My School is Going International!

Quite by surprise our school recently learned that there is a good chance that our school will be running an international school in Songdo, Korea. It will bear our name (along with International School Songdo), be governed by our board, and share our mission statement.

I am still digesting this and what it means for us. One interesting aspect is that our headmaster said that it would be a place our current students could go for an international experience and have a more seamless transition academically. However, the school will be using the IB curriculum which our school decided against several years ago. However, I, for one, thought the IB curriculum might be worth looking into. I am hoping that this may reopen that discussion at our school here in Southern California.

This will be an interesting time for our school.

Writing Comments

How do we encapsulate the whole of a students progress into a paragraph or two? That is what I am faced with at the moment as I struggle to finish writing a comment for each of my students. After awhile they all start to sound the same, and I feel obligated to make them sound different. In addition, I found at the beginning of writing my comments that I could be sure of what I was writing for each student, but as time progressed I found that the students start to blend together.

I need to figure out a better way to collect data to use for these comments so that I make sure I get them right. Some people say the parents are only interested in the grades, but as a parent myself I can’t believe that of most of them. Who would want to have their child only identified by one of five letters (with a plus or minus next to some) when they have a chance to know if their child’s teacher actually knew their child.

I was going to say there must be an easier way to do this. Then I reread the last sentence of my last paragraph and realized that maybe these are supposed to be difficult to write.

What is the point of grading students?

<I originally posted this at what was supposed to be my new blog – Mindful Teaching. I decided to keep this as my education related blog, though.>

First of all, let me make it clear that I am not asking why we assess students. These are two different questions in my opinion. What follows arose from an email/essay I wrote over 14 years ago when I was working with the Coalition of Essential Schools (So sad to see that Ted Sizer passed away recently!). I have updated some of it, but most of my questions remain the same.

There are multiple ways to determine how students will be assessed and what yardsticks are appropriate with which to measure students. Let us consider some of them.

If the point of grading students is to measure their own progress and abilities, is it not appropriate to completely individualize the goals for each student and grade them according to these goals? For instance, consider the chronically truant student. Might not a goal be for them to come to class on time and every day? Shouldn’t they receive an ‘A’ for meeting that goal? If we set the goal for a student who has demonstrated talent in a particular area to be to turn in exemplary work, shouldn’t they receive an ‘A’ for meeting that goal?

Now, if grading is to measure the amount of content a student masters, then it would be more appropriate to set certain criteria for all students and grade them against their ability to master those criteria. A student who masters all would receive an ‘A’ and those students who mastered none would receive an ‘F.’ Of course, this method fails to take into account individual abilities, home life, interests, social class, or career/college aspirations. This, however, seems to be the prevailing philosophy behind NCLB and the movement to national standards.

Thirdly, is the purpose of grading to compare students to each other? If so, then all we teachers need to do is present material, assess performance on the tests and assignments, and then compute final grades based on a curve. Half the students are above average and half below, and statisticians are happy. Of course, against what group do we set the norm? Within one classroom? By teacher? Grade level? School? District? County? State? Country? Obviously this is how standardized tests are already set up. Some, such as the ones my school uses, gives us several groups against which to measure our students. At the same time, test writers are less concerned about what the students know and more about do the questions provide enough of a “spread” to rank the students.

Fourth, do we approach this holistically and write a paragraph or an essay about each student describing their strengths and weaknesses in detail and not assign any grade. My school has done a simple version of this – although in conjunction with letter grades – and I know of other schools that only do this. However, with teacher loads of 60, 80, 120, or even 350 students (my wife had this for several years, so I am not making it up!) this is difficult at best and downright impossible at worst. Additionally, who is to say that my judgment is the same as yours or anyone else for that matter? Do we train teachers to make these judgments impartially? Who will train them and how? I know the AP does this for grading their exams, but that is one test a year (in each subject) and it is a gargantuan task. Besides, don’t we want individual differences between teachers?

Fifth, how do we integrate these disparate methods? Which method is appropriate for which situation, and how do we do it fairly? Is it enough to inform the students ahead of time and expect them (and their parents) to follow along? What if the students do not have the experience to trust that the system works? Any school should make conversations about assessments a priority on a regular basis. It is too easy to become complacent in the face of the day-to-day work of teaching.

One more important component to this whole discussion is what does the community think? Regardless of which method of assessing students is chosen (or some amalgam of the options), does the community understand and accept what the “grade” is telling them about their child? If not, what must be done? Should the school conform to what the community expects? Should the school do what it feels is right and expect the strength of its program to meet any arguments? Should there be a happy medium? Most would probably agree that a compromise is ideal, but who compromises and how much?

Although I wrote the original email on March 27, 1995, these questions continue to rattle around in my head. I left the school I was at when I wrote this email the following December due to enormous community pressure. I am now at another school where we deal with the spectre of grade inflation. I still struggle with what is the best way to assign a value to what my students have learned. In addition, I think that this discussion is not limited to the traditional A-F (or A-E) grading system. Any system that reduces the assessment to a single label (even rubrics!) fits.

Failure is Not an Option

It is a necessity.

Mr. Sweeney, over at Sweeney Math, takes a different stance, although my feeling is that we probably agree on the principles, but differ on how to accomplish things.

He says,

…in math especially it simply can’t be an option to let kids fail.  When I say “failing” I mean failing a test, or even just failing on an important concept within a test.  I’m not by any means suggesting giving students grades they don’t deserve, what I am suggesting is forcing students to deserve good grades in math.

I think there are two things in here that I do not agree with. First is the issue that we can’t let students fail a test, or a concept within the test. This just reinforces to the students that the goal of math class is to get right answers on tests. Yes, they may need to know the concept, but that is secondary to getting it right on the test. Students don’t want to hear that not understanding a concept will cause them difficulty in later math or science courses, or that it might limit their options when they graduate from high school. We, as teachers, have the experience to take the long view. The students do not. Their goal will be to get the answers right because their teacher will penalize them (their point of view) if they do not.

The second issue is that of “forcing students to deserve good grades.” Students are notoriously difficult to force to do anything. They need to be engaged and excited, and grades rarely (if ever) do that.  While definitely an extremist, Alfie Kohn makes some good points at his site, including,

Collectively, they [research studies] make it clear that students who are graded tend to differ from those who aren’t in three basic ways. They’re more likely to lose interest in the learning itself. They’re more likely to prefer the easiest possible task. And they’re more likely to think in a superficial fashion as well as to forget what they were taught.

I tend to agree with Mr. Kohn on this.

There is one other issue I have with Mr. Sweeney’s post. He states,

I agree that kids should be able to fail, but I don’t “let” them fail in my class.  The reason is because of how math is different than other subjects.  Math always builds.  That’s not to say there’s no building in other courses, but it’s more gradual, more encapsulated and there’s more chance to catch up.

This seems to be a mantra among math teachers. “Math is different.” You know what? All the subjects are different from the other subjects. Skills in history build, skills in English build, and skills in math build. And we teach too much already. Why have math textbooks in the U.S. taken to repeating material from previous years? Because we try to do too much and it doesn’t stick. I want my students to make mistakes and have time to learn from them – I have seen their understanding improve when I do this. Do I “cover” every topic I used to? No. But having taught the same students in courses that are 3-4 years apart I realized they didn’t remember a lot of what I had thought was essential in their earlier class. And I am not alone.

Of course, I do not disagree with everything Mr. Sweeney says. When he states,

…a kid fails my test on solving equations in algebra 1 and it’s totally his fault.  … if you ignore what the topic is and just look at what he did, does he deserve to fail? Sure.  Here’s where the problem sets in though.  If I just let it go here, I’m not just letting him fail.  I’m setting him up for failure.  Unless this kid is explicitly taught how to solve equations somewhere else(and he very likely won’t be), then I’m setting him up for failure in every following high school and college math class as well as Chemistry and Physics.

Of course there are essential skills that students need to master, and not helping them do that is a failure on our part. However, they need to try things, make mistakes, be given guidance, try again, and be given problems where knowing how to use these skills matter – beyond the grade on the test.

I fear that by not letting students learn that mistakes and failure is part of learning math that we set them up for dropping out of math when they first encounter failure.

Intuition & Math

Nearly two years ago I went to the workshop Teaching for Experience at the Master’s School in Dobbs Ferry, NY. David Dunbar, founder of CITYterm, runs the workshop. At the time he first introduced me to the idea of intuition in mathematics, but it took nearly a year and a half, a bottle of wine, and David for it to start to resonate with me.

As we talked about intuition, what it was, and whether it was teachable or not, I came up with a metaphor for what it looked like to me. Imagine a bag of puzzle pieces – the box with the picture long-lost. Intuition is seeing the pieces (and not necessarily all of them) spread on the table and being able to “see” the picture, and then using that image to work with the pieces and put it together. Obviously there will be missteps and wrong assumptions made, but as the pieces come together intuition guides where we should work next.

My revelation while having dinner with David (and several other teachers from my school) was that I already ask my students to exercise their intuition in this way in my classes. For years I assessed it through my “Problem Solving Tests” and now it is an integral part of my problem-based curriculum.

That being said, I have not been explicit with my students that it is their intuition we are trying to develop, nor what we can do to encourage that growth. That is what I am working on next.

Training (not teaching) students to perform skills may be a necessary part of the math classroom, but if we insist on doing this before we ask them to develop their intuition, they will never care enough to do so. If all Michael Jordan ever did was practice shooting baskets and was never allowed to play the game until he was deemed “ready,” I doubt he would have become the player he was. He developed his intuition by playing the game, and this led him to develop his skills so that he could get better. Math is no different.

As I research what it means to have and learn how to develop intuition in math, I will share what I find. Do you have any thoughts?