When I was a kid, Sundays in the summer were car washing days. The stores were closed. The roads were generally quiet. And we took out the hose and the pail, filled them with water and dishwashing soap then rubbed, scrubbed, and waxed the family car…or later our own car…beautiful again. Sundays have already substantially changed and now in an article a recent Economist magazine, one of the last of the great suburban Sunday rituals will soon be going away too. For a scientist has found a pattern made by an obscure but available laser that sheds water and dirt with it. One day in the not too distant future we should be able to buy a car that not only no longer needs waxing but will never get dirty and need washing. Perhaps, about the same time, we will no longer even own cars but instead will ask for one on our cell phone, and an Uber Self-Driving car will pull up to our house to pick us up and drop us off wherever we want to go.

Crazy ideas, great changes. Yes, this is just a tiny example of the new world our students need to be preparing for. We are all linear thinkers. We think the world will continue in much the same way it has been going, with changes that take place slowly and methodically, changes that we can get used to, changes we can plan and prepare for. But change is not linear at all. It is, like the word used by the wonderful writer and biologist Stephen Jay Gould to describe evolution, “punctuated”. Sometimes change accelerates quickly and sometimes it moves at a constant speed. This has always been the nature of change and it is evermore so true today. For things that shed water don’t get dirty and don’t need cleaning — cars, windows, even clothes. And cars that don’t need drivers don’t need parking spaces on streets, driveways, or shopping centers. Our world could, and likely will, change dramatically.

How do we prepare children for work and life in this future world? What should they learn in their school years to make them ready for a lifetime punctuated with change they cannot predict? We cannot base it on the Sunday rituals of our past like counting the cash my dad brought home from his dental practice so that he could put it into the bank on Monday morning. We cannot base it on the paper and pencil calculating rituals we spent innumerable hours on, the paper algorithms that define most of the math our students practice. We cannot base it on “What is____?” habits of thought of the past, when the answer can almost always be easily Googled. We must base it on “What if…” thinking, functional thinking, the basis of science, technology, engineering, and math, the heart of business planning and quantitative reasoning, the question the future depends on.

Sunday rituals will come and go. Technology will sometimes change rapidly and sometimes slowly. But we can prepare our children for their future by making their education about “What if…”, their practice and mastery not off paper-based algorithms but off open-ended problem solving, their focus not on facts in today’s data-rich world but on thinking, their vision directed not on finding the right answer but on seeing outside the box.

Today, I attended an ancient ceremony. It is called “Hooding”. An elaborate and beautiful hood is given to students who have completed their scholarship and are ready to receive a doctoral degree. The Hooding Ceremony at Lesley University today with its rich pageant and sweet music took me back to the 12^th and 13^th centuries when the doctoral degrees were first given out. I quote from the program booklet.

“Doctoral means teacher or instructor. In ancient Rome, people who delivered public lectures of philosophical subjects were called doctors. During the 12^th century, doctor became an honorary title bestowed on men and women of great learning.”

The ceremony features professors and recipients in full academic regalia marching into the theater to receive their hoods and their applause. The rainbow of rich colors laid on velvet black, and sometimes gowns of other vibrant hues worn by professors to feature the ceremonial colors of the institutions they received their degree from, grab our attention. Elegant, beautiful, and wonderfully solemn yet buoyant, the processional music punctuated by the cries of babies in the audience, was a family celebration.

“Most colorful and distinctive of the academic regalia is the hood, which drapes around the neck and extends down the back.”

As each person came up to be hooded by their dean, I could not help but think of the 8 or more centuries and countless people who had been part of the history of this service. So few very very long-lasting traditions remain. So many of our ancient traditions like old artifacts are either lost, destroyed or closeted in museum exhibits.

At the same time I could not help but think of Leonardo of Pisa and the tradition in mathematics he initiated, a tradition about Hooding’s age. But Leonardo’s math medieval tradition is no longer beautiful, no longer meaningful, no longer relevant, and yet we continue to cling to this academic tradition. Some traditions are precious connecting us to the past and enriching our lives. Some traditions bind us to activities that have long since lived out their usefulness, ending up not as things to cherish but as things that impoverish.

So as we enter this season celebrating successful scholarship, we should look to those who will not have anything to celebrate, who will have failed because they were made to follow a tradition no longer of value, no longer of use, no longer necessary. And we must ask ourselves, “What traditions do we cherish, preserve, and pass on to the next generation as their heritage, and what traditions must we shed to enable everyone to gain the education of their dreams.

What if I could give you a magic wand to wave over our educational system and make it fulfill our dreams for our children? What would you have it do?

I find this question stumps most people.

We all know education in America is far from what we either want or need it to be. We all know it lacks the essential creativity our children will need for 21^st century work and life. We all know it fails even the least stringent tests for those who need it most. We hear the same refrain again and again. More money — even though we have tripled our per pupil expenditures over the past half century without any significant improvement in performance. Better teachers and teacher training – even as we have taken away the opportunity to be imaginative and entrepreneurial which brings the best and brightest into a discipline. More demanding – even though we have not a shred of evidence that our children are responding by caring more and working harder. Science – even if what we are measuring will not be a useful life and work skill. To make matters even worse, education in America seems so resistant to change, so overwhelmingly complex, so replete with attempts to transform it, no wonder my question stumps most people.

No doubt great teachers are transformative but until we make their jobs transformative we will just have to hope research into cloning makes a huge breakthrough, because we will never get enough great teachers, never ever. No doubt more money is necessary in many places, but we have cloaked our schools in so many narrow demands that we starve the essential. No doubt we need to demand more of our children but more of what, for we have asked them to work harder and not work smarter even though school today should be about smarter and not harder. And no doubt we require more learning science and more learning research, but when we study the same old we get the same old, it does not take any scientific research to find out that barely 1/5^th of our students really master the required content.

We know what we need. Sir Ken Robinson’s TED Talk has been watched more times than any other. Not just any other on education, but any other TED Talk, now approaching 30 million times. Ken talks about creativity in education. We are starving for it. So how do we get it to happen?

What could a magic wand do?

If I had such a magic wand I would use it to make a minor change in the instructions of our new Common Core Tests. The tests are designed to be given on internet-connected computers. I would change the instructions to enable every student full educational access to the Internet at any time during the tests. The Web is certainly full of strange beasts and of course we should protect our students from accessing those, but everything else, sites like YouTube that are today blocked by many school systems should be accessible, spreadsheets, Google searches, Wikipedia, sites designed to help students take tests, yes even help from a friend. Anything of educational value.

When our students leave our classrooms and go to work they will live in the real world where they will have such full Web access. Don’t we want them to learn those things that will enable them to use that access to solve problems and to learn to do things? Don’t we want them to use this incredible new tool that is defining 21^st century work and life to its fullest advantage? Don’t they need their schools to prepare them for the kinds of tasks they will perform which almost certainly will involve the Web?

The Common Core tests are redefining education. If we give our students full educational Web access when they take these tests, they will be able to take charge of their learning, and they, not the tests, will redefine education. Oh, for sure the tests will have to change and our classrooms and teachers will most certainly change, because there will be no reason to teach our children the long division algorithm any more then we should go back to teaching them the square root algorithm. They will not get “What is ____?” questions whose answer could be easily found on the internet. They will have to get “What if…” questions that will challenge their creativity, demand knowledge, and engage their insight. The tests will have to be designed to represent the real world and not an artificial one that has produced profound and fatal flaws as described by Steve Rasmussen.

Such a minor change in the instructions will change our schools in dramatic ways and open a floodgate to creativity for both our teachers and our children. Magic wands are simple things, but they have the capability to make wonderful happenings. Opening the internet door to our tests and our schools would profoundly change education.

If a mathematician were asked what these two numbers had in common, she might wonder if they were both primes. They are not. A gambler might consider them lucky numbers because one of the prime factors of 209 is 11 (as you could find out by asking google) and 11 goes with 7. But that, like most gambling, is most likely just a random act. I got to thinking about these two numbers when I counted the appearance of two words in the Common Core Standards in Mathematics, fraction and spreadsheet.

Yes, fraction as you might guess appears 209 times and spreadsheet appears just 7 times in the K-12 math standards. Fraction appears very nearly 30 times as often in the Standards as spreadsheet does. And to make this ratio even worse, spreadsheet almost always appears in league with “calculators, spreadsheets, and computer algebra systems” or “other technology.” And in the Content Standards spreadsheet only appears in the high school portion.

Now I ask you which of these terms represent what our 21^st century students will be working with as adults? Today our business and STEM workforces use spreadsheets as their primary quantitative tool and few people in business or in STEM professions manipulate fractions in either their workplace or home. Oh sure, we use ratio and proportion which produces rational numbers, and we use fractions in some of our recipes and in the headmath we do. But we no longer calculate in fractions on paper or on computers, and fractional values are today almost always dealt with as decimals and not common fractions. By the way the word decimal appears in the Standards only 48 times.

A 21^st century curriculum would certainly seem to focus on those tools, skills, and concepts that would be of most use to our students when they enter the workforce. Now I grant you that fractions do have some uses, and manipulating fractions would help a student handle rational algebraic equations in case you feel strongly about that. But does it make any sense in this internet/spreadsheet age to spend the one to two years of every student’s math education focused on fractions? Does it make any sense that fractions should be a stumbling block that we require of every student? Does it make any sense to think of spreadsheets are only faster calculators relegated as an afterthought in the Standards or in our math curriculum? Should functions which are the heart of scientific thinking, spreadsheets, and programming appear less often (172 times in the Standards) than fractions and only then starting in 8^th grade.

The fundamental question we teachers must always ask is: “Are we educating our students for the past or for the future? If we are educating our children for the future as, of course, we must, then what should the spreadsheet to fraction ratio be in those 21^st century standards?