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.

~~~~~~~~~~~~~~~~~~~~~~~

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.

Mathematical engagement - images to delight, ignite and excite

Let’s be honest about this - in some classrooms the teaching of mathematics is as dry the Sahara Desert - and perceived to be as endless by many students. As a result engagement is lower than we would like. This is significant since student engagement is correlated to student success.

Whilst this statement is almost self evident we should be wary of accepting such comments unreservedly - evidence based practice requires that we support our beliefs.  Fortunately this is easy to do.  Any number of studies have endorsed this notion that engagement enhances achievement.   

With this strongly established the next issue is how to generate engagement? Jill Fielding-Wells and Kellie Makar of the University of Queensland found that “Research indicates  that student motivation and engagement are increased if instruction is authentic and relevant...”  Authentic here was defined as that which was cognitively challenging and connected to the world beyond the classroom.  The study found that student engagement could be improved by up to 22% by shifting to inquiry based problem solving as the method of instruction.

For those comfortable with a less  academic but equally authentic anecdotal style there is this piece showing how a high school in the USA significantly improved results in mathematics by introducing a curriculum based around problem solving with an emphasis on generating student engagement - the percentage of students “passing” mathematics skyrocketed from an admittedly low 20% to 60%.   There is thus both academic and “real world” evidence  that engagement is linked to achievement and that engagement can be increased by including certain features into  learning experiences.     In terms of student engagement generally,  it has been found that student engagement is enhanced when students are interested, challenged and feel that the work / task is important.

Several educational reformers,   such as the teams at the Apple Classroom of Tomorrow Today and the Partnership for 21st Century Skills, also advocate the increased and improved use of technology and multimedia in our classrooms to enhance both engagement and learning.

Fortunately the Internet is a rich source of motivational material.  Presenting clips such as the following could be one way of increasing interest and engagement in mathematics lessons.

The following are samples of video that could both ignite interest and engagement.

Ma and Pa Kettle Math.

While it is not the intent of this post to provide lesson plans I would suggest that this video cries out for “unpacking”.  Why do the flawed approaches used here produce the correct answer? Does this approach always “work? Are there other numbers that could be substituted for the numbers in the clip? How might Ma and Pa Kettle be convinced that their techniques are, in fact, wrong?

Pattern blocks


Even very young children could benefit from video enhanced lessons. After watching this clip an obvious question might be “Who would like to create their own version of this?”  Given that this is created via the  “stop motion” technique a simple digital camera and one of the many free video creation programs is all that would be created to really involve the students.  


LEAF TESSELATION

As well as being fascinating viewing this clip dealing with leaf tessellation lends itself to further investigation of the topic. ( Instructions for making non-regular tessellating shapes abound on the Internet - here’s one - and every free drawing package on the Internet or buried within operating systems has the capability of creating them.)
NATURE BY NUMBERS

Older students could unpack just some of the elements of this wonderful video.  I’d suggest that if students were able to identify and explain all the concepts embedded in this engrossing video then their mathematical knowledge would be well beyond the norm - and the beauty of it is, in order to do so, some reasonably advanced teaching and learning would be required.  


The Internet is a rich source of such videos.  There is clearly scope for including web based video into our mathematics classrooms - especially as motivators at the early stage of projects. The use of such images is one way that we can delight,  ignite and excite our students - or at least increase engagement.




Those who found these videos interesting and can see a place for them in their practice might also enjoy an earlier post with a similar collection of clips here.

Those who are interested in using such images but would like some guidance on how they might be included meaningfully into a classroom project might find this post on Project Based Learning useful.



Acknowledgements:
All links go to original sources of documents.
Image: http://www.dailygalaxy.com/photos/uncategorized/2008/04/27/stella_2.gif

Tesselating shapes PPt;

www.curriculumpress.edu.au/sample/pages/tessellated_shapes.ppt