEg158BHm
From AMSP, a new magazine for current Year 10 students – Quick Maths.
Do you have students who ponder the questions: What do you want to be when you grow up? or Ever feel like you’re never going to be good enough? Your students will learn about ‘Maths Anxiety’, hear from students and their experiences of post-16 maths and more in this issue of Quick Maths.
Seeing Sarah Farrell’s first comprehension task on the solar system reminded me of all the educational resources available from NASA. Space Math @ NASA introduces students to the use of mathematics in today’s scientific discoveries. The site includes Mathematics in the news – a look at the Mathematics involved in NASA press releases together with resources.
Check the Space Math Educator Guide and note the Problem Books and Problem Archives which contain an extensive collection of problems. Several booklets are also available, see for example Exploring Space Mathon Standard Form which includes full solutions.Bookletsinclude introductory pagesincludinga table showing the topics covered by each activity. Why not use some solar wind magnetism data when teaching directed numbers or use solar flares when looking at equations and substitution?
