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Reducing Circuits: Solve for Everything, Everytime

October 16, 2014

With circuits this year, I’ve been teaching a “solve for everything” approach that balances circuit reduction with reasoning about Kirchoff’s rules. First students reduce the circuit and then work to determine the current, potential differences, and power outputs of each device.

For example, on the student whiteboard below, they were supposed to find the power output at Resistor Three. I’ve been pushing for solving for the power input/output of everything, so they can check energy conservation.

Circuits

I worried about teaching them to use the table, that maybe it would turn it into a mindless numbers game, but the organization actually allows students to spend energy on reasoning for how currents / potential differences should relate. It also just helps with the book-keeping so keeping track of what they know and don’t know easy. It also makes checking work easy. The first two columns should multiply to the third column by Ohm’s Law. And the 2nd and 3rd columns should multiply to the 4th column by the power relationship. A colleague of mine extended my table method to include all the equivalent resistors along the way as well.

Overall, I’m pretty happy with this approach. One tweak I would make would require them to write/diagram their reasoning about how the Kirchoff’s reasoning–either in algebra or using the diagrams.

Broadening Participation Research in PER: A Slightly More Comprehensive Look

October 13, 2014

I really enjoyed reading and thinking about this post: What Computing Education Research does that Engineering Ed and Physics Ed Research doesn’t

One of the claims put forth in the post is the Computing Education Research (CER) community seems to have more lively and stronger focus on broadening participation than either the Physics Education Research (PER) of Engineering Education Research (EER) communities. From that post:

“Carl [Wieman] said that gender diversity just wasn’t a priority in PER. I dug into the PER groups around the US. From what I could find, he’s right. Eric Mazur’s group has one paper on this issue, from 2006 (see here). I couldn’t find any at U. Washington or at Boulder. There probably is work on gender diversity in physics education research, but it certainly doesn’t stand out like the broadening participation in computing effort in the United States.”

I thought I would dig a little deeper, and do just a quick survey of all articles published in Physical Review–Special Topics in Physics Education Research, which touched upon gender, participation, or highlighted international research. I should note that the list below is based on titles only–I didn’t read the abstracts or the papers. While this isn’t a thorough analysis, it paints a slightly less bleak picture than one paper published almost a decade ago.

Note: I’m certainly not looking to pick a fight about PER vs. CER or EER. I feel much like the author of the post, who writes:

I don’t have a deep bottom-line here… My exploration of EER and PER gave me a new appreciation that CER has something special. It’s not as big or established as EER or PER, but we’re collaborative, international, working on hard and important problems, and using a wide variety of methods, from in-classroom to laboratory studies. That’s pretty cool.” 

The authors post has made me pause to think about our priorities and prodded me to dig a little deeper into the data to see what the situation is beyond just trusting Carl’s Wieman’s comment and a quick examination of just two research groups.

Note 2: I also added relevant presentations from most recent PER Conference.

Gender Studies

Gender gap on concept inventories in physics: What is consistent, what is inconsistent, and what factors influence the gap? Adrian Madsen, Sarah B. McKagan, and Eleanor C. Sayre Phys. Rev. ST Phys. Educ. Res. 9
Comparative analysis of female physicists in the physical sciences: Motivation and background variables .Katherine P. Dabney and Robert H. Tai Phys. Rev. ST Phys. Educ. Res. 10, 010104 (2014) – Published 3 February 2014
Female physicist doctoral experiences Katherine P. Dabney and Robert H. Tai. Phys. Rev. ST Phys. Educ. Res. 9, 010115 (2013) – Published 10 April 2013
Factors that affect the physical science career interest of female students: Testing five common hypotheses. Zahra Hazari, Geoff Potvin, Robynne M. Lock, Florin Lung, Gerhard Sonnert, and Philip M. Sadler. Phys. Rev. ST Phys. Educ. Res. 9, 020115 (2013) – Published 22 October 2013
Preliminary investigation of instructor effects on gender gap in introductory physics. Kimberley Kreutzer and Andrew Boudreaux. Phys. Rev. ST Phys. Educ. Res. 8, 010120 (2012) – Published 4 May 2012
Gender disparities in second-semester college physics: The incremental effects of a “smog of bias” Lauren E. Kost-Smith, Steven J. Pollock, and Noah D. Finkelstein. Phys. Rev. ST Phys. Educ. Res. 6, 020112 (2010) – Published 3 September 2010
Characterizing the gender gap in introductory physics Lauren E. Kost, Steven J. Pollock, and Noah D. Finkelstein. Phys. Rev. ST Phys. Educ. Res. 5, 010101 (2009) – Published 8 January 2009
Gender differences in the use of an online homework system in an introductory physics course Gerd Kortemeyer Phys. Rev. ST Phys. Educ. Res. 5, 010107 (2009) – Published 26 May 2009
Reducing the gender gap in the physics classroom: How sufficient is interactive engagement? Steven J. Pollock, Noah D. Finkelstein, and Lauren E. Kost. Phys. Rev. ST Phys. Educ. Res. 3, 010107 (2007) – Published 5 June 2007

Participation Studies

How do they get here?: Paths into physics education research Ramón S. Barthelemy, Charles Henderson, and Megan L. Grunert. Phys. Rev. ST Phys. Educ. Res. 9
Physics teachers’ perspectives on factors that affect urban physics participation and accessibility Angela M. Kelly. Phys. Rev. ST Phys. Educ. Res. 9, 010122 (2013) – Published 19 June 2013
Educational trajectories of graduate students in physics education research . Ben Van Dusen, Ramón S. Barthelemy, and Charles Henderson. Phys. Rev. ST Phys. Educ. Res. 10, 020106 (2014) – Published 21 July 2014
Toward equity through participation in Modeling Instruction in introductory university physics
Eric Brewe, Vashti Sawtelle, Laird H. Kramer, George E. O’Brien, Idaykis Rodriguez, and Priscilla Pamelá. Phys. Rev. ST Phys. Educ. Res. 6, 010106 (2010) – Published 20 May 2010

International Studies

Secondary implementation of interactive engagement teaching techniques: Choices and challenges in a Gulf Arab context G. W. Hitt, A. F. Isakovic, O. Fawwaz, M. S. Bawa’aneh, N. El-Kork, S. Makkiyil, and I. A. Qattan. Phys. Rev. ST Phys. Educ. Res 10, 020123 – Published 6 October 2014

Introduction of interactive learning into French university physics classrooms Alexander L. Rudolph, Brahim Lamine, Michael Joyce, Hélène Vignolles, and David Consiglio. Phys. Rev. ST Phys. Educ. Res. 10, 010103 (2014) – Published 27 January 2014

Validating the Japanese translation of the Force and Motion Conceptual Evaluation and comparing performance levels of American and Japanese students Michi Ishimoto, Ronald K. Thornton, and David R. Sokoloff. Phys. Rev. ST Phys. Educ. Res. 10, 020114 (2014) – Published 19 August 2014
Effectiveness of Tutorials for Introductory Physics in Argentinean high schools J. Benegas and J. Sirur Flores. Phys. Rev. ST Phys. Educ. Res. 10, 010110 (2014) – Published 24 March 2014
Introducing Taiwanese undergraduate students to the nature of science through Nobel Prize stories Haim Eshach, Fu-Kwun Hwang, Hsin-Kai Wu, and Ying-Shao Hsu. Phys. Rev. ST Phys. Educ. Res. 9, 010116 (2013) – Published 25 April 2013
Student effort expectations and their learning in first-year introductory physics: A case study in Thailand U. Wutchana and N. Emarat. Phys. Rev. ST Phys. Educ. Res. 7, 010111 (2011) – Published 24 June 2011

Other

Validation study of the Colorado Learning Attitudes about Science Survey at a Hispanic-serving institution Vashti Sawtelle, Eric Brewe, and Laird Kramer Phys. Rev. ST Phys. Educ. Res. 5, 023101 (2009) – Published 28 August 2009

Presentations at 2014 PER Conference:

Exposure to underrepresentation discussion: The impacts on women’s attitudes and identities by Geoff Potvin, Zahra Hazari, Robynne Lock

Female Students’ Persistence and Engagement in Physics: The Role of High School Experiences by Zahra Hazari, Eric Brewe, Theodore Hodapp, Renee Michelle Goertzen, Robynne M. Lock, Cheryl A. P. Cass

The Impacts of Instructor and Student Gender on Student Performance in Introductory Modeling Instruction Courses by Daryl McPadden, Eric Brewe.

The Long Term Impacts of Modeling Physics: The Performance of Men and Women in  Follow-on Upper Level Physics Courses by Idaykis Rodriguez, Eric Brewe, Laird H. Kramer.

The Experiences of Women in Post Graduate Physics and Astronomy Programs: The Roles of Support, Career Goals, and Gendered Experiences by Ramon Barthelemy  Melinda McCormick, Charles Henderson

Discussing Underrepresentation as a Means to Increasing Female Physics Identity by Robynne M. Lock , Zahra Hazari, Reganne Tompkins

Exploring the gender gap in one department’s algebra-based physics course by Twanelle Walker Majors, Paula V. Engelhardt, Steve J. Robinson

Race and Gender and Leaving STEM: Preliminary Results of The Roots of STEM Project by Melissa Dancy  Elizabeth Stearns, Roslyn Mickelson, Stephanie Moller, Martha Bottia

Concluding Comments:

I’m not sure what this mean, if anything yet, but that’s what I did this morning. Making this list doesn’t prove anything about our fields priority in these matters–we’d have to look at funding, impacts, white papers, etc. But for me, it’s a beginning in looking into it

If you feel I missed an important Physical Review paper or PERC 2014 presentation, let me know in the comments.

Logic and Reasoning– Tools for Empowerment or Coercion?

October 11, 2014

We just came into that week in Physics Licensure–the week where students start asking, “Did I learn anything in Physics I?”

As I’ve talked about before, Physics Licensure I and II are very much a band-aid sequence of courses for our future physics teachers–helping students to develop the reasoning skills and conceptual understanding they didn’t have much opportunity to learn our introductory physics sequence.

Students are really struggling with reasoning about Newton’s Laws. The course, being a band-aid, isn’t really providing the right kind of opportunities either. We go through tutorials each week, students do tutorial homework, and they have to write brief reflections each week. In addition they work some AP physics problems, and they have to make ongoing concept map to make connections among what they are learning. In all that, students get a fair amount of practice building concepts and reasoning, but they don’t get enough opportunity to explore and grapple with actual phenomena.

We’ve encountered many days where students seem to follow along with a guided line of reasoning stemming from Newton’s Laws (not easily).  At the end of it, someone will say, ‘That makes no sense”. In that, they are understanding and can produce the logic of the argument, about how if N2nd Law and N3rd law are true, it implies that some other conclusion must be true. To students, N2nd and N3rd law are not ideas they “own”; they aren’t using these ideas to discover puzzling implications about the world. Rather, the guided reasoning they are asked to follow coerces them into concluding things they’d really rather not say and definitely don’t believe. They aren’t happy about it.

My sense as a instructor is that many of our students still largely think that force is in the direction of motion, that you have to push harder than friction (or up against gravity) to keep an object moving steadily, that pushing harder will result it moving faster. Sure, you can remind them of Newton’s 2nd Law, and they can be coerced into saying something more correct, but it’s definitely coercion.

That’s how we’ve gotten to the place where students are saying, “I think I learned nothing in Physics I”. These students need a lot more experience with phenomena and grappling with their own ideas, the ideas of each other, etc. Right now, I don’t think I’m providing what they need.

Aggregating Three Posts on Research (and the FCI)

October 11, 2014
tags:

I’ve written a few posts about research (and the FCI) that I’d like gather in one place:

Physics Education: Research, Assessment, and Poverty

http://teachbrianteach.wordpress.com/2013/07/20/physics-education-research-assessment-poverty/

Disaggregating Learning Gains

http://teachbrianteach.wordpress.com/2013/08/09/disaggregation-of-learning-gains-please-argue-with-me/

Standards of Reporting FCI Data

http://teachbrianteach.wordpress.com/2014/07/16/per-standards-of-reporting-fci-data-mixed-results-on-recent-papers/

A pretty decent warm-up: Comparing & Contrasting Blackbody Radiation and Photoelectric Effect

September 19, 2014

Yesterday, we had a break from the pace in Physics II, Instead of introducing new material, we had a day to review what we had learned about blackbody radiation and the photoelectric effect. So far this semester, most have my warm-ups have been forward looking–the aim being to prepare students to maneuver more efficiently and confidently through the rest of the day. But today, the warm-up was backward-looking.

The warm-up consisted of a table I had constructed at the front board. The two columns were, “Blackbody Radiation” and “Photoelectric Effect”. The rows of the table were the following questions

– What is being emitted? Where is it being emitted from?
– What causes this emission to occur?
– What physics quantity (or quantities) characterize how strong the emissions are? (words, symbols, units, any relevant equations)
– What, if anything, does “color” have to do with it? (words, any relevant equations)
– In the situations/problems we’ve discussed, what’s typically happened to the emissions after being emissed?

Students were in groups of three and were asked to discuss each question as a group, and then to write their response on a sticky note. Groups populated the board with their responses, and were asked to look over other groups responses.

Students took to the task pretty well–seriously engaging in the questions and in the efforts to compare and contrast what’s happening in each case. What was nice is the range of “correct” answers. For example, with the photoelectric effect someone might say,”Light is emitted” or “Electromagnetic radiation is emitted” or “Photons are emitted”. For what causes this, someone might write, “Light that is incident on metal,” or “Photons colliding with electrons”. For what happens to blackbody radiation, students might say, “It spreads out and gets less intense”, or “It goes off and heats up a planet =)” While some of what students was more vague or more precise than others, very few things were way off the mark.

After they were done, I mostly just reviewed the things that students had written and helped connect their ideas to the more precise ideas and quantitative relationships they had learned. The one place we needed to talk about the most was the role that “color” played in the photoelectric effect. I asked students to talk about that one in particular back in their small groups. Back in whole class discussion, the main idea that came up was, “Bluer light tends to be more effective at ejecting electrons from the metal”. When I asked how we knew that was true, there were two different ways that students offered for making sense of this. First, was reference to observations with the PhET simulation, that we found that UV light almost always emitted electrons but red light almost never emitted electrons. I added how, when the light got even bluer, the electrons came off faster as well. Another student worked through the reasoning that bluer meant lower wavelength, and that lower wavelength meant higher frequency, and that higher frequency meant more photon energy, which meant larger lumps of energy to give to electrons” That chain of reasoning, of course, involves drawing on several different relationships and chaining them together, so I did some work to clarify that. Looking back, I could have slowed down even more on that reasoning, asking students to go through that reasoning careful amongst themselves in groups.

In general, the warm-up went well, with student engagement being high; contact with important disciplinary ideas being high; and students expressing that they felt like it was a valuable activity from which they learned a lot (and being able to articulate what they had learned). It’s a good day when you get all three of those things. I think it’s fairly easy to get either of the first two–engaged students but not with important disciplinary ideas or a lesson that should put students in contact with disciplinary ideas but they aren’t engaged. And then, even when you get both of those things occurring, it’s not necessarily true that students leave class feeling like they have learned a lot and can express what learning took place.

Two other things on my mind are these:

– The activity went well, in large part, because of the students. I more and more see how–despite the fact that I do have a strong influence on student engagement–a good classroom is really a mutual activity in which the teacher and students coordinate their activity to achieve engagement and learning (or don’t). In particular, this activity of writing on sticky-notes and putting them on the board is not something we typically do in this class, and it might have been easy for students to think it was juvenile or just weird, and disengage as a kind of passive resistance. For whatever reason, that didn’t happen. It makes me think about Dewey’s notion of submitting to an experience–letting the experience happen to you.

– Compare and contrast is not a strong part of our curriculum. Students are rarely asked to think about how ideas or phenomena are related. We just march through… one thing to the next. I’m hoping that by asking students to do more compare and contrast that students can, to a limited extent, experience a more coherent curriculum. Not sure, exactly how it will unfold, but returning the comparison contrast makes sense as next week we encounter atomic spectra and nuclear radiation. Many of the same questions above are relevant…

More on Mediocre Warm-Ups that Pay Off Well

September 12, 2014

I’m following up my previous post about warm-ups in Physics 2, where I’ve been trying to use warm-ups as a venue for extracting more value out of class without giving up much time. So far, the experiment seems to be paying off.

But, what do I do on a day when I really don’t have much time to give up to warm-ups and I really don’t have much time to plan a whole activity? For this, my go to move over the past few weeks is to just look at some of the tricky mathematical or procedural aspects of the problems we will be solving and make them warm-ups.

For example, we were doing problems with diffraction earlier this week. I know that students struggle with unit conversions in these problems because the exponents are large. For example, in diffraction problems you are dealing with nanmeter wavelengths, micron apertures, grating densities described in cm or mm, lengths describes in m or cm, and diffraction patterns described in mm. I also know that students do not know or remember anything about the small angle approximation, which comes up in a our lab. So there you go, two warm-ups for the day– a little bit of practice doing unit conversions with a focus on talking about different strategies, and little mini-exploration of how tan, sin, and theta compare for different triangles. I actually pick values for them to practice that show up in my example problem, their problem, or the lab.

During class, I realized another warm-up that we needed was thinking about how to relate “slit density” to “slit spacing”. Not sure exactly what that warm up would be, but that reasoning is always a struggle for students. It’s the same reasoning that shows up elsewhere in physics, so I’ve seen students struggle this and resort to memorization of formulas like T = 1/f.

All and all, the key I think to these “obstacle” warmups is to emphasize the reasoning and strategies, and this alone helps makes them pretty good warm-ups even if how I structure the warmup isn’t all that great. By front-loading some of the obstacles well before they encounter them in the midst of problem-solving, it makes the classroom more manageable. Without warms ups, I’ll often get six of out of eight groups stuck at the same spot at the same time. With warmups, maybe only one or two groups will need some help from me on those areas, and usually it’s just a reminder of the strategies we talked about in the beginning. Students feel a little more equipped to tackle the problem.

I imagine you could certainly go overboard, trying to frontload all the obstacles and that would be a mistake. I think my goal is to front-load the obstacles that obscure thinking about the underlying physics.  I could also think about front-loading such obstacles for pre-class assignments, but then I think it would be harder to focus students on the reasoning and strategies.

Note: I think one reason I’ve been thinking about this part of my planning so much is this: I want to be able to circulate around the room and have interesting conversations with my students about their understanding of the physics, but that just doesn’t happen if my students are frustrated, or bogged down in things like unit conversions, or all simultaneously stuck on the same part of the problem. My best attempts at proximal formative assessment (e.g., listening to students, asking good probing questions) get destroyed if I am circulating around the room putting out fires.

I’ve known for a long time that planning has always been the weakest part of my skillset, having written almost 4 years ago:

I will say that my weakest area is as architect (choosing tasks to use with student as well as deciding how those tasks should be carried out), especially thinking about the design of a whole course. I haven’t had a lot of experience designing courses, but I think I am also weakest here because I am a decent enough in the other areas that I get away with not being a good architect. In this sense, the willingness and ability to improvise is both an asset and a liability.”

I think now that I wasn’t getting away with anything. And I even think my thinking about planning (or warmups more specifically) now is nothing unique or special, and not even particularly great. What I think is amazing is how much even small improvement to my planning (and my thinking about planning) can make a difference.

Meandering Thoughts: Trying to Get the Most of Out Warm-ups in Physics 2

August 30, 2014

Our second-semester introductory algebra-based physics course is jam-packed with labs. In 13-14 weeks, we do 22 labs! Combined with the in-class problem-solving students are expected to work through, I found it very difficult to find time for meaningful discussion questions or mini-activities that help build conceptual understanding or connections with the everyday world. 

So, this fall is my second semester teaching the course, and I have been taking the route of using warm-ups as an opportunity to build in a few discussion and mini-activity opportunities. The constraints in doing so are the following:

  • The discussion questions or mini-activity must flow into problem-solving or lab fluidly so as to be coherent to the students’ overall experience in class. It should emphasize key ideas they need that day, not just be enrichment ideas that I think are valuable in the big picture.
  • The discussion or mini-activity cannot take up much time, because we are pretty squeezed for time. Furthermore, the activity should be designed to actually save me time later. In reality that means, I get some of the invested time back, but not all of it. So, a 10 minute mini-activity might mean students take 5 less minutes struggling with the problem or mean I can take 2-3 less minutes with a particular part of my sample problem. 

An example of the kind of things I’ve been aimed for is this:

On Thursday, I was supposed to model how to solve a thin-lens problems, and then have students work together on a thin-lens problem, and then have students take data for a thin-lens lab. I had the following warm-ups:

– The opening question revolved around getting students to think about what they know about a camera, a projector, and a magnifying glass.  On the front whiteboard I had made a table, which prompted students to consider whether or not the each of these technologies involved (i) capturing an image on a screen or viewing an image through a lens, (ii) whether it typically involved creating an image that was bigger or smaller than the actual object, and (iii) whether the image was viewed relatively close or relatively far from the apparatus. I had students discuss briefly in groups and then quickly collected student responses on the board in a whole class format. To make links to the their reading and later problem, I introduced the relevant vocabulary (e.g., virtual and real image, magnification, and image distance). 

– The 1st mini activity involved giving students a converging lens and giving them the challenge of using the lens, a whiteboard, and some power point images to emulate a camera, a projector, and a magnifying glass. We turned off all the lights, so the only light was coming from the powerpoint slides. The slides were just a small, medium, and large yellow arrows. I circulated around, being more helpful than I should, due to need to keep the activity compressed in time. We then added one more column to our table, which was whether the image was right-side up or inverted. I then linked this again to concept of magnification and its sign.

– The 2nd mini-activity involved a powerpoint slide at the front of the room with nine different paths that a red laser light took through a lens. The optical axis and focal lengths were shown (but not in words). Basically, there were three examples of each of the principal rays. I briefly explained what the images were showing (a red laser light shining through a lens), and students were prompted to “Discuss what they notice” and then “See if they can come up with any generalizations or rules ” I circulated around. To keep time down, I didn’t collect responses. Rather, I talked about the patterns like, “One pattern I heard come up while I was circulating was concerned Image B, E, and F… In each of these cases, we see.” I then had a quick power point slide that summarized the three principal rays.

– Afterwards, the day proceeded as normal. I modeled how to predict where an image will form using ray diagrams and the Thin Lens equation. My example was a camera situation. Students’ first problem was a projector situation, and then their extension problem was a magnifying glass situation.

So, how did the warm-ups go in terms of my goals and constraints?

– The opening discussion took a little too much time, but I could easily tighten up my facilitation. It didn’t drag on per se, but it needed a quicker pace. It definitely helped students have a concrete understanding of the concepts of real/virtual and magnification, and help them see how what they were doing was related to their everyday world. It was easy to follow up with students, asking, “So is this situation like a camera, a projector, a magnifying glass, or none?” This prompted students to interpret the meaning of their work, which is good. This activity may not have paid back time, but it did pay back in terms of engagement (because students felt what they were doing was relatable) and in terms of sense-making (students had a feel for the important features of an image and what concepts describe them).

– The “Notice and Generalize” activity went quickly. My sense is that this paid off in terms of time in two ways. First, when presenting my example problem, I wasn’t introducing the principal rays in the middle of the problem. This saved me a few minutes. Second, I think students procedural fluency was bolstered just enough that it took them significantly less time to draw correct ray diagrams. During the problem-solving, there were no groups whose hands were up signaling they had no idea how to proceed and no groups that had diagrams that were way off the mark. 

Both of the activities clearly supported students needs for learning that day, so I think we met the first constraint pretty well.

My memory is that each of the warm-ups took about 10 minutes, which means I invested up 30 minutes up front (within a 2.5 hour class). I think, we made up about 15 of those minutes. I think my goal should be invest 20-25 minutes, and hope to get 10-15 minutes back. 

Final Note: What I find pretty interesting about my own learning to teach recently is this. More and more, I find myself being able to throw together warm-ups like this with very little time investment in planning. Before I might spend hours planning a warm-up that didn’t go very well or went well but didn’t pay off. Now, I can drum up a warmup that is fairly effective in less than 30 minutes. And while I know I must *know* things that allow me to do this, almost none of seems very conscious. I actually that I think plan most of these activities in my sleep, because I’ll some half-baked ideas when I go to bed, and then I wake up, sit down in front of the computer, and its done in about 10-15 minutes. I’m not saying my activities are gems, but teaching becomes a lot easier when what you throw together in 15 minutes is better on average than what used to take your hours. 

Final Final Note: 

OK, I partially change my mind. I think that my activities have gotten a lot better because I care more about the coherence of students’ learning experience. By that I mean, my activities are almost always designed to slip into the flow of the curriculum I have to follow.   Previously, I would want to take too many side trips–to destinations that I felt were important to understand the material. And while I do take some detours, I use them sparingly. I’ve let go of some ego which says, “I know best what’s needed for students to understand this material”, and instead accept that, “The curriculum we are working with needs them to understand these things in this manner”. I’m much more willing (and able) to enhance students’ experience of a learning trajectory that I don’t necessarily think is so great. And the truth is, working to make the overall experience more coherent is way better than trying to sprinkle on top what I think is best. Within that analogy, I think it’s been better to try to improve the existing cake batter than to smatter it with fancy ingredients from a different recipe. 

 

 

 

 

 

 

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