Page 20 – iteration, making, building, and coding in education

2012-2013 Year In Review – Learning Standards

This is the second post reflecting on this past year and I what I did with my students.

My first post is located here. I wrote about this year being the first time I went with standards based grading. One of the most important aspects of this process was creating the learning standards that focused the work of each unit.

What did I do?

I set out to create learning standards for each unit of my courses: Geometry, Advanced Algebra (not my title – this was an Algebra 2 sans trig), Calculus, and Physics. While I wanted to be able to do this for the entire semester at the beginning of the semester, I ended up doing it unit by unit due to time constraints. The content of my courses didn’t change relative to what I had done in previous years though, so it was more of a matter of deciding what themes existed in the content that could be distilled into standards. This involved some combination of concepts into one to prevent the situation of having too many. In some ways, this was a neat exercise to see that two separate concepts really weren’t that different. For example, seeing absolute value equations and inequalities as the same standard led to both a presentation and an assessment process that emphasized the common application of the absolute value definition to both situations.

What worked:

The most powerful payoff in creating the standards came at the end of the semester. Students were used to referring to the standards and knew that they were the first place to look for what they needed to study. Students would often ask for a review sheet for the entire semester. Having the standards document available made it easy to ask the students to find problems relating to each standard. This enabled them to then make their own review sheet and ask directed questions related to the standards they did not understand.
The standards focus on what students should be able to do. I tried to keep this focus so that students could simultaneously recognize the connection between the content (definitions, theorems, problem types) and what I would ask them to do with that content. My courses don’t involve much recall of facts and instead focus on applying concepts in a number of different situations. The standards helped me show that I valued this application.
Writing problems and assessing students was always in the context of the standards. I could give big picture, open-ended problems that required a bit more synthesis on the part of students than before. I could require that students write, read, and look up information needed for a problem and be creative in their presentation as they felt was appropriate. My focus was on seeing how well their work presented and demonstrated proficiency on these standards. They got experience and got feedback on their work (misspelling words in student videos was one) but my focus was on their understanding.
The number standards per unit was limited to 4-6 each…eventually. I quickly realized that 7 was on the edge of being too many, but had trouble cutting them down in some cases. In particular, I had trouble doing this with the differentiation unit in Calculus. To make it so that the unit wasn’t any more important than the others, each standard for that unit was weighted 80%, a fact that turned out not to be very important to students.

What needs work:

The vocabulary of the standards needs to be more precise and clearly communicated. I tried (and didn’t always succeed) to make it possible for a student to read a standard and understand what they had to be able to do. I realize now, looking back over them all, that I use certain words over and over again but have never specifically said what it means. What does it mean to ‘apply’ a concept? What about ‘relate’ a definition? These explanations don’t need to be in the standards themselves, but it is important that they be somewhere and be explained in some way so students can better understand them.
Example problems and references for each standard would be helpful in communicating their content. I wrote about this in my last post. Students generally understood the standards, but wanted specific problems that they were sure related to a particular standard.
Some of the specific content needs to be adjusted. This was my first year being much more deliberate in following the Modeling Physics curriculum. I haven’t, unfortunately, been able to attend a training workshop that would probably help me understand how to implement the curriculum more effectively. The unbalanced force unit was crammed in at the end of the first semester and worked through in a fairly superficial way. Not good, Weinberg.
Standards for non-content related skills need to be worked in to the scheme. I wanted to have some standards for year or semester long skills standards. For example, unit 5 in Geometry included a standard (not listed in my document below) on creating a presenting a multimedia proof. This was to provide students opportunities to learn to create a video in which they clearly communicate the steps and content of a geometric proof. They could create their video, submit it to me, and get feedback to make it better over time. I also would love to include some programming or computational thinking standards as well that students can work on long term. These standards need to be communicated and cultivated over a long period of time. They will otherwise be just like the others in terms of the rush at the end of the semester. I’ll think about these this summer.

You can see my standards in this Google document:
2012-2013 – Learning Standards

I’d love to hear your comments on these standards or on the post – comment away please!

Editing Khan

Let’s be clear – I don’t have a problem with most of the content on Khan Academy. Yes, there are mistakes. Yes, there are pedagogical choices that many educators don’t like. I don’t like how it has been sold as the solution to the educational ills of our world, but that isn’t my biggest objection to it.

I sat and watched his series on currency trading not too long ago. Given that his analogies and explanations are correct (which some colleagues have confirmed they are) he does a pretty good job of explaining the concepts in a way that I could understand. I guess that’s the thing that he is known for. I don’t have a problem with this – it’s always good to have good explainers out there.

The biggest issue I have with his videos is that they need an editor.

He repeats himself a lot. He will start explaining something, realize that he needs to back up, and then finishes a sentence that hadn’t really started. He will say something important and then slowly repeat it as he writes each word on the screen.

This is more than just an annoyance. Here’s why:

One of the major advantages to using video is that it can be good instruction distilled into great instruction. You can plan ahead with the examples you want to use. You can figure out how to say exactly what you need to say and nothing more, and either practice until you get it right, or just edit out the bad takes.
I have written and read definitions word by word on the board during direct instruction in my classes. I have watched my students faces as I do it. It’s clearly excruciating. Seeing that has forced me to resist the urge to speak as I write during class, and instead write the entire thing out before reading it. Even that doesn’t feel right as part of a solid presentation because I hate being read to, and so do my students. This doesn’t need to happen in videos.
If the goal of moving direct instruction to videos is to be as efficient as possible and minimize the time students spend sitting and watching rather than interacting with the content, the videos should be as short and efficient as possible. I’m not saying they should be void of personality or emotion. Khan’s conversational style is one of the high points of his material. I’m just saying that the ‘less is more’ principle applies here.

I spent an hour this morning editing one of the videos I watched on currency exchange to show what I mean. The initial length of the video was 12:03, and taking out the parts I mentioned earlier reduced it to 8:15. I think the result respects Khan’s presentation, but makes it a bit tighter and focused on what he is saying. Check it out:

The main reason I haven’t made more videos for my own classes (much to the dismay of my students, who really like them) is my insistence that the videos be efficient and short. I don’t want ten minute videos for my students to watch. I want two minutes of watching, and then two or three minutes of answering questions, discussing with other students, or applying the skills that they learned. My ratio is still about five minutes of editing time for every minute of the final video I make – this is roughly what it took this morning on the Khan Academy video too. This is too long of a process, but it’s a detail on using video that I care too much about to overlook.

What do you think?

2012-2013 Year In Review – Standards Based Grading

This is the first in a series of posts about things I did with my classes this year.

When I made the decision last fall to commit to standards based grading, these were the main unknowns that hung at the back of my mind:

How would students respond to the change?
How would my own use of SBG change over the course of the year?
How would using SBG change the way I plan, teach, and assess?

These questions will all be answered as I reflect in this post.

What did I do?

In the beginning of the year, I used a purely binary system of SBG – were students proficient or not? If they were proficient, they had a 5/5. Not yet proficient students received a 0/5 for a given standard. All of these scores included a 5 point base grade to be able to implement this in PowerSchool.

As the semester went on, the possible proficiency levels changed to a 0, 2.5, or 5. This was in response to students making progress in developing their skills (and getting feedback on their progress through Blue Harvest but not seeing visible changes to their course grade. As much as I encouraged students not to worry about the grade, I also wanted to be able to show progress through the breakdown of each unit’s skills through PowerSchool. It served as a communication channel to both parents and the students on what they were learning, and I could see students feeling a bit unsatisfied by getting a few questions correct, but not getting marked as proficient yet. I also figured out that I needed to do more work defining what it meant to be proficient before I could really run a binary system.

By the start of the second semester, I used this scheme for the meaning of each proficiency score:

1 – You’ve demonstrated basic awareness of the vocabulary and definitions of the standard. You aren’t able to solve problems from start to finish, even with help, but you can answer yes/no or true or false questions correctly about the ideas for this standard.
2 – You can solve a problem from start to finish with your notes, another student, or your teacher reminding you what you need to do. You are not only able to identify the vocabulary or definitions for a given skill, but can substitute values and write equations that can be solved to find values for definitions. If you are unable to solve an equation related to this standard due to weak algebra skills, you won’t be moving on to the next level on this standard.
3 – You can independently solve a question related to the standard without help from notes, other students, or the teacher. This score is what you receive when you do well on a quiz assessing a single standard. This score will also be the maximum you will receive on this standard if you consistently make arithmetic or algebraic errors on problems related to this standard.
4 – You have shown you can apply concepts related to this standard on an in-class exam or in another situation where you must identify which concepts are involved in solving a problem. This compares to success on a quiz on which you know the standard being assessed. You can apply the content of a standard in a new context that you have not seen before. You can clearly explain your reasoning, but have some difficulty using precise mathematical language.
5 – You have met or exceeded the maximum expectations for proficiency on this standard. You have completed a project of your own design, written a program, or made some other creative demonstration of your ability to apply this standard together with other standards of the unit. You are able to clearly explain your reasoning in the context of precise mathematical definitions and language.

All of the standards in a unit were equally weighted. All units had between 5 and 7 standards. In most classes, the standards grade was 90% of the overall course grade, the exception being AP Calculus and AP Physics, where it was 30%. In contrast to first semester, students needed to sign up online for any standards they wanted to retake the following day. The maximum number of standards they could retake in a day was limited to two. I actually held students to this (again, in contrast to first semester), and I am really glad that I did.

Before I start my post, I need to thank Daniel Schneider for his brilliant post on how SBG changes everything here. I agree with the majority of his points, and will try not to repeat them below.

What worked:

Students were uniformly positive about being able to focus on specific skills or concepts separate from each other. The clarity of knowing that they needed to know led some students to be more independent in their learning. Some students made the conscious decision to not pursue certain standards that they felt were too difficult for them. The most positive aspect of their response was that students felt the system was, above all else, a fair representation of their understanding of the class.
Defining the standards at the beginning of the unit was incredibly useful for setting the course and the context for the lessons that followed. While I have previously spent time sketching a unit plan out of what I wanted students to be able to do at the end, SBG required me not only to define specifically what my students needed to do, but also to communicate that definition clearly to students. That last part is the game changer. It got both me and the students defining and exploring what it means to be proficient in the context of a specific skill. Rather than saying “you got these questions wrong”, I was able to say “you were able to answer this when I was there helping you, but not when I left you alone to do it without help. That’s a 2.”
SBG helped all students in the class be more involved and independent in making decisions about their own learning. The strongest students quickly figured out the basics of each standard and worked to apply them to as many different contexts as possible. They worked on communicating their ideas and digging in to solve difficult problems that probed the edges of their understanding. The weaker students could prioritize those standards that seemed easiest to them, and often framed their questions around the basic vocabulary, understanding definitions, and setting up a plan to a problem solution without necessarily knowing how to actually carry out that plan. I also changed my questions to students based on what I knew about their proficiency, and students came to understand that I was asking a level 1 question compared with a level 3 question. I also had some students giving a standards quiz back to me after deciding that they knew they weren’t ready to show me what they knew. They asked for retakes later on when they were prepared. That was pretty cool.
Every test question was another opportunity to demonstrate proficiency, not lose points. It was remarkably freeing to delete all of the point values from questions that I used from previous exams. Students also responded in a positive way. I found in some cases that because students weren’t sure which standard was being assessed, they were more willing to try on problems that they might have otherwise left blank. There’s still more work to be done on this, but I looked forward to grading exams to see what students did on the various problems. *Ok, maybe look forward is the wrong term. But it still was really cool to see student anxiety and fear about exams decrease to some extent.

What needs work:

Students want more detail in defining what each standard means. The students came up with the perfect way to address this – sample problems or questions that relate to each standard. While the students were pretty good at sorting problems at the end of the unit based on the relevant standards, they were not typically able to do this at the beginning. The earlier they understand what is involved in each standard, the more quickly they can focus their work to achieve proficiency. That’s an easy order to fill.
I need to do more outreach to parents on what the standards mean. I thought about making a video at the beginning of the year that showed the basics, but I realize now that it took me the entire year to understand exactly what I meant by the different standards grades. Now that I really understand the system better, I’ll be able to do an introduction when the new year begins.
The system didn’t help those students that refuse to do what they know they need to do to improve their learning. This system did help in helping these students know with even more clarity what they need to work on. I was not fully effective in helping all students act on this need in a way that worked for them.
Reassessment isn’t the ongoing process that it needs to be. I had 80 of the 162 reassessment requests for this semester happen in the last week of the semester. Luckily I made my reassessment system in Python work in time to make this less of a headache than it was at the end of the first semester. I made it a habit to regularly give standards quizzes between 1 or 2 classes after being exposed to the standard for the first time. These quizzes did not assess previous standards, however, so a student’s retake opportunities were squarely on his or her own shoulders. I’m not convinced this increased responsibility is a problem, but making it an ongoing part of my class needs to be a priority for planning the new year.

I am really glad to have made the step to SBG this year. It is the biggest structural change I’ve made to my grading policy ever. It led to some of the most candid and productive conversations with students about the learning learning process that I’ve ever had. I’m going to stop with the superlatives, even though they are warranted.

Milestones at the start of summer: A tribute

I used this LEGO car in a five minute demo lesson – my first lesson ever – on Newton’s laws of motion. It was a gimmick to get the people in the room thinking about what they knew about forces, and served this purpose perfectly. This was in the beginning stages of my decision during my senior year at Tufts to pursue teaching rather than engineering after graduation.

It sat on the bookshelf next to my desk in both of my New York City apartments. It made its way into a suitcase that a friend took to Zambia. It was one of the items that I took out of the storage last summer with a smile, and was among the knick-knacks that didn’t get tossed in the move to the apartment in Hangzhou for next year.

This LEGO car rolled across the floor of the new apartment last week, the final week of my tenth year teaching. It made me think back to the many adventures that have been my life ever since I received my acceptance letter to the New York City Teaching Fellows program in 2003. I worked with an incredible group of teachers in the Bronx for seven years, helped open the KIPP NYC College Prep high school, and then made the move to Hangzhou where I have enjoyed teaching kids and working with some fantastic folks from all over the world.

Even though it is the start of summer vacation, my head is still very much in the teaching game. It’s gratifying to know that I can reinvent myself every year after a summer of reflection and meditation on what went well and what did not. I am motivated by my students comments in end-of-year surveys that my enthusiasm for learning and sharing new things gets them excited to be in the classroom with me. The unique experience of working with teenagers compels me to still devote energy and time to making myself better at what I do.

To the students that I have worked with over the past ten years: thank you for giving me the most exhilarating, satisfyingly unpredictable, and meaningful ten years I never knew I wanted in a career. To my colleagues: thank you for teaching me what it means to work hard for the right reasons and toward the right ends. To my family: thank you for supporting me in all that I do.

Have a great summer everyone!

Three Acts – Counting with dots and first graders

I had an amazing time this afternoon visiting my wife’s first grade class. I’ve been talking forever about how great it is to take a step out of the usual routines in class and look at a new problem, and my wife invited me in to try it with her students.

Here’s the run-down.

Act 1

[wpvideo 8kq5u3Cf]

Student questions (and the number of students that also found the questions interesting):

Why do the dots come together? (8)
Why are the dots making pictures and not telling us what they mean? (8)
Why are some dots going together into big dots, and others staying small? (13)
Why do some of the dots form blue lines before coming together?

My questions (and the number of students that humored me):

How many dots are there at the end? (8)
What is the final pattern of dots after the video ends? (11)

Guesses for the number of dots ranged from a low of 20 to a high of 90.

Act 2

What information did they want to know?

They wanted to see the video again.
Seven students asked about the numbers of tens or ones in each group. (I jumped on the use of that vocabulary right away – it seemed they are comfortable using this vocabulary based on my conversations with them.)

I showed them the video and gave them this handout since I didn’t have video players for all of the students:
grouping dots

What happened then was a series of amazing conversations with some really energetic and enthusiastic kids. They got right to work organizing and figuring out the patterns.

Act 3

We watched the video and discussed the results and how they got their answers. Lots of great examples of student-created systems for keeping track of their counting. We then watched the Act 3 video:
[wpvideo N9OYqdqx]

While nobody had the total number correct, I was quite impressed with their pride in being close. More interesting was how little they cared that they didn’t get the exact answer. I asked who was between 70 and 80, and a few kids raised their hands, and then the same with 50 – 70. One student was one off. Most were within ten or so of the correct answer. The relationship between the guesses and their answers after analysis was something we touched upon, but didn’t discuss outside of some one-on-one conversations.

The absolute highlight of the lesson was when I asked why they thought nobody had the exact answer. One student walked up to the projector screen with out hesitation and pointed here:

She said “this is what made it tough” and then sat back down.

We had a little more time, so we watched a sequel video:
[wpvideo xjc26Gjj]

I asked what they saw that was different aside from the colors. One student said right away that he figured it out, the same student that first shouted out ‘tens!’ in Act 1. We lacked the time to go and figure it out, so we left it there as a challenge to figure out for the next class.

Footnotes:

Any high school or middle school math teacher that wants to see how excited students can be when they are learning math needs to go take a group of elementary students through a three act. I wish I had done this during the dark February months when things drag for me. My wife asked me to do this to see how it works, but I think I got a lot more enjoyment out of the whole experience.
I made a conscious decision not to include any symbolic numbers in this exercise. It adds an extra layer of abstraction that takes away from the students figuring out what is going on. I almost put it back in when I wasn’t sure whether it was obvious enough. I am really glad I left it out so the students could prove that they didn’t need that crutch.
This is written in Javascript using Raphael. You can see a fully editable version of the code in this JSFiddle.
All files are posted at 101 Questions in case you want to get the whole package.

My latest app project: 5K Race Timer

I happened to attend a meeting a little more than a month ago for the committee that organizes the Dragon Run. This is one of the school’s biggest events and requires quite a group of people to make happen. One of the biggest challenges that the group faces is the timing of the race and management of this data for the 120+ runners that participate in the official event.

The scheme used in previous years has been a very well thought out system of spotters with pencil and paper lists and a race timer placed at the finish line. When runners register, they give an estimated time for their run, which places them in a few different speed categories. Each spotter has a list of runner numbers from each category so that they are searching for particular runner numbers throughout the time span of the race. When a runner crosses, the spotter records the time on their sheet. This time is then later fed into a spreadsheet that gives everyone’s time. These results are then collated and printed to give the results list after the race.

I’m trying not to be a hammer looking for a nail here, but this seemed like a perfect opportunity to try to use the power of the computer to reduce some of the mental and paper load of this task. My learning obsession with Python web apps and even more recent desire to learn about databases quickly helped me see some easy ways to do this. These were the main points that I wanted as part of the UI:

Upon seeing a runner approach the finish line, the spotter should be able to send a ‘stop’ command at the moment that runner crosses the line. Calculating the finish time relative to the start of the race and recording that information is screaming for a computer solution. This capitalizes on the human spotter’s ability for to recognize a runner’s number by sight, leaving the rest of the work to the program to do.
We would need a simple interface for starting the race and stopping individual runners with a button press.
A non-trivial number of runners register on the day of the race. There needs to be a way to manually add runners to the database easily.
Mistakes also come up in recording times and entering data. Editing a runner’s information, including finish time, is a necessity.
Manually entering all the runners into the database before the race? Heck no. The organizers use a spreadsheet to record all of the registration information, which is a CSV file asking to be made and inputted to the database automatically.
Creating a list of runners based on category and ranked according to race finish time is another exhausting task when done purely by spreadsheet. This process in the program should make the most of SQL queries and Python/Bottle template features to generate the race results automatically.
To properly see if this system would work, I’d need a way of showing numbers passing by similar to what actually happens during a race. I put together a Javascript simulator to do this using Raphael that can be found here. This was especially important in testing the system with my student volunteers.

The organizers agreed to let me run my software as a beta test to see if it would work for future years. More insight and conversation led to the idea of a mobile application to be used to enter runner numbers. I agreed that this would be an easier way to locate runners than looking down a list, but had no idea how to do this. I did research and figured out the jQuery Mobile would be the way to do it. This was a difficult learning process having never done this sort of thing before. I battled with the “ghost click” problem for a while until discovering that the ‘touchend’ event was an easy fix.

~~Here’s the software as used on race day:~~

Running code at http://timekeeper.evanweinberg.org
Try the mobile app on your mobile device at http://timekeeper.evanweinberg.org/mobile/
Code source at Github is here.

UPDATE Mar. 2016: I’ve taken down the site to save some memory on my server. Write me if you are interested in the details.

The system worked really well, but ran into some of the same challenges that the pencil-and-paper spotters have been battling since the event’s inception. It’s really hard to simultaneously grab the numbers of a group of 4-5 runners that all come in at once. The system that my students devised for identifying who was going to enter a particular runner approaching the finish line broke down in two specific instances of this, and we missed runners. Luckily pencil and paper picked up the ones we missed. Definitely still in beta. The process of generating results lists and recording times overall worked quite smoothly, and I’m really happy with how it turned out.

Notes:

Bottle, Twitter Bootstrap, jQuery Mobile, and vanilla Javascript were all in play.
I learned at the race that there are already software packages out there. Now that I’ve done a quick search, it seems that while there is a lot of software out there, the ease of running it through a web interface (and snagging runners through a mobile interface) is a relatively young feature. This project was about me learning to do some new things, and in the end it cost me (and the school) nothing other than time.
I learned a lot about user centered design through this project. Usability was a necessity, so I had to start from there and work backwards to build the code needed to make it happen. I really like thinking this way,

Speed of sound lab, 21st century version

I love the standard lab used to measure the speed of sound using standing waves. I love the fact that it’s possible to measure physical quantities that are too fast to really visualize effectively.

This image from the 1995 Physics B exam describes the basic set-up:

The general procedure involves holding a tuning fork at the opening of the top of the tube and then raising and lowering the tube in the graduated cylinder of water until the tube ‘sings’ at the frequency of the tuning fork. The shortest height at which this occurs is the fundamental frequency of vibration of the air in the tube, and this can be used to find the speed of sound waves in the air.

The problem is in the execution. A quick Google search for speed of sound labs for high school and university settings all use tuning forks as the frequency source. I have always found the same problems come up every time I have tried to do this experiment with tuning forks:

Not having enough tuning forks for the whole group. Sharing tuning forks is fine, but raises the lower limit required for the whole group to complete the experiment.
Not enough tuning forks at different frequencies for each group to measure. At one of my schools, we had tuning forks of four different frequencies available. My current school has five. Five data points for making a measurement is not the ideal, particularly for showing a linear (or other functional) relationship.
The challenge of simultaneously keeping the tuning fork vibrating, raising and lowering the tube, and making height measurements is frustrating. This (together with sharing tuning forks) is why this lab can take so long just to get five data points. I’m all for giving students the realistic experience of the frustration of real world data collection, but this is made arbitrarily difficult by the equipment.

So what’s the solution? Obviously we don’t all have access to a lab quality function generator, let alone one for every group in the classroom. I have noticed an abundance of earphones in the pockets of students during the day. Earphones that can easily play a whole bunch of frequencies through them, if only a 3.5 millimeter jack could somehow be configured to play a specific frequency waveform. Where might we get a device that has the capacity to play specific (and known) frequencies of sound?

I visited this website and generated a bunch of WAV files, which I then converted into MP3s. Here is the bundle of sound files we used:
SpeedOfSoundFrequencies

I showed the students the basics of the lab and was holding the earphone close to the top of the tube with one hand while raising the tube with the other. After getting started on their own, the students quickly found an additional improvement to the technique by using the hook shape of their earphones:

Data collection took around 20 minutes for all students, not counting students retaking data for some of the cases at the extremes. The frequencies I used kept the heights of the tubes measurable given the rulers we had around to measure the heights. This is the plot of our data, linearized as frequency vs. 1/4L with an length correction factor of 0.4*diameter added on to the student data:

The slope of this line is approximately 300 m/s with the best fit line allowed to have any intercept it wants, and would have a slightly higher value if the regression is constrained to pass through the origin. I’m less concerned with that, and more excited with how smoothly data collection was to make this lab much less of a headache than it has been in the past.

Visualizing the invisible – standing waves

I wrote a post more than a year ago on a standing waves lesson I did. Today I repeated that lesson with a few tweaks to maximize time spent looking at frequency space of different sounds. The Tuvan throat singers, a function generator, and a software frequency generator (linked here) again all made an appearance.

We focused on the visceral experience of listening to pure, single frequency sound and what it meant. We listened for the resonant frequencies of the classroom while doing a sweep of the audible spectrum. We looked at the frequency spectrum of noises that sounded smooth (sine wave) compared to grating (sawtooth). We looked at frequencies of tuning forks that all made the same note, but at different octaves, and a student had the idea of looking at ratios. That was the golden idea that led to interesting conclusions while staring at the frequency spectrum.

Here is a whistle:

…a triangle wave (horizontal axis measured in Hz):

…a guitar string (bonus points if you identify which string it was:

…and blowing across the rim of a water bottle:

The ratios of frequencies for the guitar string are integer multiples of the fundamental – this is easily derived using a diagram and an equation relating a wave’s speed, frequency, and wavelength. It’s also easily seen in the spectrum image – all harmonics equally spaced with each other and with the origin. The bottle, closely modeled by a tube closed at one end, has odd multiples of the fundamental. Again, this is totally visible in the image above of the spectrum.

I’m just going to say it here: if you are teaching standing waves and are NOT using any kind of frequency analyzer of some sort to show your students what it means to vibrate at multiple frequencies at once, you are at best missing out, and at worst, doing it plain wrong.

Rethinking the headache of reassessments with Python

One of the challenges I’ve faced in doing reassessments since starting Standards Based Grading (SBG) is dealing with the mechanics of delivering those reassessments. Though others have come up with brilliant ways of making these happen, the design problem I see is this:

The printer is a walk down the hall from my classroom, requires an ID swipe, and possibly the use of a paper cutter (in the case of multiple students being assessed).
We are a 1:1 laptop school. Students also tend to have mobile devices on them most of the time.
I want to deliver reassessments quickly so I can grade them and get them back to students immediately. Minutes later is good, same day is not great, and next day is pointless.
The time required to generate a reassessment is non-zero, so there needs to be a way to scale for times when many students want to reassess at the same time. The end of the semester is quickly approaching, and I want things to run much more smoothly this semester in comparison to last.

I experimented last fall with having students run problem generators on their computers for this purpose, but there was still too much friction in the system. Students forgot how to run a Python script, got errors when they entered their answers incorrectly, and had scripts with varying levels of errors in them (and their problems) depending on when they downloaded their file. I’ve moved to a web form (thanks Kelly!) for requesting reassessments the day before, which helps me plan ahead a bit, but I still find it takes more time than I think it should to put these together.

With my recent foray into web applications through the Bottle Python framework, I’ve finally been able to piece together a way to make this happen. Here’s the basic outline for how I think I see this coming together – I’m putting it in writing to help make it happen.

Phase 1 – Looking Good: Generate cleanly formatted web pages using a single page template for each quiz. Each page should be printable (if needed) and should allow for questions that either have images or are pure text. A function should connect a list of questions, standards, and answers to a dynamic URL. To ease grading, there should be a teacher mode that prints the answers on the page.
Phase 2 – Database-Mania: Creation of multiple databases for both users and questions. This will enable each course to have its own database of questions to be used, sorted by standard or tag. A user can log in and the quiz page for a particular day will automatically appear – no emailing links or PDFs, or picking up prints from the copier will be necessary. Instead of connecting to a list of questions (as in phase 1) the program will instead request that list of question numbers from a database, and then generate the pages for students to use.
Phase 3 – Randomization: This is the piece I figured out last fall, and it has a couple components. The first is my desire to want to pick the standard a student will be quizzed on, and then have the program choose a question (or questions) from a pool related to that particular standard. This makes reassessments all look different for different students. On top of this, I want some questions themselves to have randomized values so students can’t say ‘Oh, I know this one – the answer’s 3/5’. They won’t all be this way, and my experience doing this last fall helped me figure out which problems work best for this. With this, I would also have instant access to the answers with my special teacher mode.
Phase 4 – Sharing: Not sure when/if this will happen, but I want a student to be able to take a screenshot of their work for a particular problem, upload it, and start a conversation about it with me or other students through a URL. This will also require a new database that links users, questions, and their work to each other. Capturing the conversation around the content is the key here – not a computerized checker that assigns a numerical score to the student by measuring % wrong, numbers of standards completed, etc.

The bottom line is that I want to get to the conversation part of reassessment more quickly. I preach to my students time and time again that making mistakes and getting effective feedback is how you learn almost anything most efficiently. I can have a computer grade student work, but as others have repeatedly pointed out, work that can be graded by a computer is at the lower level of the continuum of understanding. I want to get past the right/wrong response (which is often all students care about) and get to the conversation that can happen along the way toward learning something new.

Today I tried my prototype of Phase 1 with students in my Geometry class. The pages all looked like this:

I had a number of students out for the AP Mandarin exam, so I had plenty of time to have conversations around the students that were there about their answers. It wasn’t the standard process of taking quiz papers from students, grading them on the spot, and then scrambling to get around to have conversations over the paper they had just written on. Instead I sat with each student and I had them show me what they did to get their answers. If they were correct, I sometimes chose to talk to them about it anyway, because I wanted to see how they did it. If they had a question wrong, it was easy to immediately talk to them about what they didn’t understand.

Though this wasn’t my goal at the beginning of the year, I’ve found that my technological and programming obsessions this year have focused on minimizing the paperwork side of this job and maximizing opportunities for students to get feedback on their work. I used to have students go up to the board and write out their work. Now I snap pictures on my phone and beam them to the projector through an Apple TV. I used to ask questions of the entire class on paper as an exit ticker, collect them, grade them, and give them back the next class. I’m now finding ways to do this all electronically, almost instantly, and without requiring students to log in to a third party website or use an arbitrary piece of hardware.

The central philosophy of computational thinking is the effort to utilize the strengths of computers to organize, iterate, and use patterns to solve problems. The more I push myself to identify my own weaknesses and inefficiencies, the more I am seeing how technology can make up for those negatives and help me focus on what I do best.

Assessing assessment over time – similar triangles & modeling

I’ve kept a question on my similar triangles unit exam over the past three years. While the spirit has generally been the same, I’ve tweaked it to address what seems most important about this kind of task:

My students are generally pretty solid when it comes to seeing a proportion in a triangle and solving for an unknown side. A picture of a tree with a shadow and a triangle already drawn on it is not a modeling task – it is a similar triangles task. The following two elements of the similar triangles modeling concept seem most important to me in the long run:

Certain conditions make it possible to use similar triangles to make measurements. These conditions are the same conditions that make two triangles similar. I want my students to be able to use their knowledge of similarity theorems and postulates to complete the statement: “These triangles in the diagram I drew are similar because…”
Seeing similar triangles in a situation is a learned skill. Dan Meyer presented on this a year ago, and emphasized that a traditional approach rushes the abstraction of this concept without building a need for it. The heavy lifting for students is seeing the triangles, not solving the proportions.

If I can train students to see triangles around them (difficult), wonder if they are similar (more difficult), and then have confidence in knowing they can/can’t use them to find unknown measurements, I’ve done what I set out to do here. What still seems to be missing in this year’s version is the question of whether or not they actually are similar, or under what conditions are they similar. I assessed this elsewhere on the test, but it is so important to the concept of mathematical modeling as a lifestyle that I wish I had included it here.

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