Presentations · Science of Learning · Teaching Methods

Toward Expert Level Thinking: Talk for AAPT SM 2021

One of the distinguishing attributes of first year physics students is the novice-style approach to solving problems, typically based upon common variables or equation hunting. Having students shift to more expert-like strategies, based upon more over-arching ideas or concepts is often a challenge in physics teaching. This talk will discuss several strategies implemented in an urban-emergent high school for both traditional junior level students, as well as AP level students to help shift student approaches from novice to expert.

If you plan on attending AAPTSM21 I hope you will engage in conversation with me! If not, this talk is accessible to all!

Slides, citations and resources available here

Science of Learning · Teaching Methods

Introducing Physics Students to PER

Physics Education Researchers know that active learning is better for students than lectures. At the same time, anyone who has attempted active learning environment knows that students do not always believe this to be true. The same holds true for study methods and habits. Instead students will balk and complain that “my teacher doesn’t teach”. Most recently a student told me they believed that by asking them to actively learn and collaborate, “the burden of the teacher has been placed on me”. I believe it was at this point I was ready to post Rhett Allain’s Telling you the Answer isn’t the Answer on every tangible and virtual learning environment I occupy. I didn’t do that.

At the end of Chapter 6 of The Science of Learning Physics, Mestre and Docktor share that students should learn about the research surrounding effective studying. I would argue that the same should be true about the active learning environment. In the past I have mentioned this casually to students, however the challenges of COVID required me to shift casual mentions to intentional direction.

Brian Frank shared that Jennifer Docktor had a webinar on the book. Excited and curious I watched the video. I was most excited that it was only 30 minutes, meaning it would be digestible for my students. The talk is an overview of the highlights of each chapter of the book. If you haven’t already ordered it and are interested, this is a great entry point!

Shortly thereafter I assigned the video in google classroom and provided the following:

  • As you prepare for finals and reset for semester two, I’d like you to listen to this talk by Dr. Jennifer Docktor.
    She is a professor of physics at UW Lacrosse and recently co-authored a book about how students learn physics.
    Watch the talk and write a short reflection. Include the following. Remember, you should be digging deep and synthesizing, rather than simply agreeing or disagreeing.
    • What resonated with you?
    • What ideas challenged your current thinking about how we learn and learn best?
    • What do you now wonder after listening to this talk?
    • What resulted in an “aha” moment for you.
  • Lastly, as a student, what can YOU take away that you’ve learned in order to improve your learning next semester?

I will be completely honest. I have a few students who have been extremely verbal about their hatred for active learning. I read their reflections last. I was also nervous because as a teacher, I’m a life-long learner. There are components that Docktor discusses and shares that I haven’t yet implemented or perfected, especially thanks to the COVID monkey wrench. Would students call me out? However, I was really impressed by what the students had to say.

Some students reflected on recognizing the intentionality put into our classes:

“I like our weekly practice tests, but I didn’t know they had an educational backing. When she started talking about interleaved practice, I thought about the momentum problems with a twist and some other homework problems that we’ve had.”

I had several students comment about applicability and connections to education outside of physics

“I now wonder, after listening to this talk, if other fields of science education, and other education in general, put this much effort into how material is taught to students, or if I have just never been aware of how I am being taught in the past.”

Another student actually posed that physics exposure happen at the elementary level so that kids have a better scaffold of experiences, rather than needing to uproot firmly held misconceptions in high school. (Big YES to that!)

What I really enjoyed, however, was students seeing themselves in the studies. Many students admitted to equation-hunting rather than starting with the big picture. I found this particular statement to be really fascinating about why they default to equation-hunting,

“I do this myself sometimes the reason why I do this is when I don’t feel confident in the work or I don’t know what I’m doing.”

Students overwhelmingly reported that an idea that resonated with them was how they are not blank slates, and experiences shape misconceptions. They saw themselves in the research and were shocked (and in some cases bothered) to hear that lecture and note-taking are ineffective, along with many of their tried and true, but passive study habits. One student who has been particularly insistent shared “the studies she talks about seem to prove me wrong about the lecturing method being more effective”

After completing this excersise here are my lingering questions:

  1. Given the demands of AP 1, how can we encourage students that they are growing and learning by leaps and bounds, even if they aren’t at a 4 or 5-level for AP yet? I feel this is easy for me in my non-AP courses because I set the bar, and so I can raise the bar as the year progresses, without students realizing this has occurred.
  2. Many students shared the sentiment of “well everyone is different, and this doesn’t apply to me” neglecting that this is a large body of work and research spanning decades and involving thousands of students. I’m wondering if more work in the realm of cognitive science and how we learn would be beneficial. But how to weave this into the structure of my courses?

I’d love to hear your insights!

Science of Learning · Teaching Methods

The Science of Learning Physics: Practice and Study Skills

In my previous post we discussed strategies for metacognition to help provide students a clear, objective judgement of learning in order to help students see their own improvement and laser-focus where they need to put in more time.

Today we are going to further explore practice and studying.

We have already discussed some of the following: that students tend to judge their own competence poorly, students mistake familiarity with competence, and student study habits, if existent, tend to rely on passive methods such as “looking over notes” and highlighting. This is part of the reason why active learning is so beneficial in the physics classroom; it creates a norm for how we approach any problem.

In the book The Science of Learning Physics, Mestre and Docktor discuss the work of cognitive scientists Elizabeth Bjork and Robert Bjork of UCLA that suggests the implementation of “desirable difficulties”. Implementing these desirable difficulties is providing students with a challenge that is just out of their comfort or familiarity zone, but not so far removed that the student shuts down. Desirable difficulties can be produced by creating certain experiences for students that, in a way, de-contextualize the problem. These methods include varying the condition of practice, spacing and interleaving.

Spaced practice is commonly known: we don’t really learn much by cramming, but students will cram nevertheless. Knowing this reality we, as teachers, can incorporate spaced practice into our classroom as part of our warm-ups and retrieval exercises or focused activities. We can also incorporate these practices in order to help students built their own study guides (particularly when combined with metacognitive strategies) I really enjoy embedding spacing as a retrieval practice like the one below. You’ll notice I give students a single word to help jog their memory just a little, because remembering from a week or two ago can be really hard!

This practice also works excellently with interleaved practice, which is when students are asked to use multiple ideas at once or in random succession (the opposite is blocked practice such as items 1-10 are newton’s laws and 11-12 are energy). Physics truly lends itself beautifully to this process because, in truth, working through a semester of physics is really working through new and layered understandings and models for how and why things happen.

Last year I had my students do a retrieval exercise to get them to retrieve everything they could remember about reflection and refraction. After cycling through pairs and groups of fours I asked them to create a Venn diagram of the two concepts. This got students actively thinking about how refraction and the problem-solving tools connected to reflection and lead to some phenomenal conversations. It also produced a desirable difficulty: students had not thought about refraction in this way before and they were asked to interleave with reflection. Students got to walk around and look at the other boards and then come back to their board to shift or add anything they felt needed to move.

Goall-less problems are a really great way to incorporate these practices. In a goal-less problem you take off the last part of the sentence that says “find the velocity” and so on. Instead, students are asked to write down and solve everything they can about the problem. The benefit to this method is that it is the epitome of a low floor, high-ceiling activity. Even your poorest performing student should be able to draw a picture or write at least one thing down. It also removes the narrow student focus of trying to solve for the specific thing asked for, and rather makes students consider all of the possibilities. In my on-track physics classes I typically put a list of all of the representations and options they have available up on the board the first few times we do this. Goall-less problems also make for fantastic final review or assessment items.

One final note that is more personal experience than anything else. I really, really hate Webassign and other similar online homework platforms. I worked as a full time tutor in a school for two years and I was typically inundated with physics students wanting to get all of the green checks. No matter my goal, hope or intent, the majority of students generally did not care until I got them through all of the steps. In contrast, the couple of students I tutored from small, private schools without an online platform were far more interested in process. There is something about the green check and the correct numerical answer that strips away all of the process and metacognition that we work so hard to cultivate in our classrooms. I’m not sure what the answer is to this (other than this type of homework being worth close to nothing). But I am sure that when the focus in class is truly about helping students create their own knowledge that much of this type of homework becomes obsolete. I would much rather have students working out solutions on paper that they can then bring to class and have a conversation. In Webassign success is binary: you get a red X or a green check, but comprehension and learning are not binary processes, they are fluid and messy. Students need to work through the mess and celebrate the small wins along the way.

Science of Learning · Teaching Methods

The Science of Learning Physics: Metacognition Strategies

This post is part of a series on the Science of Learning Physics


I distinctively remember this being a topic in one of my teacher prep classes. I also remember several failed attempts at weaving metacognition into my assignments. I don’t know about you, but trying to get students “thinking about their own thinking” seems really challenging, clunky and too often inauthentic. Students are fantastic at sniffing out inauthenticity, and the moment they recognize something as garbage, they approach it in full B.S. mode.

The challenge with this, of course, is that metacognition is an incredibly powerful tool within the cognitive science toolkit, and is one of the marked differences between expert vs novice thinking.

Metacognition allows students to evaluate their learning and problem solving approach, and focus for studying. Unfortunately, students frequently misjudge their skills and abilities, often confusing familiarity with content for competence. Furthermore, students who struggle may lack enough familiarity to properly identify the edge of their learning. So how do we teach students to be authentic reflective learners?

One of Mestre’s suggestions in The Science of Learning Physics is to provide students objective measures to judge their learning. Specifically, access to old exams and questions. While this is an excellent method, many high school and AP teachers may lack a deep pool of questions to make available to students. Additionally, this is limited to student studying outside of the classroom. What Dr. Agarwal suggests in her book Powerful Teaching is “engagement with feedback” in other words, whenever we have students working in our classroom, they should have the opportunity to receive meaningful feedback on their work in short order so they can reflect on their process while it is fresh, and course-correct as needed. How often do we ask a student to tell us their thought process and they respond, “I don’t even know anymore”

A method I’ve adapted to aid in this task weaves together retrieval practices with metacognition. Recall in the retrieval process students first write. down everything they can remember using only their brain. Then, if you so desire, students can pair and share (I typically do a pair and then have pairs get together into groups of four). Last, you permit students to dive into their notes. In each of these progressive phases, students should be adding the parts they received from. other sources to their papers. Adding the metacognitive level is as simple as a highlighter. Perhaps students highlight everything from their partner in yellow. Then, they highlight everything they added from their notes in green. This produces a very clear visual of what they know and what they do not know. It also produces a visual of how much they can reap from their friends and what topics or ideas were “really hard” for everyone because no one could remember it.

If. you’ve started to dig into retrieval ideas on twitter or on Dr. Agarwal’s. book or website, you’ve. seen that there are so many different ways to do retrieval, from lists to graphic organizers. Any and. all of these can utilize this highlighting method. Not only does this allow for metacognition. and accurate judgement of learning, over. time it demonstrates to students how much they have learned over a time-frame and how their own retrieval improves with practice.

Here is another brilliant idea by Jess Kirby. Not only does this incorporate metacognition and judgement of learning, it also requires students to organize the questions by the big idea (another “expert-level” concept).

For a more complex version of this process as it relates to problem solving I have had students combine retrieval with cornell notes.

In this example I had lectured students on how to solve this exact problem the previous day. I provided them with the following notes sheet

First, I asked students to solve this problem as best they could using only their brain and what they could remember from the previous day. I only asked them to focus on the left hand side where they solved the problem.

Next, I allowed students to pull out their notes and add, edit or correct any of the steps they had missed. I asked them to color code these edits and then write out the steps in words on the right hand side.

Finally, I told students to look over their paper. Anything that needed an edit or addition (especially if “I just forgot that..”) needed to go down in the “reminders to yourself” box.

These three ideas really only scratch the surface of what is possible! If you have picked up Powerful Teaching, head over to chapter 5 for more great ideas and then share what you’ve implemented in your own classroom!

Science of Learning · Teaching Methods

The Science of Learning Physics: Active Learning part 2 – Convincing the Student

This post is part of a series on the Science of Learning Physics

I’m going to make an assumption that most readers of my blog do not need any convincing of the benefits of an active learning environment. Even still, in the name of these posts starting from a solid research foundation I will briefly discuss the value. However, I think the bigger challenge teachers face is persisting with the active learning environment in spite of feedback from students, parents and perhaps even colleagues along the way.

The active learning model is a natural consequence of constructivist learning. Active learning has been shown to be more effective than traditional lecture, as well as most effective at uprooting and replacing common student preconceptions.

In an active learning environment the teacher takes the role as coach, facilitator and guide. Not leaving students to their own devices, but rather carefully crafting the learning experience so as to set students upon a fruitful path. Mestre lays out in his text that active learning could consist of the following:

  • Opportunities for students to share their ideas and reasoning individually or with their peers
  • Encouraging qualitative reasoning based on physics concepts
  • Encouraging construction and sense-making of physics knowledge; for example students are prompted to figure things out for themselves
  • Providing opportunities for students to engage in the process of “doing science”
  • Providing opportunities for students to apply their knowledge flexibly across multiple contexts (transfer to new contexts)
  • Helping students organize content knowledge according to some hierarchy
  • Teaching metacognitive strategies to students

For the first time this year, and thanks to an idea from a friend and college, Joe Milliano, I had this discussion of “where the learning happens” with my students at the start of the year, anticipating more push-back than usual due to the hybrid environment

Part of my intent in this was to point out how the “information getting” part of the class is really small compared to the student-centered and constructivism part of the class.

Mestre, likewise, encourages teachers to be completely upfront with students regarding the science of learning in order to provide them with the context for the journey we are about to embark on together. It’s important for students to know we’re not just doing this “to them” but rather we are doing this for them because it is truly the best model for their learning.

Unless your school or department is built on a Problem Based Learning model, or something comparable it is very likely that your students have not engaged in an active learning environment to this extent before, ever. Your students will likely cite that they learn best based on their learning style, they enjoy lectures and seeing examples and they study by going over their notes and re-reading the text. In fact, you can fully expect your students to think and feel like they are not learning, when they really truly are!

These common student responses are riddled with challenges for the teacher and their own learning. The best thing you can do as the instructor is to begin to have these conversations from the first day of school. Firstly, while learning preferences is certainly a thing, the truth is that difference courses require students to perform in different ways, and the way in which we ask them to perform may not match their learning style, this mismatch can then appear as incompetence if we teach to the learning style rather than the intended performance objective. Next, lectures, watching examples, going over notes and re-reading the text are all ways in which students can gain familiarity with content, but students confuse familiarity with competence. How often have you heard a student report “I get it when we do it in class, but then I forget everything on the test”.

Eugina Etkina has a wonderful, non-physics exercise to discuss the importance of students “doing the doing” as I call it. She calls it the expert game. You ask students to go around and share their “thing” that they are really interested in or really good at. Then, you group the students based on similar interests. Students are asked to come up with a flow-chart or visual on how you go from being a novice to an expert in that craft. Inevitably the results consists of things like “watch an expert” “practice” “get feedback”. This conversation then comes back around to the work in the physics class. I can watch Michael Phelps all day long, but I’m never going to be able to even swim unless I jump in the pool. Same goes for the work of physics!

Students begin to get on board with the idea of active learning when they see they are reaping the benefits. Unfortunately, physics tests do not always reflect this for our students. Enter the retake. I do retakes in a very special manner in my classroom. It’s something of an adjustment from an idea I read in an old Physics Teacher journal. I have not let students do this until the energy unit exam, only because I want students to get through that “adjustment period” I’ve mentioned previously.

Students complete the energy exam and I tell them the following day that they have a retake opportunity. Here is how it works.

I will be upfront with scoring. Students will take the exact same test over again. They must score 100% in order to get the bump.

Students do NOT get to see their original exam. They do not know their score, they do not know what they missed. This is really important.

I arrange a designated day and time in which students can come to my room to collaborate. They will receive a blank copy of the same exact test they originally took. They can use any print resource. They may not ask me questions.

One week after the collaboration students come in at a designated time to take the retake.

Scoring is easy because I’m looking for perfect papers. The bump works on a square root curve, so if the original score was a 64, the bump will be 10*sqrt(64) = 80. I really like this way of adjusting since the student who had a 96 to begin with only goes up to a 98, which makes sense since they had small errors, but the student who had a 64 and pulled of a 100 gets up to a respectable 80.

The design is where and how the magic happens. They know that 100 is possible because they are ALL together. The teamwork and camaraderie is palpable and the energy in the room is invigorating! Students also realize that they are all in this together: there’s no geniuses here, and working alone is not the best use of time. Because they need 100, students argue their point to the finish. Because they need 100 a week after they get to talk, students are making sure they fully understand how to answer the questions.

I was really nervous the first time I did this with my students, but I knew I did the right thing at the end of the first session when my top student walked out of the room and said, “I thought I knew what I was doing on that test, but there was a lot I needed to learn” This student had an 87 on the first round!

I have found that one of the most critical components of an effective active learning model is creating the classroom culture where students not only feel safe to take risks, but feel safe to work together with every single student in the room. This takes a great deal of time and effort on the part of the teacher to properly construct. (Head over to Kelly OShea’s blog to learn about board meetings and speed dating, two of my favorites for building classroom culture!) Our current situation with the pandemic has made it much worse and I’m not sure how I can roll out my most favorite teaching tool under all of the current constraints (if you have ideas, drop them in the comments!)

To that end, if you are a new or novice teacher, or are looking to begin using active learning in your classroom, I would strongly encourage you to seek out teachers who also use active-learning in their classrooms. Create your own Professional Learning Network (PLC) of incredible teachers from across the country, sign up for the workshops at AAPT, or an AMTA modeling workshop so you can not only network, but have a place to have conversations about what is working and not working. Just as I tell my students, we are better together.

Science of Learning · Teaching Methods

The Science of Learning Physics: Teaching Students Expert Thinking

This post is part of a series on the Science of Learning Physics

One of my favorite discoveries in my cognitive science journey is the expert vs novice thinker conversation, particularly as it relates to physics. Daniel Willingham discusses this in his book Why Students Don’t Like School, “experts don’t think in terms of surface features, as novices do; they think in terms of functions, or deep structure.”  In Dr. Jose Mestre’s book he talks about an experiment where students were asked to sort physics problems. The experiment showed that novice students tend to sort problems by surface features  whereas the “experts” sorted the problems by the big idea, specifically the major physics concept used to approach the problem. 

Part of what makes physics, as a course, so difficult for all students is the necessity to move towards an expert type of thinking in  order to approach problems. It is an experiment I would love to run formally, but in my experience there is a marked difference between the first 2 weeks of physics and week 10. By week 10 it’s like a switch has flipped for all of the students and the impossible is suddenly possible. Of course, there is no magic switch, rather students have begun to adapt more “expert” ways of approaching problems. 

A really great example of exposing novice vs expert thinking is card sorts. Brian Frank has created an abundance of these sorts and they are amazing to work with. I particularly like the way Kelly O’Shea runs her kinematics exercise with students. First students are given just the graphs and asked to organize the cards in any meaningful way. Every time I do this assignment students decide to organize the graphs based on their shape OR they put all of the position graphs together, velocity graphs and so on. They make little to no connections between graphs (such as a parabolic position graph goes with a linear velocity graph etc). When students are satisfied the teacher realizes she forgot to pass out some cards” and drops label cards. These cards begin to get students to reorganize the cards in order to make the cross-connections. This also gives students a “second pass” with the material.

Ok, so it’s easy to see students acting like students, but how to we get them to think like physicists?

Strategies for Training Students

I love this puck problem below. The premise is beautifully simple. Same force, one puck has more mass, compare the change in momentum.

The novice student thinking looks like this:

  • Change in momentum is mΔv.
  • M is bigger on A, so A has the bigger momentum change.
  • M is bigger on A and now I need to calculate v (lots of calculations later and fumble around with force).

The expert thinking looks like this:

  1. Impulse is equal to change in momentum.
  2. The force on both is the same.
  3. The mass on A is bigger, so it will take longer to get it to the finish line.
  4. Therefore Ft for A is bigger, so mΔv must be bigger.

Students are in shock by how simple and elegant the expert solution is. But it really just comes from ONE critical shift, pulling out the big idea rather than pointing to where change in momentum is explicitly stated.

AP provides another sweet opportunity to practice this skill and it is embedded in the paragraph-length response. Too often students see the format and just start to free-write. I discuss with them that they need to draft their response, much like a typical essay, but in a physics-friendly manner. They should (1) determine the big idea (2) set up the problem as if they were to solve it (3) Any step along the way becomes a sentence or bullet point towards the answer.

I work with students directly on this skill during classwork. I have a series of energy problems that I love to do this with. I have them whiteboard answers for speed and accuracy and I provide some very specific directions (1) Write your conservation statement (2) Write your proportionality statement (3) write your answer.

AP Physics 1 Multiple Choice: The Exemplar of Expert Thinking Processes

Every year I have a few AP students who are so close to an A but can’t seem to push over the edge. Additionally, I often have a handful of students who, if you were to talk to them, clearly have a solid grasp of the content but they absolutely tank the AP Physics 1 multiple choice items. The beauty…and poison of  AP Physics 1 multiple choice items is their requirement to think like an expert. The questions and responses are immensely loquacious and even though AP provides students with nearly two minutes per item students tend to fall into two traps: first, they are so used to multiple choice being factual items that you either know or don’t know and move and, and second, they try to be so careful that they lose sight of the forest for the trees. After the exam students frequently get mad that the questions were so “easy” or “obvious” “when you explain it” often placing the blame on me for not providing enough worked examples. Instead, we need to shift the narrative and turn the ownership back to the student. We cannot shame them, instead we need to train them on how to better approach any problem, not the 10 on Tuesday’s test.

I have found that having small group conversations with students about this to be highly effective. Willingham further describes in his chapter about novice vs expert thinking that experts have conversations with themselves which allows them to dissect the problem, focus on the important information and test ideas. Novices, on the other hand, rarely do this due to the cognitive load required of them. Having these conversations with my students helps train them in this type of procedure in order to make them more readily do the process on their own. 

We go through the multiple choice items together and I ask them a lot of questions. I ask them to identify the big idea, then I probe them to tell me about components of that big idea that relate to the problem. Only then do we begin to look at the answer options. When you probe about the big idea first, several options quickly show themselves as incorrect. A wonderful example are the multiple choice items that you might label “Newton’s third law”. As soon as a student sees the phrasing how does the force of A on B compare to the force of B on A, the rest of the problem should be irrelevant, whether there are numbers, masses and so on. So if I were working this problem with a student I would ask them to identify it as a force problem, then I would ask them what our class definition of forces is (an interaction between objects) and since a force is defined as such, we can cut through the distractors and identify the correct answer. 

Another strategy I use in my classes is I will literally hand them the exam a week prior to test day. However, I have made one very important adjustment: I take the question and all of the letter options off. Instead, students are presented with a scenario and they have the freedom to discuss with their peers the possibilities for the exam. I do this as an in-class activity, so students are not leaving the room with exam questions. Some students have reported back that this process makes them more anxious for the exam because they come up with exceedingly challenging possibilities, however in the end what it does is it allows students to perform on assessment day at the level they deserve. What happens here is, once again, students are engaged in conversations. They can transform these conversations into self-talk when they take the test. The idea that they have the actual exam in their hand means they know a 100% is possible if they talk to everyone, so they do not waste time working alone.

My tagline on this blog is “infecting students with passion” I definitely try to infiltrate their brains in several ways, and moving them towards expert thinking is one of them. As I tell them often, it’s my goal to get them to have conversations with me in their head when they sit an take the exam so it can feel as easy as a real-life conversation and they can knock it out of the park.

So tell me…

  1. What does expert vs novice thinking look like in your classroom?
  2. How have you tried to model or scaffold expert thinking and practices for your own students?
  3. What are you ready to commit to doing differently when we return in January?

In My Class Today · Teaching Methods

Day 2: Thinking about Relationships

Day 1 I run a HUGE physics smorgy: 11-15 demos/lab set ups with minimal directions. Students are told to play, investigate, explore, PAY ATTENTION and ask lots of questions. This is my hook into the class for the year. I’m able to observe the students, act ridiculous and ease the MASSIVE anxiety they walk into this class with.

The next four days we actually spend working with data and relationships. Specifically to build the skills necessary to analyze data on a graph and straighten it when needed. I have a reading I ask students to do ahead of time and then we go through the straightening process. These brilliant students (half of whom are in AP Calc) are completely flabbergasted by the straightening process. It just doesn’t. make. sense to them.

I decided to try something different today on the fly, and it brought about some great conversations. First I put up blank sketches of graphs depicting a linear, squared, inverse and square root function. I asked them to put the graphs on their white boards and write the relationships. The answers consisted of the following:

  • “linear, squared, inverse and square root”
  • y=x, y=x^2 (etc)
  • y∝x y∝x^2 (etc)

This kicked off some great conversations. Are we in agreement, generally, about which is which? (yes). Are the equations really representative of the sketches? (We don’t know, there are no labels or numbers on the axes)

Next, I gave students four statements

  1. “Momentum is proportional to velocity”
  2. “A spring loaded gun is fired upward. The height of the bullet is proportional to the compression squared”
  3. “Velocity is inversely proportional to mass”
  4. “The period squared is proportional to the length of a simple pendulum”

I asked them to label the axes of their graphs with the physical quantities to match the statements. Here’s where the fun began. Students took a lot longer than I had originally anticipated completing this task. Here were the great conversations to be had:

  • In science, we usually put the independent and dependent variables on the x and y axis. With these statements, is it obvious which is which?
  • Since it’s not obvious, are answers where the axis are flipped wrong? (Not if they picked the appropriate shape!)
  • So, we often are going to use slope to talk about relationships. Like, say, if we plotted distance on the y and time on the x what would we get? (speed…minds are blown)  The cool thing is if you plot the graph “wrong” you can look at the units,  and decide if they need to flip because you’d have seconds per meter or something. The important thing is whatever you tell me the relationship is, needs to match your graph.
  • Then, of course, I let them in on the secret: we always list the y thing first. Literally all we are doing in these sentences is taking the math proportions, like y∝x^2 and saying, instead, height ∝ compression^2. It’s like the hugest lightbulb moment for students ever.

Now that they have that substitution thing in their brain, explaining how to straighten graphs is a snap. I was really pleased with the lack of frustrated and confused faces. Last year, I sadly, lost several kids during this unit. I wanted to cry so hard because we hadn’t even started physics and seriously questioned my lesson plans.

Tomorrow they finish their pendulum labs, so we’ll see how this all goes.

Meanwhile, AP Physics C is dabbling in computational physics for kinematics. More on that later.


In My Class Today · Teaching Methods

I did something I would NEVER do in most classrooms

Anyone I have spoken to one on one knows that my group of AP Physics C students is truly a unique group. They are the kind of group that comes around once every few years and makes your teacher heart soar…so you bring them up with you and cast them off and they fly higher than even you could have imagined.

So I thought I’d try something radical. Work on a skill that was far greater than their ability to do physics. I wanted them to focus on the learning process.

We are starting the Biot-Savart Law. Students need to do the derivations for a line, ring and ring segment of current. The reality is that the math skills are no different from anything they haven’t already seen before. But as we know, often times when students are presented with a new application it’s like everything they’ve learned is back to zero. The reality, of course, is that they lack the experience and mastry to be able to make those connections as we do as teachers. So I assigned the reading several nights ago. I asked students to take particular note of the three examples, and then I assigned the students in groups to one of the three examples.


The paper they received, however, was not a carbon copy of the book’s example. Because we know what students do when we ask them to read. They skim. They decide they can understand how the author got from step 1 to step end and they move on. But we know if we asked them to do a similar problem they would barely know where to start. I wanted them to actively engage in the material in the text. So I told them they had to prepare their assigned problem to teach to the class, instead of me teaching it.

Students had 2 nights to prepare plus 30 minutes to discuss in their groups the day before. Today was presentation day.

Imagine your first year teaching and that lesson you thought you’d be fine at, so you didn’t quite prepare it the way you should have. That’s what happened. But it was ok because I knew that all of my students would be ok. They challenged each other, they forced the students presenting to slow down, they asked the necessary clarification questions that required the presenters to really think about what they were doing rather than regurgitating text.

After the group had come to the end, I stepped in. I asked the group to step back for a moment so we could summarize (because we all know what happens when we get lost in the details and the mistakes…) I asked the students to explain why we did each step and connected it to what they had seen before. If notes or annotations needed to be added to the board, we added them. Once we were certain everyone was securely on the same page we moved on.

At the end I explained my goals of this exercise  to my students. Not only do I want them actively engaging and learning (and seeing you CAN learn) from the text, the reality is that since they are ALL pursuing STEM majors there is a VERY REAL possibility that they will each be in a teaching assistantship in the next 3-5 years. They are going to need to learn how to teach what they are comfortable with, what they may not have been comfortable with, or something they learned 4-5 years ago. These teaching and communication skills are so valuable and go well beyond the world of academia.

I almost backtracked on this assignment and took over today, but I’m really glad I didn’t. My students once again rose way above and beyond what I expected. Working with a group of gifted AP Physics C students can be really challenging because finding the sweet spot of struggle vs overwhelming is a lot higher than one might anticipate, and in this course I think that sweet spot is higher than even the students realize. But that sweet spot is where the largest amount of growth happens, and I think we hit it today.

Concept Modeling · In My Class Today · Teaching Methods

Pass Along – Modeling Waves

The pass along activity is one I developed shortly after attending a Kelly OShea workshop. I wanted to combine modeling with the strengths of white board speed dating and board walks. At the time I didn’t have the large whiteboards and for this particular activity I decided a piece of paper would work best.

Students have already done a reading on waves ahead of time (hopefully).

Part I: I ask students to draw in a pictorial representation of what a longitudinal and a transverse wave might look like.

This is inevitably the most common drawing. Students obviously did the reading, but struggle with a pictorial representation

Students are then told to pass along their paper. I predetermine groups randomly for this activity. Three is best, but if I don’t have a factor of 3 then I put the stragglers into groups of 4. It looks like this:

Student 1 -> Student 2 -> Student 3 -> Student 1

Part II: After students have passed along, they are required to look at the work done by their peer and explain, in words, why that person drew what they drew. Much like speed dating, this requires each of the students to get in the minds of their peers, but without the opportunity for their peers to explain.


Students then pass along again.

The third person takes a look at the previous two answers and then has to think of a way to model each wave type with their bodies.

After the three pass alongs, students get into groups, at this point each paper has been touched by the same persons. They discuss their answers and then they have to get up in front of the class and model with their bodies each wave type.


The physical modeling is great in that the kids are up and moving, but it also provides an opportunity to have a discussion about the model. 7th hour we had a discussion about whether or not doing the worm accurately models a wave (nope, the particle is moving across the room). Similarly, I had a few groups move their whole line down the room which brought up the discussion point about what a wave transfers and doesn’t transfer.

Afterwards, we will go out as a whole class and model transverse and longitudinal waves using an 8-step count.

A unique representation of a longitudinal wave I hadn’t seen before

Teaching Methods

AP Physics C in the Accelerated Classroom: Addressing the Needs of the Gifted and Talented in Physics

Gifted and accelerated learners have specific needs in the classroom that frequently go unmet. It is a grievous error to assume that just because a student is gifted they will be successful. Differentiation is often viewed as incredibly labor-intensive on the part of the teacher with difficulty in grading different products fairly. This is of particular challenge in the current Advanced Placement (AP) Physics C program since, under the college board recommendations, many physics C students already have a strong foundation in mechanics from AP Physics 1 (algebra-based). This paper will share a particular example used in the lab in an AP Physics C gifted classroom and how the products are easily differentiated and scored in a fair manner.


Introduction to Gifted and Talented Learners

The first thing that must be noted is that gifted learners exist in every classroom. The second thing that must be noted is that gifted and talented looks different on each individual. Additionally, when students are put through an identification process, minority and English language learner students are overwhelmingly unidentified.

Identification of gifted and talented students is immensely important because research has shown that in the absence of the ability to nurture student talents, many of these students will, in fact, underperform. Students are either placed in environments that lack rigor and challenge and so they disengage because they are bored, or if the teacher identifies the student as “smart” the teacher often does not recognize specific markers of giftedness that contribute to student behavior in the classroom, prohibiting the teacher from allowing appropriate accommodations.

It is important that every classroom teacher become aware of giftedness so that they can best address their students. Much in the same way that we will readily allow a student with ADHD to stand during class, or use a fidget, we must also recognize that gifted and talented students have their own set of needs to be challenged and to grow.

Although there is no one blanket description for students who are gifted and talented, there are some unique markers. Much like a student who may be diagnosed with a special need, gifted and talented students’ brains are physiologically different. They have a thicker pre-frontal cortex that develops differently from their peers and they, in fact, have more and stronger neural pathways than their peers2. Not only do they think differently, they perceive the world in a different manner. In the absence of development of talent, gifted individuals can lose the strength of their pathways, rather than expanding them.

One of the most clear differences in gifted students is that they exhibit one or more over excitabilities. Overexcitabilities describe a series of traits and/or behaviors that gifted individuals feel on a level that is far more intense than the general population. These include the following: intellectual, emotional, psychomotor, sensory and imaginational. Intellectual is what people are most familiar with when they think of giftedness: avid readers, love of learning, independent thinking etc. Emotional are the students who often have an overwhelming sense of empathy for their friends and family. Due to this they are often the ones who will take up causes for advocacy. They also may exhibit extremely intense anxieties. Individuals with psychomotor over excitabilities are often misdiagnosed as having ADHD, they may talk fast, act impulsively and seem to run on little sleep. Sensory have a heightened sense in the five senses, they are often extremely interested in the arts and have a depth of interest in aesthetics. They may also, however, be unusually sensitive to smells and tastes. Individuals with imaginational overexcitabilities are the ones who are constantly daydreaming, visualizing, Males tend to score higher on the intellectual and psychomotor areas while females tend to score higher on the emotional and sensual over excitabilities3

AP Physics C for the Gifted and Talented

Acknowledging these needs for gifted students, what is a teacher to do? Two of the most important tools are acceleration and differentiation.

We often think of acceleration as grade skipping. While this is useful for many students, it is not in our grasp as classroom teachers. We should, however, not prohibit say, a sophomore, from enrolling in physics if they have met the appropriate math pre-requisites. Surprisingly, acceleration at the grade level has shown to somewhat close the gender gap in publication and salary for female students4. At the classroom level, where we have control, this means compaction of curriculum. I lean most heavily on this for my students.

Since the students in my class have all taken AP Physics 1, they have an incredible depth of conceptual foundation as it relates to mechanics. This was, indeed, the goal of the revised course. The challenge now, however, is to make AP Physics C exciting, interesting and challenging. At the same time the goal of any high school teacher should be to equip their students with the foundation for the skills needed in college.

For any STEM field, we know well that lab skills are indispensible. At the same time, we also know that creating a genuine lab experience when students have little to no lab experiences is extremely challenging. There is a certain level of base knowledge needed to have a valid lab experience from start to finish. Fortunately, students in AP Physics C have already obtained that base knowledge. The only difference is that now my students are required to incorporate calculus.


The Flipped Accelerated Classroom

I operate on the premise that first, the majority of the physics concepts should be review, and second, the lab experience is the most important experience in my classroom. While it is not imperative to student success that they be able to determine an obscure moment of inertia, it is imperative that they enter college with a basic skill set that includes troubleshooting, use of basic equipment, creativity, critical thinking and problem solving strategies. On the first day of school I gave my students the following assignment: design a product that demonstrates to me that you have mastery over all of the AP learning objectives for kinematics.

Immediately this assignment is differentiated: students have almost endless choice. They have full access to all lab equipment plus anything else they would like to use or bring in. This is, at first, an extremely challenging prospect to students. They are not used to having so much choice, their activities have more or less been dictated by the goal and/or equipment available. This is not true of real research; in that case you must select a project, investigate, and produce results.

We recently did the same with momentum. Since this topic is much more in-depth than kinematics, I assigned nightly homework sets and provided solutions the following day. The homework was not collected or scored as I am leaving it in the student’s hands to determine how much repetition is necessary for themselves. In this unit they were asked to design a lab in which all of the objectives are present. Since this project would inevitably include many other topics within mechanics I provided a little bit more guidance, encouraging students to start with a question. Within the first class period I had a group investigating a buoyant object dropped into a container of water (Fig 1)

and analyzing with Vernier VideoPhysics, another group analyzing the deflation of a balloon attached to a string with a straw, a third looking at spring pendulum, and a fourth examing a dynamics car attached to a spring on a horizontal surface. Each of these involved a varying force (not a requirement, but an option for the exemplary plus mark) and in the case of two of the experiments, students needed to study topics they had not yet covered as it related to their problem.

Student Products, Evaluation and Presentation

Student products vary n terms of level of complexity and interest, but they have always been exciting to grade. The first challenge, naturally, is scoring the product in a way that is fair for all students, given the large variety. To this end, I grade the products based on how well they meet each of the objectives, from Exemplary to Unsatisfactory. In order to permit students who are more mathematically advanced or who would like to go for the challenge, I include an exemplary plus category. At the beginning of the year this category was for any correct application of calculus, once the year progressed this category needed modification to ensure the same level of challenge.

Students are also expected to present their results and provide feedback to their peers. We do a type of poster presentation session. Students put their procedure, lab design and results on a large whiteboard. (Figure 2) , one partner circulates the room while the other remains at the board to present to their peers. During this time period students are to ask one another questions, whether it be for clarification, or as a way to offer a suggestion. (Figure 3) After students have moved through the room, original partners move together. The partner who circulated initially now must explain each board to their partner. As they do so, they are asked to leave feedback on a smaller board. At the end of this exercise, groups return to their boards and review the feedback. I then give students another few days to make adjustments and corrections before turning in the lab.

Applications for the Mixed Classroom

Allowing student choice and differentiation for gifted students is just as important as allowing other students extra time on exams or the ability to use a fidget. The reality is that just as our classrooms often will have students with special needs due to a disability, we likely also have a non-zero number of gifted students as well, who’s needs must also be met. In a mixed classroom, this might mean generating both the guided and open-ended lab. The modeling curriculum works very well for all students, but the differentiation component is key. Gifted learners should be permitted to do less repetition as long as they can prove mastery. They should be permitted to work together in class sometimes (ability-based grouping), rather than always grouped with the struggling students so they have the opportunity to flourish with like minds, much as we appreciate upon entering college.


Conclusions and Benefits

This type of activity and assessment has served multiple purposes. First, it allows for differentiation within the gifted classroom. Students have the ability to make their products as simple or complex as they determine, while still meeting the learning objectives. Secondly, it requires students to make a variety of considerations and assumptions such as which equipment will be best, how to control for a variety of variables, and which variables can be simplified due to assumptions or uncertainty measurements. (For example, in my group that examined the deflating balloon, they massed the weighted balloon on an extremely precise scale and noted it was loosing mass, even while tied. ) Students are using and improving on lab skills and techniques. Lastly, students are learning the importance of clear communication and critical evaluation. In a time where even undergraduates are expected to produce publishable research, communicating, evaluating and responding to evaluations become ever more important skills. By focusing on these at the high school level, students become better equipped for whatever their future holds.