A long hike with no trail

Of course, the most rewarding part is the “Aha” moment, the excitement of discovery and enjoyment of understanding something new – the feeling of being on top of a hill and having a clear view. But most of the time, doing mathematics for me is like being on a long hike with no trail and no end in sight.

I find discussing mathematics with colleagues of different backgrounds one of the most productive ways of making progress.

Maryam Mirzakhani, who recently won the Fields Medal prize, talking about what she finds the most rewarding or productive. I was struck between the similarity of this and Steven Johnson’s ides of the slow hunch.

There is also this:

The beauty of mathematics only shows itself to more patient followers.

Sitting alone

[The exam system] obliges students to sit alone at their desks in preparation for a world in which, for much of the time, they will need to work collaboratively.

Tony Little, head of Eton College, on why England’s exam system is out-dated.

Although he doesn’t offer an opinion on what we can replace it with, I’m beginning to think that we can look to teachers like Dan Meyer, Elizabeth Green and Ramsey Musallam to give us an idea of what need to change: children need to sit alone less, they need to be encouraged to be curious, they need to explore different ways of answering a question with their classmates. Certainly, this is already happening to an extent, and these types of methods are not necessarily incompatible with testing.

Still, you are what you measure. These exams measure the ability to take an exam at least as much as—if not more than—they measure what has been learned. Because this is what it measures, this is what is taught and what comes across as important to students, but the ability to take an exam is of exactly zero value once students leave school.

And here lies the difficulty. The government and the bureaucracy that has grown up around the education system is obsessed with measurement. It’s the only way it can determine whether it has been successful. (Actually, I’m not sure if that’s entirely true; there must be better criteria for success.) The rest of us—the parents and the teachers—are more concerned that kids are learning the skills they will need out in the real world. At the moment, I’m not entirely convinced that this is the case.

Again, I’m reserving judgement as I learn more about the National Curriculum, the exams system and the education system in the UK and elsewhere.

Festina lente

I always say, ‘Look, I’d rather you take an extra minute or two and slow up service to get it right.’ Because the one minute behind you are now is going to become six minutes behind because we’re going to have to redo the plate.

Bill Telepan explaining one of the principles of mise-en-place: speed up to slow down.

I read this a day or so before I read Stef Lewandowski’s essay on makefulness, in which he discusses the Latin phrase festina lente:

There are many historical and cultural references to the flow state, yet many people seem to be unfamiliar with it. If we go back to Roman times, we have the concept of festina lente — which roughly translates as “make haste slowly”, and gave rise to the idea of “slow is smooth, smooth is fast”. The phrase has its roots in military strategy—by going slowly you make progress, whereas rushing ahead recklessly could result in casualties. It has adapted over time and many people now take it to mean that it is important to balance urgency and diligence, and that a state of flow is where that occurs on a personal level.

I like the idea of balancing urgency and diligence. Putting too much emphasis on urgency is almost always counterproductive. This is about prioritization: taking time to do the things the things that matter, rather thank trying to do everything in as little time as possible.

Numbers game

By dragging children into a stupid numbers game with us, we do them a great disservice. They don’t respond well to the pressure, and levels and targets don’t tell the tale of their primary education. But many schools make children believe it really matters. Of course it matters to teachers and management, because that is what we as professionals are judged on, but it is of little consequence to the children themselves.

The Guardian’s Secret Teacher is concerned about passing on educational jargon to students.

To me it’s interesting that a practicing teacher seems to agree that standardized testing is about a bureaucracy measuring itself, but has little to do with the education of children.

Of course, I’m also aware I picked up on this because it reinforces my existing beliefs. It’s worth reminding myself that standardized testing has its place and that there is more to school than standardized tests. That may alleviate my concern as a parent (a bit), but I still think I see the current testing culture as a problem to be solved, rather than a situation that I’m willing to accept.

Harkness table

I work as a tour guide at Phillips Exeter and one of the most common questions I get is, “how do students learn math at a Harkness table?” This is a very good question. For those of you unfamiliar with the Harkness method, it involves students sitting around an oblong table and is entirely discussion based. Students do not raise their hands to answer questions, but are expected to learn from and teach, the students around them.

Tim Wu answering the question How do I learn without memorising? on Quora.

It find it interesting that the collaborative model that Dan Meyer, Elizabeth Green and others are advocating in primary and secondary education is also being used at the university level. Even more interesting is that it’s been used and refined at Phillips Exeter Academy since 1930.

After a bit of digging, I was able to find some more information on teaching with a Harkness Table.

There is never any busy work at the Harkness Table. Instead of a math book with an endless number of identical problems and the answers in the back of the book, your math teachers write their own text and design problems that will challenge you. In your history class, you move beyond dates – instead, you are asked to consider what “the facts” mean and why you think they are important. In your English class, your teacher wants to know which books you and your classmates have already read and which ones you want to read. Sometimes, the class syllabus may even grow out of everyone’s ideas. You go to school to challenge yourself with the unknown, not the known. That’s what makes class absorbing and keeps you immersed in it all.

I personally love the collaborative nature of a Harkness table. Working with other people on finding the answer to a problem is the way I learn and work best, but I can’t help but wondering if it’s the best approach for everyone. While I’m not an extravert, I’m certainly not an introvert either. I think I would thrive in an environment where this type of discussion is the norm, but I wonder about people who are more introverted than I am.

I suspect that like any good collaborative process, the Harkness Table is actually more about listening than about speaking, but I still wonder if introverts wouldn’t find this type of learning overwhelming. In the case of Exeter, they could simply choose another university. But if this kind of collaborative learning becomes more commonplace, I’d like to know that it isn’t solving one problem while creating an other.

There is no right answer

Education should be an education in how to live in this kind of world. And so it should an education in how you work within constraints, defined questions that you don’t know the answer to—and there will more than many more than one answer to—in collaboration with other people and how you learn to make things together. And you produce things, and you do it in the real world as much as the classroom. That’s what education should be.

Of course it should also be about learning English and maths and doing it through geography and history. Of course it should be that, and you need some element of structure. But actually we need to educate entire generations of people to go and look for problems and opportunities and collaborate to solve them.

And the trouble is that we don’t have any political leadership that is willing to speak that truth because they want to speak a language of safety, caution and education as a sixteen year apprenticeship in diligently coming up with the right answer at the right time. How is that going to help? How is that going to help in this world? There is no right answer. There are new problems the whole time. You have to find new collaborators. You have to think in fresh ways. You have to make and fail and try again. That’s that world. That’s the world they’re already in.

If you judge the education system by whether it did any harm, then we’d be really failing it seems to me.

Charles Leadbeater’s response to a question about education during his brilliant talk on the frugal innovator. His assertion that education is largely about finding the right answer at the right time. This was certainly the case with much of my own education.

I certainly think I would have benefited from an education that provided me with many stories rather a single correct answer. That didn’t expect a right answer, but expected me to use a set of tools to find the best possible solution given my resources, context and situation.

It’s what I’ve spent much of my adult life doing, and I feel that my education left me poorly prepared for the real world. In fact, I feel that I’ve spent much of my adult life unlearning what I was taught in school.

Two sides of the same coin

It can be tempting to ask families receiving food assistance, If you’re really hungry, then how can you be—as many of them are—overweight? The answer is “this paradox that hunger and obesity are two sides of the same coin,” says Melissa Boteach, vice president of the Poverty and Prosperity Program of the Center for American Progress, “people making trade-offs between food that’s filling but not nutritious and may actually contribute to obesity.” For many of the hungry in America, the extra pounds that result from a poor diet are collateral damage—an unintended side effect of hunger itself.

National Geographic has a disturbing portrayal of hunger in America. Like many places in the world, obesity in the United States has become a sign of hunger, as people struggle to afford (and sometimes to find) anything other than cheap junk food.