Wednesday, September 28, 2011

Talking of teachers

Teaching is one of the oldest professions on Earth. (Well, one of the oldest legal professions.)  Western education can trace its origins back to such notables as Aristotle, Socrates and Plato. Although in those days the curriculum was less crowded, less rigidly defined and not subject to national testing these men were teachers,  albeit non-accredited ones.

In the years since then education has gradually become a universal experience, at least in developed countries, and “schooling” has become synonymous with “education”.  The difference, according to George Savile, is clear. “Education is what remains when we have forgotten all that we have been taught.

Is he dead... or teaching school?
Since everyone receives an education of some kind or other, everyone has an opinion about education in general, and about their own teachers in particular.  Often these opinions are far from flattering. But then, holding teaching in low esteem has a long history.  A hundred years before Christ, Zenobius dismissed an inquiry about a colleague with the words, “He is either dead or teaching school.

More recently, Irish playwright George Bernard Shaw used his literary prowess to the full when he coined the expression, “Those who can, do; those who can’t, teach.”  (Those who can’t think for themselves now quote George Bernard Shaw.)

I’m sure Shaw taught himself to read and write, as did the people who read his workd. Showing similar disdain for teachers, Author J. D. Salinger said “You don’t have to think too hard when you talk to a teacher.” (It is unlikely he meant that teachers are articulate, make their meaning clear and are therefore easy to understand.)

Perhaps the most sobering observation about teachers was made by Henry Adams, one of the framers of the Constitution of the USA: “A teacher affects eternity; he can never tell where his influence stops.”  Whether you think this thought is valid or not will probably depend on whether a future Mother Teresa or a Charles Manson passes through your class.

Not all political leaders have held education so highly. When former US President Ronald Reagan was desperate to find funds to support his pet Star Wars project he suggested taking funds from other areas, such as education, asking “Why should we subsidise intellectual curiosity?”  Another former governor of California, Jerry Brown,  wondered about the priorities of educational leaders: “I question whether we can afford to teach mother macrame when Johnny still can’t read.” But Brown would have won a few friends in the educational fraternity with this observation: “Why in the world are salaries higher for administrators when the basic mission is teaching?

Just the facts?
The debate over what to teach in schools comes a close second to scandals in the House of Windsor for tabloid newspaper copy. There is seemingly endless criticism of current teaching methods and curriculum. Schools are expected to teach everything from sign language to cosines.  This debate also has a long history.

Charles Dickens, expressing an opinion not necessarily his own, had one of his characters - the odious Gragrind, in Hard Times, say, “Now, what I want is facts. Teach these boys and girls nothing but facts. Facts alone are wanted in life. Plant nothing else, and root out everything else...This is the principle on which I bring up these children. Stick to facts, sir!” Samuel Crothers highlighted the flaw in this approach when he said, “The trouble with facts is that there are so many of them.

This begs the question - which facts do we teach? And that is where the debate branches. Russell Green summed up well the choice between the process versus product, personal growth versus utilitarian function argument: “The advantage of a classical education is that it enables you to despise the wealth which it prevents you from achieving.

Perhaps the best thing for primary teachers to do is treat knowledge like grass seed - spread appropriately, cover a wide area, and be prepared to do a lot of follow-up work.

A little learning may be a dangerous thing - but a lot of ignorance is far worse.  Teachers try to reduce this ignorance a little - which is not always and easy task. Fortunately, there is no shortage of advice from past pupils on how to improve our teaching.

Albert Einstein, who is often portrayed as a “struggling student” despite report comments to the contrary, thought that “Everything should be made as simple as possible, but not one bit simpler.” This is sound advice, but relatively lacking in detail. William Ward went a little further, and told teachers how to do it: “The mediocre teacher tells. The good teacher explains. The superior teacher demonstrates. The great teacher inspires.”    Unfortunately, Ward stopped short of telling teachers precisely how to be be inspirational. This literary observation contrasted with the homespun advice of Austin O’Malley: “When you are dealing with a child, keep all your wits about you, and sit on the floor.”

A Japanese proverb, true to the Japanese tradition of stylistic simplicity, said “To teach is to learn”.  No doubt this is a worthy sentiment, but it is also rather vague on how to go about the actual task of teaching.  However, an ancient Chinese adage gives clear advice on how to do it. This maxim is probably the earliest known reference to hands-on, child-centred teaching: “What I hear I forget, what I see I remember, what I do I understand.”

These words of wisdom take the emphasis off the teacher and place it where it belongs - on the student. What teachers teach is not the central aspect of education. The truly significant aspect is what students learn.

The human factor
How do teachers know when their students have learnt? There is a bewildering array of tests, check lists and performance criteria by which we assess our students. Usually the instruction manuals are thicker than War and Peace, and read as if they were written by the same person who writes the handbooks for electrical appliances.

Sir Richard Livingstone had a more humanistic method: “If the school sends out children with a desire for knowledge and some idea of how to acquire and use it, it will have done its work.

When people talk of education systems they forget that schools are people places. A school building has exactly the same material and equipment in it over a holiday period as it does during a term. Yet a school without students is a barren place, devoid of life. It takes people to  make a school - or, for that matter, an education system.

Sidney Hook high-lighted the significance of teachers in the system: “Everyone who remembers his own educational experiences remembers teachers, not methods and techniques. The teacher is the kingpin of the educational situation. He makes and breaks programs.

And that just about says it all.

This piece first appeared in Classroom - the magazine for teachers, vol. 8, 1993.

The story behind the story...

I’ve always wanted to be a teacher and never really had serious thoughts of becoming anything else. Hence, at the tender age of 17, I began my training and have been involved with education ever since. Yet, I was aware that, for many people, school was not the generally happy place that it was for me.  For some people schools, and by extension,  teachers, were not held in high esteem.  Others felt the job itself was distasteful - a pretend profession with a modest pay cheque but major work requirements.   This attitude was incomprehensible to me.  True, the pay was (and remains) modest - but the privilege of working with developing minds and seeing the smile on a face of a student as a concept is mastered is priceless - literally beyond price.

Hence this piece.

Best teacher graphic::

Monday, September 19, 2011

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.  


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.)

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.

All links go to original sources of documents.

Tesselating shapes PPt;

Tuesday, September 13, 2011

Learning Styles - When a myth becomes a legend

When a myth becomes a legend.
Like, many others, I love this prose.
I like the tone, the sense of pathos, the sense of learning something too late - or perhaps in the nick of time. I like the imagery of it all.  The prose is inscribed on the tomb of an unnamed Anglican Bishop buried in Westminster Abbey and dates to around 1100 A.D.
When I was young and free and my imagination had no limits, I dreamed of changing the world. As I grew older, and wiser, I discovered the world would not change, so I shortened my sights somewhat and decided to change only my country.
But it, too, seemed immovable.
As I grew into my twilight years, in one last desperate attempt, I settled for changing only my family, those closest to me, but alas, they would have none of it.
And now, as I lie on my deathbed, I suddenly realize: If I had only changed myself first, then by example I would have changed my family.
From their inspiration and encouragement, I would then have been able to better my country, and who knows, I may have even changed the world.

What a pity it isn’t true. 
No such tomb exists.  
This will no doubt come as a surprise to many - the legend of the prose features heavily on poetry and self help sites across the Internet,  is featured in books such as “Chicken Soup for the Soul” and is regularly emailed around the globe.  However, as appealing and entrenched as belief in the poem is, the fact that many people believe something doesn’t make it true. The legend is a myth.
Education is not immune from widely held and deeply cherished ideas that are also based on belief rather than fact. One of these is the notion of “learning styles”.
Consider the following from Professor Daniel Willingham,  Department of Psychology, University of Virginia.
For some this challenge to the notion of learning styles is akin to heresy.  And perhaps heresy is exactly what is  since - heresy is the term usually used to describe those who oppose the teachings of a church.  I  don’t wish to get into the field of religion here - but religion is based upon faith - not logic. Religion neither relies upon nor requires logic.  But education should.
For those who might require further convincing I recommend reading this.   

And this.

Or this.
Or even this.

How did this unsupported belief become so wide spread? Possibly because it appears to work. Certainly teachers who subscribe to the belief and accommodate it in their practice appear to reap the benefits.  However, with a moments thought we can see why - catering for “different learning styles” means providing variety, it means designing lessons that are more than “chalk and talk” or lecture style, or worksheet based instruction. It may mean that material is presented from more than one perspective - which of course takes time - and we know that time on task is associated with learning. In short, it means putting effort into pedagogy - it results in improved teaching.  So, the misguided belief in learning styles actually produces better teaching,  which leads to engagement - which leads to concentration - which leads to learning.  
Thus, this flawed theory leads to improved teaching.   So, if this is the result, what’s the problem?
The belief in “learning styles” has no more scientific support  than the study of phrenology once  claimed, or the notion that ability is fixed (as in the belief of a static I.Q.). Surely our professionalism should dictate that we only advocate those practices that can be supported with evidence?  After all, it is evidence that separates informed practice  from mere opinion or entrenched habit.   It is evidence based practice that will enable us to improve our instructional techniques.
If we, as a profession, begin to insist on evidence based practice in this matter we may start questioning other aspects of our practice - the notion of assessment techniques could bear close scrutiny for example, or how computers can be used to  teach effectively, or the benefits of delaying the introduction of algorithms until at least grade 4, or the benefits of Project Based Learning, or the benefits of a “growth mindset” approach... the list is endless.  Evidence based practice can lead to innovation and improved education.
If we are to improve education we need to ensure that we as educators know why we do what we do - and can demonstrate that it is more effective than other approaches.  If there is a truth in the “learning style” myth it is that teaching style matters.  
And that is something we can all learn from...
All links go to external sources.
(I stress this is NOT the tomb of an Anglican Bishop in Westminster Cathedral.)

ADDENDUM. A post on the same theme by Steve Wheeler can be accessed here.

Friday, September 2, 2011

Project Based Learning – meaningful action … or merely activity?

The world is awash with people and groups wishing to reform education.  Some want to go “back to basics” while others want to go “forward to the future”.       Amongst the more progressive groups there is a surprising degree of similarity in what they propose. Thus, the RSA “Opening Minds” project in the UK or the US based P21 or the Apple Classroom of Tomorrow Today all have a high degree of overlap - indeed a Venn diagram of their views would be almost a single circle.  

One thing that is common to reformist groups is the emphasis placed upon students working together in authentic project based learning (PBL).  As Alan November clearly demonstrates there are many valid humanistic reasons for this.  However, as in all approaches, there are dangers inherent in this technique. Done poorly this method can consume vast amounts of time for minimal return.  However, when done well  the returns can be astounding.  

John Lartimer and John Mergendoller, writing in Educational Leadership,  have identified seven essentials for PBL.  They identify two important criteria that define a project as meaningful.  The work must be personally meaningful to the students and it must have a valid educational purpose.  I’d interpret this last aspect as meaning that the PBL must have clear links to the curriculum.

The seven criteria are;
  1. Students have a  need to know the topic.  It is no secret that many students are not engaged with their schooling.  Lartimer and Mergendoller maintain that this is often because students don’t see a need to know what they are being taught.
  2. A driving question.  Many of the educational reformers refer to a curriculum based upon questions. Lartimer and Mergendoller maintain that a good driving question is clearly stated and provides purpose and challenge.  They should be open ended and link to the core of what students want to learn.  It is no surprise then that they also advocate that the students be involved in framing the guiding question.
  3. Student voice and choice.  Students should be able to make genuine choices and decisions relating to the task - this is not to suggest “free reign” by the students but they should be able to suggest what artifacts they could produce and the methods by which they create them. Depending on circumstances students might also have meaningful input into time and resource use. (Teachers would have a “gate-keeper” role here).
  4. 21st Century Skills are developed.  This is becoming an overused and under-defined expression generally.  However,  Lartimer and Mergendoller envision it as involving genuine collaboration, critical thinking and the use of technology.  It also must have an important purpose - just like the work place.  These skills are not just nurtured by the teacher - they are explicitly taught.  These could include production of simple videos or podcasts as well as print based work.
  5. Inquiry and Innovation.  This should be genuine and meaningful - it is not simply format shifting provided  information or regurgitating  data from texts.  Students follow their driving question, form hypothesise, test them, revise them, summarise their results - which may be the solution to a real world problem in the student’s context.  This contrasts with “research” where students are given set information to locate and then supply to the teacher - information that the teacher, in all probablility, knew in advance.
  6. Feedback and Revision.  Feedback provided to students is delivered during the process - which enables them to revise and hopefully improve their work.  As Edison is reported to have said “Genius is one per cent inspiration, ninety-nine per cent perspiration".  Or, in less well know parlance - “the only job in which you start on top... is a grave digger.”  Our students need to understand that first efforts are usually drafts - drafts, that need editing and improving.
  7. A publicly presented product. Key in many reformists writing is the notion of public performance / presentation of work. Obviously, the nature of the task would reflect the audience - but a significant aspect of authentic PBL is that the artifact created is shared with an audience.  So, if a “project” is not shared outside the probably isn’t really authentic PBL.   (Steven Levy addresses this well in his article “The Power of Audience.”)

The team at edutopia (  have produced a free resource called “Top Ten Tips for Assessing Project-Based Learning” PDF.  Not surprisingly it has much in common with Lartimer and Mergendoller’s piece.  Their advice includes:

  1. Keep it real with authentic products.  “Authentic products naturally reflect the learning goals and content standards you have identified during project planning. They don’t feel fake or forced.”
  2. Don’t overlook soft skills.  “Soft skills” echos some aspect of 21stC skills above - creative problem solving, critical thinking and global awareness.  In what universe are these really “soft” skills?
  3. Learn from Big Thinkers.  The concept of “assessment” needs to be rethought with this approach. It is not always sensible to assess in a traditional manner when using PBL.  Fortunately the  PDF provides links to leaders in the field - including James Paul Gee and Grant Wiggins.  Good practice would suggest that the assessment criteria would be assessed with students at the start of the PBL.  Gee would suggest that, if the task has been well designed, then successful completion of the task is itself the assessment.  
  4. Use formative strategies to keep projects on track.  A teacher using PBL is less of a lecturer out the front of the class and more of a “guide on the side”, constantly moving around the classroom and offering advice...and asking questions.  The metaphor of project manager is not entirely inappropriate.
  5. Gather feedback - fast. Providing feedback quickly is important in PBL - especially as the students are likely to be working in territory that is uncharted for them personally.  However, it is not just about providing feedback - it is also about receiving it.  There are many  activities that allow students to provide a quick snap shot of their learning and understanding to teachers.  It is important that this is done - not only does it inform the teacher about student learning, but it also indicates how the creation of artifacts is progressing.
  6. Focus on teamwork. Teamwork is another one of those highly prized 21st century skills. It doesn’t always develop naturally - and a range of strategies that both scaffold and direct team work are required for effective PBL.
  7. Track progress with digital tools.  A rough rule of thumb when working with”digital natives” is “think digital”.  The details will differ from project to project - but in general terms, the use of digital technology for recording work and providing feedback is recommended.  This could also include student reflection throughout the process - for example, instead of writing a reflection about progress students could do the same thing in a group wiki, individual blog, or perhaps even a podcast.
  8. Grow your audience. Think back to Steven Levy’s “The power of audience” article.  Think outside of the classroom - have the students contact the local, state, national, or even global “experts” in a given area.  Send links to completed digital artifacts to them and ask for feedback. Share work on appropriate social media.  The classroom no longer has walls.
  9. DIY Professional Development. It is likely that your skill set as a teacher will need to improve rapidly to enable you to assist students in their PBL.  Fortunately, there are experts galore online - use the internet as an online training facility to learn the skills you need - as you need them.
  10. Assess better together. Depending on how and what you decide to assess, don’t do it alone. Ask a colleague to assist you. (The guide suggest some specific sites to assist in this).

Although no single educational technique holds all the answers to educational reform there is certainly a sizeable movement of significant people advocating PBL as being one of the important components of providing sensible educational reform.  Maybe PBL could be your next personal learning experience.

(To see where PBL fits into the broader educational agenda you may like to follow this link to TARGETS - Educational Reform in Three Minutes.)

Credits and acknowledgments:

Both main articles used in this blog are both highly readable and highly recommended.

Steven Levy URL =

Edutopia guide URL =

Alan November link =

PBL graphic =,r:15,s:133