(From the outstanding Nrich, Countdown Fractions, one of their many Interactivities.)
See ‘Searching for things‘ for more on using Evernote.
If you are searching for a particular kind of resource then do use the comments to let me know.
To begin the carnival we will as is the tradition look at some properties of the number 22, additionally we can look at some sites which provide information on number properties.
A good place to start is the NumberADay blog from the Mathematical Association of America. Every working day, they post a number and offer a selection of that number’s properties.
Here we learn for example that 22 is a pentagonal number and is the smallest number that can be expressed as the sum of two primes in three ways: 22 = 3 + 19 = 5 + 17 = 11 + 11.
A great site for finding out about the properties of a number is Tanya Khovanova’s Number Gossip. Whilst we all know that 22 is even, did you know it is odious?
From Cool Numbers we learn that 22 is seriously cool!
For other sites with information on number properties see What’s Special About This Number?, Amazing Number Facts, a site with many fascinating articles and Mudd Math Fun Facts, where we could search for all the Number Theory Fun Facts. We could of course enter 22 as a WolframAlpha query.
So, to the posts, as it’s a carnival it seems appropriate to start with the party post!
Bon Crowder describes a fabulous party for her soon to be three year old in Birthday Party Fibonacci Style! There are some fabulous ideas here, I want a party like that!
Shaun Klassen presents a clear description with accompanying diagrams in his Asymptotes at Maths Concepts Explained. Reading Shaun’s post it struck me that we could provide a Desmos graph where students could experiment (click on the image and change the sliders).
For more on the outstanding Desmos graphing calculator see my own series of posts.
One of Rocky Roer’s series of Summer Maths series posts is What’s the comma good for? where he describes what you can do with that comma key on your calculator!
In case anyone is wondering about the calculator font I have been using, you can download such fonts free. The Calchux font is available on the resources page (scroll right down to Miscellaneous) of subtangent.com.
John Cook was asked this question on Twitter ‘Is there a trick to make an singular (non-invertible) matrix invertible? He posted his response Making a singular matrix non singular on his blog The Endeavour. John’s mention of Twitter reminded me of the value of developing contacts on Twitter.
Guillermo Bautista tells the story of Andrew Wiles in solving Fermat’s Last Theorem in his post The Man Who Solved a Math Problem for 8 Years on Math Palette.
It seems most appropriate to conclude the carnival with Guillermo’s post on 10 reasons why Maths teachers should blog. I know I have learned a great deal, found a fantastic library of resources and made many contacts since starting my own blogs. Thank you so much to all of the contributors here.
That concludes this edition. Thank you for reading. Submit your blog article to the next edition of Mathematics and Multimedia Blog Carnival#23 (a happy event as 23 is a happy number!) which will be published on Math Palette using our carnival submission form, the deadline for submitting articles is August 18th.
A great way to get students thinking about mistakes and misconceptions and hence deepen their understanding of topics is to have them mark the work of others. There are some great resources hosted on TES that will allow your students to do just that.
Particularly excellent resources come from Andy Lutwyche, look at his excellent Erica’s Errors seriesfor Spot the Mistake activities. See also, on TES – further Spot the Mistakes resources from Andy Lutwyche.
Edexcel’s A Level Teaching and Learning Materials, a growing library of resources offer excellent support for teachers.
The exemplar answers with examiner comments provide a particularly valuable resource. These booklets look at questions from the AS and A level Sample Assessment Materials, which was used in the trial undertaken in summer 2017. Real student responses are shown together with commentary showing how the examining team apply the mark schemes. The commentary includes always useful notes on common
errors. These could be used in class and students asked to find errors.
TES resources I have come across include:
R Barnard’s Bob’s Ratio Homework
Craig Barton’s lovely little starter on Algebraic Misconceptions (this one is truly tried and tested – I used it as a starter for a lesson observation and followed it up with a class discussion on what advice students would give to students making the kind of errors here – it went down rather well with the observers!)
Kaszal’s Fractions Mistakes
and Damian Watson’s
Transformations AfL Spot the Mistakes
Enlargement Spot the Mistake Booklet
Fractions AfL Plenary Spot the Mistake Booklet
Thank you to all the great authors of these resources.
On the subject of mistakes, the Classic Mistakes website has a gallery of posters of classic errors made in Mathematics. These could be a prompt for a useful discussion starter activity. Note that an audio file is also available for each poster.
See also: Rich Tasks and the Questions page updated, 2016.
Ofsted (The UK Office for Standards in Education, inspect and regulate services which care for children and young people, and those providing education and skills for learners of all ages) as part of their judgement on the quality of teaching quite rightly include ‘the extent to which teachers’ questioning and use of discussion promote learning’. Research has shown that often teachers’ questions are closed questions which require only lower order thinking skills from students. There are some excellent resources available to help teachers think about the types of questions they can use to support students’ learning. Not just for Maths but applicable to any subject I’d recommend very highly the Brighton and Hove Assessment for Learning project – Questions worth asking. This includes many practical suggestions for the classroom and concludes with a self analysis.
The project includes the use of Bloom’s Taxonomy as an aid to thinking about the level of challenge / thinking required for a question. One of the consistently popular posts on this blog is Bloomin’ Mathematics which has links to several resources on Bloom’s Taxonomy. Of particular interest here on questions is an excellent resource: This booklet of sample questions has been created as part of a project funded by the NCETM on Questioning the use of Bloom’s Taxonomy.
Blooms Questions NCETM
For further questions which require higher order thinking skills see the Levelopaedia from Kangaroo Maths which has numerous probing questions and also the focused assessment materials which make it clear what students should be able to do and give probing questions. Whilst we happily don’t have levels any more these remain great questions.
Focused Assessment Level 4 Focused Assessment Level 5 Focused Assessment Level 6
Focused Assessment Level 7 Focused Assessment Level 8
Diagnostic Questions – brilliant diagnostic questions – use this with your classes and find out what your students know – or are in a muddle with!
Further Resources:
Multiple Choice questions can really help expose misconceptions as mentioned above, there are many other sources too and note Daisy Christodoulou’s comments on the use of Multiple Choice questions.
Hosted by the National STEM Centre I do like Susan Wall’s Thinking Questions, open–ended questions which should certainly make your students do just that – really think.
Nrich have some excellent advice on questioning, see Working Effectively with All Learners which offers questions and prompts to encourage discussion and Using Questioning to Stimulate Mathematical Thinking.
See Dylan Wiliam’s paper on Rich Questioning.
For more always / sometimes / never and also some true/false questions use CIMT’s excellent Mathematical Proof.
See also: Rich Tasks and the Questions page.
For many Proof resources – see Proof – 2021.