From the New Yorker.

“I’m sorry, Jeannie, your answer was correct, but Kevin shouted his incorrect answer over yours, so he gets the points.” November 22, 2016





Disenchanting Student Assessment Part 1

What’s the big deal with student assessment?

In simpler times, student assessment/grading/marking or what have you seemed a fairly straightforward thing. Teachers assigned tasks. Students completed tasks. Teachers graded tasks. Assigned marks were amalgamated (“averaged”) to assign an overall grade for the student. Only in recent years have educators begun to wonder: What does “Janie got 75% in science” really mean?

Several possibilities come to mind.

1.       Janie understands and can perform 75% of the curriculum.

2.       Of the questions answered, Janie got 75% of them correct.

3.       The teacher judges Janie to be a very good, but not an outstanding science student.

It is a curious thing that before the 20th century, there was very little concern over how to interpret student marks. The public had a rough idea of what the scores reported, and life went on. In many jurisdictions, students were required to write external examinations for post-secondary entrance (e.g. the A-levels in the UK since 1918 and the Scholastic Aptitude Test in the USA since 1926), and herein begins the curious evolution of some modern ideas about student assessment.

Here’s an amusing interlude. It isn’t a history of report cards, as it is titled, but rather a personal reflection (with 19th century American Sunday School and Harvard thrown in for good measure).

I’m getting a bit ahead of myself. I want to make the next several entries about assessing student understanding and achievement. Of course, this assessment should ultimately be reported, but that’s not quite what I’m about here. It’s important though: we assess what we think is important, and we report what we think is important. But who is “we”? Therein lies a tale.

As in the video, we see that earlier student reports were mostly open comments from the teacher about things that they believe will be of importance to parents. Cooperation, hard work, personal characteristics were pretty darned important. But something changed in the middle of the 20th century. Report cards became more about academics and less about personal development. As in the video, my personal experience was that as technology became involved, teachers began using “canned” comments, and grades. The humans fell out of the picture.

In the first decades of the 21st century we are seeing an increased emphasis on reporting ONLY on the student’s performance relative to some standard (usually the approved curriculum) with comments about personal development expressly forbidden. The idea, rightly or wrongly, is that in the 21st century teachers should assess student performance and nothing else. All else is subjective and irrelevant to the progress of public education. Worse yet, it gives a platform to teacher biases, explicit or hidden.

As I go through the next few entries, I’ll look at what I think it means to assess student achievement. I’ll contrast this with a number of ongoing trends in assessment, and I will suggest that the teacher’s biases continue to be present in student reports, but in a hidden and subtle way.

Stay tuned. If you’re new here, I hope you’re stoked. If you’re an old friend, please forgive the delays that inevitable sneak into this blog.

Student Assessment—A Parable

Once there was a teacher called Sam. Sam always tried to apply life lessons to school and school lessons to life.

One summer, Sam decided to build a cupboard. The main body was completed to Sam’s satisfaction; all that remained was to cut the cupboard door, assemble the cupboard and stain it. Sam was excited.

After running the wood through the saw, Sam grabbed a measuring tape to make sure the door was just right. Imagine Sam’s disappointment at seeing that the door was ¾” too short!

After a few moments’ reflection, Sam remembered a student assessment session from the previous year’s professional development. Perhaps the measuring tape was faulty! Sam ran to the garage and grabbed every measuring device in sight. If ever there was a time to triangulate evidence, this was it!

Poor Sam! All 3 measuring tapes gave the same disappointing news. The square rule was too short, but with a pencil and some effort, it too showed that the door was not quite up to the acceptable standard. “Perhaps,” thought Sam, “this requires my professional judgment!” So, Sam looked at the door. It looked pretty good, but Sam was not quite sure.

Fortunately, Sam remembered a TED talk. Since all children are different, we should not measure them the same way. Same with doors! This was a breakthrough! The door was fine the way it was, and Sam had imposed a restrictive regime of testing that was preventing it from being properly understood.

Feeling liberated, Sam took his original measuring tape, and made a little kink between the 3” and the 4” marks. The door was perfect! All that was required was the understanding of the importance of individual differences.

Sam hung that door, and Sam’s family all smiled and paid compliments. If they felt that the door was in any way deficient, they kept that opinion to themselves.

Easter and Ishtar: A Little Critical Thinking

For the past several years, this meme has made the rounds at Easter time.


A number of issues come to mind:

  • What’s the point?
  • Is it true?
  • What is that amazing relief in the background?

The Point

Clearly the meme is intended to belittle and/or demean the Christian celebration of Easter. We see the “insider’s” poke at the fertility symbols associated with Easter—eggs and bunnies. It’s pretty obvious that eggs and rabbits are associated with birth, just as Easter is about rebirth. Perhaps some Christians haven’t thought too terribly much about it, but it should surprise no one that the secular celebration of Easter is associated with the symbolism of the religious observance. Of course, it’s always cool to throw the word “sex” into the discussion, so that those who missed the egg, rabbit, birth connection can play along too.

It seems to me that the mask is pretty transparent anyways. The new bit is the connection to the “Assyrian and Babylonian goddess Ishtar”. Again, this appears to be an attempt to discredit by association. It is true that there are symbolic, mythological and name connections throughout the Bronze Age Near East. This is an interesting phenomenon, worthy of considerably more space than I will give it.

Is It True?

It’s tempting to just google “Easter and Ishtar” and snoop (or should I say Snope?) around. Fair enough. From the point of view of critical thinking, this is one approach. Unfortunately, it tends to simply shift “I believe this meme” to “I believe this website” which runs the risk of not being very critical at all. (I think I’ll write about this another day. The question of the critical use of authorities remains interesting and educationally important.)

Let’s just apply a bit of logic to the meme’s central claim. The claim is that “Easter” is historically, religiously and linguistically connected to “Ishtar” and that the connection is explicitly connected to Constantine and the Roman Empire’s adoption of Christianity. Given that Constantine spoke Latin, you would expect the Latin word of Easter to be as close or closer to “Ishtar” as the English word. Not even close. In Latin, Easter is Pascha—a word recalling the Hebrew Passover. In fact, most European languages seem to have words derived from Pascha for Easter. Here’s a small sample:

  • Italian—Pasqua
  • Spanish—Pascua de Resurrección
  • French—Pâques
  • Swedish–påsk

No Ishtars in sight. Well not quite; you do see something that looks rather like “Easter” or “Ishtar” in German: Ostern. (Other Germanic languages such as Danish or Dutch have Pascha-related words; other languages, such as Polish or Lithuanian have words that appear unrelated to either. I leave that for the interested reader to explore.)

Easter and Ostern do appear to have something to do with the East, as does the name Ishtar, so at least we have that. But the claim that there is a straight line from Ishtar to Easter, running through Constantine appears to be complete rubbish. (It’s unlikely that Constantine spoke either English or German 😊)

That Amazing Relief

The image on the meme is from the British Museum. It is a fired clay relief known as The Burney Relief (boring) or The Queen of the Night (love it!).


In the dry British Museum style:

Rectangular, fired clay relief panel; modelled in relief on the front depicting a nude female figure with tapering feathered wings and talons, standing with her legs together; shown full frontal, wearing a headdress consisting of four pairs of horns topped by a disc; wearing an elaborate necklace and bracelets on each wrist; holding her hands to the level of her shoulders with a rod and ring in each; figure supported by a pair of addorsed lions above a scale-pattern representing mountains or hilly ground, and flanked by a pair of standing owls; fired clay, heavily tempered with chaff or other organic matter; highlighted with red and black pigment and possibly white gypsum; flat back; repaired.


Is it Ishtar? Maybe. If we can trust Wikipedia, there is some scholarly debate on that issue.


So what is my educational point? Critical thinking is important, it can bring a great deal of fun and entertainment, and it requires some patience and thought. In the case at hand, I asked two critical questions: What is the point? And Is it true? I’ll return to these another day. Often critical thinking exercises ignore the first and do a poor job of the second. I’ll keep these in focus for a while.

Until then, enjoy the season. If you celebrate Easter or Passover, let the depth and solemnity of the days guide you. If you enjoy a bit of secular chocolate and fun, enjoy that too. And enjoy the voluptuous sexuality of Ishtar or whoever it is depicted in the Queen of the Night relief.

Jump Math

Just completed our annual Teachers’ Convention. It was not particularly eventful for me, but as always, I walked away with something to think about.


1403816949849On Friday, I caught two sessions with playwright-mathematician John Mighton. Mighton is an interesting character. After an undergraduate degree which, in his words, left him with the impression that he wasn’t much good at anything, he put his energy into learning to write. He developed a modestly successful reputation as a playwright in Toronto, but still found by his early 30s that this was a tough way to earn a living. He made ends meet by tutoring kids and discovered that he was able to learn (re-learn) mathematics if he managed to break the learning into small, concrete steps. And he found that his pupils learned the same way. This led Mighton to graduate school and a career as a mathematician.

Somehow, Mighton maintained his interest in student learning, and put together the basic structure of Jump Math, which has grown to a not-for-profit organization championing Mighton’s vision and cooperating with university researchers to provide a research base to support, refine and change the program.

I’ve linked to the organization above, so I won’t repeat their basic information. Rather, I’ll recall and reflect on Mighton’s sessions.

Mighton hits on some themes that I’ve reflected on in the past—mainly the virtues of practice and mastery—but he takes it further. Jump Math is predicated on the principles that

·       Scaffolding is essential to learning.

·       The teacher is responsible for making the scaffolding increments small enough so that every student can make every move.

·       Every child must climb every rung of the scaffold before the class can move forward.

·       Success is its own reward.

·       Every child (with enough cognitive capacity for language) can make significant progress in elementary mathematics.

·       Competence precedes understanding.

On the one hand, this is a pretty unsurprising list of principles (do remember that this is my reading of the talk, not necessarily the voice of John or of the organization). On the other, it’s about as un-trendy as you can be in contemporary education.

Before I go further, a note about the Jump Math materials. You can buy stuff from them, but the teachers’ guides (Grades 1-8) are available for free on the website. Mighton emphasized that the student materials are quite uninteresting, as they are nothing more than overly-large practice sets. They’ll save you time and effort, but they are the least important part of the program. The teacher’s guides articulate the recommended scaffolding for the classroom lesson. If you only have one thing from Jump Math, Mighton says, make sure it’s the teacher guide. This seems eminently sensible to me.

So how might a teacher prepare a lesson utilizing the Jump ideas?

First you need to know where on the continuum of background knowledge and skills each child in the classroom lies. This is relatively straightforward. Mighton used the miniature whiteboards that are common in classrooms today. (Actually, it was a sheet of white paper inside a plastic folder; participants wrote in dry-erase marker on the folder.) The Do Now activity is simple and relevant to the activity. If today’s lesson, for example is the addition of simple rational expressions, then I need to know if each student is comfortable adding fractions. So I might put a simple fraction addition on the board, and ask each student to perform the addition on the white boards and hold it up. We’re talking simple 10-second stuff here. When each student holds their board up (no exceptions; no one is allowed to opt out) then you can see if you’re ready to move forward. If anyone requires attention, do it now. Again, you move together in a group.

Side note: it’s easy to see Mighton’s background in theatre. When an audience is unified, there is an energy in the room, that far exceeds the energy of individuals working separately.

The key part of the lesson is “what’s next?” When the simple addition is successfully performed, add a SMALL bit of extra complexity to the problem. The idea is that even fairly simple mathematics requires a surprisingly large number of small pieces for it to be sensible. If I am going from 2/3 + 4/5 to (x+1)/(2x-3)+5/(x-6), I should do it in baby steps. Make sure that every idea of common denominator, gathering of like terms, reducing fractions, etc. is in place. If I give all at once, I can be sure that some will get it (eventually) and some will not. The belief behind Jump is that everyone can and should get each step before moving on.

I’ll not belabour the lesson further, as I think the point of the lesson is reasonably clear. In a sense, I think every teacher is onside with much of the above, but there are still moments of uncertainty. Am I going to slow? Am I going to bore my brighter students? What if someone doesn’t catch on? Do I have time for all of this?

Of course, the answers to these questions are found in practice, not theory.

The other family of concerns is with the “richness” of the problems. There is a powerful movement in mathematics education that asserts that openness, richness and exploration are the keys to mathematical learning. I’ve looked at this in the past, with my reflections on a video by Dan Meyer. Mighton is even more skeptical than I am about the virtue of open problems for most students most of the time.

Ultimately, the sessions have provoked me to look harder at my scaffolding and to be more precise in my progression. I have always taught in a similar way, but I have not been as scrupulous as I might have been about always taking small steps and always ensuring 100% understanding before moving on. In my defense, I teach high school academic mathematics, and students are capable of storing anomalies for now, and resolving them later. Or have I been assuming too much? How big do these steps need to be? I will report back.

Finally, Mighton offers a view of inclusion that is curiously out of sync with most established views. In most of the literature on inclusion (see my earlier entries on UDL, for example) we plan for multiple entry points for students with multiple means of participating in activities at their own level. Jump suggests that this is excessive. Jump Math claims that we can harness the group dynamic (Weber’s “collective effervescence”) and differentiate by working together at all times. If this is so, then much can change in education—well, mathematics education at least. It is likely that this structured approach is well suited to mathematics because of its rigid internal structure; learning to read is likely a different sort of cognitive experience. But that’s a talk for another day.


Critical Thinking: UFOs

The press is having fun with the discovery that the Pentagon has spent a few million dollars checking out UFO claims.

Here’s a little video of Neil deGrasse Tyson talking about the program. In his typically witty way Tyson points out that the presence of unidentified flying objects does not imply that they are evidence of alien visitation.

It’s ok not to know. It’s just fine to suspend judgment. Admit that you don’t know things. But there’s a huge gap between something defying explanation, and its being explained by guesses like “aliens” or “gods” or “ESP” or “magic” or what have you.

Not knowing is ok. It’s what pushes us to look for evidence. Recognizing your limitations, recognizing that there is work to do, and actually doing the investigation is at the heart of critical thinking. When you have decent evidence, be prepared to revise your position. Easy to say. Sometimes not so easy to do.