Category Archives: Uncategorized

Standards Based Grading and Leveling Up

I've been really happy since joining the SBG fan club a few years ago.

As I've gained experience, I've been able to hone my definitions of what it means to be a six, eight, or ten. Much of what happens when students sign up to do a reassessment is based on applying my experience to evaluating individual students against these definitions. I give a student a problem or two, ask him or her to talk to me about it, and based on the overall interaction, I decide where students are on that scale.

And yet, with all of that experience, I still sometimes fear that I might not be as consistent as I think I am. I've wondered if my mood, fatigue level, the time of day affect my assessment of that level. From a more cynical perspective, I also really really hope that past experiences with a given student, gender, nationality, and other characteristics don't enter into the process. I don't know how I would measure the effect of all of these to confirm these are not significant effects, if they exist at all. I don't think I fully trust myself to be truly unbiased, as well intentioned and unbiased as I might try to be or think I am.

Before the winter break, I came up with a new way to look at the problem. If I can define what demonstrated characteristics should matter for assessing a student's level, and test myself to decide how I would respond to different arrangements of those characteristics, I might have a way to better define this for myself, and more importantly, communicate those to my students.

I determined the following to be the parameters I use to decide where a student is on my scale based on a given reassessment session:

  1. A student's previously assessed level. This is an indicator of past performance. With measurement error and a whole host of other factors affecting the connection between this level and where a student actually is at any given time, I don't think this is necessarily the most important. It is, in reality, information that I use to decide what type of question to give a student, and as such, is usually my starting point.
  2. The difficulty of the question(s). A student that really struggled on the first assessment is not going to get a high level synthesis question. A student at the upper end of the scale is going to get a question that requires transfer and understanding. I think this is probably the most obvious out of the factors I'm listing here.
  3. Conceptual errors made by the student during the reassessment. In the context of the previous two, this is key in whether a student should (or should not) advance. Is a conceptual error in the context of basic skills the same as one of application of those skills? These apply differently at a level six versus a level eight. I know this effect when I see it and feel pretty confident in my ability to identify one or more of these errors.
  4. Arithmetic/Sign errors and Algebraic errors. I consider these separately when I look at a student's work. Using a calculator appropriately to check arithmetic is something students should be able to do. Deciding to do this when calculations don't make sense is a sign of a more skilled student in comparison to one that does not. Observing these errors is routinely something I identify as a barrier to advancement, but not necessarily in decreasing a student's level.

There are, of course, other factors to consider. I decided to settle on the ones mentioned above for the next steps of my winter break project.

I'll share how I moved forward on this in my next post in the series.

Unit Circle Practice (#TeachersCoding)

I've always wanted a simple interface to help my students practice the unit circle. I've found Quizlet sites that help with this, as well as the occasional Khan Academy exercise that approaches what I want. The big issue I find with most of these is that the interface and the questions ask much more than what I'm looking for. I want a simple flashcard-like situation with no bells and whistles that gets my students the repetition and opportunity to think through the functions with feedback.

Over the winter break, I decided I needed to build the resource I had in mind. Here's the result:

The live site can be accessed here: http://codepen.io/emwdx/full/bgEJYK/

This is essentially a digital version of a set of flash cards, but they never stop. The angles rotate around the unit circle and the trigonometric function used is randomized. Since I am holding my PreCalculus students responsible for the reciprocal functions, but my IB students don't need them, I added the ability to flip those on and off.

I decided to do this on CodePen in case you want to look under the hood to see how it works. The editor view that contains my code is here. Let me know if you use it for something useful.

Releasing Today: States-n-Plates

I'm excited to share States-n-Plates , a project I built with Dan Meyer.

Dan proposed the idea for this activity a while ago with his typically high level of excitement about activities that provoke interesting and productive classroom conversation. This time, however, it wasn't about mathematics. I was looking for a bigger scale project to help me develop my ReactJS skills, so I took it on. Dan was patient enough to let me hack away at the project in this context. Though I could have certainly done it more quickly using jQuery or another framework, I wanted to try building this project in a particular way.

Specifically:

  • I wanted to be able to play the game myself when I was done. Hard coding everything into a series of HTML pages would have likely resulted in my seeing each plate and the answer over the many times I reloaded during development. By abstracting the behavior of the game to be automated for each group of license plates, I saw most of the plates for the first time during testing.
  • I wanted to experiment with a drag and drop library for React as an exercise for use in future experiments.
  • I also wanted to have a slightly different UI behavior for the desktop and mobile versions. This functionality came from Bootstrap. This led to a bit of wonkiness on small phone displays, but larger tablets work great using touch, and the desktop version works well using drag and drop.
  • I also wanted to experiment with modularity of both files and React component JSX files. I used Webpack. I don't understand Webpack.

As in my past collaborations with Dan, I learned to do a number of things I didn't think I could do. For example, I told Dan 'no' on the fading effect at one point, and then subsequently figured out how to make it happen through lots of searches, StackOverflow, and careful reading of the React documentation.

If you want to play with the code, the Github repository is at https://github.com/emwdx/states-n-plates/. You don't need the big node_modules directory for this to work locally, but it is required if you want to change the bundle.js file.

I have more thoughts on the learning process I went through, but that will be shared soon. Have fun and share with your friends.

Computational Thinking and Spreadsheets, Teacher Edition (#TeachersCoding)

I ran a workshop last week giving some teachers ideas on how to use computational thinking to improve their workflow. I've written in the past about how spreadsheets can serve as a way to get students thinking like programmers, without the intimidation of a text-based development environment. I don't find teachers any different in this regard.

I spent the beginning of this workshop sharing a bit about my views on why teachers should develop their computational thinking skills. I then set them off to work through answering the following questions about each task in the video below:

  • What is the spreadsheet being programmed to do?
  • What commands are being used?
  • How would I use this in my own practice?

I'm reasonably sure that a majority of teachers have a spreadsheet somewhere that contains student data like the one in the video. My hope is that teachers that watch the video and see what I've done with this spreadsheet will have one of a few possible responses:

  • Wow, I do that by hand right now. Now I know there's an easier way that will save me time.
  • That isn't useful to me, but it does give me an idea of how to do some other task that involves iteration, sorting, or another task best suited for a computer.
  • I do that already. Is that computational thinking?

If I elicit any of these responses, and then get someone to then build a tool that is useful to him or her, I think I've done my job. Learning to code for its own sake isn't necessarily worth a teacher's valuable time. Outsourcing tasks that computers do best to a computer can free a teacher to have more time for those tasks that require the expertise, experience, and a personal touch that only a person can provide. If learning a bit of computational thinking can do that, doing so might be worth the time.

Please comment on the video or below to let me know what you think.

Let's Collect Some Data Together!

I've hacked together a data collection tool with the Desmos API for an activity tomorrow - I'd love if you could help me test it out.

Please visit https://emwdx.github.io/groupData/index.html and enter 3DR9 as the name of the data set. Then enter an ordered pair in the form (age, # of years teaching).

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If everything works correctly, we'll be able to put together a data set across the world and see it graphed in real time.

I'll talk more about this soon - thanks in advance for helping out, folks.

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.

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.

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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.

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.

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.

example1

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 http://question-builder.evanweinberg.org, 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 evanweinberg.com) if you have questions or suggestions.

Endings and Beginnings

Today, I bid farewell to my home away from home for the past six years.

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When I first moved away from New York, I had shed all doubts that the teaching career was for me. I knew that learning and exploring were important elements of a meaningful existence on this planet, both for me and my students. I knew that few things were more satisfying than spending time with good people around plates of food. I knew that not knowing the local language or the location of the nearest supermarket was a cause for excitement, not fear. Purposely putting one's self into situations with unknown outcomes is not a reckless act. It is precisely these challenges that define and refine who we are so that we are better prepared for those events that we do not expect.

I knew these things already. And yet, I leave China today as a changed teacher. I met students from all around the world. I made connections not just with new people in the same building as me, but with teachers in many distributed time zones. People that I respected and admired for their ideas humbled me as they invited me to join in their conversations and explore ideas with me. I found opportunities to present at conferences and get to know others that had also fallen in love with the international teaching lifestyle. I started this blog, and surprisingly, had people read it with thoughts of their own to share.

I also learned to accept the reality that life continues in twenty four time zones. News from home made it seem more foreign and paradoxically more connected to my own experiences here. When opening my eyes and my various devices in the morning to see what had happened while I slept, I again never knew what to expect. I lost family members both suddenly and over stretches of time. Kids grew up. Our parents sold their houses and apartments. Friends put prestigious letters at the end of their names.

Our world changed as well. We added new countries to our passports and got lost in cities that refused to abide by a grid system. We fell in love with our dog and his aggressive sneezing at harmless bystanders. We tried to address the life and work balance through weeknight dinners and mini vacations. We repeatedly overcommitted to traveling during our summers off and time went too quickly. We became parents.

I write this not because anything I'm saying is especially new. The 'time marches on' canon is well established. That does not invalidate the reality that we're all experiencing life and its passage for the first time ourselves. This is the magic that we, as teachers, witness between the end of one year and the beginning of the next. We tweak our lessons from the previous year with the hope that they prompt more questions and productive confusion on the next iteration. Our students do experience some of the ideas we introduce for the first time in our classrooms, and it is unique that we get to design those experiences ourselves. 

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The best way to understand the rich range of emotions that our students experience while in our care is to live deeply and richly in our own lives. We need to learn to know and love others, explore and make mistakes, and be ready to move forward even when the future is uncertain. My time abroad thus far has given me numerous journeys through these human experiences. I would not give them up for the world, and luckily, I do not have to do so.

I'll write more about my next move in a future post. 
Until then, I wish you all a summer full of good times with good people.