computational-thinking

Global Math Department – The How and Why of Computational Thinking

I had a great time presenting to a group of good people last night at the Global Math Department meeting for the evening. Thanks to Michael, Megan, Jonathan, and the rest of the team that helped make it happen.

The recording of my talk is now available, so check it out when you get a chance. You can access that here: https://www.bigmarker.com/GlobalMathDept/20Jan2015

Here’s an executive summary to discuss at the water cooler:

Let computers do what they do best, so that we can use our brains to do what they do best.
Numbers first, abstraction later. Computers serve to link concepts of specific numbers to the more abstract idea of variables.
We often use computation as a gate-keeper to get to the more interesting problem solving and higher level reasoning. Students can learn to use computational models and tools to get to that reasoning directly.
With spreadsheets, you (and your students) don’t have to know a programming language to get in the game.

Students and Working With Big Data

I happened upon this tweet today:

Teachers: How are you teaching #data skills to your students? Tell us! #mathchat #scichat #STEM

— Oceans of Data (@oceansofdata) January 9, 2015

I hadn’t heard of the Oceans of Data Institute before, but a quick look at its website revealed some interesting areas of focus:

Designing interfaces to let students interact with large sets of data
Defining the skills profile of big data scientists explicitly

As an example of their projects, the page includes a link to http://oceantracks.org, which allows students to visualize the movement of different animals in the ocean. In the image below, red is the track of an elephant seal, yellow is a blue-fin tuna, and turquoise is a white shark.

I like the idea of students getting large data sets and learning to play with them. I agree with the idea that students need to understand the role of data in the world given how frequently it is used to guide decisions. Having students collect, manage, model, and understand data is key to the scientific method and the learning process. Feeling comfortable drawing conclusions from data is crucial to being considered quantitatively literate today. I really like that ODI is putting in the effort to make this sort of exploration possible, while also acknowledging that there is a lot of work to be done.

Here is an example of the curation they are doing to share best practices:
http://oceansofdata.org/instructional-sequences-are-thought-scaffold-students-exploration-data

All that being said, here’s one quote from an executive summary about the skills profile for big data specialists that surprised me:

Unexpectedly, “soft skills” such as analytical thinking, critical thinking, and problem solving dominated the 20+ big data skill and knowledge requirements identified by the panel and endorsed by experts who completed the validation survey.

As a teacher, I find that this isn’t unexpected. The skills in the profile (which can be downloaded here) include skills that I’m interested in cultivating in my students. These soft skills are the key to students being successful in any field, not just big data. These are the truly transportable skills that I hope my students have long after they have left my classroom. The executive summary also identifies “defining problems and articulating questions” as one of the key tasks that are essential to the work of data scientists. I also believe this to be a focus of my time with students, and a focus of the work of most K-12 teachers.

The site also links to this article, which suggests that the conclusions drawn in the executive summary are more declarative and alarmist than I interpret them to be:

The skills necessary for the data analytics jobs of tomorrow aren’t being taught in K–12 schools today, according to a new report released by the Education Development Center, Inc.’s (EDC) Oceans of Data Institute.

I’m not sure how the Oceans of Data Institute feels about the comparison, but they do link to the article in their page about the project. I’m a big believer in teaching computational thinking skills. I acknowledge that getting more data scientists is an obvious goal for an organization with ‘data’ in their name. I think that using data is a nice way to tick off the ‘real-world relevance’ box along the way to the bigger picture skills that students need to develop.

I just don’t think we need another bold statement about a skill set that is missing from today’s curriculum. I want more tools that get students interacting with data, the creation of which ODI states and has demonstrated is its goal. That’s certainly a better way to get educators on board.

Coding For The Classroom: SubmitMe

For more than a year now, my process of sharing student work involves me going around the class, snapping pictures on my phone, and uploading the results through a web page to my laptop. It’s a lot smoother than using a document camera, and also enables students themselves to upload pictures of their work if they want, or if I ask them to. This is much smoother and faster than using a native application in iOS or Android because it’s accessed through a web page, and is hosted locally on my laptop in the classroom.

I’ve written about my use of this tool before, so this is more of an update than anything else. I have cleaned up the code to make it easier for anyone to run this on their own computers. You can download a ZIP file of the code and program here:
submitMe

Unzip the file somewhere convenient on your computer, and make a note of where this is on your computer. You need to have a Python compiler installed for this to run, so make sure you get that downloaded and running first. If you have a Mac, you already have it on your computer.

Here’s what you need to do:

Edit the submit.py file in the directory containing the uncompressed files using a text editor.
Change the address in the line with HOST to match the IP address of your computer. You can obtain this in Network Preferences.
Change the root_path line to match the directory containing the uncompressed files. In the zip file, the line refers to where I have these files on my own computer. These files are located in the /Users/weinbergmath/Sites/submitMePortable directory. This needs to be the absolute address on your file system.
Run the submit.py file using Python. If you are on a Mac, you can do this by opening a terminal using Spotlight, going to the directory containing these files, and typing python submit.py . Depending on your fire-wall settings, you might need to select ‘Allow’ if a window pops up asking for permission for the Python application.
In a web browser, enter the IP address you typed in Step 2 together, port 9000. (Example: http://192.168.0.172:9000). This is how students will access the page on their computers, phones, or tablets. Anyone on the same WiFi network should be able to access the page.

That should be it. As students upload images, they will be located in the /images directory where you unzipped the files. You can browse these using Finder or the File Browser. I paste these into my class notes for use and discussion with students.

Let me know if you need any help making this work for you. If needed, I can throw together a screen cast at some point to make it more obvious how to set this up.

Analyzing IB Physics Exam Language Programmatically

I just gave my IB physics students an exam consisting entirely of IB questions. I’ve styled my questions after IB questions on other exams and on homework. I’ve also looked at (and assigned) plenty of example questions from IB textbooks.

Just before the exam, students came to me with some questions on vocabulary that had never come up before. It could be that they hadn’t looked at the problems as closely as they had before this exam. What struck me was that their questions were not on physics words. They were on regular English words that, used in a physics context, can have a very different meaning than otherwise. For these students that often use online translators to help in decoding problems, I suddenly saw this to be a bigger problem than I had previously imagined. An example: a student asked what it meant for an object to be ‘stationary’. This was easily explained, but the student shook her head and smiled because she had understood its other meaning. On the exam, I saw this same student making mistakes because she did not understand the word ‘negligible’, though we had talked about it before in the context of multiple ways to say that energy was conserved. Clearly, I need to do more, but I need more information about vocabulary.

It got me wondering – what non-content related vocabulary does occur frequently on IB exams to warrant exposing students to it in some form?

I decided to use a computational solution because I didn’t have time to go through multiple exams and circle words I thought students might not get. I wanted to know what words were most common across a number of recent exams.

Here’s what I did:

I opened both paper 1 and paper 2 from May 2014, 2013, 2012 (two time zones for each) as well as both papers from November 2013. I cut and pasted the entire text from each test into a text file – over 25,000 words.
I wrote a Python script using the pandas library to do the heavy lifting. It was my first time using it, so no haters please. You can check out the code here. The basic idea is that the pandas DataFrame object lets you count up the number of occurrences of each element in the list.
Part of this process was stripping out words that wouldn’t be useful data. I took out the 100 most common words in English from Wikipedia. I also removed some other exam specific words like instructions, names, and artifacts from cutting and pasting from a PDF file. Finally, I took out the command terms like ‘define’,’analyze’,’state’, and the like. This would leave the words I was looking for.
You can see the resulting data in this spreadsheet, the top 300 words sorted by frequency. On a quick run through, I marked the third column if a word was likely to appear in development of a topic. This list can then be sorted to identify words that might be worth including in my problem sets so that students have seen them before.

There are a number of words here that are mathematics terms. Luckily, I have most of these physics students for mathematics as well, so I’ll be able to make sure those aren’t surprises. The physics related words (such as energy, which appeared 177 times) will be practiced through doing homework problems. Students tend to learn the content-specific vocabulary without too much trouble, as they learn those words in context. I also encourage students to create glossaries in their notebooks to help them remember these terms.

The bigger question is what to do with those words that aren’t as common – a much more difficult one. My preliminary ideas:

Make sure that I use this vocabulary repeatedly in my own practice problems. Insist that students write out the equivalent word in their own language, once they understand the context that it is used in physics.
Introduce and use vocabulary in the prerequisite courses as well, and share these words with colleagues, whether they are teaching the IB courses or not.
Share these words with the ESOL teachers as a list of general words students need to know. These (I think) cut across at least math and science courses, but I’m pretty sure many of them apply to language and social studies as well.

I wish I had thought to do this earlier in the year, but I wouldn’t have had time to do this then, nor would I have thought it would be useful. As the semester draws to a close and I reflect, I’m finding that the free time I’ll have coming up to be really valuable moving forward.

I’m curious what you all think in the comments, folks. Help me out if you can.

Computational Thinking in Teaching and Learning (Re-post)

A modified version of this post appeared on the Techsmith Blog here and in their quarterly newsletter, the Learning lounge. I appreciate their interest in my perspective. I hope to continue this important discussion here with my readers.

The idea of computational thinking has radically changed my approach to teaching over the past few years. This term, first coined by Jeanette Wing, a professor of computer science at Carnegie Mellon University, refers to several key ideas of thinking that are essential to computer science. The paper clearly identifies the reality that there are some tasks that computers do extremely well, and others that are better suited to the human brain. Traditionally, computer scientists have worked to outsource the calculating, organizing, searching, and processing work for task X to a computer so that they can focus on the more complex, challenging, and engaging aspects of the same task. According to Wing, one of the most essential skills we should develop in students is sorting tasks into these two groups.

My classroom, at its best, is a place where maximum time is spent with students wrestling with an engaging task. They should be working together to develop both intuition and understanding for required content. I can read the smiles or frowns and know whether I should step in. I can use my skills to nudge students in the right direction when I think they need it. Knowing precisely when they need it can’t easily be determined by an algorithm. For some students, this moment comes early on after encountering a new concept. Others require just one more minute of struggle before the idea clicks and it’s in their brains for good. Knowing the difference comes from the very human experience of time in classrooms with learners.

This is the human side of teaching. It is easy to imitate and approximate using technology, but difficult to produce authentically. Ideally, we want to maximize these personal opportunities for learning, and minimize the obstacles. For me, the computer has been essential to doing both, specifically, identifying the characteristics of tasks that a computer does better. If a computer can perform a task better than me or my students alone, I’m willing to explore that potential.

The most consistent application of this principle has been in the reduction of what I call ‘dead time’. I used to define this as time spent on tasks required for learning to be possible, but not actually a learning task itself. Displaying information on the board, collecting student answers, figuring out maximum and minimum guesses for an estimation problem – these take time. These sorts of tasks – displaying, collecting, processing – also happen to be the sort at which computers excel. I wrote a small web application that runs from my classroom computer that allows students to snap a picture of their work and upload it to my computer, anonymously if they choose. We can then browse student answers as a class and have discussions about what we see. The end result is equivalent to the idea of students writing their work on the board. The increased efficiency of sharing this work, archiving it, and freeing up class time to build richer activities on top of it makes it that much more valuable to let the computer step in.

I’ve also dabbled in making videos of direct instruction, but I have students watch and interact with them while they are in the classroom. During whole class instruction, I can’t really keep track of what each student is and isn’t writing down because I am typically in a static location in the classroom. With videos simultaneously going throughout the classroom, I can see what students write down, or what they might be breezing through too quickly. I get a much better sense of what students are not understanding because I can read their faces. I can ask individualized questions of students to assess comprehension. The computer distributes and displays what I’ve put together or curated for my students – one of its strengths. My own processing power and observation skills are free to scan the room and figure out what the next step should be.

Letting the computer manage calculation (another of its strengths) enables students to focus on the significance of calculations, not the details of the calculations themselves. This means that students can truly explore and gain intuition on a concept through use of software such as Geogebra or a spreadsheet before they are required to manage the calculations themselves. For students that struggle with arithmetic operations, this enables them to still make observations of mathematical objects, and observe how one quantity affects another. This involvement has the potential to inspire these same students to then make the connections that underlie their skill deficiencies.

Full disclosure though: I don’t have a 100% success rate in doing this correctly. I’ve invested time in programming applications that required much more effort than an analog solution. For instance, I spent a week writing all of my class handouts in HTML because the web browser seemed like a solution that was more platform independent than a PDF. That ended when I realized the technology was getting in the way of my students making notes on paper, a process I respect for its role in helping students make their own learning tools. There are some tasks that work much more smoothly (or are just more fun) using paper and a marker.

I value my student’s time. I value their thoughts. I want to spend as much class time as is possible building a community that values them as well. Where technology gets in the way of this, or adds too much friction to the process, I set it aside. I sit with students and tell stories. I push them to see how unique it is to be in a room for no other reason but to learn from each other. When I can write a program to randomize groups or roll a pair of dice a thousand times to prove a point about probability, I do so.

Knowing which choice is better is the one I wish I could write an algorithm to solve. That would take a lot of the fun out of figuring it out for myself.

Standards Based Grading(SBG) and The SUMPRODUCT Command

I could be very late to the party finding this out. If so, excuse my excitement.

I gave a multiple choice test for my IB Physics course last week. Since I am using standards based grading (SBG), I wanted a quick way to see how students did on each standard. I made a manually coded spreadsheet eight years or so ago to do this. It involved multiple columns comparing answers, multiple logical expressions, and then a final column that could be tallied for one standard. Multiply that by the total number of standards…you get the drill.

I was about to start piecing together an updated one together using that same exhausting methodology when I asked myself that same question that always gets me going: is there a better way?

Of course there is. There pretty much always is, folks.

For those of you that don’t know, the SUMPRODUCT command in Excel does exactly what I was looking for here. It allows you to add together quantities in one range that match a set of criteria in another. Check out the example below:

The column labeled ‘Response Code’ contains the formula ‘=1*(B6=E6)’, which tests to see if the answer is correct. I wanted to add together the cells in F6 to F25 that were correct (Response Code = 1) and had the same standard as the cell in H6. The command in cell I6 is ‘=SUMPRODUCT((F6:F25)*(E6:E25=H6))’. This command is equivalent to the sum F6*(E6=H6) + F7*(E7=H6)+F8*(E8=H6)+…and so on.

If I had known about this before, I would’ve been doing this in some way for all of my classes in some way since moving to standards based grading. I’ve evaluated students for SBG after unit exams in the past by looking at a student’s paper, and then one-by-one looking at questions related to each standard and evaluating them. The problem has been in communicating my rationale to students.

This doesn’t solve the problem for the really great problems that are combinations of different standards, but for students that need a bit more to go on, I think this is a nice tool that (now) doesn’t require much clerical work on my part. I gave a print out of this page (with column F hidden) to each student today.

Here is a sample spreadsheet with the formulas all built in so you can see how it works. Let me know what you think.
Exam Results Calculator

Sensors First – A Changed Approach

I presented to some FIRST LEGO League teachers on the programming software for the LEGO Mindstorms EV3 last week. My goal was to present the basics of programming in the system so that these teachers could coach their students through the process of building a program.

The majority of programs that students create are the end product of a lot of iteration. Students generally go through this process to build a program to do a given task:

Make an estimate (or measurement) of how far the motors must rotate in order to move the robot to a given location.
Program the motors to run for this distance.
Run the program to see how close the robot gets to the desired location.
Adjust the number in Step 1. Repeat until the robot ends up in the right location.

Once the program gets the robot to the right location, this process is repeated for the next task that the robot must perform. I’ve also occasionally suggested a mathematical approach to calculate these distances, but the reality is that students would rather just try again and again until the robot program works. It’s a great way to introduce students to the idea of programming as a sequence of instructions, as well as familiarity with the idea that getting a program right on the first try is a rarity. It’s how I’ve instructed students for years – a low bar for entry given that this requires a simple program, and a high ceiling since the rest of programming instructions are extensions of this concept.

I now believe, however, that another common complaint that coaches (including me) have had about student programs is a direct consequence of this approach. Most programs (excluding those students with a lot of experience) require the robot to be aimed correctly at the beginning of the program. As a result, students spend substantial time aiming their robot, believing that this effort will result in a successful run. While repeatability is something that we emphasize with students (I have a five in a row success rule before calling a mission program completed) it’s the method that is more at fault here.

The usual approach in this situation is to suggest that students use sensors in the program to help with repeatability. The reason they don’t do so isn’t that they don’t know how to use sensors. It is that the aim and shoot method is, or seems, good enough. It is so much easier in the student’s mind to continue the simpler approach than invest in a new method. It’s like when I’ve asked my math students to add the numbers from 1 to 30, for example. Despite the fact that they have learned how to quickly calculate arithmetic series before, many of them pick up their calculators and enter the numbers into a sum, one at a time, and then hit enter. The human tendency is to stick to those patterns and ideas that are familiar until there is truly a need to expand beyond them. We stick with what works for us.

One of my main points to the teachers in my presentation was that I’m making a subtle change to how I coach my students through this process. I’m calling it ‘sensors first’.

The tasks I give my students in the beginning to learn programming are going to require sensors in order to complete. Instead of telling students to program their robot to drive a given distance and stop, I’ll ask them to drive their robot forward until a sensor on their robot sees a red line. I’ll also require that I start the robot anywhere I want in the test of their program.

It’s a subtle difference, and requires no difference in the programming. In the EV3 software, here’s what it looks like in both cases, using wheels to control the distance, and a sensor:

What am I hoping will be different?

Students will look to the challenges I give them with the design requirement built in that aim-and-shoot isn’t an option that will result in success. If they start off thinking that way, they might always think how a sensor could be used to make the initial position of the robot irrelevant. FLL games always have a number of printed features on the mat that can be used to help with this sort of task.
When I do give tasks where the students can start the robot wherever they choose, students will (hopefully) think first whether or not the starting position should matter or not. In cases where it doesn’t, then they might decide to still use a sensor to guide them (hopefully for a reason), or drop down to a distance based approach when it makes sense to do so. This means students will be routinely thinking what tool will best do the job, rather than trying to use one tool to do everything.
This philosophy might even prompt a more general need for ways to reduce the uncertainty and compound error effect associated with an aim and shoot approach. Using the side of the table as a way to guide straight line driving is a common and simple approach.

These sorts of problem solving approaches are exactly the way successful engineering design cycle works. Solutions should be found that maximize the effectiveness of a design while minimizing costs. I’m hoping this small change to the way I teach my students this year gets them spending more time using the tools built into the robot well, rather than trying to make a robot with high variability (caster wheels, anyone?) do the same thing two times in a row.

The Nature of Variables for Students vs. Programmers

Dan Meyer has provoked us again with this post questioning the meaning of variables in programming compared with how they exist in the minds of our students.

I previously wrote about something I tried at the beginning of last year with my students that probed this question a bit. My contention then was that writing expressions is something that occurs with students only in math class world, and that it is an inherently non-interactive process. The spirit of what variables do is something with which students have familiarity. It’s the abstraction of the mathematical representation that pushes that familiarity away from them.

I’m going to use a different expression problem since the one in Dan’s post doesn’t do it for me.

Dan estimates that around 3/4 of any group of people drink soda.

I’d start with this activity that students would be able to answer:

Students could each click on the people go through the process of figuring out how many in each group drink soda according to Dan’s estimate, and would record the number in each group. The third group serves to construct a bit of controversy for discussion purposes. In doing this four times, students are presumably going through a similar process each time.

Mathematics serves to create structure for this repetition, but on its own, is not necessarily in the realm of what our students would do to manage this repetition. Programming provides a way to bridge this gap using the same idea of variables that exists in the mathematical realm, and here is where the value sits for this discussion.

In the post I mentioned previously, I said that I briefly showed students how to type expressions into a spreadsheet and play around with inputs and outputs so that they match concrete values. In a non 1:1 laptop classroom, I might start with this:

A calculation links the outputs to the inputs in each of these tables. Students have concrete values sitting in front of them, so they will notice that each of these tables must be making the wrong calculations, even though they each have one correct value. Here, we have the computer making the same calculation each time, but these calculations do not work in each case. This is the wrong model to match our data. The computer is doing exactly what we are telling it to do, but the model is wrong.

How do we fix this, class? Obviously we use a different computational model. I might have students decide in a group what calculation I need to do to correctly reproduce the values from the exercise, and elicit those suggestions from them.

Once we establish this correct model, this calculation we are making is common to every set of data. We can show that this calculation makes an interesting prediction of 7.5 people liking soda in the group of 10. We can use this calculation to predict how many people in a group of 28 drink soda (and in a 1:1 classroom, I’d have them go through this entire programming process themselves.)

I might now generate a table hundreds of entries long and ask whether there is a better way to represent the set of all possible answers to this question. The table will work, but it is tedious. We need a better way. How do we do this? Here is where variables come in.

Programmers use variables because they want to build a program that produces a correct output for every possible input that might be used to solve a given problem or design. Mathematicians also want to have the same level of universality, and have a syntax and structure that allows for efficient communication of that universality. Computers are really good at calculating. The human brain is really good at managing the abstraction of designing those calculations. This, ultimately, is what we want students to be able to do, but they often get lost in both the design stage and the calculation stage, especially because these get divorced from the actual problem students are trying to solve.

If we can have students spend more time in the design stage and get feedback on whether their calculations are correct, that’s the sweet spot for making the jump to using mathematical variables.

Curated review for finals

I really don’t like reviewing for exams. I don’t think I’m the only one that thinks this, by far.

If I create a the review sheet, I’m the one going through all of the content of the unit and identifying what might be important. It would be much more valuable to have students do this. I’ve also been filling the school server with notes and handouts of what we do each day, so they could be the ones deciding which problems are representative of the unit.

Suppose I do make a new set of review problems available to students. If students have this set of problems to work through during class, I spend my time circulating and answering questions and giving feedback, which is the best use of my time with students. Better yet, students answer each other questions, and give each other feedback. They lose the opportunity to see the scope of the entire semester themselves because, outside of the set of problems I prepare for them, they don’t actually take the time to see that scope on their own. They only see my curated sample and interpret it according to their own understanding of the relationship between review problems I select and problems I select for an exam.

I’ve had students themselves create review sheets, but this always has its own set of issues. Is it on paper or online? If on paper, how does this sheet efficiently get shared with other students? The benefit of an online resource is the ease of sharing. The difficulty comes from (1) the difficulty of communicating mathematics on a computer and (2) compiling that resource in one place. It’s a lot of work to scan student work and paste it into a document. Unless I am meticulous in making sure that all students are using the same program (which is a lot of work for a class of twenty-four students all with their own laptops) this becomes a lot of work (again) for me. I’ll do it if I really believe it is worth the effort for students, but I’m always looking to be efficient in that effort. I also don’t want to put this effort on the shoulders of a student to together. And before someone tells me to use Google Docs and its amazing collaborative tools, I’ll bring up the governmental disruption of Google services and leave it to you to figure out why that isn’t an option for me and my students.

In the end, I have to decide which is the most valuable for students relative to a review. Is it getting feedback on what a student does and does not understand? Is it going back over the entire semester’s material and figuring out what is important relative to a cumulative final?

If I have to pick a theme of my online experiments this year, it has been the search for effective ways to leverage social pressure and student use of technology to improve the quality of the time we spend in the classroom together. In the past, I have been the one collecting student work and putting it in one place when I’ve tried doing things differently for exam review. That organization is precisely something computers do well if we design a scheme for them to use.

Here’s what I have had students do this year:

Each student has a blog where they post their own review sheet for one standard. They submit the URL of their post and their standard number through the same site through which they sign up for SBG reassessments. They see a list of the pages submitted by other students:

This serves as a central portal through which students can access each other’s pages. Each student controls their own page and URL information, which saves me the effort to collect it all.

Why am I really excited about this list?

I curate the list. I decide whether a page has met the requirements of the assignment, and students can see those pages with a checkmark and a WB for my initials. If a student needs to improve something, I can tell them specifically what isn’t meeting the requirements and help them fix it. Everyone doesn’t have to wait for everyone else to be finished for the review process to begin. I don’t decide what goes into each page generally, but I do help students decide what should be there. Beyond that, I don’t have to do any compilation myself.
Students (ideally) vote on a page if they think it meets the requirements. Students can each vote once for each page, and see a checkmark once they have voted. This gets them thinking about the quality of what they see in the work of other students. I have been largely impressed with what students have put together for this project, and students are being fairly generous with this. I’m ok with that at this point because of the next point:
Students have an incentive to actually visit each other’s pages. I have no idea how many students actually use the review sheets we’ve produced together in the past. I doubt it is very many. There’s some aspect of game theory involved here, but if a student sees that others are visiting his or her own pages, that student might feel more compelled to visit the pages of other students. Everyone benefits from seeing what everyone else is doing. If some review happens as a result, that’s a major bonus. They love seeing the numbers adjust real time as votes come in. There is a requirement that each vote include a code that is embedded in the post they are voting for, just so someone isn’t voting for them all without visiting the page.
Students were actually using the pages to review today. Students were answering each other’s questions and getting feedback sometimes from the authors themselves.
I get to have valuable conversations about citing resources online.

Right now, students can vote as much as they want, but I plan to introduce one more voting option before this is entirely done which allows students to vote on their top three favorites in terms of usefulness. I am not sure how I would do this without it turning into a popularity contest, but I might try it and see how their sense of quality relates to mine. I would also love to use this next year as a Reddit style resource where students are posting problems and solutions potentially for specific standards and can vote on what is particularly helpful to them. Again, just an experiment.

I really loved how engaged students were today in either developing their pages or working on each other’s review problems. It was one of the most productive review days I’ve had, particularly in light of the fact that I didn’t have to write a single problem of my own. I did have to write the code, of course, but that was a lot more interesting to me today than thinking of interesting assessment items that I’d rather just put on an exam.

Standards Based Grading: Bridging the Gap

I ended last semester feeling pretty discouraged about my implementation of standards based grading. I still felt pretty good about what it was doing for students. For the students that were actually taking advantage of the system and initiating reassessments, it seemed to be helping. Some examples:

Students were getting frequent assessment over the different standards of the course through quizzes, and got feedback on their learning the same day since the quizzes were short.
Some students understood that they could request reassessment on their own to show progress on standards that previously were not marked as proficient.
On a day that I gave one of these standards quizzes, I was guaranteed to have a conversation on content, albeit sometimes a short one, with every single student. I can’t guarantee that I get to every student, every period, though I’d like to think that I do.
Students seemed to be less frustrated or scared by unit exams, and I received (anecdotally) fewer blank problems since students had an incentive to try anything.

By the end of the semester, I had 248 student-initiated reassessments. I don’t know how that compares to others, but that number seemed to be an indication that something was going well. Then I looked at the numbers. Of those reassessments, eighty-eight of them were in the last week of the semester. Roughly 1/3 of the total were taken by the top five most frequent assessors.

I wasn’t getting to many of the students. Despite my efforts to constantly ask students to do so, talk about opportunities to reassess in class, and target students that needed extra help with suggestions to come see me after school, some students didn’t know that they could reassess. Some students didn’t make the time. In fact, most didn’t. I was also tolerating a fairly heavy end of semester reassessment rush that seemed higher than what I’d like to see happen.

The other concept that also bugged me was that in this system, I wasn’t placing value on those behaviors that would lead to higher standards scores. No, I wasn’t about to go back to a system of checking homework, and giving extra credit – the grades reported through standards were a pretty good measure of what students knew. On an end of semester survey, a majority of students confirmed this fact. Students also understood that reassessment without preparation wouldn’t result in increased scores. I had students that said, however, that doing homework, getting help after school, teaching concepts to other students – those things that result in improved understanding – weren’t accounted for in the grade. If I valued those as part of the process, why was I not assigning any value to them in the grade?

I spent a lot of time thinking about this over the winter break. In my system, there was a fundamental gap between the behaviors I wanted students to develop, and the way I was measuring the learning happening in my classroom. Students understand the system this way:

There is a visible wall between what students know I value and what they see measured in their grade. This is the philosophical basis of standards based grading – the grade is a measure of learning content, not necessarily of completion of activities. It is fundamentally different from other grading systems. We don’t see it this way as teachers, however.

We see it like this:

I have the conversation with students all the time about the difference between these two conceptions. They do understand. It just doesn’t fit with the rest of what they have been told in school, where learning sometimes takes second fiddle to being a student.

This is a communication design problem. After a lot of thinking and designing, I came up with a new computer based system using the Meteor JS framework that I’ve been using since January.

Some parts of it have helped bridge this gap (and other problems) in some ways that have been quite productive – I’ll go through them piece by piece.

Problem 1 – Google Forms are not reliable in China.

I previously used a Google form to collect reassessment sign-up data. Students would frequently (and with good reason) say that they couldn’t log on to sign up because of this issue. While there are still internet issues with the new site, this is less of a problem. They can log in with their own email address, their own secure password, and I can control the input/output of information much more reliably since it’s a database, not a spreadsheet.

Problem 2 – I don’t want students signing up for reassessments the same day.

I really want students planning ahead. The Google form didn’t have the option of limiting which days they could sign up for based on the time of sign up, at least I didn’t see how to do this easily. It’s true that I could simply see which students signed up from the Google form results spreadsheet, but that involved scrolling, searching, and mentally filtering results. That was more work than I wanted to be doing.

With some Javascript, I make it impossible to do this. Students log in, click on ‘Reassessment Sign-up’ and see this form:

Problem 3 – Students forget which standard they signed up to reassess on.

I received an email every time students signed up for a reassessment through the Google form. I never figured out a slick way to do this through forms – I’m sure it’s possible. With this system, students can click on ‘My Reassessments’ and see what they’ve signed up to do:

If they miss the bus and have to reschedule for later the same day, they can log in and edit the reassessment themselves. Because of Meteor’s realtime system, those changes instantly show on my browser when they happen.

Problem 4 – Students sign up to reassess without any preparation.

This was a big one I wanted to solve. On my previous form, there was just a check box that said “I promise to prepare for this reassessment” along with a box where they describe what they did to prepare. I wasn’t directly able to check this, and usually didn’t have time to do so beyond noting that it was more substantial than ‘I studied’.

When students log in and sign up for a reassessment now, they see a little badge called ‘Reassessment Credits’. Each reassessment costs them one credit. What happens when they try to sign up for a reassessment without any credits left?

They can’t do so. No way around it, at least without learning some Javascript to hack my system.

This is where I find I am doing the work to educate students in what I am looking for. I value the work that they do in preparing for reassessments. I show that value through giving students credits, a token for whatever it is they choose to do to improve their understanding. These credits then directly convert into opportunities to show what they have learned through reassessment. I have the flexibility to give credits for different things that students do – tutoring other students, sitting in the classroom and doing homework with me, or simply showing me the homework they did after the previous class. This value is separate from the grade. Students have also found that through doing the work to earn a credit, I have directly increased their standards grade because I’ve seen evidence of higher understanding there.

Problem 5 – Students don’t know that their peers are reassessing.

I’m not ashamed to say that I also wanted to call upon the fact that students (and all of us) are influenced to some extent by our social community. I added one more part to the page that some students have reported has pushed them to sign up and complete reassessments.

When I first added this feature, a student said she was disappointed when she saw her proportion of the total decreasing, so she felt compelled to figure out what she might reassess over based on her progress.

Problem 6 – Staying organized with reassessments from four different classes is difficult

This system is computerized, so it’s easy to sort which reassessments I have on a given day.

Rather than skimming a spreadsheet and figuring out which quizzes to prepare, I have an easy list that allows me to prioritize and plan which quizzes I need to have available for which part of the day.

I’ve taken a lot of the obstacles out of the way that have made it stressful for me to stay organized in reassessments, and for students to opt not to do so. I am not trying to make a point about quantity vs. quality here, but I’m really pleased with how the system has worked for students.

So far this semester, I’ve had 221 reassessments through the system at this point in the semester, and we’re only in the first quarter. Thirty seven out of 55 students have assessed multiple times. Eleven students thus far have not reassessed at all, and I’ve seen that information easily through some database queries, which has prompted some conversations with those students about why they haven’t. It’s far easier than it used to be to get this information out.

Students also have great ideas for making it better. They know themselves, and know what would help them stay on top of their needs. I enjoy the challenge of learning to build this for them, and they seem to appreciate the effort.

I am not sharing the URL quite yet since there is student user information in there, and haven’t built a nice sandbox login yet to see the features. That will come when I have the time, whenever that is.

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