**1998**

**2005**

**2012**

What do these three years have in common? For me, they represent the times that I have collectively been the most nervous, the most uncertain, and the most excited regarding the start of a new school year. In 1998, fresh out of college, I started my teaching career. In 2005 (a seven year itch, perhaps?) I adopted the Modeling Method of physics instruction. And now, in 2012 (another 7 years, hmm….), I am about to embark on yet another fundamental shift in my teaching practices…. standards-based grading (SBG).

**Standards-Based Grading**

I spent the better part of the last school year thinking about the meaning of grades and how a standards-based grading system would help students to focus on actual learning rather than the accumulation of points. I also spent a great deal of this time trying to develop a vision for how an SBG system could work in my classroom and in my school district. After a lengthy and deep conversation with my principal in May, I got the go ahead to implement SBG. Now, with less than ~~two weeks~~ one week before the start of school, it’s time to deliver. The following post is as much for me to keep myself oriented and on track throughout the year as it is for anyone else who might be considering this approach. I doubt that there’s anything really new here for SBG veterans, but I would welcome any feedback you might have.

*Full Disclosure: In typical teacher fashion, I have borrowed heavily from those who have gone before me (particularly the thoughts and practices of teachers like Frank Noschese, Kelly O’Shea, and Shawn Cornally). For a more thorough description of SBG I recommend checking out their sites.*

In researching SBG, I have come to realize that there are as many different ways to implement the process as there are teachers who do. Everyone seems to create a system that will work for them within their classrooms and school districts, while still maintaining some of the guiding principles of SBG.

- A focus on learning rather than the accumulation of points
- Development of a growth mindset (effort creates ability, learning from mistakes, persistence)
- A classroom atmosphere in which students are free to take risks and embrace challenges without fear of failure
- Development of student metacognitive abilities (self-reflection and assessment)
- Providing a summative grade which is reflective of a student’s true knowledge and abilities, regardless of when they achieved mastery of the knowledge and abilities

**Learning Objectives (aka standards)**

In SBG, there are no real points to add or subtract from a student’s grade and no final averaging of a student’s accumulation of points on things like homework, labs, quizzes/tests, and participation at the end of a grading period. There is no extra credit, nor are their penalty points for late or missed work. Instead, students are evaluated solely on the basis of their ability to demonstrate their understanding of the key learning objectives of the course. Developing and refining these objectives was one of the first steps that I took on the SBG planning ladder. Below are the final(?) versions of my objectives for the first few models of the school year. In this case, I borrowed heavily from Kelly O’Shea and Frank Noschese but there are a few key differences. I decided (perhaps to my downfall) that having one objective to deal with student understanding of position, velocity, and acceleration vs. time graphs, as well as motion maps, was just too much content to include in a single objective. While I know that it may be difficult to assess these graphing objectives in isolation (and after the students have had some time to work with the graphs I probably will not want to) I have observed students who were perfectly capable of interpreting a position vs. time graph falter when it was time to interpret a velocity vs. time graph. I wanted the opportunity to target my assessment and feedback, as well as their own remediation and practice on the key areas they were struggling with. It might become a bit unwieldy when re-assessment time comes, but we’ll see how it pans out. Another key difference is the separation of some of the objectives dealing with vectors into a broader general category as I don’t see these objectives as necessarily part of any one particular model. You can also see that I decided to separate the objectives into two levels. The core objectives (C-Level) are the basic physics understandings that I would expect my students to be able to demonstrate, while the advanced objectives (A-Level) require a somewhat deeper knowledge of physics and usually require the ability to understand the core objectives.

2012-2013 Physics I Objectives (Partial Listing)

**Measuring a Student’s Level of Understanding**

The next decision on the SBG planning ladder was exactly how I would evaluate a student’s level of understanding of each objective. Some teachers choose to rate a student’s mastery on a numerical scale of 1-4 or 1-5, while others use words like basic, developing, proficient, and advanced, still others use a binary approach (either the student understands the objective or they don’t). Since I wanted to distance myself and my students from points as much as possibly and avoid any possible confusion with a points-based system, I decided not to use a system involving numbers. I also think that in the end, a student can either interpret a position vs. time graph or they can’t. So I decided to use the following three designations:

**M – Mastery**

The student’s work clearly shows that they understand and know the objective and can explain the objective in detail. Depending on the objective, this level of work could require the student to correctly and appropriately:

– Apply the relevant model

– Use multiple representations (pictures, diagrams, graphs, etc.)

– Show mathematical work

– Provide a detailed explanation with accurate and logical scientific reasoning

**DM – Developing Mastery**

The student’s work shows that they generally understand the objective, but still possess some degree of confusion regarding some component of the objective. In other words, at least one of the components required for mastery are not present in their response.

**NE – No Evidence**

The student did not respond to the question or their response shows that they have no understanding of the objective.

Student responses on frequent short formative assessments throughout a model’s development (as well as a more involved assessment at the end of each model) will be evaluated on the basis of the above three descriptions. Only the score on the most recent assessment (or re-assessment) counts. In the end, only the objectives on which a student has demonstrated the Mastery level will be considered in the determination of their numerical grade. Speaking of….

**Determining a Numerical Grade**

One of the issues created by the averaging of points in a traditional grading system is that a student’s poor understanding of a key topic can be masked by a higher level of understanding in another. It all, well, averages out. I felt that in order for a student to earn at least a C, they should be able to demonstrate at minimum a basic understanding of all the physical models we study. This is why I separated the objectives. Since the core C-level objectives represent what I consider to be the most basic and fundamental understandings a physics student should posses, a student must demonstrate mastery on each C-level objective in order to earn at least a 70%. If a student fails to achieve mastery on each C-level objective (a regrettable circumstance I will work hard to avoid), their grade will be interpolated from 50-70% based on the percent of C-level objectives they have mastered. For example, if no mastery has been shown on any C-level objective, the student will earn a grade of 50%, while mastery of half the C-level objectives will correspond to a 60%.

Assuming a student has shown mastery on all the C-level objectives, their grade will then be interpolated from 70-90% based on their mastery of the A-level objectives (i.e. mastering half the A-level objectives would correspond to an 80%, while mastery of all the A-level objectives would correspond to a 90%). Uh, oh. Why shouldn’t mastery of all the objectives earn the student a 100%? This was something that I thought deeply about and struggled with for quite some time. In the end, I was uncomfortable with the isolated conditions in which a student could demonstrate mastery of an objective. In order to earn an A, I truly believe that the students need to show me they have the ability to synthesize and combine separate objectives, and to utilize multiple models and representations when confronting “messy” situations.

*So how does a student earn a grade above a 90%?*

Great question, and one I didn’t really have an answer to until recently. I briefly toyed with the idea of some type of culminating project, or lab practical, or activity at the end of each grading period, but I just didn’t see a way to make it work. The juniors in my classes have so much school related stress to begin with that I thought something along these lines would only exacerbate the problem and not really provide me with the information I needed anyhow. At the end of a grading period, I want my students to be focused on mastering any lingering objectives without having the specter of some required project looming over their heads. So, I once again decided to borrow/steal an idea from Kelly O’Shea and include goal-less problems on their assessments at the end of each grading period. I used goal-less problems last year with some success and found that the really good problems allowed students to combine multiple models and representations together (exactly what I want them to demonstrate to earn above a 90%). So, student performance on goal-less problems will translate into increasing their percentage grade above the 90% threshold. Now, admittedly, I’m not quite sure how this translation will occur. I think this will have to be something that is determined with some student input near the end of the first grading period and after I get a handle on how this entire process is working.

*What about those grading periods?*

Our school has 4 nine week grading periods, as well as a midterm and final exam. At the end of the year, a student’s final percentage grade for a course is determined by the following weighted average calculation:

– 1st grading period – 20%

– 2nd grading period – 20%

– Midterm exam – 8%

– 3rd grading period – 20%

– 4th grading period – 20%

– Final exam – 12%

Yep, that means that I must be able to have an accurate percentage grade that *counts* at the end of each nine week grading period (I can’t easily go back and change prior grades). This is another reason why I opted not to use a project for determining grades above 90%. There just isn’t enough time between grades and I did not want students (and me) dealing with projects four times a year at nine week intervals. It would all just be too much. So, at the end of each nine weeks, students will need to take a final assessment on which they can demonstrate their mastery on all lingering objectives and goal-less problems. I know that this will take away some valuable class time, but I have come to be at peace with this solution. As it is, I still have questions regarding how I will handle the midterm and final exams, as well as how objectives should carry over from one grading period to another without diluting more recent objectives. More things I’ll have to work out (and blog about) as the year progresses.

**To be continued…**

Well, if you’re still with me, I think that this is probably a good stopping point for this already too long post. I still need to get my thoughts down in writing regarding some of the implementation aspects of SBG, particularly how I intend to handle homework, labs, the process by which students will assess and re-assess on objectives, and keeping track of it all. But that will have to wait for future posts. Until then, I welcome any questions, comments, or concerns you may have regarding the approach I have taken. I know there are many of you who have gone before me with SBG and I look forward to any advice and guidance you can provide.

My typical introduction to the Galilean version of relative motion has usually involved some teacher led discussions regarding reference frames, usually using examples of “freeway” relativity with cars passing each other on the highway at various relative speeds, followed by a teacher led derivation of the Galilean equations for relative motion and the ever present S and S’ observers. Ho hum. Where was the student thinking here?

This year, I was determined to do it differently. As I thought about alternate approaches I recalled a Dan Meyer posting where he had created a video of himself walking up and down stairs and escalators. I think his intention was to use the video to get students to work with systems of equations, but I thought it could be used to analyze relative motion. Particularly, I thought it could be a good way to practice “ninja physics.” The students would be using relativity concepts without really knowing they were doing relativity.

I showed the video clip of Dan walking up and down stationary stairs and walking up an escalator that was also moving upwards. The clip ends with Dan about to walk up the down escalator. Afterwards, I had the students write down three questions they had after watching the video. I immediately saw where some of them were going with this and decided that in order to reign in their, um, “creativity”, they were allowed one question that probably couldn’t be answered by using physics, and two questions that could. After we laughed a bit about questions like:

- Where did he film the video?
- Was the person in the video a clone/quadruplet? (four videos of Dan are shown simultaneously)
- Why did he choose that particular music?
- Where did he get the cool shirt? (actually, one of the students realized he possessed the exact same shirt and wore it the following day just to verify).

On the physics front, there were questions regarding the individual velocities of both Dan and the escalators, as well as the $64,000 question, “how much time will it take Dan to travel up the down escalator?” With this, we were off discussing things they felt they needed in order to answer the question. In the end, the students decided that they would need the time information provided by the video, as well as the height and depth dimensions of each step on the stairs and escalators (conveniently available on the additional images Dan provides).

The students then went into their lab groups and started to work things out on whiteboards. There were some questions about whether or not they could assume that the stair distance and the elevator distance were equal, some groups decided they could, while others decided to treat them separately. A couple of the groups did stumble at first, trying to quantify everything they could about the situation before they realized that in terms of answering the question, most of the information they were attempting to find was not necessary. In the end, after some great student to student discussions and some mental exertion, the groups each arrived at an answer (values ranged from as low as 19 seconds to as high as 45 seconds). I had students present and compare their thinking processes to each other and made sure that they were explicit about any assumptions they had made. I was actually a bit surprised at the diversity of solutions the students came up with. Most groups determined the velocities of Dan and the escalators in inches/sec, while one group used a rate of steps/sec. Another group determined the distance traveled per step in inches/step and then used a step rate of seconds/step to determine the velocities. Some of their board work is shown below.

As they presented and discussed their work, I surreptitiously recorded their findings on a whiteboard of my own:

I asked the students what they noticed about their different approaches and if there was anything the approaches had in common. In very little time they noticed that, without even explicitly realizing they had done it, they had used vector addition of velocities because it just “seemed” right to them. In general, they determined that they had used the following relations:

velocity on steps + escalator velocity = velocity of Dan going up the up escalator

velocity on steps – escalator velocity = velocity of Dan going up the down escalator

Eureka! They had just used and determined the Galilean equation for the superposition of velocities!

I then decided to take this a step farther and asked them if they could use their information to determine an equation that relates Dan’s position on the escalator at any time with the velocity of the escalator if they knew how far Dan had traveled relative to where he started on the escalator? Admittedly, I’m not too happy with how I asked this question. I think I may have guided them to a place where they might not have naturally gone by limiting them to the specific terms that I wanted them to have in the equation. Next time, I think I’ll try to phrase the question more generally. Perhaps have them come up with several different expressions that all describe his position on the escalator. With multiple options, we can then discuss the advantages/limitations of each one and see if we can come to a group consensus on the most useful expression.

In any case, the students went back into their lab groups and after some group discussion about the necessity to include/not include Dan’s velocity relative to the escalator, within about 5-10 minutes they had all determined some form of the following relation:

position relative to ground = position relative to escalator + (escalator velocity)t

Eureka again! The Galilean expression for relative position!

By this time, the students were *dying* to see how close their results were to reality, so in addition to checking the answer video Dan provides for the actual time, we also used it to check their position equations. Obviously, the groups that had arrived at a time that was closer to the actual time (~ 22 secs) had better luck in verifying their position equations, but overall, the students felt they had done a reasonable job at describing the escalator/stair scenario.

Following this, we formalized their relationships into the traditionally accepted forms of the Galilean relativity equations. We also discussed the S and S’ reference frames and how the students had already used these two different frames (stairs and escalator) to analyze the situation. We also tested the waters a bit and tried to switch reference frames to describe what someone traveling on the escalator would see if they were describing the motion of the camera or of someone walking on the stairs.

So, how did this different approach to introducing relative motion impact student learning? Primarily, it took me off the center stage, which is always a good thing. It provided the students with an opportunity to develop an intuitive sense for relative motion first, before we officially formalized the concept. They also exercised their abilities to approach new questions, determine a possible path to a solution, and try to take that path to a sensible conclusion (with some back tracks and stumbles along the way). Particularly, they had to critically evaluate the assumptions they could or could not make as well as determine how to best use the video to obtain the information that they needed in order to answer the question. Additionally, I think it helped that we focused on some key concepts before getting bogged down in discussions of S and S’ or x and x’. Many of the students were surprised to find out that they had done “relativity” on their own without even realizing it. Interestingly, a few astute students did mention that it would seem like somebody would have already developed equations to deal with these types of scenarios. To which I smiled and replied that it was possible, but I doubt they would have used such a cool video to do it!

It’s still early in the relativity unit and I’ll be continually checking to see if the intuitive sense they developed regarding reference frames and observers as a result of working with the video carries over into their work on other everyday situations. From there, we’ll see if it helps them to deal with the non-intuitive cases of relative motion at close to the speed of light. I’m still trying to come up with ways to approach the ideas of Special relativity in a more student-centered way, so feel free to offer any advice/suggestions you may have in the comments below.

]]>In my school district, I am the only physics teacher (it’s a very small public school in the suburbs). And while I value the relationships I have with the other teachers in the district, especially my fellow modeler in crime, the chemistry teacher, I still possess a certain feeling of professional isolation. There is no sounding board for discussions regarding the benefits/pitfalls of teaching specific physics topics in a certain way. After all, just what is the best way to conduct a paradigm lab for the unbalanced force model? How can I teach modern topics such as particle and nuclear physics, or Special and General relativity using models? How can I get students to truly understand the implications and subtleties of Newton’s Laws without them thinking that they “understand” them because they’ve managed to memorize them? These and other questions are ones that I’ve struggled with throughout my 14 years of teaching, and still do. However, aside from the modeling workshops I’ve attended, opportunities to discuss these ideas with fellow physics teachers have been few and far between. When I stumbled upon the blogging community, I saw the opportunity to engage in these discussions with other like-minded individuals who were not satisfied with traditional instruction methods.

I started subscribing to and devouring blog posts in order to incorporate new ideas into my classes. I started the year with a marshmallow challenge activity after reading posts by John Burke at Quantum Progress and Frank Noschese at Action-Reaction. I had discussions regarding growth and fixed mindsets with my classes after reading another of John’s posts. I began to follow Kelly O’Shea’s example and challenge my students with goal-less problems that allowed them the opportunity to really stretch their understanding of the applicability of models and to show them that they are capable of more than they give themselves credit for. I improved my introduction to force interactions by providing students with rubber mallets and bowling balls (mallets were MUCH better than the broomsticks I had been using). And just recently I incorporated a WCYDWT scenario of Dan Meyer’s regarding relative motion on an escalator as an introduction to relativity in my Physics II class (more on this in a future post). In the long term, I’m even contemplating using standards based grading next year due to the continual opportunities for feedback and mastery such a system provides and the focus on learning rather than the accumulation of points. Although I relished the changes I was making in my classroom and the responses from the students have been positive, I still felt a bit guilty. I had been a consumer who observed from the sidelines. Like someone attending their first junior high dance, I stood near the punch bowl, drank a lot of punch, and watched.

So, the day has arrived.

I’ve started this blog to organize my own thoughts and reflections regarding the teaching and learning of physics, and I hope along the way to at least be able to contribute in some small way to help others via my posts and the feedback I can provide. I’ve also created a Twitter account (@BEphysics), something I thought I would never do, but I’ve seen the value of these online interactions and I’ve decided to try to become a part of the community from which I have learned so much these past few months. I’m not sure exactly what my role can be, nor where this journey will take me, but simply standing by the punch bowl isn’t quite enough anymore.

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