Dancing the Bubble Sort

Teachers of Decision Mathematics will be familiar with sorting algorithms which put elements in a list in order. A bubble sort is a sorting algorithm that works by working through the list to be sorted, comparing each pair of adjacent items and swapping them if they are in the wrong order. The pass through the list is repeated until no further swaps are necessary, the elements are then all in order having ‘bubbled’ to their correct positions.

Check Nathan Yau’s Flowing Data blog where he has embedded this video created by Sapientia University in Romania showing a bubble sort illustrated by a Hungarian folk dance.

For further dancing of sorting algorithms see this YouTube channel.

Teaching sorting algorithms will never be quite the same again! If you look at the comments on Nathan’s blog some users have spotted errors but it certainly illustrates the comparison of adjacent pairs very well indeed.

And a little Dancing with Desmos!

Math Contest – University of Mississippi

For weekly problems try the challenges from the University of Mississippi.
Four problems are set every week.

The Problem of the Week and Algebra in Action challenges are open to anyone from anywhere of any age! The Middle School Madness and Elementary Brain Teaser problems are for school age children, Middle School Madness for grade 8 (age 14 and under), the Elementary Brain Teaser for grade 6 (age 12 and under). If you submit a correct solution by the deadline that week your name will be published on the website. You might even win a T-shirt!

I have posted details for students here.

Time for some games …..

Thinkfun provide an excellent range of games, some of which are available to play online including the very popular Rush Hour. The other games are for younger players including ‘What’s Gnu?’ – a verbal game.

Thanks to Andrew Jeffrey for the link to Chocolate Fix in his latest newsletter.

There is an online version of Rush Hour programmed by Mark Riedel including 40 different challenges from beginner to expert available on Thinkfun’s Puzzles.com site.

This has been added to the puzzles page on the Mathematics Games blog which includes many favourites from Nrich which have all worked very well in the classroom. Many of the Nrich games work very well on the interactive whiteboard as full screen versions are available.

The extensive and excellent resources collection on Mathisfun includes numerous games. Many of my students tried and enjoyed RayRay recently.

Can you make these little people all stand up?

For all my favourite games see this blog – Mathematics Games and Puzzles.

Bloomin’ Mathematics

 (checked & updated February 2018)

It seemed that everywhere I looked today I kept finding Kathy Schrock’s ‘Bloomin’ Google‘ where she has categorised Google tools according to Bloom’s revised taxonomy. Her blog post explains its origins.

My Digital Tools blog has information on Bloom’s taxonomy, in particular, the digital version of the taxonomy which accounts for the new technologies and the processes and actions associated with them.

Thinking about the different levels of the taxonomy is useful when planning questions for students. So often questions relate only to the lower order thinking skills.

Nrich has a small number of articles on Bloom’s taxonomy, this by Jennifer Piggott showing the hierarchy of thinking skills together with skills and question cues and this by Jenni Way on using questioning to stimulate mathematical thinking, with an addendum also which includes ideas for questions to use for student investigation.

Lindsey Shorser has written a short paper on the interpretation of Bloom’s taxonomy for Mathematics.

A very useful resource is this booklet of sample questions which has been created as part of a project funded by the NCETM on Questioning the use of Bloom’s Taxonomy. I have tried many of these in the classroom, they really make students think and encourage a deep understanding. 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.

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 provides probing questions. (No levels any more – but still some great questions).
Focused Assessment Level 4   Focused Assessment Level 5   Focused Assessment Level 6
Focused Assessment Level 7   Focused Assessment Level 8

Diagnostic Questions - Algebra
Diagnostic Questions – 
brilliant diagnostic questions – use this with your classes and find out what your students know – or are in a muddle with!

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 Questionsopen–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 always / sometimes / never resources and also some true / false questions use CIMT’s excellent Mathematical Proof. There are many such resources on TES – try some of these resources. See this post for further Proof resources.

Underground Mathematics
For questions to really get your older students thinking, try these resources.

For younger students try Andrew Jeffrey’s lovely free gift ‘What’s the same, what’s different?