Tag: journal

Letting Students Personalize their Grading Scheme

How do you know if a student has mastered a subject? How do you get students to better understand how they learn and take more control of their education? I’ve been thinking that giving them more control of their grading might be the answer.

Test grades give some information, but experiments can be just as, if not more, informative. Much depends on the learning style of the student and how they express themselves. Verbally oriented might be good at processing written information and putting what they learned on paper. Kinesthetic-oriented students are likely to do better with practical demonstrations and labs that require movement and coordination.

Since there’s some merit to both exams and laboratory experiments – tests are good for checking the understanding of basic facts, while good labs require application of concepts – they have to be somehow added together to determine if and how well as student has mastered the topic.

Usually, the different types of assessment are combined with different weights. 60% of the total grade for a class might come from exam scores, and 40% from labs. But, given the different talents of different students, might it not make more sense to adjust the weights based on the specific student.

In fact, it would probably be even better to have the students decide for themselves on their own personal grading scheme. It could be part of a classroom contract.

Students would have a strong incentive to come up with their own most beneficial grading system, and, if you gave them a little time to understand the exam and lab requirements (say half a semester) before coming up with the weights, they’d have a lot of incentive to really try to understand how they learn best, and how to demonstrate that knowledge.

Once they’d made a decision on grading weights, they could then focus more energy on the parts of the class they find interesting, which, if we’re lucky, make them more motivated to learn the subject. Then they could set out to acquire the same information and concepts from what is to them a more interesting perspective, without having to worry so much about the stress of struggling through those activities they find difficult and tedious.

A student who is good at experiments might learn the facts in the textbook better if they were looking up information for an experiment – a big picture to little picture perspective – while a student who’s read and understands the text might find the experiments a lot easier to deal with (and so perform better) if they’re less worried about getting the perfect grade.

There would probably have to set some limits as to how much they could play with the weights, say plus or minus 15%, but individualized, self-assigned weights could be a very powerful way of tailoring education, especially in a context where grades are necessary.

A Few of My Unpublished 9/11 Pictures

Lower Manhatten on the evening of 9/11 2001.

I was sorting through my slide collection, while preparing for our recent move, and came across my binder of slides from New York on 9/11. These are actual, physical slides, organized neatly in plastic binder pages, not digital images.

If I remember correctly, I was just visiting the city that day, staying with my grandparents in Brooklyn. The visit was for work, I’d a post-doc lined up at Columbia and I’d lived in the city before, so I’d not thought to bring my camera with me.

So I walked into Manhattan, against the crowds turned out by the silent subways. Edging against the flux of humanity walking across the bridges away from the tragedy.

And I bought a camera, on the afternoon of September 11th, in a small shop somewhere around 32nd Street. The proprietor was sitting behind the glass cases, following what was going on outside on a small television set. Fortunately, the electricity and credit card system were still working. He was happy to sell me a good, used, fully manual Pentax K1000 (just like the one I’d left at home), and enough slide film to get me through the day.

I’ve always had faith in the strength and resiliency of New York. It’s where I’d spent my first four years, as an impressionable teenager, after immigrating to the U.S., but I would not have been able to harbor any doubts about those first, likely naive, impressions after that day. And this was without seeing or even knowing about the heroics at the World Trade Center. All I could see was the calm and matter-of-factness of the people on the street. Though the arteries had clogged, the blood of the city, its people, still flowed.

Nor was I the only one headed towards the dense clouds of smoke, made eerily attractive by the clear sunlight and pellucid skies of that clear September day. I don’t think I would have made it over the bridge if there were not a few other people, hugging against the railing, edging their way across. That infinitesimal trickle turned into a small but steady stream on the streets of Manhattan itself, which was then dammed up by the police line at Canal Street. Being unable to see anything from there, I turned left and joined the crowd this time as took me back across the Manhattan Bridge back into Brooklyn.

A flag flies over the Brooklyn Bridge.

I figured the opposite waterfront would be the best place of any for me to get any glimpse of what was going on. So, once across, I looped under the eastern side of the bridge and walked along the roads that edge the shore until I ended up in Brooklyn Bridge Park.

The picture at the top of the post is from the Brooklyn Bridge Park. I managed to get two major icons into the frame that are important personal symbols: a piece of the Brooklyn Bridge is on the right edge and, if you squint, you can see the Statue of Liberty (my favorite landmark) on the left. They’re a good reminder of the history and purpose of this great city. I also like that the picture captures the silhouette of the city dove, a graceful symbol of peace, standing against the roiling clouds of smoke, dust and turmoil.

Scaffolding and Peer-learning: Thinking about Vygotsky’s “Zone of Proximal Development”

When a student is struggling with a problem, and they just need that little boost to get them to the next level, they’re in Vygotsky’s Zone of Proximal Development, and it’s appropriate for the teacher to give them that crucial bit of help. The idea implies that students really have been trying to solve the problem so the help they get will be useful.

It also implies that the teacher can recognize precisely the help they need and deliver it, which is often easier than it sounds. As an adult, from a different generation and culture, and with more experience with these problems, I see problems very differently from my students. Indeed, experts solve problems by developing rules of thumb (heuristics) that speed problem solving by amalgamating large volumes of information. Unfortunately, for these heuristics to be meaningful, students often have to arrive at them themselves. Thus the student looking at the details is unable to communicate effectively with the expert who sees the big picture.

Peer-Teaching

One remedy Vygotsky advocated was peer-teaching. By letting students of similar but differing abilities work in groups, they can help each other: often a lot more effectively than a teacher would be able to. The teacher’s main interventions can be with the more advanced students who do not have anyone more knowledgeable to help, but who are best able to communicate with the teacher because of a smaller knowledge gap.

Practically, this suggests multi-aged classrooms, and a high level of vertical integration of the subject matter. Consider, for example, which topics from algebra, geometry and calculus might be appropriate for students from middle to high school to be working on together at the same time in the same room.

Scaffolding

Another, more typical, approach to this problem would be to provide all the extensive scaffolding – all the information including explicit demonstrations of ways of thought – that students need to get started, and then gradually take the scaffolding away so that they have to apply it all on their own.

In a high school laboratory science class, a teacher might provide scaffolding by first giving students detailed guides to carrying out experiments, then giving them brief outlines that they might use to structure experiments, and finally asking them to set up experiments entirely on their own.

Slavin (2005) (online resources): Classroom Applications of Vygotsky’s Theory.

In Combination

Elements of both these approaches are necessary – and they’re not mutually exclusive. The scaffolding perspective is most important when introducing something completely new, because they’re all novices at that point. But as you build it into the classroom culture in a multi-aged classroom where there is institutional memory and peer-teaching, then the job of the teacher evolves more into maintaining the standards and expectations, and reduces (but does not eliminate) the need for repeatedly providing the full scaffolding.

Building the Machine: The Role of the Teacher in a Montessori Middle School

With students working on different things at the same time, sometimes collaborating, sometimes working individually, a fluidly function Montessori classroom is somewhat akin to a complex but well-oiled machine: there are lots of individually moving parts that sometimes interact and sometimes not, in an ever-changing configuration. As a result, the job of the middle school teacher is less to convey information than it is to develop a successful classroom culture and ensure its efficient working.

Building the machine starts with the teacher as a role model. The teacher is a role model at all levels, but in middle school this takes on a slightly different color. After all, your adolescents are furiously figuring out how to be adults, so they’re taking a lot of clues for their behavior from the adults in their presence. The key things they’re looking for are, in Montessori’s (1948) words, “a sense of justice and a sense of personal dignity.” The trick is that underneath all the cynicism, they’re all idealists.

Justice is a particularly important and delicate concept because students want justice badly, but they tend to see it as distributive justice, where everyone is equal and get equal rewards and punishments. Unfortunately, this view tends to lead to an over-expansive expectation of rights and often to a sense of entitlement: the belief that if that person is getting something, I should get the same thing too. What’s too often missing, is the recognition that beyond the basic human rights, rights and privileges have to be earned.

This is something I find that I have to explain again and again for everyone to internalize what it means. It does not help that adolescents’ frontal cortex, the part of the brain responsible for critical thinking and impulse control, are not yet fully developed. What makes things even more interesting is the fact that girls tend to cognitively mature a lot faster than boys.

In addition, my own philosophy is that there are two key things I want to impart to my students: a love of learning and the willingness to try new things. This is somewhat contrary to where students are going developmentally. Adolescents tend to chase certainty as they change physically and mentally, all the while trying to establish their personal identities and place in the world; their focus tends to narrow toward what they’re good at and where their interests lie; there is “an unexpected decrease in intellectual capacity” (Montessori, 1948).

To encourage independence and creativity, and to build the sense of personal dignity through accomplishment, I sometimes break the pattern of the Montessori three-part Lesson (introduction, practice, application), and throw them assignments that they should have most of the background tools and knowledge to deal with, but have never encountered in this particular way. The Student Run Business is great for this, as unexpected problems are always cropping up, and, in case of emergency, it’s easy to create extra problems and challenges if you need to. When our bread-baking ovens started acting up, the oven calibration provided a great opportunity. It needed to be done, and students could figure it out on their own. Mostly. Eventually.

Developing a good classroom culture is probably the hardest challenge for those new to Montessori, especially with early adolescents who tend to have their own ideas and know everything already. However, with a few carefully designed lessons and exercises, the machine takes care of most of the teaching and learning of math and science and social studies and whatever else the curriculum requires students learn, peer-teaching and collaborative learning are all part of the classroom culture. The best part though, is that, once well established, the teacher ends up with a lot less work to do, and with a culture that propagates itself from year to year in our multi-aged classrooms.

So while we want to create a well organized, fluidly functioning classroom, it’s sometimes useful to introduce a little extra friction to keep things interesting. Of course, most often you don’t have to do this yourself. A lot of friction will come from the students themselves, and then the trick is anticipating it, allowing students the chance to deal with it, and then finally using it as a lesson so students learn from their experience if it gets beyond them. All the while, you must recognize that your every word and action is being carefully scrutinized with an eye for justice, even though you and they may not have the same definition for the word.

References

Grazzini, C., 1996. The Four Planes of Development, The NAMTA Journal, 21 (2), 208-241.

Montessori, M., 2005. From Childhood to Adolescence, The Montessori Educational Research Center, Trans. New York: Schocken. (Originally published in 1948).

Moving on

Break, break, break,
On thy cold gray stones, O Sea!
And I would that my tongue could utter
The thoughts that arise in me.

–Tennyson (1842): Break, Break, Break via the Poetry Foundation.

I feel as if I’ve been posting more poetry than normal. I know I’ve been reading a lot more. It’s a habit I fall back into at major transitions. I’m leaving Lamplighter Montessori in Memphis and instead of doing everything in the Middle School, I will be taking a more Math and Science oriented position at the Fulton School at St. Albans near St. Louis. I’ve really enjoyed being the Middle School teacher at Lamplighter, so it is hard to leave, but the hardest part of moving on is that, in my multi-age, single-teacher classroom, there are seventh graders who I won’t be able to take through the full cycle.

It’s particularly hard because I’m leaving behind an exceptional group of students that any teacher would love to have in their classroom. They’re kids who love to learn, are serious about their work, and are well-balanced, “normalized” Montessori students; the epitome of constructivist education. For this reason, I know they’ll do well, which is some consolation (I also have a lot of confidence in their new teacher), but I will miss not being able to work with them.

Saying goodbye to the graduating students was also more difficult than I expected. There’s always some sadness in seeing them move on, but it is part of the normal progression of things, so it is a sweet sorrow. Now, however, my moving to another city introduces another element to a naturally traumatic change, especially for the kid who have had a harder time making the transition. Part of the safe anchor back to middle school, which some students need during that first year of high school, has become untethered.

At least, with the blog and email it is harder to loose all contact, but electronic communications cannot always satisfy the need to know that there is something, somewhere, safe behind you, somewhere that will provide a little unconditional positive regard we all need sometimes. Admittedly, this is often an illusion, institutions evolve, but I think it is a useful fiction we all need sometimes.

There is a lot to commend my new position, which I will undoubtedly be writing a lot about over the summer as I prepare classes, but after talking to my students individually today, I feel like I need to take a moment to reflect on what has been a few, wonderful years. Hence my need to resort to poetry.

At the Closing of the Year

‘Tis true, the stuff I bring for sale
Is not so brisk a brew as ale:
Out of a stem that scored the hand
I wrung it in a weary land.
But take it: if the smack is sour,
The better for the embittered hour;
It should do good to heart and head
When your soul is in my soul’s stead;
And I will friend you, if I may,
In the dark and cloudy day.

— Alfred Housman (1896): from A Shropshire Lad via USCC.

Power Down and Disconnected

Like addicts racing to get their overdue fix, my students raced to the computers this afternoon after having had to survive all day without power and without the internet. I’ll confess that I felt the same urge, but was able to restrain it. Until now.

We usually don’t have internet access during our immersions, but then it’s expected and students are not inside needing to refer to the study guides to figure out their assignments. At the beginning of the year I gave everyone paper copies of the study guides, but now there are just a core few who request them.

Fortunately, we had a couple of smart-phones so one student would look up the reading assignment and post the page numbers on the whiteboard. Fortunately, the reading assignments were out of the book.

We weren’t quite surviving without technology, but it was close, and students were getting innovative.

We’ve had storms every few days for the last couple of weeks, which is typical for Memphis at this time of year. Over the last few days a frontal system has just been pushing back and forth over us. When it pushes south we get a cold front with thunderstorms and rain, but clear skies afterward. When the front pushes north it gets warm and humid, and the sky goes overcast for most of the day.

Weather map for Wednesday, April 20th. The blue and red line passing through the southeastern U.S. show the mixed warm and cold fronts that have been oscillating past Memphis for days. Image from the National Weather Service.

This line of fronts marks the general location of the sub-polar low, which is moving north with the spring. But more on that tomorrow.

Epic Rain-Garden

They're making dirt-angels, actually.

Talk about a long day! (“What an understatement,” she says.)

The 'before' picture.

We moved about 45 tons of sand, gravel and compost today, filling in the moat we dug last week. We were lucky enough to have the help of a backhoe for the digging, but all the filling in today was done by hand, with shovels and wheelbarrows.

Digging the moat.

Despite rumors about it being a first line of defense against the Cordovan barbarian hordes, the moat was actually intended to become a rain garden, which was designed by the Rhodes College Hydrogeology class to intercept some of the runoff slope that funnels water directly down toward the school during the intense rainfall that we get with our spring and fall mid-latitude cyclones.

So we had to get rid of the heavy, dense, silty-loam soil that is really slow to let water seep through, and makes it hard to grow anything on the Memphis side of the Mississippi River. The fine grained silt was blown over from the Mississippi River floodplain about 20,000 years ago when the ice-age glaciers were melting and all their ground up rock flour was being washed down the Mississippi. This type of wind-blown sediment is called loess. I like the sound of the word because if you stretch out the “oe” properly it does something to the back of your throat that feels distinctly German; however, if you ask someone from the deep south to pronounce it, you’ll hear the name of Clark Kent’s girlfriend.

Middleschooler pushing a wheelbarrow full of silty-loam.

The backhoe dug two trenches, each about 2 m wide, 6 m long, and about 60 cm deep, and piled the soil up next to the holes. Moving this stuff is not trivial. My middle-school students gave it a try on Friday afternoon and though they made a small dent, there is an awful lot more to do (my students also helped figure out how long it would take to finish pumping out Friday morning’s collected rainwater from the trenches).

Five cubic yards of pea gravel.

Then, on Saturday, with large piles of the old soil still sitting there, we replaced the impermeable loam with a fifty-fifty mix of sand and compost, underlain by five centimeters of pea-sized gravel on top of five centimeters of crushed limestone. This material was delivered by dump truck on Friday afternoon, while school was still in session. It was loud, exciting, and according to one member of the pre-school aged audience, “the best day ever!”

Enjoying the 'best day ever.'

I have to agree. It was kind-of exciting. Although for me, the bright, brown pile of pea gravel evoked fond memories of pyramids of powdered curry, saffron and tummeric sitting on the spice-seller’s stall in a market in Morocco .

Rhodes students slacking off (after lugging soil and gravel all day).

For others the pea gravel was a more tactile experience: snuggling into it, after a hard day’s work, appeared to be quite therapeutic.

Girl Scouts taking a well earned break.
Middle school students slacking off (after ...?).
Hauling silty clay.
Dr. Jen raking in the first of the gravel in the not yet drained pit.
Wagon team.
Team Z. on the top of the mound.
Gravel tossing.
It begins.
Mixing soil.
More mixing.
Grading.
The last of the pile. Job well done.

To be continued…