Tag Archives: new ideas

modphys 32/180: Atomic Model

On a superficial level, atomic scattering of alpha particles is a simple process to understand. My students have usually been able to repeat back the main observations and conclusions: most alphas pass straight through but few are significantly deflected, so atoms are mostly empty space, with a small, hard nucleus. However, I have always suspected that my students didn’t really understand how the experiment worked theoretically, nor why this complex system was required.

Last year, I began to use a simulation in which I hide an object under a board and have students try to figure out what it is by shooting marbles at it.

image

I use blocks to hold up the edges or the board. It is good for these to stick out a bit so the students don’t conflate their effect with that from the hidden object. For objects, I have tried a number of things. A water balloon or barely-unflated rubber balloon provides a good elastic collision. A heavy round mass is good too, but produces a distinctive tink, which sort of ruins the mystery. One good way to get an inelastic collision is to increase the rolling friction in a region by putting down a piece of thin felt or newspaper. The former represents the Rutherford atom, while the latter is more of a plum pudding model.

It is hard to assess the effect of an activity like this, but it seems to me that my students have been able to talk more cogently about the Geiger-Marsden experiment when they do the hidden object activity first.

A problem we run into is the direction the marble flies out of our clumsy hands. I think I will try to make some launchers, similar to what you would find in a pinball machine. Such launchers could also be good for studying projectile motion.

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A Student Research Journal

I’ve just published the second volume of Three Stars, a journal of student research that I created and edit. My goal is to create a forum for students to share their investigations with the broader school community, to take pride in their scientific work, and to encourage students to try going to the next level with their science projects.

I had originally planned to publish twice annually, but since we’re a small school there really hasn’t been enough work in the autumn. I rely on a few of our students’ Group 4 (integrated sciences) projects, which take the form of single-page “letters”. Longer “papers” are derived from lab reports, the extended essay, and other internal assessments. If you don’t know what these things are, you’re probably not an IB teacher, but it doesn’t matter: they are all science-y projects.

When I first created the journal, I ran into some conflicting ideas about what the publication should be. The English teacher thought it might be partly a literary magazine and feature creative writing, for example, and I’ve yet to convince any of our humanities teachers to encourage their students to submit work. Currently, we’ve published physics, chemistry, biology, psychology, computer science, and mathematics — that feels about right.

Probably the most difficult part is getting the student work, which usually consists of awkwardly-written prose in a specific hard-to-parse format, into a shape that looks and scans well. I’ve adopted stylistics similar to those of Nature, and I think the result looks quite good. It’s certainly more approachable than APA or MLA… although since our middle school is adopting an MLA use policy, I might need to start using MLA-style citations in the next volume.

Once I’ve compiled, formatted, and copy-edited everything, I go to a local printer and have a couple dozen copies run off in booklet form. I try to get a nice picture (either student artwork, or science-related photography) for the cover. I registered the journal with the international organization that does such things, and so we have an official ISSN, although I haven’t created the appropriate barcode yet.

You can see an electronic copy of the journal on its web site or, if you’re at my school, there should be a copy at the front desk to peruse.

Weekly Email Update

Over the past few months, I’ve been trying to do a better job of helping my students see the “big picture” view of what they’re learning. It’s easy to get bogged down with particular equations or specific problem types. I want my students to know what they’re study, and why, at all times.

One way of meeting this goal is to send out a weekly email update. In addition to assigning homework, delineating support and extension readings, and restating the major ideas and themes, I try to give a picture of how this topic fits into the larger panorama of science, math, or human knowledge.

The advantage of doing this via email, as opposed to posting it on the class website, is that students are already comfortable with the email reading apparatus. They’ve also incorporated it into their lives. I want my students to reflect on the value of set theory at precisely the time when they’re relaxing after dinner, or riding the bus home from school — not while they’re elbow-deep in homework.

Further, by putting the homework assignment into email (as opposed to posting it online), it is accessible in a familiar way. I don’t need to worry about students having difficulty accessing it, not looking at it until the last minute, or conveniently forgetting they have to do it. Simply by typing my words into a different box, I’ve moved the out-of-class portion of my class from a passive to an active form of communication.

The students have responded to it, too. During class today, approximately half of the students had read and thought about a syllogism I’d written at the bottom of the email update I’d sent the previous evening (formal logic starts next week).

Points for Grades

During the summer and autumn, I became interested in “gamification” approaches to education. The idea is to use the psychological tools and strategies commonly found in video games to make education more effective. There are numerous problems with this approach, if taken at face value, but I think there are lessons to be learned.

One common feature of video games is the idea of points. Cookie Clicker is a game that consists entirely of accumulating points by clicking the mouse (or purchasing upgrades using points), and it is fiendishly addictive. I wanted to try replacing my traditional grading scheme with a points-based system. The use (or abuse) or such points-based systems is often called pointsification.

The Process

For my Math Studies classes, we used the following system to generate quarterly grades:

100 points (max) for weekly quizzes
50 points (max) for weekly homework
35 points for serving as the class Scribe or Artist [to be explained in a future post]
10 points for attendance, thrice weekly
and bonuses worth between 10 and 200 points for optional extra assignments

Before the quarter began, I calculated a grade scale based on the IB system of 1-7 points.

7 is the point equivalent of 100% on all homework and quizzes, and perfect attendance
5 is the point equivalent of 70% on the homework and quizzes, and perfect attendance
3 is the point equivalent of 0% on the quizzes, and perfect homework and attendance
1 is the point equivalent of 0% on the homework and quizzes, and perfect attendance

Our school uses PowerSchool for grading and attendance, but the PowerSchool GradeBook package isn’t able to create the sorts of progress bars and reporting that I wanted. Thus, I did my grading in a Google Spreadsheet.

Screen Shot 2014-02-08 at 8.52.14 PM

Some of the students’ grades appear in columns J to O in this image. I’ve “frozen” rows 1-2 and columns C-D, which is invaluable when scrolling around a large spreadsheet. The green boxes (above the blurred-out students’ names) indicate the total cumulative points so far.

After the first quarter, two of my students suggested that I include some guidance as to what is a satisfactory grade during the middle of the quarter. In other words, after three weeks, is 400 points good? Column P is my solution to that problem: it is a running total of the maximum scores for all attendance, homework, and quizzes. The current “maximum” score appears in the red box.

Our school uses Google Apps for Education, so I have a Google Site for each of my classes. On the site for this class, I created an individual page for each student. With a few clicks, I’m able to make these pages viewable only to the student and myself.

Screen Shot 2014-02-08 at 9.08.43 PM

Now, I inserted the points and target cells from the Spreadsheet into the page of this Site, using a process I put together previously.

The progress bar is done differently, as Google Sites have a built-in capability for inserting charts from a Spreadsheet into a Site. Creating the progress bar required a bit of playing around: it’s a stacked horizontal bar chart, with the grades (column Q above), grade bounds (column R), and the total number of points as (respectively) the three data series.

The Results

Without a control group, I cannot draw a conclusion from this experiment. Instead, I’ll list a few ways in which this points-based approach seemed to change the learning process:

  • It was new. Students always seem to have some enthusiasm for newness, and that was apparent. There was a great deal of curiosity when I first explained the system, and I think the reaction to the individualized web pages with the progress bars was something like, “that’s cool.”
  • Progress was clear. I was careful to stay up-to-date with my grading, and most of the time I got the points updated within a day or two. That meant the students had a (nearly) real-time picture of how they stood in the class, and they could see the result of their work visually. I think this was appreciated.
  • A couple students relied on last-minute bonus assignments (especially the 200-point project of creating a video solution to an exam-style problem) to boost their grades at the end of the semester when they realized they could go from a 4 to a 6 with a few extra hours’ work. I wasn’t unhappy with this, although allowing such an approach isn’t promoting efficient time management.
  • For the “slackers”, it didn’t seem to provide much benefit, as their attendance and grades continued to be poor.
  • It was more work for me, both (a) to create and maintain the individual sites, the points  box and progress bar, and (b) to maintain a careful record in a spreadsheet in addition to PowerSchool. While there was clearly a reward, in increased student understanding and motivation, I think I could have used the time more effectively by planning more-engaging learning activities, conducting after-school tutoring with struggling students, and so forth.

Ultimately, our program coordinator decided that all grading should be done, and published for student access, on PowerSchool. Thus, I had to stop my pointsification experiment after two quarters.

Idea: Students create charities

In my view, empathy is the most important skill we should be teaching students (see Jackie Gerstein’s excellent post).

  • In the IB program, doesn’t “internationalism” just boil down to empathy + geography class?
  • The increasingly-networked world will require increasingly-sophisticated emotional competences (ie: the opposite of YouTube comments)
  • The gap between rich and poor seems to be growing in nearly all countries

Here’s the idea: give each student some seed money to start and run a charity. This can be connected to class content by requiring a business plan, promotional materials, a mission statement, a cash-flow model, etc. It might be best to hold on to the cash until the students have laid all the groundwork.

I started this project with my senior math class, but it looks like we won’t have the time to carry it through to completion with looming exams and conflicts from other demands (university applications, etc). Nonetheless, I was very excited with the progress we made. Here are just a few of the students’ ideas for how they would leverage €100) to create a lasting change in a community they cared about:

  1. Set up an after-school art program for local kids, and sell their work to tourists during the summer.
  2. Use the start-up to print t-shirts saying “I love dogs”, then sell the t-shirts at school and use the profits to buy vaccines for a local animal shelter
  3. Create an activity day to bring together kids from different schools in the local community
  4. Use kiva.org to make microloans

I think that a bit more time would have streamlined and fleshed out these ideas. Maybe next time.

Idea: Pythagoras Cult

As a math teacher, I’m all too familiar with the phenomenon of students learning, and then promptly forgetting, concepts and skills in maths. In fact, our system of teaching maths — revisiting the same concepts year after year after year — seems to be predicated on this very principle. It seems like such a waste of time, of energy, and of instructional headwind.

Thus, I’ve been wondering lately how math teachers can make the key concepts more “sticky”. I’m referring to Malcolm Gladwell’s popular book The Tipping Point, in which he analyses attempts to make key ideas “stick” in the minds of an audience (summary). The memorable example involves Sesame Street and Blue’s Clues, two American television shows that were designed to be “sticky”.

Sesame Street simplified and highlighted key concepts, used colourful muppets, and produced carefully-timed segments. Blue’s Clues, the successor, appears in shorter episodes, with simpler characters and purposefully abrupt dialogue that is designed to draw in the viewer.

Here’s my idea for making Pythagoras’s theorem sticky: Once a class has been introduced to the concept, and learned how to use the basic formula to solve simple problems, the teacher will host an initiation in which students are inducted into a secret society of Pythagoreans.

Pythagoras did, in fact, establish a sort of cult that was part school, part brotherhood (but inclusive of both genders*), and part religion. They were secretive, yet venerated mathematics. A famous tale about a student discovering the irrationality of the square root of 2 may help to illuminate the Pythagoreans, even if the story is invented.

The initiation ceremony should be secretive and it should require that students demonstrate a knowledge of Pythagoras’s theorem. I think it would also be great to make a web site for students to share Pythagorean artwork, proofs, and so forth.

This will be memorable, surely. If we ensure the maths takes center stage, it might also help students to form lastings understandings of this key concept.

* There is very little written record about the activities of Pythagoras and his followers. One clue comes from this description of Plotinus, a sort of academic leader who identified with both the Platonic and Pythagorean traditions, as recorded by Porphyry (source (line 9)):

Several women were greatly attached to him, amongst them Gemina, in whose house he lived, and her daughter, called Gemina, too, after the mother, and Amphiclea, the wife Ariston, son Iamblichus; all three devoted themselves assiduously to philosophy… Not a few men and women of position, on the approach of death, had left their boys and girls, with all their property, in his care, feeling that with Plotinus for guardian the children would be in holy hands. His house therefore was filled with lads [and] lasses…

If this is true, it’s a stunning reminder that the patriarchal inclinations of Western history were not absolute. Here’s some background about our developing understanding of gender role in ancient Greece.

 

Scrum Education

Last spring, a visitor to our school introduced me to the Scrum framework for software development. The name “scrum” (borrowed from rugby) represents the goal of getting a group to push together for a short burst of time. Here are some highlights of the Scrum method:

  • Goals are prioritized and assigned estimated completion times
  • A handful of goals are chosen for a “sprint” that typically lasts two weeks
  • The team meets daily to resolve issues
  • Progress is tracked using a “burndown” chart (more below)
  • Once the sprint has been completed, the process begins again

The most interesting part of this, from my perspective, is how the burndown chart provides a clear picture of the team’s progress. Could I do something similar with student assessment? It turns out that Google Apps for Education [GAFE] allows you to do this, although not easily.

I started by creating a Form containing questions lifted from, and inspired by, the IB Physics course guide (ie: my content standards). The example below is a knowledge question; other questions required that students applied their understanding of concepts or employed formulae.

a

The results from that Form are saved automatically on a Spreadsheet in Google Drive. I use the Spreadsheet to create the burndown chart using the following process:

  1. Copy all the data to a new sheet, so I can add new columns, ie:
    =arrayformula(‘Sheet1’!A1:L99)
  2. Create 10 new columns (one for each question) that compare the student’s answer with the first submitted answer (which are my own answers), printing a 1 if correct and a 0 otherwise, ie:
    =if(C3=C$2,1,0)
  3. Tally the score in an 11th new column, ie:
    =sum(M3:V3)
  4. Create a new sheet for each student. Cell A1 contains the student’s GAFE email address. The two columns we need are the test date and the test score. For the date, filter through all the submissions, looking for the correct student, ie:
    =filter(‘Sheet2′!A1:A127,’Sheet2’!B1:B127=A1)
  5. For the score, filter through the submissions, looking for the correct student, ie:
    =filter(‘Sheet2′!W1:W127,’Sheet2’!B1:B127=A1)
  6. To make the graph, we want the number of questions that were wrong, not the score. Also, to make the graph automatically, we need to make sure that there’s no number in this new column unless it corresponds to an actual score. Thus,
    =if(D4<>””,10-D4,””)
  7. The burndown chart is a column graph. Here’s what mine look like:

b

 

Notice that I put a “100% wrong” bar at the start of the chart, for the sake of comparison. The 18th of September is empty because the student got all the questions correct.

Now, in order to share this chart with the student, I created a page on our class GAFE Site that is visible only to the student and I. The chart is inserted into the student’s individual page. (I also use these pages for our gamified points system — more about that in a future post)

Conclusions:

  1. Since I have to create a spreadsheet and a page for each student, this method doesn’t scale. I could use a script to automate the spreadsheet work, but (probably correctly!) Google doesn’t allow automated website creation on Sites.
  2. Once the students have seen the same question a couple of times, their understanding is no longer being evaluated effectively. Knowledge-based questions seem to hold up better (after all, the point is being able to answer such a question correctly) but have limited educational value.
  3. The Scrum method uses remaining man-hours as the value on the y-axis of these burndown charts. Knowledge/understanding, however, surely is not linearly related to the amount of time spent learning. Thus, a key insight to be gained from these charts — the ability to estimate a completion date — is lost.
  4. Perhaps unsurprisingly to those who are familiar with GAFE, this system hiccups. One day, the scores weren’t (automatically!) saved from the Form into the Spreadsheet for several hours. Students who are logged into personal Gmail accounts (in addition to their school GAFE accounts) experience bizarre and unpredictable errors.

To see my full burndown quizzes (if they’re still online), check out my physics and maths class web sites.