Monday, 31 December 2012

School Is Dead - Chapter 8

Education for freedom

I think the opening paragraph speaks volumes. I've broken it up into sentences so that you can ponder each and consider their meaning.

"Alternatives to schools must be more economical than schools: cheap enough so that everyone can share them."

"They must also be more effective so that lower costs do not imply less education."

"Monopoly must be avoided."

"The school system must not be replaces by another dominant system: alternatives must be plural."

"There should be competition between alternatives, but some of them, at least, should not involve competition between students, especially for lifetime prizes."

"One student should not learn at the expense of another, nor should success for one student imply failure for another."

"Alternatives to schools should not manipulate individuals but, on the contrary, should prepare individuals to direct and re-create institutions, including their governments."

"Education should not be separated from work and the rest of life, but integrated with them."

"Educational environments should be protective only to an unavoidable degree."

"Education should not, primarily, prepare for something else nor be a by-product of something else."

"It should be a self-justified activity designed to help man gain and maintain control of himself, his society and his environment."

School Is Dead - Chapter 7

Are democratic institutions possible?


But we can dream...

"The history of institutions is a history of domination."

"(True) democratic institutions offer a service, satisfy a need, without conferring advantage over others or conveying the sense of dependence that institutions such as welfare agencies do."

Reimer imagines a democratic institution as being more a network of equal participants rather than a hierarchy of bosses and workers.

"Institutions which confer or maintain an advantage over others...tend to be production systems rather than networks."

He predicts that the wealthy will suffer under a truly democratic institution, those with advantage will need to give up some of their power and possessions in favour of those weaker, less powerful, less wealthy.

"The choice ultimately is between two completely different styles of life. One is egalitarian, pluralistic and relatively sparse in the kinds of products and services it provides. People have to do things for themselves, but have time and freedom to do what they want. The other kind of life is based on a unified hierarchy of privilege,maintained by international, inter-class and inter-personal competition."

So we are left with a choice - democracy or domination?

I haven't read much provocative stuff like this in the last 20 years. 

Have the idealistic hippy radicals of the 60s and 70s been consumed by the commercialism and materialism of the 80s, 90s and 00s? 

What happened to our dreams of a better (=simpler) world? 

Just as video killed the radio star, did the internet kill the interpersonal-network?

Sunday, 30 December 2012

School Is Dead - Chapter 6

An inauspicious start to the chapter but he got there in the end

"Churches were remarkable among other institutions, until recently, only for their hypocrisy."

Really? Churches have a monopoly on hypocrisy? What about governments? families? armies? community groups? sporting clubs?

I get the point - yes, churches were, are and always will be flawed, just like any organisation that is run by people. And yes, they are full of hypocrites - come along and see, we can always use a few more.

I think the important point is that there are no "perfect organisations" - no perfect schools, no perfect governments, no perfect families.

Confusing "need" with "product"

One big problem that Reimer identifies with a consumer society is that products are always promoted as "needs" - and our need to consume is constantly growing.

And people can be controlled and manipulated by whoever controls the supply of the product, much as a drug addict is controlled by his/her supplier.

He sees schools as being a product that is presented as a "need" - we are told that we cannot get education without attending school and being a part of the system. And the controllers of this product can control the consumers.

Developing countries can never catch up to the developed world

The temptation for developing countries is to try to improve their own standards by imitating western countries. To improve your education system, you need to copy the system that is successful elsewhere.

"Brazil, spending fifty dollars per student per year, can never have the schools which in North America cost a thousand dollars."

Trying to copy the systems and organisations of the developed world will never elevate developing countries out of their poverty. Developing countries do not have the money or resources needed to catch up. To do so, they would need more money, more food, more schools, more technology than the western countries that they are chasing.

"The follower must, therefore, not only remain behind but fall further behind as long as he adopts the means of development of the leader."

Finally, a suggestion of a solution

I've been struggling with the negative approach of this book. I have been tempted to put it down and give up, turned off by the constant complaints about what is wrong with the system and how it all needs to change.

But (finally) we have the first glimpses of a possible solution.

"Developing nations must invent their own institutions." Copying the western model isn't going to work.

"What must be new and indigenous are the institutional patterns" - how needs will be met, how people will be fed, educated, protected, clothes, sheltered - all this needs to be defined and organised under a new framework, decided by the people that it seeks to serve.

One big problem here is that "developed nations now have an effective, if not necessarily deliberate, monopoly on the means of modern invention." What hope is there then?

Revolution? Throw out the despotic rulers of the world? Up-turn the apple cart of history? Throw off the yoke of the oppressors?

Maybe it will come to that. 

But maybe we need to ensure that what we replace the old machinery with is going to be an improvement.

School Is Dead - Chapter 5

Where schools come from

In this chapter, Reimer presents a historical view on how schools have evolved over time. Starting from prehistoric times (not sure where he got his evidence for this part -seemed pretty speculative) he wanders through time up to the present (1971) day and makes the following point:

Schools proliferate "when traditional value systems were in jeopardy". In these times "schools were seen as a way of preserving a set of values which were losing their dominance."

He points to two examples to support his case:

  1. Alexandrian Greece - when Greece had established colonies around the Mediterranean, schools flourished because the colonists were desperate to maintain their traditional values and sense of "Greekness". "It was insecurity rather than the dominance of the Greek colonies of Alexandrian times which caused them to build and depend upon schools.
  2. The Jesuit Schools - these flourished in Europe under in the Jesuit order in the 16th century. Once again, it is the insecurity of the church at the time that prompted this rapid growth in schools.

Alexander and the Jesuits - an unbeatable combination. Surely if anyone was going to implement a world-wide network of schools, these guys were the ones for the job.

This raises a few questions for me

  • Do we really just build schools to preserve the past? Is there no future focus in education and schools?
  • Is a school that good an investment in times of trouble? When the roman Empire was going down the tube, did the Emperors embark on a massive campaign of free education for all children in the hope that it might keep the barbarians from the gates of Rome?
  • Is this view of "school as a conspiracy to manipulate the population" believable? Are there no other altruists out there who believe that schools can be good things?
  • Schools have also proliferated in the late 20th century. What is the crisis in our value system that is behind this rapid growth?
  • Are there other times in history when schools have grown rapidly that are not accounted for in Reimer's explanation?


Interesting historical perspective - I'm not convinced by the conclusions drawn - must read more myself to clarify this.

Saturday, 29 December 2012

School Is Dead - Chapter 4

How Schools Work

Reimer is very interested in the place of rituals in society and uses this in his explanation of the way that schools operate.

"Schooling is social ritual, bridging the gap between social theory and social practice."

We need these rituals because we don't always act in accord with our beliefs.

He identifies four ideologies that play a prominent role in society, examines their realities and then describes the rituals in schools that bring the two together.

1. The Ideology of equal opportunity

The ideology:
  • people can advance themselves solely on their own merits
The reality:
  • "all advancement is at the expense of others."
  • "one can rise to the top only over the heads of thousands."
  • "the odds of staying near the bottom (are) many times higher than the odds of getting to the top."
The ritual of schools:
  • annual progression to the next grade helps us believe that we are all going somewhere
  • "There are enough steps so that everyone can climb a few. Grades in school are easy enough at first, in rich countries, and almost everyone passes these early grades."

2. The ideology of freedom

The ideology:
  • all men have certain unalienable rights
The reality:
  • we have oppressive governments, wars and repression of these rights in many countries around the world, including some that describe themselves as democratic
The ritual:
  • Democratic elections can be a ritual that makes people believe that they have a say in government. Yet the choice of candidate is often manipulated by the hierarchy of political parties. These elected candidates have little personal say when it comes to voting in parliament, being required to vote along party lines.

3. The ideology of progress

The ideology:
  • everything is improving and will continue to improve forever and always
The reality:
  • things cannot continue to keep improving in a finite world with finite resources, serving a growing population
The ritual:
  • "The ritual of research induces the belief that new discoveries change the whole picture, that every day is a new day with a new set of rules and possibilities."
  • Curriculum renewal offers the promise of revitalised, more relevant and more effective teaching. And if we do it every  3-5 years, we will never have to stop and see if we are actually going anywhere or if we are just shuffling the deck chairs. 
Deck chairs on the Titanic

4. The ideology of efficiency

The ideology:
  • We can solve our problems by being more efficient
The reality:
  • We can employ more people if we are inefficient. Or, if we get too efficient, people will lose their jobs.
  • We spend a lot of time and money producing things we don't really need.
  • Efficiency is not always desirable or enjoyable.
The ritual:
  • "Schools learned a long time ago that the way to keep children from thinking is to keep them busy."
  • the ritual of activity helps us believe that we are doing something, that we are moving forward, that we are achieving something.


I quite liked this chapter. It was well structured and made some kind of sense. I do think that some of our "rituals" are based on self-deception (we don't want to see what the problem is), rather than some external conspiracy (someone else doesn't want us to see).

So good news - I will continue reading to see what other ideas will be presented. Looking forward to it.

Friday, 28 December 2012

School Is Dead - Chapter 3

What Schools Are

Might seem a little bit obvious this, but think about it - what are the features that define a school?

Well, according to Reimer, schools are "institutions which require full-time attendance of specific age groups in teacher-supervised classrooms for the study of graded curricula."

Further into the chapter, Reimer find problems with each component of schools:

  1. Children - "Childhood becomes a problem when extended over too many years and too many aspects of life."
  2. Teachers - "Teaching becomes a problem when students depend upon it for most learning."
  3. Classrooms - "Classroom attendance becomes a problem when it builds sterile walls around too much of normal life."
  4. Curriculum - "Curriculum becomes a problem when it approaches international universality."

Other interesting points raised by Mr Reimer:

  • "Once knowledge becomes a product, the graded curriculum follows - an ordered array of of packets of knowledge each with its time and space assignment, in proper sequence and juxtaposed with related packages."
  • "Schools treat people and knowledge the way a technological world treats everything: as if they could be processed."
  • "In this specialised (classroom) environment, knowledge must be transmitted, it cannot merely be encountered, since in most instances it has been taken out of its natural habitat. It must be processed, not only to clean it up but also to facilitate transmission."

My Response

But hang on - don't throw out the baby with the bath water. Surely schools have some good attributes too. I'm getting a bit tired of this negative attitude from Mr Reimer. It lacks balance and perspective. Let me propose the following:

  1. Children - Childhood is more than just a time for avoiding responsibilities. It is also a time of growth and learning. Children are receptive to new ideas. Their brains are developing and their understanding of the world around them is expanding daily. Surely this is a time to prolong if possible, even perhaps beyond the 12 odd years of formal school education. I aim to be a "life-long learner" and I'm not Robinson Crusoe in this. 
  2. Teachers - The best teachers are those who inspire students to learn things for themselves. I think one of the big changes in pedagogy in the last 25 years has been the redefinition of the role of the teacher, no longer the "instructor" or even the "coach on the sideline" but now the "meddler in the middle", provoking and challenging the students.
  3. Classrooms - The physical aspects of classrooms have changed a lot since 1971 - carpet, air conditioning, plastic chairs and tables, computers. But more than just the physical layout of the room, other things have changed too. I don't see too many sterile walls isolating students from normal life. I see stimulating classrooms that bring the wider world into the lives of the students, prompting them to think and respond, to create and to dream.
  4. Curriculum - Yes - we have national curriculums and international assessment devices and TIMMS but...all the curriculum documents I've seen allow for, and encourage or require, local variation and implementation based on regional conditions. I actually think we need some kind of accountability for what goes on in each school, so that we can have confidence in the "product". Curriculum can provide both standardised expectations and flexible interpretation of their implementation.

School is not all bad.

School Is Dead - Chapter 2

What Schools Do - 4 Functions of Schools

According to Reimer, schools have four social functions:

  1. custodial
  2. social role selection
  3. indoctrination
  4. education
Let's consider each of these in turn.

The Custodial Function of Schools

  • schools provide child care - this allows parents to get to work. If only Reimer could have predicted in 1971 the explosion of this function in today's world - he would have invested heavily in before- and after-school care facilities and made a million.
  • communities that do not have schools do not seem to need this function
  • as children get older, child care gets more expensive. Kids spend longer at school. And it costs more to educate older kids as well.
  • the custodial function of schools prolongs childhood. Children are forced to stay in schools for many years. Some are still full time students at the age of 25. This prolonged childhood is unnatural, in fact the whole concept of "childhood" is a fabrication invented less than 300 years ago.
  • children who are in the school system are not required to take responsibility for themselves, their families, their finances, their homes. Not so long ago, children were required to do all of these things. While this may not have been a good thing - 8 year olds working down the pit or in the mill - I'm not sure the current alternative - 25 year old dependents living at home - is much better.

Child labour in a coal mine

The Social Role Selection Function of Schools

  • schools sort kids into the social slots that they will occupy in adult life.
  • schools are part of the system designed to perpetuate privilege.
  • "The major part of job selection is not a matter of personal choice at all, but a matter of survival in the school system. Age at dropout determines whether boys and girls will be paid for their bodies, hands or brains and also, of course,how much they will be paid." The longer you can survive "in the system", the better your chances of getting a high paid, white collar job. Unless of course you get stuck in Grade 3 for seven years - doing the same grade for seven years doesn't really count as seven years of education.
  • tertiary education also plays a significant role in determining social position. Graduating from Oxbridge, an Ivy League college or one of the sandstone universities (Australia's equivalent to the Ivy League), will have a big influence on an individual's access to the top levels of social hierarchy.
  • "It is no wonder, under these circumstances, that some children drop out while others work to win rather than work to learn."

The Indoctrination Function of Schools

  • schools teach values that a student needs to accept in order to succeed (in school - not necessarily in life). Sometimes I think that we punish kids at school for the things that will help them achieve in the business world - cooperation, collaboration, creativity. These are not things encouraged in a formal exam context where each student is required to work by themselves, not communicate with anyone else and produce predictable responses to questions that have been prepared by someone else.
  • schools teach the importance and value of conformity.
  • schools give priority to "dominant languages, both natural and technical." Reimer points out the priority of Spanish over native languages in Latin America and also to Russian over other languages in the former USSR. This is also very true in Australia where indigenous students were forces to learn English and forget their native tongue. A similar pattern of events happened in many other countries, including Wales and Scotland, where children were punished for speaking their "home" language at school.

The "Welsh Not" worn on string around the neck if caught speaking Welsh at school. The wearer was expected to pass it to another child that they heard speaking Welsh. Whoever was wearing it at the end of the day got a beating.

 The Educational Function of Schools

  • while this might be thought to be the main function of schools, apparently as little as 20% of school time is spent in learning
  • schools claim to be the sole purveyors of literacy and numeracy skills, yet Reimer quotes census data that records more literate individuals that the number of those who attended school
  • schools are promoted as the only place where children can learn. Schools also teach children to depend on what they are taught, reinforcing the message that people cannot learn things for themselves. Many "unschooled" and illiterate people learn how to use money, to barter and trade efficiently, to add, subtract, multiply and divide. Not many people can do much more maths than this after 12 years of formal schooling.
  • "Einstein, commenting on a short period he had spent in school preparing for a degree examination, said that as a consequence he was, for several years afterwards, unable to do any creative work."

The man himself, not a big fan of school

In Conclusion

Looks like there is more to school than just learning stuff. I agree that there are many agendas underlying the education systems around the world but I am hopeful that the promotion of the inquiry process in schools is a good step away from students depending on what they are taught and a movement towards acknowledging the individual's responsibility for their own learning.

Thursday, 27 December 2012

School Is Dead - Chapter 1

In my enthusiasm to start reviewing this book, I got a bit carried away. Some of the comments I made about the Introduction were in fact relating to content from Chapter 1. However, there is still much to learn from the first chapter, so here goes...

The Case Against Schools

1. "Most of the children of the world are not in school."

This is the opening sentence from this chapter. Can this still be true today? Maybe it was the case back in 1971 but how about now?

Freidrich Huebler in his blog suggests that in 2004, 86% of all primary aged children were enrolled in schools worldwide. While there is always going to be a big difference between enrolment and attendance, this is an encouraging improvement on figures from 1970.

World Bank data suggests, for example, that in 2010 in Timor Leste, 117% of primary aged students were enrolled at school. (Apparently figures above 100% are explained by over-aged or under-aged enrolments and grade repetitions.) Even so, talking with colleagues who have worked in Timor Leste, attendance at school is irregular and infrequent for most students, despite the enrolment data.

2. "No country in the world can afford the education its people want in the form of schools."

Even in affluent Australia, the government is hard-pressed to provide funding for schools. The Australian Bureau of Statistics reported that enrolments in non-government schools in Australia increased by 35% between 2001 and 2012. Currently about a third of all Australian students attend non-governemnt schools. The annual budget fights over allocation of funds between government and non-government sectors is an indicator of the financial pressure that schools face in trying to provide the education that is expected of them.

3. "While children who never go to school are most deprived, economically and politically, they probably suffer the least psychological pain."

Reimer makes two points here. The first is that school education gives economic and political power, or is provided for the children of those who already possess this power. 

The second point is that those who are "unschooled", who live outside the parameters of schools, including the indigenous and tribal communities of the world who have no schools, suffer no great loss as a result of not having schools. In fact, he suggests that those who have a little bit of schooling suffer great damage psychologically because they learn that they have no power, that they will never be free of the domination of others and that they will be condemned to a life of poverty. While the idea of living an idyllic life in the jungle in a traditional community far from the influence of schools smacks of the "noble savage" character popular in Victorian fiction, perhaps there are some benefits to be gained from such a lifestyle. Or has the progress of the world gone so far as to bring disease, hunger, war and pollution to even the most remote corners of the globe?

4. "The main thing children learn in school is how to lie."

What? That's a rather bold statement. Where is he coming from?

Well the idea is that schools require children to complete a set curriculum. Success at school is a product of being able to "play the game" or "beat the system", authentic learning is compromised in favour of studying for the test. Tom Chapin sings a great song about this - "It's not on the test". 

Reimer also suggests that the pressure that schools put on students to conform forces them to be untrue to who they really are. 

While we may have made some progress in this area over time, involving students in curriculum choices and encouraging individual research and inquiry, there remains in many education systems a Day of Judgement - the SATS, the HSC, the GCSE etc.


So there are many ideas here to think about. Good luck with your own personal journey.

By the way, Craig Dwyer (@DwyerTeacher), a colleague in Japan, found a .pdf copy of "School is Dead". Just click on the title. Thanks Craig. Hope you enjoy it.

Monday, 24 December 2012

School Is Dead - Introduction

A radical book for radical times

When it was published in 1971, this short book, or "essay" as it describes itself, was a provocative and subversive bombshell. 

It starts with a quote from Margaret Mead:

"My grandmother wanted me to have an education, so she kept me out of school."

Margaret Mead - educated but unschooled

The 60s and 70s was a time of radical social and political change. Set in this context, "School is Dead" asked some significant questions about the purpose, value and effectiveness of schools. 

These questions are still being asked today - one of my Grade 4 students asked in a reflective moment last term, "Why do we have schools?" 

When I shared this with a colleague, she sat back and nodded her head. "I ask myself the same thing every day," she said.

But interestingly, when you google the phrase "school is dead" these days, you don't find links to philosophical discussions on the meaning and purpose of a formalised education system, you get instead references to the horrific tragedy of mass shootings in schools across the USA. 

Where did this book come from?

The author, Everett Reimer, describes the book as a result of a conversation with Ivan Illich held over 15 years, starting with their first meeting in Puerto Rico in 1954. 

Ivan Illich - proponent of the de-schooling movement

This book has a very keen awareness of and focus on the needs of Third World countries, an important perspective that can be easily forgotten in our western affluence.

"Schools are an essential element in a world in which technology is king."

This was written in 1971 - before the computer, the mobile phone, the internet - but is a more accurate prediction than any Mayan calendar.

And the problems with technology being king? Well...

  • technology promises unlimited progress to unlimited numbers of people - which is not possible as the population will reach a point that is unsustainable. Reimer states, "We retain breathing space only by letting poor babies die at ten times the rate of privileged babies."

  • the promise of unlimited progress implies that all people in the world can have the same standard of living as that enjoyed in the USA. "Raising world consumption standards to US levels would multiply the combustion of fossil fuels by fifty times, the use of iron a hundred times, the use of other metals over two hundred times." - and this written in 1971? Seems almost prophetic in terms of global warming and fossil fuel consumption.

  • schools perpetuate "the system" and the dependence on technology. Reimer says that at the start of the 20th century, schools were a minority institution and there were alternative educational options for people not suited to schools. He attributes the rapid growth of schools to the needs of a rapidly growing technological society - the monopoly that schools have over education feeds and is feed by the monopoly that technology has on the world. He suggests that other alternatives to schooling provide an escape from these monopolies.

"Our main threat today is a world-wide monopoly in the domination of men's minds."

So we are not dealing with small, insignificant issues here. I will be interested to read the rest of this book.

Another candidate for worldwide domination

Saturday, 22 December 2012

School Is Dead

My holiday book review project

I am moving classrooms at the start of next year and consequently I have been packing up boxes of accumulated "stuff" to move to the other side of the school.

There are a lot of books involved in this move - and packing each one was like meeting an old friend, so the box packing took a while.

And thus I came across this little treasure. It had belonged to the greatest teacher in the world, my mother, before her retirement a few years ago. I had "borrowed" the book from her but had never really got around to reading it so I have decided that here is a worthy holiday project.

I will use my time over the next few weeks to read this short book and post a review of each chapter. Hope you enjoy the reviews.

And if you get a chance, see if you can track down your own copy.

Or else borrow a copy from your mother.

Merry Christmas and happy holiday reading!

Monday, 10 December 2012

If Everyone in the World had a Candy Cane

...and we put them end to end, how far would they reach?

This was a bit of a "Christmas" problem I put to my class as we were one day away from finishing school for the year. Thought we might as well see if they have learnt any problem solving skills this year...

And what did they do?

1. Reach for a calculator

"The answer is 6.4429235." came a confident and speedy reply.

Really? What type of units are we talking here.

2. Give up

Checking on a website ( that showed real-time statistics, we quickly found that the population of the world is constantly changing?

"The numbers keep changing! It's impossible to work out!"

3. Make some "assumptions"

All good maths is based on assumptions and we sometimes need to rely on approximation.

For example, we decided to take the world's population as 

7 084 224 052 people

which is what it was at about 10.00am Australian EDST on 10th December 2012.

Also, we recognised that not all candy canes are the same - so we agreed to measure the one I had been given earlier by a generous student, that was about 9cm long - the candy cane, not the student.

4. Some calculations

Now we had some numbers to work with, we could play!

Number of people x length of candy cane =

63 758 016 468 cm

or 637 580 164.68 m

or 637 580.16468 km

So how far is that???

Not content with just having a number like that, the cruel and demanding teacher asked for a real-life example of how far the line of candy canes would reach.

"Can we get to the moon?"

After much googling and discussing...

"The moon is about 357 000 kms away from the Earth at its closest point."

"Yes - we can get to the moon!"

"But can we get back???"

More googling and discussing...

"Well, we're going to be short of the Earth by about 76 417 kms."

"So we can get there and then get 3/4 of the way back to Earth."

"What if we stretched it around the equator?" asked the unsatisfied teacher.

Well, more calculating and googling ensued. 

Soon we knew that the distance around the equator is about 40 000 kms. 

Brains were starting to flag now so I suggested we try a few of the problem strategies we had sung about in our class play - "Mastering Math" - like draw a picture, make a table etc.

"Can we act it out?" asked one enthusiastic student.

"Sure!" I replied. "This group of desks can be the earth. How far around is the equator again? Oh - 40 000 kms! Right, so each time we walk around the desks, that's going to be 40 000kms. Let's go!"

And off we went. A group of 5 or 6 students and me walking around "the earth", counting by 40 000 for each lap.

I paused at the end of 5 laps - 200 000 kms - to see if anyone was going to make the intuitive leap to 600 000 ( 3 x 200 000) but no-one did so we kept walking.

I stopped again at the end of 10 laps (400 000 kms) but again no spontaneous flash of recognition.

We ended lap 15 (600 000 kms) and the students realised that we couldn't do any more laps - we only had 37 580 kms of candy cane left - it wouldn't stretch to a 16th lap.

Using this as our remainder, we used a calculator to work out that this was about 0.9395 of a lap.

So our line of candy canes would go around the world 15.9395 times.

I wonder...

I asked the students to come up with some questions of their own - how would they like to extend the inquiry?

Here's what they came up with:

  • How many more candy canes would we need to complete the trip back from the moon?

  • How many candy canes would you need to go to the moon 7 times?

  • How many candy canes would you need to get to Pluto and back?

  • How much sugar would you need to make all these candy canes?

  • How many candy canes are made every year?

I think this was a great thing to do on the second last day of the school year. 

Which leads me to say that my blogging may slow down a little over the Christmas break as we take our summer holiday in Australia. Thanks for reading this far and for following the blog. 

Normal service will resume sometime in late January.

Have a great holiday season.


Wednesday, 5 December 2012

Finding the Area of a Picture Frame

Once again 4BF joined up with 4RB and @CapitanoAmazing ( to explore the exciting world of 2D shapes.

Our recent focus has been on finding the area of a shape.

We started with a look at one of those activities that gives you a picture in a frame and asks you to find the area of the picture - but you only get the dimensions for the frame and the distance from the edge of the frame to the edge of the picture:

This activity was taken from the Mathletics e-book "Length, Area and Perimeter"

Can you work backwards to create your own?

We had been talking a lot about problem solving strategies lately and so the suggestion was made that if we worked backwards, we might create our own similar puzzle.

SO, starting with a picture from a magazine, the kids got busy. 

The initial task was to create a frame that was equal in area to the picture itself. The simplest strategy to do this was found to be trace the outline of the photo onto the coloured paper and then slide the photo across and do it again.

But some students quickly realised that there were problems here. If their photo was very square or very elongated, they were in trouble. To keep it simple, we agreed that they could make their frame from a piece of paper that was four times larger than their photo - and therefore their frame would be three times the area of their photo, with the photo covering 1/4 of the coloured space.

The cutting and pasting was impressive but the most significant dimension of this activity was what the kids wrote about their learning and use of mathematics.

Here's the explanations and reflections the kids produced:

 When explaining this one to me, the student said, "So my picture has an area of  30cm2

and the frame has an area of 88cm2  which is twice the size of....Hey! No it's not!"
Much interesting learning occurred following this reflection.

Two students explaining their calculations

 A bit hard to read but if you zoom your screen in you might be able to read it

Here's what the whole thing looked like..

....and here's a few close-ups of the comments....

And again - the whole picture (above) and the close-ups (below)

So what?

Well, we got to apply the "work backwards" strategy to create our own puzzles.

And we explored area a bit more deeply.

We applied fractions and decimals in our measurements and calculations.

We wrote explanations and reflections on our investigation.

And we got to do some quality cutting and pasting, the life-blood of primary education.

And with five days to go to the end of the school year, they're still working hard in Year 4!