IB Physics vs GRE Physics

Can you tell which problem is from a test designed to assess the skills of high school students, and which problem is from a notiously difficult test used to rank applicants for graduate school?

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A student needs to get 70 to 80% of these questions correct to be eligible for the top graduate schools in the USA (MIT, CalTech, Harvard, Stanford, etc). The same percentage is required to achieve a “7” (the top grade) in IB Physics.

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The GRE consists of 100 of these multiple-choice problems. For IB physics, it is 30 or 40 (depending on the level) and then two more papers with longer-form questions. Students generally find the multiple choice questions easiest.

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So which are IB and which are GRE questions? (hint: the GRE questions have five possible answers)

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Gender Balance

This is the story about how I learned the real meaning of gender balance.

A couple months ago, I heard of this great way to integrate the Theory of Knowledge (the philosophy hub of the IB diploma) into my math classes. I took it a bit further, and ended up creating posters for eight different ways of knowing. These include reason, emotion, sense perception, language, faith, etc. My posters featured a picture of a famous mathematician whose work epitomized that way of knowing, along with a (carefully sourced!) quotation where they describe their process.

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Making these posters was challenging but fun. Some were easy: Bertrand Russell’s work was pivotal to the language of math, Cantor’s work with infinities was deeply religious, and Edward Frankel’s great emotional love for the field is a great modern example. I sought mathematicians the students might encounter (Venn, famous for his diagrams), attempted to include those whose work is accessible to students, and tried including various cultural backgrounds where possible (Ramanujan for imagination).

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Throughout the process I knew that I was failing to include women. Noether almost made the cut, but I couldn’t find the right quotation. Partly, I felt that no female mathematician deserved to be on the wall beside Hilbert, Poincaré, and von Neumann (except for, perhaps, Noether).

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I don’t think this was a sexist viewpoint, but rather a reflection of the reality of a past in which women were barred or strongly disincentivized from participating. I provide plenty of female role models for my students, do interventions when necessary, and build discussions about the culture of sexism that is currently poisoning much of STEM into my classes. But these posters were historical, and so I figured it would be okay.

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When I first put them up, I asked my classes why they thought there were no women, and whether they thought it was fair. They understood: we can celebrate the history of mathematics while also recognizing its faults.

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After a couple months, a colleague challenged me to create posters with women. We played a game on the bus ride home of coming up with role models for the eight ways of knowing. I tried to provide only female physicists (physics is my other subject) but found it challenging.

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So I took a couple weeks to work through it, reading biographies and wikipedia articles when I could find time, searching for the origins of pertinent quotes. Finally, I had a set. But these women were not like the men.
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Three of the women were still living (compared with only one for the men). Several had contributed in ways that would not arouse the suspicion of the Fields Institute. One, a lecturer on hyperbolic surfaces, was better known for her crocheting than her equations. Few had names that appear in math textbooks. Several were unmarried throughout their lives. All had experienced sexism that slowed or derailed their careers.

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So, what did I learn from the inclusion of these women? That math is about people, not theorems. That contributions to the subject come in many shapes. That, contrary to my expectations, the history of mathematics is rich with female role models. And that gender balance is a necessary condition for cultural balance.

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You can download PDFs of the 16 posters here.

IB Physics is Too Hard

For several years, I have harboured the notion that IB Physics is too hard. I suspect I’m not the only one:

For a student, the difficulty of physics is perhaps easier to explain: the ways of constructing meaning are challenging, the models of knowledge demand careful study for mastery, and the assessments are notoriously hard to bluff your way through. For educators, however, these difficulties are part of the trade. Textbooks, lesson plans, and pedagogical approaches provide good ways for students to overcome these issues.

Even as an educator, however, IB physics still seems hard. Some people believe that the syllabus is too broad, encompassing too many topics like particle physics, wave interference, thermodynamics, and the greenhouse effect. Others point to the depth of understanding required to score well on the exams. However, I don’t think that either of these dimensions is sufficient to explain what is so hard about the syllabus.

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I’ve added a third dimension to the “iceberg” of physics. Thickness is about the skills students need to acquire in order to do physics. To see this, let’s look at some examples.

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Example 1: There’s a car on a hill, with lots of known properties.

  • Depth – what is the car’s velocity at the bottom of the hill? what is the efficiency of the car’s motion? if the car were to roll back up a similar hill, how far would it go?
  • Breadth – what would be the impact of a non-zero drag force? how does the calculation change if you consider the angular momentum of the wheels? at what rate is the car increasing the temperature of the hill?
  • Thickness – how do we know to use energy conservation? what does our model include? how can we understand the energy transformations within this model? how do we know if our answer is reasonable?

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Example 2: A past IB exam problem (above)

In this problem, students are expected to use the Rayleigh criterion to estimate resolution. It is a simple calculation that they have already done a few times, using a formula from the data booklet. This topic demonstrates both the breadth and depth (this is from a unit on single-slit interference) of the IB physics curriculum. It also demonstrates thickness: conceptually understanding what is going on here is very challenging. Although this appears on an exam, I suspect most IB physics students have just memorized how to use the formula.

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Thickness in physics involves the skills, approaches, mindsets, and contextual knowledge that allows physicists to do physics. This includes things like critical thinking, building models, visualizing phenomena, drawing representative diagrams, working fluently with numbers, dimensional analysis, and using the right model at the right time.

IB Physics is hard because we neglect the thickness of physics, focusing on solving standard problems and preparing for tests instead of learning the skills of physics. And when students do well in this hard course, it isn’t because they mastered physics: it is because they did well on the test.

Let’s return to the tweet by @AfroRose_: “I remember when I was in IB physics, it was so hard. What’s crazy was in class I always got the answers right, but I couldn’t explain myself [emphasis added]”. Here is a student who studied hard and succeeded at IB physics, but never became competent with the skills involved in the discipline itself. For her, physics was deep, broad, and thin.

Over the past two years, I have tried to reconcile a deep, narrow, thick pedagogy (Modeling instruction) with a deep, broad, thin syllabus. There have been productive moments — the thickness is especially valuable in preparing students for their independent investigations — but any concession toward thick teaching comes at a cost in contact hours and, since the alternative is to prepare students directly for their exams, potentially a decrease in student grades.

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How can IB Physics be more thick?

The AP and A-level boards have both done an admirable job in their past revision cycles of cutting down the amount of material students need to learn, that is, decreasing the breadth. The IB revision cycle sort-of-not-really did this, by reducing the number of optional topics, and shoehorning some extra particle physics into its place. A decrease in breadth is necessary because of the limited amount of time available for learning.

With a bit more time allowed for the development of skills with mechanics, for example, we could include system schemata, LOL diagrams, or graphical vector addition for forces. If we keep Feynman diagrams, we could have enough time to develop students’ understanding of them. With scaffolds like these, we could be confident that students will be better prepared to tackle unfamiliar, complex problems on exams. This could even allow for the use of open-ended problems. I think that would be pretty cool.

A change to a syllabus that seems to make it less hard will always be met with concern. I want to smart-up students, not dumb-down the curriculum. In any case, I wouldn’t be worried about blowback.

Classroom Culture

The thing I worry about most is the nature of my students’ interactions with me, with my subject, and with our shared environment. Lately, I’ve come to think of all these things as (my part of) the culture they encounter in, and around, school.

I want to be clear, in my use of the term “culture”, that I am not referring to climate of the school. The attitudes, behaviours, and discourse of the people in the school are like the motion of iron filings, and the pattern they form locally is the climate. Culture is the magnetic field.

Culture is, as Geertz puts it, “an ordered system of meaning and symbols, in terms of which social interaction takes place” (p 144). The meaning includes things like our values and our core beliefs, the symbols include the things we put on our walls and the vocabulary we adopt; the social interaction is education.

Creating a positive culture in a school or classroom has become a popular discussion-point for the education advice sector (example, example). Teachers should collaborate, listen, enact classroom rules that promote respect and sharing, and directly instruct children about community values. That’s a good start, and it is probably enough for the beginning teacher. But for those of us who really, genuinely care about our students, we are often compelled to do more.

Jose Vilson, in typically concise honesty, described what he learned teaching a difficult class during his first year in the classroom: “When I took off my mask and invested myself in a group of kids, the homeroom became a home. For all of us” (p 87). For him, the next step to creating a positive classroom culture was appreciating the students as individuals, with hopes and needs and fears. How else can we reach out to students, and establish the sort of culture the beginning teachers cannot?

Love Your Students

Love your students. Take them for who they are, flaws and all, and love them anyway. Love them when they are causing trouble, and you will see their misbehaviour as symptomatic of some deeper need. Love them when they do poorly on assessments, and they will learn that some things are more important than test scores. Love them for their humanity when fellow teachers blame them for their failures. Don’t be afraid to tell them so, at the right time.

I once had a troublesome high school math class that missed the deadline for an important project. They assumed I would treat them as their other teachers did: admonishment, an extended deadline, and complaints home. I told them that my love for them wasn’t contingent on their work.. They should finish it at their own pace, but that it was necessary for the course. That changed the dynamic of our classroom: mutual trust and affection meant that we could navigate problems, rather than butting heads against them.

Accept Friend and Follow Requests

We all know that our social media need to be sanitized. So what’s the problem with connecting with our students online? I tried to answer that question last year.

On Facebook, I can wish happy birthday and celebrate achievements outside of school. I can keep an eye out for dangers, too, and help students learn about privacy and the internet.

Develop Respect Beyond “Mister”

My students have called me a lot of things, but they rarely call me my name. Even after years of developing and displaying their deep respect for me as their teacher, my students use an awkward and unnecessary formality: “Mr Doucette”. I would rather that my students show their respect for me and my classes through their actions, and by accepting me as a human being — which is something quite difficult when you’re not even allowed to use my name.

Dress Appropriately

Several years ago, I developed a teacher costume. At the time, as a young male teacher, I needed to send the appropriate cue to female students whose crushes distracted them from their work. I typically wear a white or blue shirt with a bow tie, a v-neck sweater or cardigan, a tweed jacket, corduroy trousers, and brown dress shoes. It is almost comically professorial, and it makes me a well-known character in my school.

Recently, however, I’ve found that my style of dress makes it difficult for students to conceptualize me as a human beyond the teacher character they’ve framed in their minds. I wonder how I could dress in such a way as to promote positive classroom culture? I’ve got a great hoodie that says “Niceness is Priceless”, and I’ve worn it a few times.

Eliminate Implicit Bias and Stereotype Threat

Implicit bias is probably affecting how most teachers act in the classroom. During the past two years, I’ve kept a careful eye out, and caught myself a few times: calling more frequently on boys than girls, presuming girls are more interested in the social sciences and boys in the physical sciences, and “mansplaining” to my peers more than once. I think I’m getting better at treating everyone as an individual worthy of their own types, rather than relying on stereotypes.

Stereotype threat, on the other hand, is something I cannot eliminate, because it is brought into the class by my students. I can try to ensure that all students know their particulars are not relevant to academic success in my class. For some students, who struggle, I have had mini-interventions that seemed to be successful.

Surround Ourselves with Cultural Artifacts

The walls of my classroom are covered in student work and colourful, engaging, and useful posters. I’m happy with that. But these cultural artifacts are of my designs. Even the student work was created according to tasks and rubrics I designed. If the classroom is truly to become a shared cultural space, then I think the walls need to reflect our shared culture, even if that means posters of Rey and Biebs.

Kids Online

Cyberbullying, online harassment, or simply being inappropriate on the internet: for my students, these are becoming increasingly commonplace. I’m worried.

I want to think about what I need to do better, as a teacher and a coach. So here’s a list of the ways I’m failing my students:

  • I am not modelling appropriate behaviour on social media for them to observe
  • I am not directly instructing them about data retention policies, legalities, and (lack of) privacy
  • I am not teaching them how to deal with peer pressure online
  • I am not training them to be empathetic
  • I am not supervising, or even keeping an eye out for trouble, when they are outside my classroom
  • Since they don’t, I assume I have not made my students feel they can come to me if they are having trouble
  • I am not engaging in, or sustaining, a dialogue with the students’ parents about their engagement in social media

My school could do more to red-flag inappropriate behaviour in our Google Apps set-up. Most parents should probably be doing a lot more to monitor what is going on with their students. Yet, clearly, I feel that part of the failure is my own.

Here’s what I know about the best teachers: when they fail, they come back the next day with a new, better idea. In that spirit, here’s my plan:

  1. Work empathy-building activities into the classroom (for my middle school students), and work empathy-building into our learning activities (for my high school students, where time is a precious commodity). In addition, I will try to think of all-school activities that could help to build empathy between students who normally don’t interact.
  2. Start accepting friend requests on Facebook, returning follows on Twitter, and so forth; try to engage in a positive way with my students on social media; and keep an eye out for dark corners (I made this argument last year).
  3. For the students I advise, prepare some lessons about responsible online citizenship, and share them with my colleagues if there is interest.
  4. From there, once I know more, try to contact parents as appropriate to cheerlead, support, and inform.

It’s time to go connect with some of my students.

Modeling Thermo

In applying the modeling methodology to IBDP physics, there are a few gaps. In this post, I present a unit that uses the modeling approach for the thermal physics and thermodynamics unit of Physics.

1. Building background

Have students touch something warm and sonething cold. Ask what is happening in terms of energy in these interactions. There are two main goals for this short preliminary discussion:

a. definitions of the terms heat and internal energy
b. an agreement that heat, as a transfer of energy, is sufficient to explain thermal processes, and is what we feel

2. Paradigm Lab I

For this lab, masses of hot and cold water are mixed in an insulated cup. After a demonstration of the effect, students should walk through a variable brainstorming session (I like a version I learned from Karl Schmidt that has three steps: observations, measure-ables, manipulate-ables). The students should recognize that either the hot water mass or the cold water mass could serve as the independent variable. They will recognize that the temperatures are dependent, but might need some help to decide to use the ratio of temperature changes as the dependent variable.

The students will thus conduct two labs, perhaps by splitting into two groups and sharing in the whiteboard meeting. They should find that the ratio of temperature changes is proportional to one of the masses and inversely proportional to the other. Be careful to define the ratio of temperature changes clearly for everyone before beginning data collection.

Combining results and looking at slopes allows us to construct the equation:

mass of hot water * temperature change for hot water = mass of cokd water * temperature change for cold water

Now, the students should recognize that this reflects the heat flow discussed earlier, but since heat is n energy change the units don’t work out and we need to have a coefficient. Students should think about what this coefficient means (it is the energy released/absorbed to change the temperature by one degree Celcius for each kilogram of matter).

3. Some practice with calorimetry problems without phase changes here. I spontaneously put two on the board at the front, and had student pairs write a third.

4. Demonstrate a melting curve. This may be difficult, but at least set up the apparatus and sketch the resulting curve.

First provide students with the power output of the heater and the mass of your sample and ask them to find the specific heat capacity of the sample (ie: using the slope).

Next, point to a segment where the temperature is unchanging and ask students to try to explain what is happening here. Socratic questioning and your favourite applet (PhET, etc) is good here. There are lots of misconceptions here, so insist on very clear statements and model IB language (ie: from past exams).

Students can usually guess the form of the latent heat equation (Q=mL), so I ask them how they would design an experiment to test that, and then we move on.

5. Model deployment, proper.

Now, the students are ready for some lengthier calorimetry problems, so they do a worksheet of these.

6. Quiz

A quiz based on the worksheet.

7. Practical I

I do a calorimetry problem at the front of the room, moving a hidden mass of steel from a hot water bath to a known mass of cold water. I provide the temperatures and the students predict the mass, which we put on a balance once all the predictions are in.

8. Paradigm Lab II

This could be done using a PhET simulation, or with an apparatus like the one shown below (the block could be replaced with a heating element to manipulate the temperature, and a pressure sensor should be attached to the flask somewhere):

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Image from Purdue University (http://chemed.chem.purdue.edu/)

Briefly outline the nature of an ideal gas (no potential energy, elastic collisions providing pressure, etc). In the regular pre-lab process, students should identify pressure, volume, temperature, and number of molecules (or mols) as the relevant variables. For now, leave the number of moles aside (ie: keep the device closed): this leaves three experiments, all of which should be done:

  1. How does a changing temperature affect the pressure at constant volume?
  2. How does a changing temperature affect the volume, when the volume is adjusted (ie: by extending the syringe) so that the pressure is constant?
  3. How a changing volume affect the pressure at constant temperature? (this works better by connecting the syringe directly to the pressure sensor)

Connecting these gives that PV/T = constant. Logically, P and V should be proportional to the number of moles n, while T is inversely proportional to n (at constant P and V), so this becomes PV/T = nR, where R is the ideal gas constant.

After rearranging this equation into the familiar form (PV=nRT), as students to determine the units on the left side. This gives the units of R as J/mol/K and, more importantly, shows that the ideal gas law is fundamentally a statement about the amount of internal energy in the gas. A brief note about the Maxwell distribution and rms velocities of the particles is probably appropriate here, even though it does take us out of the modeling cycle.

9. Deployment II

Now, the students do a second worksheet, on the ideal gas law. This also includes the three constituent laws (Boyle’s, Charles’, and the Gay-Lussac/Amonton) and practice with the exam-style question “determine whether this graph shows that the gas obeys Boyle’s Law (etc)” by checking points on the graph to determine whether the relationship is proportional, inverse, or otherwise.

10. Practical II

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11. Unit Test

 

Social Justice in Physics

Moses Rifkin does a superb 6-day unit on social justice in his physics class. Here, by arguing against it, a Fox News correspondent makes it clear why social justice is needed:

I wanted to do something similar to Moses, but I had two constraints:

  1. Since I teach IB physics, and already don’t get enough contact hours, I couldn’t devote more than a class period to it.
  2. Since I teach at an international school in Northern Europe, the social justice issues experienced by my students and in our culture will not necessarily be racial in nature.

Thus, I tried to lift out my favourite parts from Moses’ curriculum, and recontextualize everything to be more universal in nature. Our discussions ended up primarily focusing on sexism, with class, religion and disabilities as other sources of examples and discussion.

We started with some ground rules, directly pilfered from Moses:

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Second, I introduced the idea of stereotype threat. Two students had studied this in a psychology class, but had difficult explaining it. I gave an example (as a North American in Europe, I fear being seen as monolingual, and am disinclined to practice languages as I struggle to learn, thus learning less well). The students brainstormed examples in pairs, then shared out. This took about 15 minutes.

Third, I had students randomly select from a list of social groups. They used their computers to quickly find and research two physicists from that social group. In a circle, they shared who they found and I probed with questions like “how did you find this person?”, “how did you choose this physicist?”, “had you heard of this person before today?” and “was it hard to find physicists in this social group?” Our list of social groups (the last two were suggested by students during our discussions):

women, men, heterosexual, homosexual, black, white, young, old, disabled, able-bodied, Christian/Muslim/Jewish, Eastern religion, European/American, not European/American, upper class, lower class

This led fairly naturally to a discussion of why some of these social groups are under-represented among physicists. I asked the students to make hypotheses to explain the under-representation, and then to offer counter-examples for the hypotheses, if they could think of any. Our hypotheses were that the distribution of physicists:

  • represents the population
  • is determined by the geographical location of universities and research institutions
  • is determined by the populations access to education
  • is determined by social expectations
  • is determined by history/politics

These were all seen to be unsuccessful as a complete explanation. Next, we switched directions, and looked at the barriers for people of under-represented social groups. Some good arguments were presented here, including the effect of expensive tuition at university, the impact of stereotypes, and the role of religion. I was able to cap-off these arguments by labeling these effects as the essence of institutional sexism, racism, classism, ablism, agism, homophobia, etc.

We finished with the Implicit Association Test about gender and science. I told the students that they need not share their scores, but many were keen to talk about it, so I know that we got a variety of results that approximately conform to what one would expect from a mixed group.

Before we left, I tried to introduce the idea of privilege, and especially of white privilege, but I think this fell flat, like everything does when you’ve got two minutes until lunchtime.