‘Just weighing a pig doesn’t fatten it’ — Obama hint on testing

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PRESIDENT Obama spoke, briefly, at his June 11 Green Bay town hall meeting on education as well as health… and gave a hint of some hope and change that may not be as bad as many educators feared when he announced the appointment of the militaristic, test tsar Arne Duncan as his education secretary.

Local teacher Matt Stein of 20 years challenged the president: “One of the things that I’ve learned in education in the last 20 years is that the system is not broken. And it bothers me when I hear politicians, and even my President, say that our educational system is broken.

“This system works in cases. There are great things happening in Green Bay and Appleton and all over the UP. And there are things that can be reproduced. My question is: When will the focus be on reproducing those things — smaller classrooms, creating communities in your classrooms — and moving the focus away from single-day testing and test-driven outcomes?”

The president responded:

“So here’s the bottom line. We’ve got to improve, we’ve got to step up our game — which brings me to the next point in your question, which is, how do we do that? I agree with you that if all we’re doing is spreading around a lot of standardized tests and teaching to the test, that’s not improving our education system.

“There’s a saying in Illinois I learned when I was down in a lot of rural communities. They said, ‘Just weighing a pig doesn’t fatten it.’ You can weigh it all the time, but it’s not making the hog fatter.

“So the point being, if all we’re doing is testing and then teaching to the test, that doesn’t assure that we’re actually improving educational outcomes.

“We do need to have accountability, however. We do need to measure progress with our kids.

“Maybe it’s just one standardized test, plus portfolios of work that kids are doing, plus observing the classroom.

“There can be a whole range of assessments, but we do have to have some kind of accountability, number one.”

Obama’s remarks heavily focused on the need for a change in health care in the US. They were reported as such.

But as the town hall was held in a school — SouthWest High School — a likely question on education was predictable. Obama’s remarks may have been less off the cuff than appears. Buried and almost lost in the extensive arguments on health care, the remarks on education could be seen as an early precursor of things to come.

Arne Duncan is at present on a “listening tour”.

When Arne Duncan was first appointed as education secretary there were fears across the education community, based on his draconian approach to bringing change to education in inner-Chicago — see Hope and change in my classroom.

But balancing Duncan, Obama also appointed the much more radical Linda Darling-Hammond, professor of education at Stanford, as head of his education policy transition team, a champion of constructivism and reduced testing. She was the choice of those who understand how children learn as Alfie Kohn put it.

Could it be that we’re going to see Duncan as the hard cop in the public eye, while some of the soft cop’s more thoughtful and intelligent policies make it into the classroom?

Stanford’s teacher training program now includes on its reading lists for aspiring teachers the radical (for the US) pamphlets and research of Kings College London’s Prof Paul Black and friends.

The record of the president’s remarks can be read at: http://www.whitehouse.gov

Below are the president’s remarks in full on education:

Well, let me — first of all, thank you for teaching. My sister is a teacher, and I think there is no more noble a profession than helping to train the next generation of Americans. (Applause.)

I completely agree with you that there is a lot of good stuff going on in American education. The problem is, is that it’s uneven. (Applause.) Well, let me put it this way. There are actually two problems. In some places it is completely broken. In some urban communities where you’ve got 50 percent of the kids dropping out, you only have one out of every 10 children who are graduating at grade level — this system is broken for them.

Q Crime — (inaudible).

THE PRESIDENT: Well, I’m going to get to that. We can’t have too big of a debate here. You got your question. (Laughter.) Don’t worry, though, I’m going to answer your question.

So there are some places where it really is completely broken. And there, yes, a lot of it has to do with poverty and families that are in bad shape. There are all kinds of reasons. And yet, even there, there are schools that work. So the question is, why is it that some schools are working and some schools aren’t, and even in the worst circumstances, and why don’t we duplicate what works in those schools so that all kids have a chance?

Now, in other places, Green Bay and Appleton and many communities throughout Wisconsin and Michigan, the average public school is actually doing a reasonably good job — but can I still say that even if you factor out the urban schools, we are falling behind when it comes to math; our kids are falling behind when it comes to science. We have kind of settled into mediocrity when we compare ourselves to other advanced countries and wealthy countries. That’s a problem because the reason that America over the last hundred years has consistently been the wealthiest nation is because we’ve also been the most educated nation.

It used to be by a pretty sizable factor we had the highest high school graduation rates, we had the highest college graduation rates, we had the highest number of Ph.D.s, the highest number of engineers and scientists. We used to be head and shoulders above other countries when it came to education. We aren’t anymore. We’re sort of in the middle of the pack now among wealthy, advanced, industrialized countries.

So even with the good schools, we’ve got to pick up the pace, because the world has gotten competitive. The Chinese, the Indians, they’re coming at us and they’re coming at us hard, and they’re hungry, and they’re really buckling down. And they watch — their kids watch a lot less TV than our kids do, play a lot fewer video games, they’re in the classroom a lot longer. (Applause.)

So here’s the bottom line. We’ve got to improve, we’ve got to step up our game — which brings me to the next point in your question, which is, how do we do that? I agree with you that if all we’re doing is spreading around a lot of standardized tests and teaching to the test, that’s not improving our education system. (Applause.)

There’s a saying in Illinois I learned when I was down in a lot of rural communities. They said, “Just weighing a pig doesn’t fatten it.” (Applause.) You can weigh it all the time, but it’s not making the hog fatter. So the point being, if we’re all we’re doing is testing and then teaching to the test, that doesn’t assure that we’re actually improving educational outcomes.

We do need to have accountability, however. We do need to measure progress with our kids. Maybe it’s just one standardized test, plus portfolios of work that kids are doing, plus observing the classroom. There can be a whole range of assessments, but we do have to have some kind of accountability, number one.

Number two, we do have to upgrade the professional development for our teachers. (Applause.) I mean, we still have a lot of teachers who are — we’ve got a lot of teachers who are well-meaning, but they’re teaching science and they didn’t major in science and they don’t necessarily know science that well. And they certainly don’t know how to make science interesting. So we’ve got to give them the chance to train and become better teachers. We’ve got to recruit more teachers, train them better, retain them better, match them up with master teachers who are doing excellent work so that they are upgrading their skills.

If after all that training, the teacher is still not very good, we’ve got to ask that teacher, probably, there are a lot of other professions out there; you should try one. (Applause.) I mean, I’m just being blunt, but we’re going to have to pick up the pace.

Now, the key point I want to make is this: We should focus on what works, based on good data. And Arne Duncan, my Secretary of Education, this guy is just obsessed with improving our education system. He is focused a hundred percent on it, and he is completely committed to teachers. We think that teachers are the most important ingredient in good schools. We’re going to do whatever works to help teachers do a better job — (applause) — we’re going to eliminate those thing that don’t help teachers do a good job. Some of it is going to require more money, so in our Recovery Act, we have more money for improving curriculums, teacher training, recruitment, a lot of these things. But you can’t just put more money without reform, and so some of it is demanding more accountability and more reform.

There’s one other ingredient, though, and that is parents. (Applause.) We’ve got to have parents putting more emphasis on education with our kids. That’s how we’re all going to be able to pick up our game. (Applause.)

Assessment… a new sort of gradebook

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WHAT could authentic assessment look like in the classroom?

For four years I have been experimenting in my math classroom to replace percentage and letter grades with much more meaningful descriptive feedback.

There’s no shortage of percentage-based grade books for teachers. Punch in the numbers and out come the letter grades.
They don’t tell the student what they need to do to improve… they don’t even tell the student what it is they have achieved.

They just divert the student’s attention with a meaningless letter grade from the essential tasks of learning. The frustrated and anxious student is left vainly to plead for extra credit in a bid to get more nonsense points.

The challenge is to create a gradebook that is not based on numbers and letters, but records descriptive progress and gives the student the sort of valuable feedback that describes just what it is they need to do to improve their learning.

Well, take a look at this powerpoint and let me know what you think.

The system is based on student-friendly learning targets. Assignments and questions are all linked to a learning target.

Against each assignment and learning target the teacher can record and feedback to the student a description — ranging from Starting through Getting it to Got it — and add a suggested revision learning target plus a customized study skill tip.

It also records the student’s own self-assessment of progress.

And rather than add up meaningless percentages, the system summarizes to what extent the teacher and student agree on their assessment of progress.

It can show a matrix of an individual student’s progress. Or, it can show, color-coded, the progress of an entire class.

Input screens allow the teacher to add questions (+ pictures, diagrams and equations), new targets, target notes and assignments — and link them together in a host of assignment designs.

Win, win not fail, fail

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GRADING day, end of the first quarter. After a long day writing individual assessments, I have some envy for my colleague teachers who have been punching in percentages into their computers for the past few weeks.

As the email reminded us at the beginning of the day: hit the yellow button and the magic software will turn all the numbers into a grade and get the report cards ready for dispatch. Bingo! Easier than punching in 180+ grades and descriptive assessments by one-by-one.

I note one of my colleagues’ students has a percentage of 92.827. Well, that’s an A, then. To three decimal places!

Clearly the assessments that built this grade had not just 100 criteria, not 1,000, not 10,000… but 100,000. Some grading!

But what is this percentage of..? What exactly has our student achieved 92.827% of..? What, exactly, is being measured?

Percentages are a mathematical nonsense, unless they are of something. Just what did our student fail to do to miss out on the last 7.133%? Nothing on the report card gives an explanation.

Even being more sensible about the three decimal places (the very expensive software used across school district spewed those out, not I), just what would, say, a rounded 90% actually mean?

More important what about the student who got a 65% and got an F? What practical advice does the 65% contain to tell the poor unfortunate who has been branded a failure need to do to become a success?

The A, B, C, D or dreaded F may contain no help in specifically describing what a student has or has not learned… and certainly contains no help in telling a student what they need to do to improve. But it does label the student.

This might be ok for the (albeit stressed-out) student labelled an A or B… but it’s not so hot for the student labelled C, D or F. Labelled a failure… but given no clue as to what to do.

And, believe me, where these percentage-based letter grading systems are used with enthusiasm, then these numbers have been pinned up fresh every week in classrooms… raising stress levels in all the students weekly and forcing them to focus and re-focus… not on the joys of learning, but on the terrors of the grade.

You might get an A one week on your assignment. The next, you miss it. That means you’re at best 50% and failing wildly. There’s plenty of teachers who practice, and defend this as a perfect reflection of their students’ learning. You get a perfect 100% A the following week… that still does not lift you back up to passing!

You might be well on top of the learning… but you can’t meet deadlines = F! What’s important here?

So, what’s on your mind? The beauties of that Shakespearean sonnet or doing something desperate to scrabble together a few more percentage points? Or, just call it quits? You can’t win.

What if you are the kid who doesn’t get As? And you miss an assignment? And you work nights?

Is this education… or just a confusing nightmare? Life was much more fair in Catch-22. Welcome to school.

❏ So, what is to be done?

Drop the As, Bs down to Fs. Learn the lessons of pre-algebra and accept that percentages without a definable “of” are a mathematical nonsense.

Instead, describe in student-friendly phrases just what it is they need to learn, what they have learned, and what is the next achievable step they need to take to improve.

And give them as many chances as they need to do it, to learn. It’s the learning that’s important, whenever and wherever it finally happens. Not the grade.

That’s a win, win. Not fail, fail.

Working inside the black box

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YET MORE research is now available to confirm that alpha-numeric grading and traditional testing not only do nothing to promote learning… but actually lower achievement.

Since the late ’90s the team assembled around Prof Paul Black at King’s College, London, has steadily chipped away at the traditionalist approaches to assessment with their Inside the Black Box series.

“In terms of systems engineering, present policies in the US and in many other countries seem to treat the classroom as a black box,” Black and Dylan Wiliam argued a decade ago. “Certain inputs from the outside — pupils, teachers, other resources, management rules and requirements, parental anxieties, standards, tests with high stakes, and so on — are fed into the box.

“Some outputs are supposed to follow: pupils who are more knowledgeable and competent, better test results, teachers who are reasonably satisfied, and so on.

“But what is happening inside the box?” they asked.(October 1998 issue of Phi Delta Kappan, Vol. 80, No. 2.)

Their books and articles have since influenced tens of thousands of teachers and educational professionals around the world. But while their reasoning has changed both thinking and practice in the UK and Europe, it has yet to take a hold in US public schools which remain fettered by traditionalist, formulaic practice and teaching children to collect points.

Now Black, Wiliam and colleagues have produced a new series of slim pamphlets taking the argument further and giving specific advice and a wealth of teaching points tailored to key subject areas, with an overall summary Working Inside the Black Box.

The pamphlets, published by GL Assessment, focus on maths, english and science.

Working inside the black box means focussing on assessment inside the classroom with the priority of serving student learning: “It thus differs from assessment designed primarily to serve the purposes of accountability, or of ranking, or of certifying competence.

“An assessment activity can help learning if it provides information to be used as feedback, by teachers, and by their pupils, in assessing themselves and each other, to modify the teaching and learning activities in which they are engaged.

“Such assessment becomes ‘formative assessment’ when the evidence is actually used to adapt the teaching work to meet learning needs.”

Research experiments have established that, whilst pupils’ learning can be advanced by feedback through comments, the giving of marks — or grades — has a negative effect in that pupils ignore comments when marks are also given (Butler, 1988).

“These results often surprise teachers, but those who have abandoned the giving of marks find that their experience confirms the findings: pupils do engage more productively in improving their work,” says the Black team.

“The central point here is that, to be effective, feedback should cause thinking to take place… the assessment of pupils’ work will be seen less as a competitive and summative judgement and more as a distinctive step in the process of learning.

“The key to effective learning is to then find ways to help pupils restructure their knowledge to build in new and more powerful ideas… that learning was not a process of passive reception of knowledge, but one in which the learners were active in creating their own understandings. Put simply, it became clear that, no matter what the pressure to achieve good test and examination scores, learning cannot be done for the pupil; it has to be done by the pupil.”

Teachers in the UK involved in a two-year experiment demanded to learn more about the psychology of learning after working on such formative assessment practice in the classroom:”Learning is not just a cognitive exercise: it involves the whole person. The need to motivate pupils is evident, but it is often assumed that this is best done by offering such extrinsic rewards s merits, grades, gold stars and prizes. There is ample evidence that challenges this assumption.

“Pupils will only invest effort in a task if they believe that they can achieve something. If a learning exercise is seen as a competition, then everyone is aware that there will be losers as well as winners: those who have a track record as losers will see little point in trying.

“Thus, the problem is to motivate everyone, even though some are bound to achieve less than others. In tackling this problem, the type of feedback given is very important.

“Feedback given as rewards or grades enhances ego — rather than task — involvement. It can focus pupils’ attention on their ‘ability’ rather than on the importance of effort, damaging the self-esteem of low attainers and leading to problems of ‘learned helplessness’ (Dweck 1986).

“Feedback that focusses on the needs to be done can encourage all to believe that they can improve. Such feedback can enhance learning, both directly through the effort that can ensue, and indirectly by supporting the motivation to invest such effort.

“When feedback focusses on the student as a good or bad achiever, emphasising overall judgement by marks, grades or rank order lists, it focusses attention on the self (what researchers have called ego-involvement).

“A synthesis of 131 rigorous scientific studies showed this kind of feedback actually lowered performance (Kluger + DeNisi 1996). In other words, performance would have been higher if no feedback had been given.

“This is because such feedback discourages the low attainers, but also makes high attainers avoid tasks if they cannot see their way to success, for failure would be seen as bad news about themselves rather than an opportunity to learn.

“In contrast, when feedback focuses not on the person but on the strengths and weaknesses of the particular piece or work (task-involving feedback) and what needs to be done to improve, performance is enhanced, especially when feedback focuses not only what is to be done but also on how to go about it.

“Such feedback encourages all students, whatever their past achievements, that they can do better by trying, and that they can learn from mistakes and failures (see Dweck 1999).”

Quotes taken from:

Working Inside the Black Box, Dept of Education + Professional Studies, King’s College London by Paul Black, Christine Harrison, Clare Lee, Bethan Marshall and Dylan Wiliam

Mathematics Inside the Black Box, Dept of Education + Professional Studies, King’s College London, by Jeremy Hodgen and Dylan Wiliam.

❏ If this article was of interest, try… No prizes in points

❏ PiFactory’s descriptive grading rubrics can be found at: pifactory.net/catalog/assess_page_one.html

Rigorously challenged

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I WAS never clear what the word “rigor” meant. Mostly, it seemed to be used either by school administrators or by those teachers who seem to take pride in how hard their courses are. The no-pain-no-gain school of education.

A college professor teaching a math course I took last summer mused that he was also unsure what rigor meant, adding, “I think it means we write things down”.

Alfie Kohn tells, in his The Homework Myth, the story of a principal who was asked by a parent if his school provided a “rigorous” education. He hesitated, and added he was unsure until he’d consulted a dictionary. He returned and declared, “Good Lord, No!”

Inspired by this, I too consulted the definition of rigor even in that most traditional and quintessential US dictionary, Webster’s.

Ask me now whether or not my classes are rigorous and I would declare, “I hope not!”

Rigor dates from the early 1300s, the time of The Inquisition.

The Inquisition ruthlessly suppressed any creative or free thought, under the label of “heresy”, as well as the likes of a Galileo. Rigor in education seems to simply equate difficulty with quality. Difficulty for the sake of difficulty doesn’t seem to promote the enjoyment of free or creative inquiry.

I know teachers who boast of rigor in their courses. Some refer to other teachers as “the slacker teachers”. For them learning is about hard work, the harder the work, the better the learning. Kids get off too easy. The way to improve learning is to make it harder and then do repeatedly more of it. They point to their successes with pride but somehow seem to forget those who don’t make the grade. After all they didn’t work hard enough.

In this harder-is-better world, late or poor homework means an invitation to a mis-named after-school homework “party”. Failure to accept the invitation means a referral, detention.

It conjures up visions not so much of the 19^th century sadism of Wackford Squeers and the crushing of the pathetic Smike in Dickens’ Nicholas Nickleby, but certainly the pompous Blimber and his academy of Dombey and Son — “a great hothouse, in which there was a forcing apparatus incessantly at work.”

In the Dickensian Mr Feeder’s class, “they knew no rest from the pursuit of strong-hearted verbs, savage noun-substantives, inflexible syntactic passages, and ghosts of exercises that appeared to them in their dreams”.

Before that at Mrs Pipchin’s, Dickens describes the pedagogy as “not to encourage a child’s mind to develop and expand itself like a young flower, but to open it by force like an oyster”.

Difficult does not equal better. Difficult is a relative term. What is difficult for one student may not be so for another. What is difficult for a student this year, may not be 12-months down the line after the brain has gone through another year of development.

The question in the classroom should not be about difficult versus easy, it should be about finding what the Soviet educational psychologist Vygotsky called the zone of proximal development — that place between the actual development achieved by a child on their own and the potential development that they can achieve with the mediation of an adult or other students.

“The trick,” said Jerome Bruner (quoted by Kohn in The Schools our Children Deserve), “is to find the medium questions that can be answered and take you somewhere.”

Maximum difficulty isn’t the same as optimal difficulty adds Kohn.

Too easy and the student feels belittled, too difficult and the student feels stupid, alienated and likely to lose all interest in the subject.

Kohn adds this footnote: “One technique for finding just the right level of challenge for each student is so simple that few of us think of it: let the student choose. As long as the classroom doesn’t overemphasize performance, doesn’t lead student to think mostly about getting good grades or doing better than others, children will generally seek out tasks that are just beyond what they’re able to do easily.”

But in the rigorous classroom grades and sorting and ranking students are fetishes. Students who suffer the rigorists are never allowed to forget the grade, that’s the point. The percentages and grades are supposed to motivate, when in fact they do exactly the opposite.

Key to finding Vygotsky’s zone of proximal development is collaboration with other students or the mediation of an adult in a cultural context. This clashes with another rigorist article of faith, that a child should prove ability in the isolation of high-stakes tests, based on lessons that are taught outside of a cultural context.

Kohn quotes educationist, reformer and philosopher John Dewey; the value of what students do “resides in its connection with a stimulation of greater thoughtfulness, not in the strain it imposes.”

Parents would be better served by asking not whether a course is rigorous, but whether or not it is engaging and meaningful.

No prizes in points

WHEN I was training to be a math teacher in Britain some years ago there was a popular satirical BBC radio program called I’m sorry I haven’t a clue, presented by legendary jazz trumpeter Humphrey Lyttelton.

Humph arbitrarily awarded points for no apparent reason. The rules of the games were far from clear.

And although the audience shouted “points mean prizes…” on cue, no one ever knew what the prizes were. The only real prize for all concerned being an addictive dose of hilarious nonsense that was also a biting weekly commentary on current events.

Reflecting on the issue of grading, I’m reminded of this farce.

Three years ago I decided to completely abandon all grading based on points, marks, percentages or letters. The only numbers in my classroom would be in the math my students and I were working on, and not in any assessment. I felt naked.

But since then, this simple decision has lead me radically to re-assess everything that goes on in our classroom — from testing, homework policies, seating plans, late work, make-up work, behavior management to the really important question… the very essence of what it is my students and I are trying to achieve in our thinking laboratory.

Now my assessment focuses on observation, listening, discussion, collaboration and increasingly on students’ own assessment of progress. I hope the result is a focus on what we’re trying to think about in the classroom, free of the diversion of worrying about some ill-defined percentage.

The prize is the achievement of just trying to get it.

Feedback is verbal and descriptive, striving to help the student find some way of constructing their own meaning and paths to mathematical thinking.

I changed career to be a math teacher at the age of 50. UK educationists were encouraging new math teachers to abandon the traditional mark-book full of numbers. Numbers have no place in assessment and feedback in the math classroom was the argument.

It was summed up: Students who get nines and tens out of ten, nearly always get nines and tens. It may make them — and their parents — happy, but the points don’t motivate them to seek out new challenges or how to improve. They coast, complacently.

Those who get sevens or sixes… well, they’re passing. They just need to survive the you-could-try-harder talk. But how to try harder? To do what, exactly?

Those with the fives, fours, threes… confused, disappointed, frightened, feeling an inexplicable shame, they give up and cover-up as best they can. I was given a class into which such kids had been herded: “Hi,” they said, “we’re the dumb class.” I felt ashamed.

Numbers in assessment de-motivate, set student against student and encourage assessment as a process of ranking and sorting.

Adding some words of encouragement to the numbers also seems to make little difference. Students still focus on the numbers, despite their lack of any real meaning. Changing the numbers to letter-grades, doesn’t shift the focus to learning either.

Only when you take away the numbers, and letter grades, and replace them with phrases such as, “well done, now you need to work on… the distributive property” does motivation get turned round.

A target, a goal, something to focus on finally clears the clouds of confusion for the student. Now the student can see just what to do to improve. With student self-esteem no longer punctured by the stark moral judgement of a number or letter dripping with blood-red ink, students are free to focus on what they need to do to improve… and work cooperatively together to collaborate and help each other.

The business of parent conferences

LIFE is like a business the father was telling me and his child. As he warmed to his theme he lost me, so I can’t recall whether his child’s grade was part of the product-mix, the prospectus or the marketing plan. Certainly it needed to be factored into the matrix for the overall offering… viewed helicopter, in the big picture on a blue sky.

This week was spring parent-teacher conferences at my school.

First, they work better when they’re student-parent-teacher conferences, with the student taking the lead.

In my old school in the UK it was really a big point that the conference was student-centered and student-lead. It works much better. Students almost always know how they’re doing and what they need to do in terms of effort, attitude and the like. And when they say out loud what’s needed for them to improve, then it comes much more forcefully than if the parent or teacher was to say the same thing.

You could call it a student self-assessment conference.

It’s also a chance for the child to see the adults most concerned about them, sit together and listen to their point of view. The listening is important. Not all parents, or teachers, are good at that.

It’s also a great opportunity to get beyond just the disciplinary stuff that parents and many teachers seem obsessed with… talking in class, not listening to the teacher and other stuff like that.

Are you happy? is a good question to ask a kid at a student conference. Is it working for you? is another. Is there anything we can do to help? What do you think? And then listen.

Paul, the head of my old maths (with an ‘s’ in the UK) department once told me one of those secrets-of-being-a-good-teacher… once the kids know you’re on their side, then it’ll work. And he was right.

The fall parent conference, in particular, is crucial to telling a kid you’re on their side. The are-you-happy? question can go a long way towards changing the student-teacher relationship overnight. If before you were adversaries, then after teacher and student can start to be a team working together to help the kid.

Here in the US the parent-teacher conference can be obsessively grade focused.

Armed with pencil and list of courses, parents go from one teacher to the next to ask the single question: “What’s the grade?” This can then be followed by versions of the good-cop/bad-cop threat and bribe speech on the need to get/keep those grades up. The kid rarely wins. Even a good grade often ends in a speech along the lines of well-we-need-to-keep-this-up-no-slacking-off-now.

Last year I had a father and daughter. He had taken an evening class in business leadership I believe. “Right,” he barked in opening, “I’m taking control of this meeting…” Clearly, it was not expected that I would respond. “Grade!?” he shouted.

She sat next to her father in terror, her face quivering with emotion. Overwhelming fear, but with a look in her eyes that appealed, screamed at me, “what you now say could condemn me to absolute misery and pain for the rest of my life… and certainly as soon as I leave this conference.”

Normally, the grade question is my cue to deliver my I’m-not-so-concerned-about-the-grade-I-want-the-student-to-be-focused-on-what-we’re-learning speech. This time it didn’t seem as if it would work.

The student in question was an absolute pain to try to teach. She was funny, cocky, self-confident, mouthy… and completely focused on destroying any progress in my class till she’d had the last word. The secret, of course, was to work out how to let her have the last word… and move on. Not always so easy. She often just got chucked out of class. Somehow all our battles, tussles every other day now made sense.

“B,” I invented. “She could get a B if…” I tried to continue, but by then the father was delivering his own speech that B wasn’t good enough. The lie had not really saved her, and alas it did not in the end do much to save or help us build a new relationship in class. In the pantheon of win some, lose some… I lost her. So, I suspect, did her father.

But back to my own don’t-focus-on-the-grade speech. Well… it’s three paragraphs above, and then I give the parent a rubric describing what it is to be an A, B or C student. I ask them to give it to their child and ask the child to tell them what their grade is. The kids are usually far more tough on themselves than I. And the rubric is like a To-Do-List of how to improve. Most parents are intrigued by the descriptions and seem to like the idea.

There are formulae describing this:

Grades = stress

Stress = no learning

The point is, judgemental letter grades (destructive, and certainly meaningless in the absence of any descriptive definition) do nothing for learning. Non-judgemental descriptions provide a learning-centered focus. And so, do help learning.

One last aside before I conclude: Grades can only serve a useful purpose if they help motivate a student to build meaning for themselves. Grades, if they must be used, need to be divorced from the destructive rank-and-sort mentality that so obsesses much of the US corporate education system.

Such grading guarantees Fs… it is a system of success and failure. The fear of the F is what motivates the successes going. You can’t have the fear, if you have no Fs. The system depends on the Fs for its seeming success. Except, it is not successful. The Fs are branded, and the successes often have little clue how to think creatively or critically for themselves… only how to collect points and jump through repeated hoops.

Many teachers feel most comfortable with a handful of As, lots of Bs and Cs and some Fs. The teacher who gets this out of balance is held in suspicion. Ranking and sorting is part of the job. Except it isn’t. The job is to help every student find their success within. Every class should be a classroom of As… or, rather, a classroom of positive and individual and unique successes.

Grades should serve the learning needs of each individual student as if they were in a bubble. The grade should have no role in comparisons with other students. Which means, of course, grades are redundant.

Far better would be to replace letter grades with descriptions… as some more progressive colleges and schools are now doing.

Finale. Of course, it is easy to be sniffy about grades and grade-obsessed parents. But there are real reasons driving very real concerns.

Grades are linked to numbers. The numbers build up an average, the Grade Point Average (GPA).

Forget the learning. The difference between an A or a B or a C could mean the difference in a GPA that qualifies for getting a scholarship or not getting a scholarship. It could mean the difference between affording a respected college or less-respected college or no college.

The obsession goes on. It could mean the difference between a good job… or even no job. A house, a health plan.

GPA is sorting, ranking and competition in an unforgiving society committed to competition… with no safety nets. This is a society that lives in fear.

For parents, it’s the stuff of sleepless nights. And for students too.

After all in America, education, as well as life, is a business.

JJ’s knock-out question

JJ’s question was a bit of a knock-out blow. Not just because it left me stumped for an answer — nor because I didn’t have the self confidence to let a class discussion find the answer — but because… well, to be frank, I hadn’t thought up till then that JJ could ask this level of question.

My mistake. My assumptions. My ignorance. Sorry JJ.

We’d been looking at writing an explicit equation for an arithmetic sequence. We’d done the recursive routine, now we were finding the equation based on the n, the position of the n^th term of the sequence. Arithmetic sequences involve repeated addition — or subtraction — of a constant, the common difference.

Over several terms of the sequence I’d tried to demonstrate, in true traditionalist didactic style, that this repeated addition was the same as multiplication.

Out of the blue JJ asked, “does that mean repeated subtraction is division?”

Wow! We’d bashed away at inverses. The inverse of addition is subtraction, the inverse of multiplication is division… I could see where JJ was coming from. But I was thrown, I didn’t even feel confident enough to say that the answer was yes.

But if JJ asked that level of question, he didn’t want a yes, he wanted the explanation. He wanted to see it built up on the board. And he deserved his explanation.

This is what is called a teachable moment. Teachable moments are supposed to be gifts for teachers. They are also tests of teachers.

Well, I failed the test.

But I was determined to try to seize the moment, even if the moment was to go through a time shift… and a couple of weeks later JJ did get his explanation (see the end of this post).

It wasn’t so much about the question or JJ’s mathematical curiosity. It was about JJ’s belief that he could build some meaning for himself in a subject he would happily tell you isn’t his favorite.

I’d first taught JJ in Algebra 1. He wanted to get it. And he’d try, he really would, but getting three or four consecutive steps correct and then getting the right answer… discouragement was always near at hand.

It was the first year I’d started to think about and experiment with throwing grades — damned confidence and learning killers — out of the window. JJ so desperately didn’t want to get the F, but he just didn’t know how not to get the F he expected. It came up again and again… his mom. It wasn’t the fear of parental anger, but he just didn’t want to disappoint his mom. JJ felt unable to deliver.

That year, I announced: if you turn up, try, don’t smash up the classroom… there’d be no Fs. I can’t remember JJ’s grade that year, but it wasn’t an F.

First lesson this year, JJ was quick to re-check the rules hadn’t changed. Smiles, thumbs up… telling the class it was going to be cool.

Since then JJ has never had the facial expression of early in his first year with me… that look of overwhelming worry, the furrowed brow, has gone. Sometimes, too often, JJ the football star talks too much about football or basketball or something to do with balls. But some work comes in, and increasingly frequently the attempts to make contributions in class discussion.

And then came the question. JJ was thinking mathematically. And he felt sufficiently confident to form the thought and say it in front of a class.

On his end-of-quarter progress report, I can remember JJ got a B. But more important were the sentences on his report card describing that he’d demonstrated mathematical thinking skills. He came up and shook my hand and thanked me for the words… his mom had been delighted he said with a huge grin.

❏ Start at 0… repeatedly add 5

0 + 5 + 5 + 5 + 5 → 20

0 → +5 → (x 4) → 20

0 ← −5 − 5 − 5 − 5 ← 20

0 ← − 5 ← 5 ← (÷ 4) ← 20

Of course, repeated subtractions are multiplications. But division is also multiplication… multiplication by the reciprocal.

My colleague, Roscoe, said that multiplication counts the number of additions from zero… and division counts the subtractions back to zero.

Any other explanations out there?

Adolescence, a time for second, third… as many chances as it takes

EIGHTY-PLUS adolescent brains are walked into my classroom each day by their legs. The following 80 minutes working with each brain can be interesting, or just plain confusing, or maddeningly frustrating. On the whole it’s fun.

Then each evening plus weekends there are the two teenage brains that sometimes I find wandering my home. They slump by and crash through a door complete with a surgically-sprouting phone, or, they rush up and give me a hug and lift me off the floor. I’m ok with that.

So, when I found a copy of Why are they so Weird? What’s really going in a teenager’s brain in Portland’s famed Powells I was intrigued.

Its theme is that it is not just raging hormones that make many adolescents such joyful hard work to be around… new neurological research indicates that major changes in the growth of the brain during the teenage years may also be having a much bigger affect than previously thought.

As author Barbara Strauch reports, “most scientists working in this area today think that changes taking place in the brain during adolescence are so profound that they may rival early childhood as a critical period of development”.

She concludes: “Indeed, the remodelling of the adolescent brain — a brain that science had considered largely finished — spreads over such a wide range of systems we should rethink how we think of teenagers altogether.”

Since the late ’90s the advent of the MRI scanner has helped scientists peer into the adolescent brain, for the first time in terms of serious research. The pioneer of this research, Dr Jay Giedd, concludes, “we shouldn’t give up any teenager, there is hope.”

There are serious implications for education in this research. Perhaps the teenage years are too early for us to be labelling our young people as successes and failures. Probably these are the years for second, third… as many chances as are needed.

Jay Giedd, a neuroscientist at the National Institutes for Health, started scanning teenage brains in the late 1990s. Hundreds of them. He detected major changes in areas of the brain associated with logic, spatial reasoning, problem solving, language… and most importantly in the frontal lobes behind our foreheads.

It is the frontal lobes that guide our reasoning, decision-making, our judgement, our motivation, that help us plan ahead, that say stop that impulse isn’t the best idea. The frontal lobes are the chief executive and the police wrapped up in one. Developed frontal lobes are what make us grown up. As neuroscientist Chuck Nelson summed it up: “This is the part that tells you to count to ten before you call your mother old and stupid.”

Giedd found the frontal lobes — the very area that makes adults do the right thing — “are one of the last areas of the brain to reach a stable grown-up state”. He adds:”… perhaps not reaching full development and refinement until well past age 20″. It can be as late as 25 in boys. 25!

The teenage brain remains far from finished, says Strauch, “it remains a teeming ball of possibilities, raw material waiting to be synaptically shaped.”

Says Giedd: “If that teenage brain is still changing so much, we have to think about what kinds of experiences we want that growing brain to have.”

Yet the teenage brain seems to be growing in an ever-confined space. One Washington DC school counsellor told author Strauch: “We’ve simply made schools impossible for the regular kid. There are not enough options for how to be a successful teenager.”

A 16-year-old told Strauch the world was too black-and-white, with academic success the only barometer for success. “It seems you have to go to Harvard — or you will be a druggie and drop out.

“There don’t seem to be any in-between choices. People just talk about getting into a good college all the time; they pound that into you. They never talk about being a nice person or having a good marriage or a nice family.

“It’s all about grades. And there isn’t any room for mistakes.”

Giedd is unsure what influence we can have on the developing brain. “We may find out that all we can do is tinker around the edges…

“But we might find out that there are things we can do to improve things. My guess is that, if that is so, it’s going to turn out to be something we already know about.

“And we could find out that the way to make a better brain is not through four hours of homework.” Knowing what he does about the teenage brain, Giedd often lets his own four children decide for themselves how to use their own free time.

“What we might find out, in the end, what the brain wants is play… what if the brain grows best when it’s allowed to play?”

Bob Blum, professor at of the University of Minnesota, who has analyzed much of the data in the National Longitudinal Study of Adolescent Health concludes of the neural development of the teenage brain: “Ten years ago there was nothing. Now, I think it will be the frontier of the field for the next ten years. It will change the whole debate about adolescents. It will have huge implications for policy, for laws.

“It will change the whole way we think about kids. Forever.”

Assessment… it’s all in the tone of the voice

DARIO is one of my outgoing, great-fun students. Fabulous and generous sense of humor, and a little loud and a little mischievous with it. Dario is fun to work with. He also enjoys his math, works hard at it and wants to get it.

Dario was frowning as he tried to follow just why ¹/_x⁻¹⁸ is equivalent to x¹⁸.

We reviewed that x⁻¹⁸ is the same as ¹/_x¹⁸. So, ¹/_x⁻¹⁸ was the same as 1 being divided by the fraction ¹/_x¹⁸.

As earlier lessons had focused on the laws of exponents, I tried a different tack… thinking about 1 divided by ¹/₄. We drew a pizza cut into four and talked about the quarters and how four of them made up the whole pizza, and how that was like division, that ¹/₄ divided into a whole pizza four times. We talked about the pattern that seemed to be there, that the denominator of ¹/₄, became the numerator in the answer 4.

Clearly my flounderings were not helping Dario construct any meaning around all this. Everything screamed that he just couldn’t see it, did not get it. There was no light bulb flashing, or even, about to flicker. But Dario looked at the accumulated doodles and said slowly, “Oh, I get it.” I clapped him on the back and said words to the effect, “I don’t think so Dario, but don’t worry, you will.”

Dario’s friend, Joe pushes across the his work to solve 125^{2x + 4} = 25. Joe is more quiet than Dario.

Dario looks to Joe for help, but also asks probing questions. Dario doesn’t just want the answer, he does want the why behind the answer.

Joe laughs at Dario’s jokes… particularly if they’re good naturedly at the expense of the teacher.

I look at Joe’s work and start to venture that “the exponent…” But before I can get any further the paper has gone and Joe quickly says, “Oh, I get it” and smiles. The work comes straight back, the exponent corrected.

Assessment isn’t right or wrong answers in a test. It’s all in the tone of the voice.