Educational reform; like building a plane - in flight!

I love this clip. To me it is a wonderful metaphor for educational reform.

One of the major issues with educational reform is that schools have to be operational while education is transformed. We can’t simply shut down the schools and learn new and more effective educational techniques. We need to test and trial our learning when and where it matters - in the classroom with our students. We need to learn new skills while we teach via established methods. There are those who suggest that teachers can learn new approaches when students are on vacation - and to some extent this is true. However, the important aspects of classroom teaching can only be learnt through implementation in the real world - and that means while the students are present. There is a time when a trainee pilot needs to land a plane in real life and not in a simulator.

There are obvious issues with this. Our students are not guinea pigs or lab rats. We should not experiment with them. On the other hand, we need to continually improve our practice - and that means we need to be constantly trialling new approaches or trying to refine and enhance established ones. This balance can be difficult to achieve - perhaps this explains the almost glacial pace of school reform.

Clearly there are risks involved in any educational reform - if any innovation is ineffective then students suffer in comparison to what they may have achieved with another approach. However, there are more risks involved in educational stagnation and ignoring new possibilities and potentials.

So how do we build an educational plane in flight? We start by being clear about what we want to do and why. We acknowledge that established techniques may not be appropriate in this operational environment. We try to anticipate any likely issues and develop responses in advance - or at least be observant and flexible to respond to issues as they arise. We clarify our roles - who does what, when and to what standard? Who checks and assists? How do we know when we have succeeded? We accept that the task may be difficult - but, if we are clear about our objectives, it should be worthwhile.


And then we take a deep breath and build our plane.

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Credits: EDS commercial via youtube @ http://www.youtube.com/watch?v=L2zqTYgcpfg

Original idea to link to education: Thanks to a long forgotten presenter at a SPERA conference in Darwin who used this clip in his session.

Ancient maths = modern learning

There are many issues of concern associated with mathematics teaching today.  One is the emphasis on procedural competence regardless of conceptual understanding. Another is the almost total lack of historical significance of mathematics. This is a pity as one can inform the other.

In our busy classrooms we tend to rush from one mathematical concept to another - often without any explanation given to the students. It is my experience that if we take the time to develop student interest in a topic then sound performance often follows  -  the “diversions” demonstrate that mathematics is more than learning algorithms  and makes the broad topic of mathematics more interesting - which engages the students - and engagement leads to understanding which in turn leads to higher performance.

My views on this are shaped not only by my experience as a teacher - but as a student. My primary years have been largely shrouded in the mist of time but I can still remember being stunned and amazed when I was briefly shown alternate historical methods of calculation. It was a revelation. Maths could be done more than one way? People once did maths differently - and accurately - and it worked … every time?  Ancient peoples were smart enough to do mathematics?  They discovered this stuff?

I’ve covered the same material myself in classrooms and  recognise the same lightbulb moment of understanding in students as they make the same discovery.  It is often the beginning of lasting interest in mathematics.

Today, thanks to web-based video we can show students “historical” mathematics as a way to scaffold and extend their mathematical knowledge.

One of the favourite “ancient” forms of mathematics taught in schools is often known as “Egyptian multiplication”.  It turns out that “Egyptian” part of the label may not be overly accurate - but the technique surely is.  This clip provides a good explanation of the process - together with a brief explanation as to why it works.

Ethiopian multiplication (also known as Egyptian)

From Egypt / Ethiopia / Elsewhere  we can make the short historical journey to the lattice method explained here.

Lattice Multiplication

The use of the diagonal columns will have parallels with the use of vertical columns in our current systems of calculations which will not escape the children and provides a useful opportunity to discuss the use of columns in modern calculations.
From there it is a short step to Napier’s Bones.  
Napier's Bones

                                        

 (This is a good clip despite it’s simplicity as it allows the students to study the structure of the “bones” and perhaps identify the pattern in the rods for themselves.) The clip below shows how the bones or rods were used.

The sense of amazement and wonder is enhanced if students actually complete some calculations themselves - in which case the pro forma here will be useful.  Once the students are capable of using the “bones” it is a useful extension to get them to use them to multiply two two digit numbers - and let them discover the technique themselves if they can.


The discussion around why devices such as Napier’s Bones were useful and necessary is a worthy way to spend some time.  Our students find it difficult to understand that it was once the norm for humans to perform all calculations, not silicon chips.  It is also worth raising awareness the universal education is a relatively new social phenomena - and discussing the impact of that.

Another avenue that can be useful is to look at numbers without using numerals at all (well, at first at least). This clip looks at the ancient Greek interest in square numbers and demonstrates the concept effectively using nothing more sophisticated than stones - which is all the Greeks needed to discover the concept.

Counting like an Ancient Greek

I’m not suggesting that the techniques presented here be “taught” in isolation - more that they can be explored and then, once students are familiar with the techniques, compare and contrast them to current methods.  It is often at this stage that students really develop an understanding of the strength of the place value system that we use today - after which their fluency with formal algorithms often improves significantly.  
If nothing else students will have enjoyed interacting with mathematics - and without a worksheet in sight.

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

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  

The most important sticky note you'll ever read?

I came across this video the other day -  a “feel good” effort with a twist at the end that I won’t spoil - all is revealed in the clip.

Video from KarmaTube


It occurs to me that this clip has implications beyond the relatively narrow focus of the target audience. So what relevance has this video to broader aspects of education?  There are several messages really - one is that  education requires open and genuine communication.  As teachers we need to listen to our students as much as we talk to them - if not more.

Another is that this relationship needed time to develop - the relationship could not blossom until there was a degree of trust.  Again, there is a message there for teachers.

But watching this reminded me of one of my favourite quotations which is attributed to Dr. James Comer;  “There is no significant learning without a significant relationship”.  Put simply, if we want our students to learn from us we need to spend the time to develop genuine relationships with them. How we do this is up to each teacher as an individual - for we too have our own personalities, interests and foibles. However,  unless we take the time to value our students they will not value us - or what we are trying to share with them.

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Dr. James Comer is more than a source of an inspirational quotation.  He has developed the Comer School Development program as a vehicle for school reform.  An interview with Dr. Comer can be accessed here.

A modern heresy?

I have a confession to make - one that will label me a heretic in this modern world, or worse, a luddite.

I turned my phone off.

Yes - my wonderful phone, miracle of modern technology, my link to the world and all the people I know - I turned it off.  Not to “in flight” mode.  Not to silent. Off.

I know, I know...my phone is really a powerful computer - I’m told that it has more computing power than NASA could muscle up in  the control room in 1969  used when they first put a man on the moon. It can find any information I think I might want to know  and much that I am sure I don’t. It can play my music or video. It can store and send email. I can read more news and current affairs than anyone outside of national security really wants to know.  I can search the data bases of the world. I can take photos, even video with it and upload it before I even leave the park.  It is my link to the world. And I turned it off.

At the time I committed my act of heresy I was at a family picnic. My loved ones were with me - I could talk to them in person. Work didn’t need to contact me - (and if it did what would that say about training, delegation and leadership density?). I did not need to access any of the social networks to which I belong. I did not need to tell the world I was having a great time.  But I needed to let my family know that they are important - much more important than the electronic distractions that masquerade  as essential elements of daily life. So I turned my phone off and “lived the moment”.

Technology might be important - but people are more so.

How often do you see people having a conversation stopping while one answers a phone? Even worse, to send a text that could be sent later when not talking to someone. Why is a person kilometres away more important than someone right there with you? Chances are they are not - so why put your face to face friend on hold?

Mobile technology is our servant - not our master.

Phone image:
http://cdn.cbsi.com.au/story_media/339302015/samsung-galaxy-s_4.jpg

The kindness boomerang

We live in an era when success at school is defined by many as achieving high marks in exams, or possibly on the sporting field.  We live in a society that boasts “life coaches” to help individuals achieve their personal goals. We live in a time where an unstated belief in “social Darwinism” is rampant - the cream rises to the top, the rest...well, they don’t deserve to be successful.  In short, we live in a society that emphasises individual achievement and success; perhaps this would be more palatable if the meaning of “success” was broadened beyond the limits of economic worth.

However, we rarely hear of the value of simply being a decent person - of helping someone else without  thought for personal gain.  For an antidote to this mode of thinking watch this wonderful video - the Kindness Boomerang.

From an educational view point this video is clearly worth sharing with students - even students from a relatively young age could appreciate this.  Those interested in helping to make the world a nicer place one person at a time (starting with themselves) might be interested in visiting the “Random Acts of Kindness” site for some ideas. This site also has some ideas suitable for using in schools.

This site also has some ideas suitable for using in schools.  Or you might enjoy reading this as an adult - especially if you appreciate the joys of a good coffee.

Teaching students that they can be people of worth regardless of their age (and income or “status” in later life) may just be one of the most important lessons we can teach them. As Martin Luther King is purported to have said “Life’s most persistent and urgent question is, ‘What are you doing for others?’”


Those who enjoyed the video above might also like to view my post “Validate - it’s great”, which features another inspiring video well worth viewing. I challenge you to watch it without smiling...

Herding cats in the classroom?

Teaching is a challenging activity.  Keeping track of a class of students who are operating at a range of different ability levels, often from vastly different socio-economic backgrounds, catering for a range of learning needs, dealing with any individual health issues class members may have, managing the administrative requirements of your school or system, attempting to match curriculum requirements to the needs of students in the class, dealing with “helicopter parents” or, even worse, parents who are as insubstantial as the abominable snowman, acting as a part of a team when your specific class requires focused and immediate attention, trying to make your lessons as interesting and engaging as possible...it takes a special type of person to do it well.
It is not unlike herding cats.



One thing we know about cats is that is easier to get them to come to you than to make them go somewhere that they don’t want to go.  With cats this is easy - entice them with food.  Although we do not bribe students via their taste buds we can learn from this approach - efforts put into developing student motivation is an important aspect of effective teaching. Structuring the educational environment to get students interested and wanting to learn through engaging and challenging activities where they value the outcomes of their efforts and feel secure as they explore their boundaries changes the educational process from that of herding cats to managing learning.
If teachers feel as if they are herding cats in the classroom it might be worth looking at what is on offer. Motivated people, even young ones, don’t need to be herded; they drive themselves.  The challenge for teachers is to guide student interest in ways that reflect the outcome requirements of the curriculum. And that is far from easy.  There are many sites and blogs offering advice or guidance in this area - a brief but worthy offering can be found here.
One important aspect of effective education is often overlooked however. Teacher reflection is an important part of becoming an expert practitioner.  Teachers need to find the time to think about what is going on in their classrooms and their educational practice - this is as important as thinking about the response of students to lessons. How else can areas for improvement be identified? Reflection is not a luxury, it is an essential part of personal professional development and adaptation.
For some personal reflection needs to be done alone - perhaps over a coffee whilst appearing to stare out the window. Others need guidance and stimulation.  Technology may come to the rescue for those in this category. Apple’s Itunes “university” section has FREE lectures on a variety of educational issues and subject areas while Harvard also offers free podcasts on educational issues.  Podcasts can be thought provoking ways to stimulate reflection - and can be absorbed during the daily commute.

To paraphrase Margaret J. Wheatley, reflection “...is not just a nice thing to do if you have the time. It is the only way you can survive.”

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Credits:
video = commercial from http://www.youtube.com/watch?v=Pk7yqlTMvp8
Embedded link via Larry Ferlazzo at Education Week.
Harvard and Itunes links go to original sources.
Margaret Wheatley link goes to source.