Posts tagged ‘percentages in grading’

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.assess_screen_02
Assignments built from learning targets with student self-assessmentassess_screen_04 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.


December 14, 2008 at 11:14 pm 1 comment

No prizes in points

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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.

April 6, 2008 at 4:40 pm Leave a comment

The research gives testing an F

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FINALS week and the school goes effectively into something akin to lock-down. Students are tense, withdrawn, depressed. So are the teachers. For me it’s the most depressing week of the semester.

For the past couple of years I’ve managed to work round it completely. Instead of a final where students work in isolation for an hour-plus to show how well they cope with stress, I’ve organized sessions where students pick a couple of challenging questions from a packet and work collaboratively in groups to show their best work.

Each question is labelled with the math skill most needed. The kids are asked to pick questions based on the skills they’ve not fully understood during the semester.

The room has usually been buzzy with chatter. If they get stuck, I help out. When everyone has had enough the kids complete a form explaining why they should get the grade they think they deserve. Then we play chess.

The final grade is based on a descriptive grades rubric which the kids were given on day one of the semester. All work throughout the semester is graded on descriptive rubrics.

The policy of other teachers varies: Some run sessions which amount to little more than giving a quiz right through to the full-blown terror thing. 

Finals brings out the simmering discussion between the Skinnerite behaviourists who sincerely believe you train students to behave like learners in the hope they become learners…and constructivists who believe students construct meaning and learning for themselves and their teachers try to create the atmosphere where that happens. 

I’m a constructivist. And I don’t believe testing helps students create their own meaning which in turn becomes learning. In fact, I believe testing can be a crippling blow to the learning hopes of many pupils.

My aspirations are summed up by this brief section from Alfie Kohn’s The Schools our Children Deserve:

“… the best teachers do not rely much on paper-and-pencil tests because they rarely need them to know how their students are doing. Teachers who base their practice on a constructivist theory of learning are always watching and listening… this kind of informal assessment is continuous, making things like quizzes very nearly superfluous.

 “We might even say that the more a teacher needs formal tests to gauge student achievement, the more something is wrong. (With direct instruction, the teacher is talking more than listening, so traditional exams would be seen as necessary.)

“As parents, we shouldn’t be worried about teachers who rarely give tests; we should be worried about those who need to give frequent tests because they have no feel fo how their students’ minds work.”

So, unburdened by the need to spend hours with my red pen ticking and counting and working out percentages to many decimal places… I spent some time reading some research on testing.

The Assessment Reform Group, based at the UK’s Cambridge University school of education, has been in the lead in argueing for constructivist forms of assessment. Its pamphlet Testing, Motivation and Learning a classic. It reviewed 180-plus studies. It is tempting to simply quote the document in full… but here’s a representative selection of its conclusions.

Testing has a negative affect on pupil motivation.

The self-esteem of low-achieving pupils is particularly adversely affected by testing.

The testing ethos narrows the curriculum.

When tests pervade the ethos of the classroom, performance is more highly valued than what is being learned.

Repeated test practice encourage pupils to avoid responsibility and effort. It is detrimental to higher-order thinking.

Pupils should not be faced with tests in which they are unlikely to experience success.

“What emerges is strong evidence of the negative impact of testing on pupils’ motivation… Many aspects of the impact have significant consequences for pupils’ future learning. and thus are causes for concern.”

“One impact of the tests was the reduction in self esteem of those pupils who did not achieve well.”

“Pupils are aware of repeated practice tests and the narrowing of the curriculum. Only those confident of success enjoy the tests. In taking tests, high achievers are more persistent, use appropriate test taking strategies and have more positive self-perceptions than low achievers. Low achievers become overwhelmed by assessments and de-motivated by constant evidence of their low achievement. The effect is to increase the gap between low and high achieving pupils.”

“Lower achieving pupils are doubly disadvantaged by tests. Being labelled as failures has an impact on how they feel about their ability to learn. It also lowers further their already low self-esteem and reduces the chance of future effort and success. Only when low achievers have a high level of support (from school or home), which shows them how to improve, do some escape from this vicious circle.”

“When tests pervade the ethos of the classroom, test performance is more highly valued than what is being learned. When tests become the main criteria by which pupils are judged, and by which they judge themselves, those whose strengths lie outside the subjects tested have a low opinion of their capabilities.”

“The use of repeated practice tests impresses on pupils the importance of the tests. It encourages them to adopt test-taking strategies designed to avoid effort and responsibility. Repeated practice tests are, therefore, detrimental to higher order thinking.”

“The evidence suggests that teachers can be very effective in training pupils to pass tests even when the pupils do not have the understanding or higher order thinking skills that the tests are intended to measure. When test results are used for making decisions that affect the status or future of pupils, teachers or schools (‘high stakes tests’), teachers adopt a teaching style that emphasises transmission of knowledge. This favours those pupils who prefer to learn by mastering information presented sequentially. Those who prefer more active and creative learning experiences are disadvantaged and their self-esteem is lowered. External tests have a constricting effect on the curriculum, resulting in emphasis on the subjects tested at the expense of creativity and personal and social development.”

“The results of tests that are ‚”high stakes” for individual pupils have been found to have a particularly strong impact on those who receive low grades. However, tests that are high stakes for schools rather than for pupils (such as the national tests in England and state-mandated tests in the US) can have just as much impact.”

“Instead of motivation increasing with age, older pupils feel more resentment, anxiety, cynicism and mistrust of standardized achievement tests. Girls are reported as expressing more test anxiety than boys. Girls are also more likely to think that the source of success or failure lies within themselves rather than being influenced by external circumstances. This has consequences for their self-esteem, especially when they view their potential as fixed.”

“Feedback from the teacher that focuses on how to improve or build on what has been done (described as task-related) is associated with greater interest and effort. Feedback that emphasises relative performance, for example marks or grades which are formally or informally compared with those of others, encourages pupils to concentrate on getting better grades rather than on deeper understanding.”

The degree to which learners are able to regulate their own learning also appears to foster pupils’ interest and to promote focus on the intrinsic features of their work (15). Pupils who have some control over their work by being given choice and by being encouraged to evaluate their own work are more likely to value the learning itself rather than to focus only on whether or not it is correct.”

The research shows that the negative impact of tests can be reduced by ceasing to focus teaching on test content. It can also be reduced by ending the practice of ‘training’ pupils in how to pass the tests and by preventing the use of class time for repeated practice tests. Pupils should not be faced with tests in which they are unlikely to experience success.”

The ARG says do more of this…

q    Provide choice and help pupils to take responsibility for their learning.

q    Discuss with pupils the purpose of their learning and provide feedback that will help the learning process.

q    Encourage pupils to judge their work by how much they have learned and by the progress they have made.

q    Help pupils to understand the criteria by which their learning is assessed and to assess their own work.

q    Develop pupils’

understanding of the goals of their work in terms of what they are learning; provide feedback to pupils in relation to these goals.

q    Help pupils to understand where they are in relation to learning goals and how to make further progress.

q    Give feedback that enables pupils to know the next steps and how to succeed in taking them. Encourage pupils to value effort and a wide range of attainments.

q    Encourage collaboration among pupils and a positive view of each others’ attainments.

and do less of this …

q    Define the curriculum in terms of what is in the tests to the detriment of what is not tested.

q    Give frequent drill and practice for test taking. Teach how to answer specific test questions. Allow pupils to judge their work in terms of scores or grades.

q    Allow test anxiety to impair some pupils’ performance (particularly girls and lower performing pupils). Use tests and assessment to tell students where they are in relation to others.

q    Give feedback relating to pupils’ capabilities, implying a fixed view of each pupil’s potential.

q    Compare pupils’ grades and allow pupils to compare grades, giving status on the basis of test achievement only.

q    Emphasise competition for marks or grades among pupils.

For a constructive alternative to testing take a look at the ARGs pamphlet  Assessment for Learning:Beyond the Black Box.

There’s lots more at The Assessment Reform Group.

And Alfie Kohn on testing is an inspiring read.

You can get my grading rubrics and some further thoughts at The PiFactory assessment page.

February 16, 2008 at 9:20 pm Leave a comment

Why I no longer set homework

I NO LONGER assign homework. That’s now a decision. I’ve told parents and guardians and I’ve a brief document that I give to them. None have complained. Some have been effusive in their thanks. I think I understand why.

The question of homework, assignments, demands some serious re-reflection. In the schooI in which I now teach, for most students and for most teachers assignments are how you get the points which get you the grade. From what I understand, my school is not unusual. Indeed, I suspect it is typical of a US public school.

The assignments are mostly written work. They are often against strict deadlines. And they’re graded with a percentage. The final percentage, calculated in a computer, defines the grade. Percentage of what exactly is not defined. Real percentages are always of something. Otherwise, they are a nonsense.

So, a student who hands in one assignment and gets an A grade score of, say, more than 90 per cent (let’s forget margins of error, rounding errors and all that math stuff), but misses a second assignment ends up getting an F according to the computer. The tough teachers who value what they call rigor say it’s an F. Softies opt for a C.

After much thought, I say such assignments are discriminatory, are more about teacher control and, most importantly,  have little if anything to do with learning. As an assessment tool they are educationally criminal.

Together with points-based grading and testing, homework assignments are about training students to focus on collecting points and jumping through hoops. Homework belongs to the school of education that believes sorting and ranking is the aim of the public school system… labelling the F students to make the As and Bs stand out more starkly.

The system is discriminatory because it sets up swathes of students to be labelled as failures, the poor students, the black or hispanic students in particular.

I have students who go to work a second day as soon as the school day ends — not for pocket money, but as key income earners for the family. Many live in a culture of poverty which has profound respect for learning, but cannot deliver any of the requirements for quiet study. 

But it also discriminates against students whose learning styles don’t fit a narrow vision of training based on written work, reproduction of algorithms, deadlines and drill-and-kill. The majority of high school drop-outs are not the supposed least able, but among the most discriminating and thoughtful students.

It discriminates against young people struggling with hormonal fluctuations, sleep patterns over which they have no control, erratic front lobal development and all the hard-wired tribulations of teenagerdom.

For many the label of F for failure is branded before they even get started.

Such an education system suits students with access to the largely white middle-class, second-chance affirmative action programs of private tutors, articulate parental advocates and their vision of education as grade-based stepping stones to the safe gated-community of college and entry to the corporate careers of laargely white America. And that requires sorting and ranking, narrowly-defined successes and failures… precisely what points, testing and homework assignments deliver.

Sadly, some parents see homework assignments as some sort of symbol of the worth of a school. A school that does not set or value homework must be a school of slackers. It could not possibly be a place where the hard work gets done inside a vibrant classroom, and which values and respects the home and the private time of students and families alike.

Yet many parents will acknowledge the nightly hell of homework, the nagging, the denials, the tears, the slamming of doors, the simmering rows and breakdown in communication between tired and frustrated parents and their tired and frustrated children as conversation and human contact is narrowed to irritable interrogations about homework completion.

Instead of a stress-free chat about what interesting stuff may have been learned, the end-of-the-day communion between parent and child becomes an exercise in rewards, punishments and time management.

Many parents are angry at the nightly and weekend intrusions into family time.

They are angry that another worksheet and more busy work dictates the time of a tired family needing time to build and maintain the fleeting relationship of child and parent.

They are angry that with no say in the matter, a stranger can impose arbitrary demands in their home and effectively pronounce judgement on the moral worth of the family with a simple letter.

They are angry at how meaningless or simply impossible are almost all of the tasks set.

And they’re the lucky ones… for the students most ill-served by the points-testing-homework trinity of tyranny there is no end-of-day solace and comfort as parents are absent at second jobs or through poverty-driven family breakdown.

If any homework should be set, it should be for parents and childen alike to recall that four innocent people were hanged to death for demonstrating for the eight-hour work day.

Yet, there is no evidence that homework achieves any positive educational gain whatsoever. Indeed, if the evidence shows anything, it is that homework is destructive of learning.

Certainly, there are plenty of pundits — and politicians — who insist on the value of the discipline of homework. Their concern seems to focus on discipline. Here we must be grateful to Mr Alfie Kohn and his excellent The Homework Myth — Too Much of a Bad Thing for exposing the chasm between the conclusions of these charlatans and the actual evidence of their data.

At best homework seems to be set because it seems common-sense to assume that it must be good. But that homework is then used as a prime basis for assigning ill-defined labels on a child’s worth is scandalous.

My homework policy now reads as follows:

“Research indicates it does little to promote real learning, and frequently is a source of conflict in the home between tired and frustrated students and their equally tired and frustrated adult supporters.

“Occasionally I do assign a project to be done in school and at home over a period of time.

“Students are welcome to work on what we are doing in school… if that gives them pleasure or satisfaction, but not if it is a source of stress or worry.

“However, I do understand that parents are anxious to help their students… and may feel homework is a discipline that will help.

“If you want to help your student at home, the most effective way, in my view, is to ask your student to explain the ideas we are tackling in class. Talking math is learning math. Exploring the ideas, is learning math.

“Try to listen and not intervene. Ask a few mildly probing questions. If the explanation does not help you understand the idea, suggest your student raises the matter in class to seek a better explanation.

“Please, do not push the conversation to a confrontation or anything that is anything other than a pleasant conversation in the evening in the home. Please do not try to teach your student the point under question. Just suggest the student seeks a better explanation in school.”

And grading? I don’t use use points in any form. Instead I rely on a description of the grades, and the students’ own self assessment based on descriptions of what it is to be on top of a subject (the descriptions can be found on the assessment page at assessment at The PiFactory).

A factory worker works in the factory. An office worker in an office. My students work in the classroom… not at home.

For a more cogent argument against homework see re-thinking homework by Alfie Kohn. 


January 1, 2008 at 12:17 am 1 comment


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