The How and Why of Standards Based Grading @ Learning2.0

For those of you that are readers of my blog, you already know that I've become a believer in the power of standards based grading, or SBG. It's amazing looking back at my first post on my decision to commit to it four years ago. Seeing how this system has changed the way I plan my lessons, think about class activities, and interact with students about learning makes me wonder where I would be at this point without it.

I'm now trying to help others see how they might make standards based grading have a similar change to their classrooms. I'm running a one hour workshop this Friday at 1:30 in room C315 to introduce Learning2 attendees to how a teacher might go about this. More important for those considering a change to such a system is the fact that I run my system in a non-standards based PowerSchool environment. Here's the workshop description:

Suppose a student has earned a 75 in your class. How do you describe that student's progress? What has that student learned in your class? Obviously a student with an 85 has done better than the student with a 75, but what exactly has the 85 student achieved that the other student has not? Is it ten percent more understanding? Two more homework assignments during the quarter? Perhaps most importantly, what can the 75 student do to become an 85 student?

Grades are part of our school culture and likely aren't going anywhere soon. We can work to tweak how we generate and communicate the meaning of those grades in a way that better represents what students have actually learned. One approach for doing this is called Standards Based Grading, or SBG.

In this one hour workshop, you will learn about SBG and how it can clarify the meaning of grades, as well as how it can be implemented effectively within a traditional reporting system. You will also learn how a SBG mindset encourages productive changes to the process of planning units, activities, and assessments. We will also discuss the ways such a system can be run in the context of various subject areas.

It's a lot to cover in an hour, but I'm hoping I can nudge a few folks to try this out moving forward.

The link to my workshop is here.

I'm really excited about the Learning 2.0 conference this year. I first attended back in 2011 in Shanghai and the experience was what prompted me to become active on Twitter and begin blogging back then. I know the next few days will be filled with inspiring conversations and ideas that challenge my thinking and push me to grow as a teacher.

Stay tuned to the blog and to Twitter to see what I'm up to over the weekend.

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Scaling Reassessments, Part 2

A quick comment before hitting the hay after another busy day: the reassessment system has hit it big in my new school.

Some facts to share:

  • In the month since my reassessment sign-up system went up, 87% of my students have done at least one self-initiated reassessment, 69% doing more than one. This is much more usage than my system has had, well, ever.
  • Last Friday was an all time high number of 53 reassessments over the course of a day. I will not be doing that again, ever.
  • Students are not hoarding their credits, they are actually using them. I've committed to expiring them if they go unused, and they will all be expired by the end of the quarter, which is essentially tomorrow.

I need to come up with some new systems to manage the volume. I'll likely limit the number of slots available in the morning, at lunch, and after school to encourage them to spread these out throughout the upcoming units instead of waiting, but more needs to be done. This is what I've been hoping for, and I need to capitalize on the enthusiasm students are showing for the system. Now I need to make it so I don't pull all my hair out in the process.

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Scaling up SBG for the New Year

In my new school, the mean size of my classes has doubled. The maximum size is now 22 students, a fact about which I am not complaining. I've missed the ease of getting students to interact with simple proximity as the major factor.

I have also been given the freedom to continue with the standards based grading system that I've used over the past four years. The reality of needing to adapt my systems of assessment to these larger sizes has required me to reflect upon which aspects of my system need to be scaled, and what (if anything) needs to change.

The end result of that reflection has identified these three elements that need to remain in my system:

  • Students need to be assessed frequently through quizzes relating to one to two standards maximum.
  • These quizzes need to be graded and returned within the class period to ensure a short feedback cycle.
  • There must still be a tie between work done preparing for a reassessment and signing up for one.

Including the first element requires planning ahead. If quizzes are going to take up fifteen to twenty minutes of a class block, the rest of the block needs to be appropriately planned to ensure a balance between activities that respond to student learning needs, encourage reinforcement of old concepts, and allow interaction with new material. The second element dictates that those activities need to provide me time to grade the quizzes and enter them as standards grades before returning them to students. The third happens a bit later in the cycle as students act on their individualized needs to reassess on individual standards.

The major realization this year has been a refined need for standards that can be assessed within a twenty minute block. In the past, I've believed that a quiz that hits one or two aspects of the topic is good enough, and that an end of unit assessment will allow complete assessment on the whole topic. Now I see that a standard that has needs to have one component assessed on a quiz, and another component assessed on a test, really should be broken up into multiple standards. This has also meant that single standard quizzes are the way to go. I gave one quiz this week that tested a previously assessed standard, and then also assessed two new ones. Given how frantic I was in assessing mastery levels on three standards, I won't be doing that again.

The other part of this first element is the importance of writing efficiently targeted assessment questions. I need students to arrive at a right answer by applying their knowledge, not by accident or application of an algorithm. I need mistakes to be evidence of misunderstanding, not management of computational complexity. In short, I need assessment questions that assess what they are designed to assess. That takes time, but with my simplified schedule this year, I'm finding the time to do this important work.

My last post was about my excitement over using the Numbas web site to create and generate the quizzes. A major bottleneck in grading these quizzes quickly in the past has been not necessarily having answers to the questions I give. Numbas allows me to program and display calculated answers based on the randomized values used to generate the questions.

Numbas has a feature that allows students to take the exam entirely online and enter their answers to be graded automatically. In this situation, I have students pass in their work as well. While I like the speed this offers, that advantage primarily exists in cases where students answer questions correctly. If they make mistakes, I look at the written work and figure out what went wrong, and individual values require that I recalculate along the way. This isn't a huge problem, but it brings into question the need for individualized values which are (as far as I know right now) the only option for the fully online assessment. The option I like more is the printed worksheet theme that allows generation of printable quizzes. I make four versions and pass these out, and then there are only four sets of answers to have to compare student work against.

With the answers, I can grade the quizzes and give feedback where needed on wrong answers in no more than ten or fifteen minutes total. This time is divided into short intervals throughout the class block while students are working individually. The lesson and class activities need to be designed to provide this time so I can focus on grading.

The third element is still under development, but my credit system from previous years is going to make an appearance. Construction is still underway on that one. Please pardon the dust.


If you're an ed-tech company that wants to impress me, make it easy for me to (a) generate different versions of good assessment questions with answers, (b) distribute those questions to students, (c) capture the student thinking and writing that goes with that question so that I can adjust my instruction accordingly, and (d) make it super easy to share that thinking in different ways.

That step of capturing student work is the roughest element of the UX experience of the four. At this time, nothing beats looking at a student's paper for evidence of their thinking, and then deciding what comes next based on experience. Snapping a picture with a phone is the best I've got right now. Please don't bring up using tablets and a stylus. We aren't there yet.

Right now there are solutions that hit two or three, but I'm greedy. Let me know if you know about a tool that might be what I'm looking for.

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Numbas and Randomized Assessment

At the beginning of my summer vacation, I shared the results of a project I had created to fill a need of mine to generate randomized questions. I subsequently got a link from Andrew Knauft (@aknauft) about another project called Numbas that had similar goals. The project is out of Newcastle University and the team is quite interested in getting more use and feedback on the site.

You can find out more at The actual question editor site is at

Screen Shot 2016-08-22 at 8.23.01 PM

I've used the site for a couple of weeks now for generating assessments for my students. I feel pretty comfortable saying that you should be using it too, and in place of my own QuestionBuilder solution. I've taken the site down and am putting time into developing my own questions on Numbas. Why am I so excited about it?

  • It has all of the randomization capabilities of my site, along with robust variable browsing and grouping, conditions for variable constraints, and error management in the interface that I put on the back burner for another day. Numbas has these features right now
  • LaTEX formatting is built in along with some great simplification functions for cleaning up polynomial expressions.
  • Paper and online versions (including SCORM modules that work with learning management sites like Moodle) are generated right out of the box.
  • It's easy to create, share, and copy questions that others have created and adapt them to your own uses.
  • Visualization libraries, including Geogebra and Viz.js, are built in and ready to go.
  • The code is open sourced and available to install locally if you want to do so.

I have never planned to be a one-person software company. I will gladly take the output of a team of creative folks that know what they are doing with code over my own pride, particularly when I am energized and focused on what my classroom activities will look like tomorrow. The site makes it easy to generate assessments that I can use with my students with a minimal amount of friction in the process.

I'll get more into the details of how I've been using Numbas shortly. Check out what they've put together - I'm sure you'll find a way to include it in part of your workflow this year.

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Context and Learning Names

I wrote yesterday about my decision to try learning names of my students on the first day.

As of the middle of week two, I've learned the names of every student within each class with few exceptions. In some of the bigger groups, I mix one or two names that start with the same first letter, but I correct myself pretty quickly. I've come to recognize some individual traits that make each student unique within the group, and am feeling comfortable building on my knowledge of their names to find out more about who they are.

In the hallways, in line for lunch, and walking around campus, I struggle. Outside of the classroom, I lack the context of those names that I can usually lean back upon to remember them. With the students all mixed up together, including with students that I don't have in my classes, it takes longer to put a name with the face. As I develop an understanding of the students beyond names, this struggle will go away.

The analogy to learning in any classroom context stands on its own, so I won't ruin it with more commentary.



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Fail Early, Fail Often: Learning Names

Learning names this year was a bigger challenge this time around in comparison to the past few years. The first reason is that my new school is substantially bigger than my previous school, as are the class sizes. Another major reason: I'm the new guy.

The students generally know each other, so I decided the first day wasn't actually about them learning each other's names. I still included activities that got them interacting with each other, but I was the one that needed to learn their names. I decided the quick forty minute block on the first day was an opportunity to model my class credo: fail early, fail often.

When they walked in, I asked them their names, and what they wanted to be called. I've learned that these are not necessarily the same. These names were noted on my clipboard. I made a big show out of going around to each student, looking them in the eyes, and saying their name. Taking attendance then became my first opportunity to assess what I remembered. The order on the roster definitely didn't match the order that the students entered the classroom.

I then had them line up alphabetically along the back wall. I had them all say their names one in a row. I had my reference material on the clipboard and went reverse alphabetical order. I publicly made mistakes, lots of them. Then I had them say the name of the person immediately to their left. For me learning the names, this meant that the voice saying the name was different, but the name was the same. I narrated that I wasn't actually looking at the person saying the name - my attention was on the person whose name was being said.

I then had them get in line in order of birthday, but without any words. Once they figured out their order, I went down the line and tried to get names. I looked at my clipboard if I needed to, and I often did, but often had them just say their names back. I explained that I made them move around because I didn't want to learn names based on who each person was next to - I needed to connect the name to the face. This ensured I was learning the right information, not an arbitrary order.

Then I had them get into two or three random orders. If there was time, I had a student go down the line reciting names. Then I went again myself, now trying not to look at the clipboard unless it was absolutely necessary. The mistakes continued to come, but I generally was having more success at this stage. I again told them that I had quizzes myself enough - it was time to let my brain do connecting behind the scenes. I emphasized that this was why cramming doesn't tend to work: the brain is really good at organizing the information if it has the time to do so.

It was great putting myself in the position of not knowing answers and having to ask students for help. The students appeared to enjoy my genuine attempt to demonstrate how I learn information efficiently, and how essential failure is to being successful in the end.

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Moving to Vietnam

After a whirlwind tour visiting family, friends, and taking care of many more errands than in a typical summer vacation, my family and I arrived in Vietnam mid-July. The 27 hours of travel went far more smoothly and quickly than expected. This was at least partly due to the fact that the under-filled coach cabin yielded our now eight-month old daughter her own seat.

All of this was a big step toward the next stage of my teaching career: I've joined the high school faculty at the Saigon South International School, located in District 7 of Ho Chi Minh City. This past week, I started my year teaching two sections of the first year of IB Mathematics SL, two sections of pre-Calculus, and a section of Algebra 2 & trigonometry. If you've heard me discuss my teaching load at my previous school, you'll know that this is half the number of preps, and one more open block in my schedule than I've had for the past six years. I've been amazed by my colleagues and their range of international experiences, both in and out of my department. The energy to try new things and a drive to challenge my teaching practices are both part of the culture here, and it's very exciting to be on this team for the new year.

Screen Shot 2016-08-15 at 9.19.47 PM

I'll continue to write on this blog, which has often played second fiddle to other obligations in the past couple of years. My hope is to reflect more regularly as part of an effort to do fewer things, but with greater focus. I hope you'll continue to join me.

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2015-2016 Year in Review: IB Mathematics SL/HL

This was my second year working in the IB program for mathematics. For those that don't know, this is a two year program, culminating in an exam at the end of year two. The content of the standard level (SL) and higher level (HL) courses cross algebra, functions, trigonometry, vectors, calculus, statistics, and probability. The HL course goes more into depth in all of these topics, and includes an option that is assessed on a third, one-hour exam paper after the first two parts of the exam.

An individualized mathematics exploration serves as an internally assessed component of the final grade. This began with two blocks at the end of year one so that students could work on it over the summer. Students then had four class blocks spread out over the first month of school of year two two work and ask questions related to the exploration during class.

I taught year one again, as well as my first attempt at year two. As I have written about previously, this was run as a combined block of both SL and HL students together, with two out of every five blocks as HL focused classes.

What worked:

  • I was able to streamline the year 1 course to better meet the needs of the students. Most of my ability in doing this came from knowing the scope of the entire course. Certain topics didn't need to be emphasized as I had emphasized in my first attempt last year. It also helped that the students were much better aware of the demands of higher-level vs. standard level from day one.
  • I did a lot more work using IB questions both in class and on assessments. I've become more experienced with the style and expectations of the questions and was better able to speak to questions about those from students.
  • The two blocks on HL in this combined class was really useful from the beginning of year one, and continued to be an important tool for year two. I don't know how I would have done this otherwise.
  • I spent more time in HL on induction than last year, both on sums and series and on divisibility rules, and the extra practice seemed to stick better than it did last year in year one.
  • For students that were self starters, my internal assessment (IA) schedule worked well. The official draft submitted for feedback was turned in before a break so that I had time to go through them. Seeing student's writing was quite instructive in knowing what they did and did not understand.
  • I made time for open ended, "what-if" situations that mathematics could be used to analyze and predict. I usually have a lot of this in my courses anyway, but I did a number of activities in year one specifically to hint at the exploration and what it was all about. I'm confident that students finished the year having seen me model this process, and having gone through mini explorations themselves.
  • After student feedback in the HL course, I gave many more HL level questions for practice throughout the year. There was a major disconnect between the textbook level questions and what students saw on the HL assessments, which were usually composed of past exam questions. Students were more comfortable floundering for a bit before mapping a path to a solution to each problem.
  • For year two, the exam review was nothing more than extended class time for students to work past papers. I did some curation of question collections around specific topics as students requested, but nearly every student had different needs. The best way to address this was to float between students as needed rather than do a review of individual topics from start to finish.
  • The SL students in year two learned modeling and regression over the Chinese new year break. This worked really well.
  • Students that had marginally more experience doing probability and statistics in previous courses (AP stats in particular) rocked the conditional probability, normal distribution, and distribution characteristics. This applied even to students who were exposed to that material, but did poorly on it in those courses. This is definitely a nod to the idea that earlier exposure (not mastery) of some concepts is useful later on.
  • Furthermore, regarding distributions, my handwaving to students about finding area under the curve using the calculator didn't seem to hurt the approach later on when we did integration by hand.
  • This is no surprise, but being self sufficient and persevering through difficult mathematics needs to be a requirement for being in HL mathematics. Students that are sharp, but refuse to put in the effort, will be stuck in the 1-3 score range throughout. A level of algebraic and conceptual fluency is assumed for this course, and struggling with those aspects in year one is a sign of bigger issues later on. Many of the students I advised this way in year one were happier and more successful throughout the second year.
  • I successfully had students smiling at the Section B questions on the IB exam in the slick way that the parts are all connected to each other.

What needs work:

    For year one:

  • I lean far too hard on computer based solutions (Geogebra, Desmos) than on the graphing calculator during class. The ease of doing it these ways leads to students being unsure of how to use the graphing calculator to do the same tasks (finding intersections and solutions numerically) during an assessment. I definitely need to emphasize the calculator as a diagnostic tool before really digging into a problem to know whether an integer or algebraic solution is possible.
  • Understanding the IB rounding rules needs to be something we discuss throughout. I did more of this in year one on my second attempt, but it still didn't seem to be enough.
  • For year two:

  • Writing about mathematics needs to be part of the courses leading up to IB. Students liked the mini explorations (mentioned above) but really hated the writing part. I'm sure some of this is because students haven't caught the writing bug. Writing is one of those things that improves by doing more of it with feedback though, so I need to do much more of this in the future.
  • I hate to say it, but the engagement grade of the IA isn't big enough to compel me to encourage students to do work that mattered to them. This element of the exploration was what made many students struggle to find a topic within their interests. I think engagement needs to be broadened in my presentation of the IA to something bigger: find something that compels you to puzzle (and then un-puzzle) yourself. A topic that has a low floor, high ceiling serves much more effectively than picking an area of interest, and then finding the math within it. Sounds a lot like the arguments against real world math, no?
  • I taught the Calculus option topics of the HL course interspersed with the core material, and this may have been a mistake. Part of my reason for doing this was that the topic seemed to most easily fit in the context of a combined SL/HL situation. Some of the option topics like continuity and differentiability I taught alongside the definition of the derivative, which is in the core content for both SL and HL. The reason I regret this decision is that the HL students didn't know which topics were part of the option, which appear only on a third exam section, Paper 3. Studying was consequently difficult.
  • If for no other reason, the reason not to do a combined SL/HL course is that neither HL or SL students get the time they deserve. There is much more potential for great explorations and inquiry in SL, and much more depth that is required for success in HL. There is too much in that course to be able to do both courses justice and meet the needs of the students. That said, I would have gone to three HL classes per two week rotation for the second semester, rather than the two that I used throughout year one.
  • The HL students in year two were assigned series convergence tests. The option book we used (Haese and Harris) had some great development of these topics, and full worked solutions in the back. This ended up being a miserable failure due to the difficulty of the content and the challenge of pushing second semester seniors to work independently during a vacation. We made up some of this through a weekend session, but I don't like to depend on out-of-school instruction time to get through material.

Overall, I think the SL course is a very reasonable exercise in developing mathematical thinking over two years. The HL course is an exercise in speed and fluency. Even highly motivated students of mathematics might be more satisfied with the SL course if they are not driven to meet the demands of HL. I also think that HL students must enjoy being puzzled and should be prepared to use tricks from their preceding years of mathematics education outside of being taught to do so by teachers.


Filed under IB, reflection, Uncategorized, year-in-review

QuestionBuilder: Create and Share Randomized Questions

I've written previously about my desire to write randomized questions for the purpose of assessment. The goal was never to make a worksheet generator - those exist on the web already. Instead, I wanted to make it easy to create assessment questions that are similar in form, but different enough from each other that the answers or procedures to solve them are not necessarily identical.

Since January, I've been working on a project called QuestionBuilder. It's a web application that does the following:

  • Allows the creation of assessment questions that contain randomized elements, values, and structures.
  • Uses regular Javascript, HTML, and the KaTEX math rendering library to create and display the questions
  • Makes it easy to share questions you create with community members and build upon the work of others to make questions that work for you.


Here's a video in which I convert a question from the June 2016 New York State Regents exam for Algebra 2 Common Core into a randomized question. Without all of my talking, this is a quick process.

I've put a number of questions on the site already to demonstrate what I've been using this to do. These range from simple algebra to physics questions. Some other folks I appreciate and respect have also added questions in their spare time.

For now, you'll need to create an account and log in to see these questions in action. Go to, make an account, and check out the project as it exists at this point.

My hope is to use some time this summer to continue working on it to make it more useful for the fall. I'll also be making some other videos to show how to use the features I've added thus far. Feel free to contact me here, through Twitter (@emwdx), or by email (evan at if you have questions or suggestions.

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Generality vs. Specificity

We want our students to have problem solving methods that are general enough to work in any situation. If we assign a series of exercises that are too similar to each other, it becomes easy for students to lock onto the wrong pattern, or to use a 'trick' that works just frequently enough to seem worth the effort to learn it.

One thing I tried this year was to prompt students to make themselves aware of the spectrum from generality to specificity. What works for solving specifically this question? What general ideas apply to answering all of the problems on the page?

I used my randomized question generator to help create problems that worked this way. Here's an example:

Screen Shot 2016-07-01 at 11.05.02 PM

I only started a deliberate effort to prompt these conversations at the middle of the second semester. I wish I was doing it all year.

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