Mathematics education - as seen on the screen

The stats for this blog indicate that my previous collections of web-based videos have been popular. Hence this post...

Why use web based video in mathematics education? Don Tapscott, author of “Grown Up Digital”, uses the expression “screenagers” to describe the youth of today. Like it or loathe it, the fact remains that our students are conditioned to interact with screens. By using their medium of choice we are more likely to engage them - assuming that the content is worthy. Video - moving pictures and sound - is the language of our students. There is considerable research evidence that interest leads to engagement - which leads, on average, to better performance.

This classic clip of Abbott and Costello demonstrates how easily errors can flow from faulty understanding of procedures - procedural knowledge without conceptual understanding.
Abbot and Costello maths 7x13=28

Apart from the appeal of seeing adults make mistakes this clip can easily move from viewing to activity by investigating where is Abbot going wrong. How could students convince him that he is wrong - and help him from making the same mistake in the future?

This clip is one of many on Youtube featuring what has been called “Mayan multiplication”. (The name may be something of a misnomer as there is some evidence that it may have evolved in India as a part of the vedic tradition.)
Mayan multiplication

This clip is clear and “lo tech” which generates the impression that anyone could use this technique. Can they? Students could explore the technique - but then contrast it with the traditional method of multiplication to compare ease of use - especially with larger numbers.

So how does it work? The wondrous Vi Hart both demonstrates and explains here.



Younger students can also benefit from drawing lines - to investigate patterns in numbers.
Number patterns


Once this video has been viewed it is a small step to recreating it in real life - and then investigating the patterns created by other numbers.

Lines - of symmetry - also feature in this clip. In an earlier collection I included an amazing clip of paper placed in water which unfolded to create a complicated flower-like shape. This is similar - but much simpler and could also be used to prompt an examination of symmetry - and being simpler might be suitable for younger students.




This site features a reasonable number of educational videos with a special section on mathematics. Included is an “inspiration” section which links to photographs with an accompanying maths challenge.
It needs to be said that I see these clips as a means of promoting interest in mathematics rather than as an end in themselves - I see these as useful ways of introducing topics which can then be explored in a more traditional manner. Using visual images in mathematics classes can help bring the subject alive while still allowing teachers to address the requirements of the curriculum.
If you enjoyed this collection you may like to see other collections  here.

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Credits: all information available by following the relevant links.
Abbot and Costello maths 7x13=28
http://www.youtube.com/watch?v=KVn0aksCzNE&feature=related
Mayan multiplication
http://www.youtube.com/watch?feature=fvwp&NR=1&v=1bhOCJ8eijU  
Vi Hart
http://www.youtube.com/watch?v=a-e8fzqv3CE
Number patterns
http://www.youtube.com/watch?v=8TnEbL9vK5A
Floating flowers
http://www.youtube.com/user/dutchpapergirl#p/a/u/2/eHMPkLE0Qs0  

Mathematics education - as seen on the screen

The stats for this blog indicate that my previous collections of web-based videos have been popular.  Hence this post...

Why use web based video in mathematics education?  Don Tapscott, author of “Grown Up Digital”, uses the expression “screenagers” to describe the youth of today.  Like it or loathe it, the fact remains that our students are conditioned to interact with screens. By using their medium of choice we are more likely to engage them - assuming that the content is worthy. Video - moving pictures and sound - is the language of our students. There is considerable research evidence that interest leads to engagement - which leads, on average, to better performance.   

This classic clip of Abbott and Costello demonstrates how easily errors can flow from faulty understanding of procedures - procedural knowledge without conceptual understanding.
Abbot and Costello maths 7x13=28


Apart from the appeal of seeing adults make mistakes this clip can easily move from viewing to  activity by investigating where is Abbot going wrong. How could students convince him that he is wrong - and help him from making the same mistake in the future?
This clip is one of many on Youtube featuring what has been called “Mayan multiplication”. (The name may be something of a misnomer as there is some evidence that it may have evolved in India as a part of the vedic tradition.)
Mayan multiplication


This clip  is clear and “lo tech” which  generates the impression that anyone could use this technique. Can they? Students could explore the technique  - but then contrast it with the traditional method of multiplication  to compare ease of use - especially with larger numbers.

So how does it work?  The wondrous Vi Hart both demonstrates and explains here.
Younger students can also benefit from drawing lines - to investigate patterns in numbers.
Number Patterns

Once this video has been viewed it is a small step to recreating it in real life - and then investigating the patterns created by other numbers.  

Lines - of symmetry - also feature in this clip.  In an earlier collection I included an amazing clip of paper placed in water which unfolded to create a complicated flower-like shape.  This is similar - but much simpler and could also be used to prompt an examination of symmetry - and being simpler might be suitable for younger students.






This site features a reasonable number of educational videos with a special section on mathematics.  Included is an “inspiration” section which links to photographs with an accompanying maths challenge.


It needs to be said that I see these clips as a means of promoting interest in mathematics rather than as an end in themselves - I see these as useful ways of introducing topics which can then be explored in a more traditional manner.   Using visual images in mathematics classes can help bring the subject alive while still allowing teachers to address the requirements of the curriculum.




If you enjoyed this collection you may like to visit others here and here - or my page of “maths” posts here.

Credits: all information available by following the relevant links.

If you enjoyed this post you may enjoy my other maths related posts available via the maths page or by clicking here.

Maths education – dire or inspire?

You could see the panic in their faces - and then the relief.

They were students in their final year of high school on a visit to campus to explore the possibility of “going to uni” after they finished their compulsory schooling.  I had, perhaps perversely, set up an experiment.  I had told them that two of them would find a red dot under their seat - and if they were one of these people they would come forward and participate in a simple mental mathematics activity. Panic turned to relief as, chair after chair, they stood and did not find a dot. It had been a trick - but one with a purpose.

It may have been cruel - but the momentary discomfort was worth the discussion. I asked them how they felt when they thought they may have to do a simple maths activity in front of their peers.  Who had a nervous uneasy reaction in the pit of their stomach? Almost everyone felt this way (except those girls too cool for school with more product in their hair than even the law of gravity could cope with  - and there a was no way that they would be going up!!!).  We discussed that fact that so many people had that reaction.

We discussed why they thought that way and what they thought mathematics was about.
The conversation quickly distilled to mathematics teaching and text books. Most of the students really do not like mathematics; many do not understand it - even if they can complete the required procedures. Most thought that mathematics was what took place at school,  or when you were shopping or later in life if you worked in an office.  

I was not surprised - for these groups mirrored previous groups;  same experiment, same reaction, same discussion - same finding. In short, most of our students leaving the mandated years of schooling do not like mathematics - especially the way it is taught.  This reaction is also wide-spread when I conduct the same experiment with pre-service teachers.

Why does this continue to be the case?  This is a deceptively simple question. The answers range from teachers teaching out of area (and therefore having both a reduced skill set and limited knowledge base), teaching to the text, the mistaken belief that “old fashioned” teaching produces better test results (assuming that we accept that as a valid indicator) and so forth.  But rather than unpack this I’d rather simply contrast traditional text book based learning with something different.

What might good mathematics teaching look like?

One thing that students consistently mention is the use of multimedia.  I’m not suggesting that we plug our students into the Khan Academy and walk away - far from it in fact.  Another item frequently mentioned is relevance or interest - statements such as “You’ll need this later in life” do not sit well with these students. They want relevance now - and why not? 

So how can we interest students in mathematics? We can start by moving away from a reliance on text books and meaningless exercises. Those who need convincing watch  Dan Meyer’s TED talk.

Why not let the beauty of maths speak for itself? Let your children watch this amazing creation by Etinne Cliquet ("Flottille") and see how many are interested in looking at symmetry then.

Flottille (detail) from Etienne Cliquet on Vimeo.

Vi Hart’s famous hi speed doodling / ranting also make good watching - and could easily prompt school based follow up lessons (which is ironic given Vi’s iconoclastic style).  

What about this amazing clip showing what happens when pendulums of slightly different lengths are released simultaneously?

Or watch Kjartan Poskitt taking his “murderous maths” to the street.  Just look at the faces of the people in the street at he performs his ABC x 7 x11 x 13 trick.  These people are fascinated - by mental mathematics!  

Or visit www.mathpickle.com for videos of children at work in real maths classrooms on real problems - visit the “Hard fun is how we learn best” clip to see primary students playing with factorisation.

I’m not suggesting that maths lessons need to be fun in the arcade game sense - but they should be engaging, stimulating and challenging (ironically, characteristics that are associated with video games). Nor am I suggesting that we replace every lesson with video oddities and novelties. However, the use of  videos such as these can encourage real life exploration of mathematics. They can provide launch pads into “hands on” investigation of mathematics.  In short, they can inspire our math classes.


Those wishing to view more videos that have the potential for use in mathematics classrooms might like to view this post.