Category Archives: year-in-review

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.

2014-2015 Year in Review: Work & Life Balance

This is more of a comment on things I did outside of the classroom rather than in, but it was something that my wife and I made a focused effort to do during the second semester.

The idea was simple: buck the routine of the house (and classroom) during the week with something specific that didn't involve work. Make dinner with friends. Go for a walk to somewhere new in the neighborhood. Watch a movie. Work on a fun side project.

These scheduled, specific plans meant I had a reason to leave my classroom and end planning earlier than the usual, which often pushed well past 5:00 PM. If there was a need to do more before the next day, I'd take a look at it before going to bed. I took the time to ask myself whether the work left unfinished was actually going to make the learning better the next day. Sometimes it was, often it was not.

I realize now that Parkinson's Law is notoriously problematic for perfectionists like me:

From Wikipedia, the free encyclopedia:


Parkinson's law is the adage that "work expands so as to fill the time available for its completion....

There is always more tweaking that can be done. The law of diminishing returns (and importance) is a major reason not to do so, particularly in light of the restorative energy that comes from spending time with good people.

These reasons for wrapping up work and being more efficient also made a big difference in my use of planning time throughout the day. I prioritized much more effectively knowing that I had a limited time to complete planning for the next day.

One important comment here: specificity was crucial. I couldn't just say I wanted to finish early to have more free time at home. It made a big difference to be able to picture the end goal of these time limitations. The goal is having a specific activity to look forward to rather than just a negative space formed by the absence of work.

I will be deliberate about continuing this throughout the coming year. This is too important.

2014-2015 Year In Review: IB Physics SL/HL

This was my first year teaching IB Physics. The class consisted of a small group of SL students with one HL, and we met every other day according to the block schedule. I completed the first year of the sequence with the following topics, listed in order:

    Semester 1

  1. Unit 1 - Experimental Design, Uncertainty, Vectors (Topic 1)
  2. Unit 2 - Kinematics & Projectile Motion (Topic 2.1)
  3. Unit 3 - Newton's Laws (Topic 2.2)
  4. Unit 4 - Work, Energy, and Momentum (Topic 2.3)
  5. Semester 2

  6. Unit 5 - Circular Motion, Gravitation, and Orbits (Topics 6.1, 6.2)
  7. Unit 6 - Waves and *Oscillation(Topic 4, AHL Topic 9, *AHL Engineering Option Topic B3.1,3.2)
  8. Unit 7 - Thermal Physics (Topic 3, Engineering Option Topic B2)
  9. Unit 8 - *Fluid Dynamics (Engineering Option Topic B3)

For the second semester of the course, there was at least one block every two weeks that was devoted to the HL student and the HL only content - the SL students worked on practice problems or other work they had for their IB classes during this time. Units 7 and 8 were concurrent, so the HL student had to work on both the thermodynamics content and the fluid dynamics content together. This was similar to how I did it previously while teaching the AP physics B curriculum.

One other fact that is relevant - none of my students are native speakers of English. More on this later.

What worked:

  • The growth students made during the year was significant. I saw students improve in their problem solving skills and their organization in the process of doing textbook style assessment problems.
  • I learned to be honest about the IB expectations for answering questions on assessments.In the beginning, I tried to shield students from questions that combined conceptual understanding, computation, and complex language, often choosing two out of the three of them for any one question that I either wrote or selected from a bank. My motivation was to isolate assessment of the physics content from assessment of the language. I wanted answers to these separate questions:
    1. Does the student understand how the relevant physics applies here?
    2. Does the student understand how to apply the formulas from the reference table to calculate what the question is asking for?
    3. Can the student process the text of the question into a physics context?
    4. Can the student effectively communicate an answer to the question?

    On official IB assessment items, however, this graininess doesn't exist. The students need to be able to do all of these to earn the points. When I saw a significant difference between how my students did on my assessments versus those from IB, I knew I need to change. I think I need to acknowledge that this was a good move.

  • Concise chunks of direct instruction followed by longer problem solving sessions during class worked extremely well. The students made sense of the concepts and thought about them more while they were working on problems, than when I was giving them new information or guiding them through it. That time spent stating the definitions was crucial. The students did not have a strong intuition for the concepts, and while I did student centered conceptual development of formulas and concepts whenever possible, these just didn't end up being effective. It is very possible this is due to my own inexperience with the IB expectations, and my conversations with other teachers helped a lot to refine my balance of interactivity with an IB pace.
  • Students looked forward to performing lab experiments. I was really happy with the way this group of students got into finding relationships between variables in different situations. Part of this was the strong influence I've developed with the Modeling Instruction curriculum. As always, students love collecting data and getting their hands dirty because it's much more interesting than solving problems.

What needs work:

  • My careless use of the reference sheet in teaching directly caused students to rely excessively upon it. I wrote about this previously, so check that post out for more information. In short: students used the reference sheet as a list of recipes as if they provided a straight line path to solutions to questions. It should be used as a toolbox, a reminder of what the relationships between variables are for various physics concepts. I changed this partly at the end of the year, asking students to describe to me what they wanted to look for on the sheet. If their answer was 'an equation', I interrogated further, or said you aren't about to use the reference sheet for what it was designed to do. If their answer was that they couldn't remember if pressure was directly or inversely related to temperature, I asked them what equation describes that relationship, and they were usually able to tell me.
    Both of these are examples of how the reference sheet does more harm than good in my class. I fault myself here, not the IB, to be clear.
  • The language expectations of IB out of the gate are more of an obstacle than I expected at the beginning of the year. I previously wrote about my analysis of the language on IB physics exams. There tends to be a lot of verbal description in questions. Normally innocuous words get in the way of students simultaneously learning English and understanding assessment questions, and this makes all the difference. These questions are noticably more complex in their language use than that used on AP exams, though the physics content is not, in my opinion, more difficult. This is beyond physics vocabulary and question command terms, which students handled well.
  • Learning physics in the absence of others doesn't work for most students. Even the stronger students made missteps working while alone that could have been avoided by being with other students. I modified my class to involve a lot more time working problems during class and pushed students to at least start the assigned homework problems while I was around to make the time outside of class more productive. Students typically can figure out math homework with the various resources available online, but this just isn't the case for physics at this point. It is difficult for students to get good at physics without asking questions, getting help, and seeing the work of other students as it's generated, and this was a major obstacle this semester.
  • Automaticity in physics (or any subject) shouldn't be the goal, but experience with concepts should be. My students really didn't get enough practice solving problems so that they could recognize one situation versus another. I don't want students to memorize the conditions for energy being conserved, because a memorized fact doesn't mean anything. I do want them to recognize a situation in which energy is conserved, however. I gave them a number of situations, some involving conservation, others not, and hoped to have them see the differences and, over time, develop an awareness of what makes the two situations different. This didn't happen, partly because of the previous item about working physics problems alone, but also because they were too wrapped up in the mechanics of solving individual problems to do the big pciture thinking required for that intuition. Group discussions help on this, but this process is ultimately one that will happen on the individual level due to the nature of intuition. This will take some time to figure out.
  • Students hated the formal process of writing up any parts of the labs they performed. This was in spite of what I already said about the students' positive desire to do experiments. The expressions of terror on the students' faces when I told them what I wanted them to do with the experiment break my heart. I required them to do a write-up of just one of the criteria for the internal assessment, just so they could familiarize themselves with the expectations when we get to this next year. A big part of this fear is again related to the language issue. Another part of it is just inexperience with the reality of writing about the scientific process. This is another tough egg to crack.

There was limited interest in the rising junior class for physics, so we won't be offering year one to the new class. This means that the only physics class I will have this year will be with the same group of students moving on to the second year of IB physics. One thing I will change for physics is a set of memorization standards, as mentioned in my post about standards based grading this year. Students struggled remembering quick concepts that made problem solving more difficult (e.g. "What is the relationship between kinetic energy and speed?") so I'll be holding students responsible for that in a more concrete way.

The issues that need work here are big ones, so I'll need some more time to think about what else I will do to address them.

2014-2015 Year In Review: Web Programming

This was the first year I've taught a computer programming course. The class was a broad survey of programming in HTML5. This was the overall sequence:

    Semester 1:

  1. Hacking a webpage from the browser console
  2. HTML tags, structures, and organization
  3. CSS - page design, classes and IDs, along with using Bootstrap
  4. Javascript - variables, structures, conditionals
  5. jQuery - manipulating the page using events and selectors, animations
  6. Semester 2:

  7. Mongo Databases & Queries
  8. HTML Templates using Blaze
  9. Writing Meteor Apps
  10. Meteor, Media, and the HTML5 Canvas
  11. HTML5 Games using Phaser

I have posted the files and projects I used with students at this repository on Github:
https://github.com/emwdx/webprogramming2014-2015

What did I do?

The class generally began with a warm-up activity that involved students analyzing, writing, or running code that I gave them. This always led into what we were going to explore on a given day's lesson. I would show the class a few lines of code, ask them to make a prediction of what they thought would happen. This might be a visual request - what will this look like? Will there be an error? Was this error intentional or not?

This was all done while students had their laptops closed and notebooks open. I usually designed a series of tasks for students to complete using some code snippets that were saved in the directory on the school server.

We didn't use any textbook, so I knew I needed to create a reference that students could refer back to whenever they got stuck. For each class, I took notes either in Microsoft OneNote or the SMART Notebook software and saved the notes in PDF form. I don't know if students used this or not.

I had three types of assessment:

  • Mini-projects, which were fairly straight forward and had unique answers. These were assessed by general completion (4.5/5) with a (5/5) given for effort to creatively make the code their own. I was fairly loose on that final half point, giving it whenever I saw students clearly engaged by the task. You can see an example of this assignment here.
  • Projects, which had clear guidelines and requirements to meet the minimum grade that ranged from 80 - 90 percent, and then a series of additional tasks that raised the grade up to 100%. The additional task points weren't awarded until the basic requirements were met, though that didn't stop students from trying (see below).
  • Blog posts, which were required for every class. The expectations required a summary of what we learned for each class, along with code snippets, questions about what we learned, or confusion about something they wanted to go over in the next class. As the students became more skilled, this turned into questions that started as "How can we.../Is it possible to...".

Once every two weeks, and usually on a Friday, I had a 20% day during which students could work on anything they wanted related to web programming. Some students worked on previous projects to resubmit them, others experimented with code from the previous class or week. In a couple of cases, students worked on their own pet projects, which included a chat application, a mathematical formula parser, and applying visual design principles to the pages we created in class. I often made suggestions for what students could do at the beginning of the class block, including providing some basic code they could use to experiment.

What worked:

  • Based on feedback from the end of the year, students enjoyed the course. They had a lot of positive comments on the ways I ran the class and that they always got help when they needed it.
  • Forcing students to write down code helped with retention and building a useful reference for later. I didn't require them to write down long blocks of code, but for things like HTML tags and Javascript, I wanted there to be some written reinforcement that things were important. I was pretty strict on deciding when I wanted students to write down code (to activate that part of the brain) and when I wanted them to copy it directly into a text editor and run it.
  • Forcing students to recreate code (and not copy and paste) led to higher activity and interaction between students while learning to code. I saved some code as images, not text, which required students to go line by line and see what they were doing. This was a decision I made early on because it helped me when learning to code. That extra step of needing to look at the code while I was typing it in led me to take a closer look at what it said, and I wanted to give a similar opportunity to my students.
  • The more open ended projects led to much richer questions and interaction between students. I really liked the range of responses I received when I gave open ended projects. Some students were exceptionally creative or went well beyond the requirements to make code that mattered to them.
  • Students were constantly helping each other with their code...when they eventually asked for this help. I was called over many times by students calling out the blanket statement "my code doesn't work" and then handing me their laptop, but over time they learned that I wasn't going to just fix their code for them. They became careful readers of each other's code, when they finally made the step to ask someone to help, though this took some time.
  • I succeeded in having students do more than listen. I never talked for more than 15 minutes before students were actually writing and experimenting with code. This was exactly what I wanted.
  • 20% days were a big hit. Some students wanted this time as extra processing time to complete the mini projects from the rest of the week. Others liked being able to ask me how to do anything, or to find tutorials for HTML elements that they wanted to learn to use. I really liked how well this worked with this group of students and looked forward to it, and not just because it was a reduction in the planning required for class.
  • Videos offered an effective and preferred method for learning to write code in this class. I put together a number of screencasts in which I spoke about the code, and in some cases coded it live. Students were able to pause, copy code to the editor, and then run it pretty easily. Some zipped through it, others took longer, but this is nothing new. The time required to do this, as is always a consideration for me, was often more than I could afford. Luckily, there is plenty of material available already out there, so I was able to step back and give another voice and face a chance to teach my students.

What needs work:

  • The bonus elements for projects were the first things most students wanted to figure out first. Many students did not put in the time to read and complete the basic requirements for projects, resulting in submitted projects that were sent right back as being incomplete. Some of this was a language issue, as there were many ESOL students in the class, but most of it was what we always encounter when working with adolescents: not reading the directions.
  • Students reused a lot of old (and unrelated) code. I emphasized creating simple code from scratch throughout the year, as my expectations were relatively simple. For many students, copying and pasting code was a crutch that led to many more problems than simply writing simple, clean code from the start. I get it - I copy and paste code myself - but I also know how to clean it up. They knew why not to do it (because they all tried it at some point) but some students continued doing it to the end. I need a better plan for helping students not fall into this trap.
  • Many students did not pick up on error messages in the console that said precisely where the problem with the code was located. At times, I expected too much from students, because the console is a scary place. That said, I think I could do a better job of emphasizing how to find the line numbers referenced in these errors messages, regardless of what the error message is.

I really enjoyed teaching this class, and not just because of the awesome group of students that took it. It helped me refine my knowledge and get better at some of the HTML, CSS, and Javascript coding skills that I had used, but often had to relearn every time I wanted to use them.

Feedback, as always, is welcome!