Category Archives: teaching philosophy

Too Many Reassessments, Just in Time for Summer

I posted this graph of cumulative reassessments versus the day of the semester on Twitter:

That, my friends, is a reassessment system gone wild. The appropriate title for that image, as one person pointed out, is Too Many Reassessments. The grand total for this semester was 711. There are obvious bunches of reassessments close to the ends of the quarters when the grade book closes.

Here is a histogram of the reassessment data for the semester. There is some discrepancy in the total number in the data here, but I haven't figured out exactly where that is.

I committed to transplanting the system I have used in the past to my new school this year, and didn't want to make a full change without seeing how this would play out. This semester I was much more consistent in the types of questions I gave students reassessing, changing grades based on a reassessment, and the choice I offered them for the level of reassessment. Some of this I wrote about at the beginning of the semester.

The most important observation I can make at this point is that this system is not sustainable as is. I cannot make my sign-up and credit system more efficient to manage the volume - that isn't the issue. I'm satisfied with the quality of the questions I give students. I've developed a pretty nice bank of questions that span the spectrum of application, understanding, and transfer. The bigger issue is my capacity to give the sort of feedback I want to give to students throughout the semester. I have many conversations about learning, and many of them are great, but I cannot multiply myself to have as many of those conversations as I want.

Here's a graph of the average learning standards grade for a sample of students compared with the number of reassessments:

This doesn't support the expectation that more reassessments implies a higher grade. Students are not necessarily doing machine-gun style reassessment. They are working on specific skills and show my what they are doing. They are responding in a positive way to my feedback. Credits, which students earn by doing work and review of concepts, are still required for students to reassess. Students are for the most part using their credits. Expiring credits, as much as I thought it would make a difference, is not making that much of a difference for behavior (i.e. signing up for reassessments) or course grade. I need to dig into the data more to be able to explain why.

In terms of moving forward, I have many things to think about.

  • The past three or four years have been an exercise in exploring a system that centers around student-initiated reassessment. I'm not sure it's time for that to completely go away, but I wonder about shifting my focus to an assessment structure centered on teacher-initiated. I already do this on unit exams, but I wouldn't say it is the focus of where I spend my time.
  • I wonder if reducing the permitted number of reassessments per student to one per week would improve their effectiveness. This effectiveness increase could be based in higher quality feedback from me, more focused effort on the part of the student for improving understanding on a given learning standard, or something else entirely. This reduces the options for students to learn on their own timeline, which isn't a good thing. While we're being honest though, that exponential curve at the end of the assessment period is all the evidence I need to accept that the timeline is based on the grading-period structure, not learning.
  • How do I most efficiently help the weak student that reassesses on the same standard multiple times and makes limited progress on each attempt?
  • How do I give meaningful guidance to the student that aces everything on the first try? How do I get them more involved in finding learning that is meaningful, rather than waiting for me to tell them what to learn?
  • What do the students think? I've collected all sorts of anecdotal evidence that students appreciate the opportunities to reassess, and not just in a superficial way related to their course grade. I've given students an end of year survey to complete, and those results are rolling in slowly as students complete their final exams.

These are the big picture questions that add one more reason to be thankful that the summer is ahead. Getting back to my main point, I am brought back to the idea that quality feedback is the main way we as teachers add value. This, like many things in education, is not easy to scale. This need for improving and scaling the transfer of feedback is really the only basis for innovation in the ed-tech realm that interests me at all these days. So far, despite the best intentions of many that are trying, machine learning is not the answer yet. Make it easy for me to organize and collect student thinking, respond to that thinking, and give helpful nudges to the resources needed to make progress, and then I'll consider your product.

Final exam marking is ahead. Stay tuned.

Assumptions About the Basics

"I'm just going to teach it again from the basics."

This approach makes some assumptions:

  • Students that didn't understand the topic on a first exposure will benefit from just seeing the topic be developed again.
  • Students that did understand the first time will get confirmation of what they remember.
  • Colleagues that taught this in the past didn't necessarily cover everything, so this ensures students see a complete presentation of the topic.

All of these are assumptions that serve a teacher-centered classroom model. No teacher wants to be to blame when a student forgets an essential component of knowledge for a given topic, I get that. I have a hard time seeing the presentation of a complete topic as anything other than a checklist of items for a teacher to present.

What does a student do in this context? Why does the student that remembers everything have to sit through tasks that they demonstrably know how to complete? Why would we expect a student that struggled after a first exposure to benefit from seeing the same sequence of topics, but made "harder" by some arbitrary measure associated with course or grade?

I prefer the idea that we instead present students with a task that demands the knowledge and skills that are outcomes of the course. Tasks like open middle and 3-Act problems let us see where students are in the continuum of knowledge and problem solving. There are plenty of resources we can use to fill in the gaps for students where they exist - this is where online resources and activities shine. As teachers, we truly add value when we can build intellectual need for what we teach and foster discussion about interesting challenges and thought process. Most importantly, we can provide feedback that is focused and personal.

If I had to identify one fundamental change to my teaching philosophy over the last several years, it would be the acknowledgement that students are not blank slates. Assuming they are doesn't serve any of them well. Teaching compliance and patience to the strongest students is a pretty low level goal. Teaching what we say are the basics to those that never understood the basics in the first place disrespects these students as well.

Let's stop assuming we need to give our own overview of a topic. We aren't as good at it as we think we are. This only reinforces the idea that students are hungry and waiting for us to give them the knowledge they can't obtain any other way.

We must aim much higher than that.

Scaling in Education

From today's New York Times article, The Broken Promises of Choice in New York City Schools.

"Ultimately, there just are not enough good schools to go around. And so it is a system in which some children win and others lose because of factors beyond their control — like where they live and how much money their families have."

The structures of education do not scale well. This is because good lessons, good classrooms, and good schools are all sourced from people, and people do not scale well. People cannot be copied. The human mind is exceedingly, beautifully complex - a fact that underlies the wonderful challenge of teaching. The talents, ideas, and experience of people that understand this reality are essential to making a school what it can be.

The work that must be done centers on building a culture that acknowledges and values the human basis of our profession. It takes energy and time from human beings to turn an empty room into a learning space. Budgeting for all of the costs of the inputs, financial or otherwise, is necessary to do this work.

Ideas scale easily because it costs virtually nothing to share them. Cultivating the relationships that are necessary to use those ideas to make opportunities for children needs to be our focus.

People matter. We should be skeptical of anyone that seeks to minimize this reality.

An Experiment: Swapping Numerical Grades for Skill-Levels and Emoji

I decided to try something different for my pre-Calculus class for the past three weeks. There was a mix of factors that led me to do this when I did:

  • The quarter ended one week, with spring break beginning at the end of the next. Not a great time to start a full unit.
  • I knew I wanted to include some conic sections content in the course since it appears on the SAT II, and since the graphs appear in IB and AP questions. Some familiarity might be useful. In addition, conic sections also appear as plus standards within CCSS.
  • The topic provides a really interesting opportunity to connect the worlds of geometry and algebra. Much of this connection, historically, is wrapped up in algebraic derivations. I wanted to use technology to do much of the heavy lifting here.
  • Students were exhibiting pretty high levels of stress around school in general, and I wanted to provide a bit of a break from that.
  • We are not in a hurry in this class.

Before I share the details of what I did, I have to share the other side to this. A long time ago, I was intrigued by the conversation started around the Twitter hashtag #emojigrading, a conversational fire stoked by Jon Smith, among many others. I like the idea of using emoji to communicate, particularly given my frustrations over the past year on how communication of grades as numbers distort their meaning and imply precision that doesn't exist. Emoji can be used communicate quickly, but can't be averaged.

I was also very pleased to find out that PowerSchool comments can contain emoji, and will display them correctly based on the operating system being used.

So here's the idea I pitched to students:

  • Unit 7 standards on conic sections would not be assessed with numerical grades, ever. As a result, these grades would not affect their numerical average.
  • We would still have standards quizzes and a unit exam, but instead of grades of 6, 8, and 10, there would be some other designation that students could help select. I would grade the quizzes and give feedback during the class, as with the rest of the units this year.
  • Questions related to Unit 7 would still appear on the final exam for the semester, where scores will be point based.

I also let students submit some examples of an appropriate scale. Here's what I settled on based on their recommendations:

I also asked them for their feedback before this all began. Here's what they said:

  • Positive Feedback:
    • Fourteen students made some mention of a reduction in stress or pressure. Some also mentioned the benefits of the grade being less specific being a good thing.
    • Three students talked about being able to focus more on learning as a result. Note that since I already use a standards based grading system, my students are pretty aware of how much I value learning being reflected in the grade book.
  • Constructive Feedback:
    • Students were concerned about their own motivation about studying or reassessing knowing that the grades would not be part of the numerical average.
    • Some students were concerned about not having knowledge about where they are relative to the boundaries of the grades. Note: I don't see this by itself as a bad thing, but perhaps as the start of a different conversation. Instead of how to raise my grade, it becomes how I develop the skills needed to reach a higher level.
    • There were also mentions of 'objectivity' and how I would measure their performance relative to standards. I explained during class that I would probably do what I always do: calculate scores on individual standards, and use those scores to inform my decisions on standards levels. I was careful to explain that I wasn't going to change how I generate the standards scores (which students have previously agreed are fair) but how I communicate them.

I asked an additional question about what their parents would think about the change. My plan was to send out an email to all parents informing them of the specifics of the change, and I wanted students to think proactively about how their parents would respond. Their response in general: "They won't care much." This was surprising to me.

So I proceeded with the unit. I used a mix of direct instruction, some Trello style lists of tasks from textbooks, websites, and Desmos, and lots of circulating and helping students individually where they needed it. I tried to keep the only major change to this unit to be the communication of the scores through the grade book using the emoji and verbal designation of beginner, intermediate, expert. As I also said earlier, I gave skills quizzes throughout.

The unit exam was a series of medium level questions that I wanted to use to gauge where students were when everything was together. As with my other units, I gave a review class after the spring break where students could work on their own and in groups, asking questions where they needed it. Anecdotally, the class was as focused and productive as for any other unit this year.

I was able to ask one group some questions about this after their unit test, and here's how they responded:

The fact that the stress level was the same, if not less, was good to see. The effort level did drop in the case of a couple of students here, but for the most part, there isn't any major change. This class as a whole values working independently, so I'm not surprised that none reported working harder during this unit.

I also asked them to give me general feedback about the no-numerical-grades policy. Some of them deleted their responses before I could take a look, but here's some of what they shared:

    • Three students confirmed a lower stress level. One student explained that since there was no numerical grade, she "...couldn't force/motivate [her]self to study."
    • Five students said the change made little to no difference to them. One student summed it up nicely: "It wasn't much different than the numerical grades, but it definitely wasn't worse."
    • One student said this: "The emojis seemed abstract so I wasn't as sure of where I was within the unit compared to numbers." This is one of a couple of the students that had concerns about knowing how to move from one level to the next, so the unit didn't change this particular student's mind.

 

  • This was a really thought-provoking exercise. A move away from numerical grades is a compelling proposition, but a frequent argument against it is that grades motivate students. By no means have I disproven this fact in the results of my small case study. If a move like this can have a minimal effect on motivation, and students get the feedback they need to improve, it offers an opportunity for considering similar experiments in my other classes.

    There are a couple questions I still have on this. Will students choose to reassess on the learning standards from unit 7, given that they won't change the numerical average when we return to numerical grades for unit 8? The second involves the longer term retention of this material. How will students do on these questions when they appear on the final exam?

    I'll return to this when I have more answers.

 

After Individualized Learning, What Comes Next?

This was my classroom in the latter part of the last block of the day.

I should point out that I usually have students seated closer together in groups. Conversation happens more organically in that configuration. I gave a quiz where I didn't want to set hard time limits. As each finished, I nudged them to work on their own on a PearDeck assignment.

This is what it looks like when everyone is working at their own pace. Each student with a single screen, each solving problems and answering questions.

I like that I can drift from student to student and either ask or answer questions when the time seems right. I can see each student's answers on the online teacher dashboard. I can decide which conversations I need to have. Students can also decide if they need to have conversations with me. I involved myself in student learning with surgical precision.

Some claim this is the future of learning in schools.

For me, the silence in the room today was unsatisfying. No sharing of ideas. No excitement shared between friends. Nothing that might compel a student to contemplate the other living, breathing beings in the room.

I don't do this every day, so I know this isn't how it will always be. Whenever I do this type of lesson, I know that the students are better off when they get what they need. I know it is good for them. My thinking always go to the next step. What will we do when we are back together in a big group, or at least in groups larger than one?

I asked the students the following question:

We have all worked independently today. What is the best way to use our time when we are back together?

Their answers gave me the direction I needed to think about the next steps:

  • Either going over answers so people who haven't put the answers in will know what to do and what the correct answer is.
  • Maybe review the questions people were confused with or got wrong a lot. This would help to review what we did.
  • Go over some of the answers together or answer some of the difficult problems.
  • I don't know.
  • To check where the majority of us got stuck and had trouble, and discuss how to figure out those problems. That, and to possibly discuss new concepts that we have yet to master.
  • Going through the questions that could be tricky and solve challenging problems together
  • I think it is good to have a mini lesson to quickly teach what we are learning and to go over, but also save time for students to work independently.
  • Give us a few examples at the beginning of class so we don't forget what we learned, and then learn new things.
  • To quickly go through and review all the topics we've learnt about polynomials.
  • Learn something new

Knowing what to go over is certainly where the online tools are helpful - they make incorrect answers or misconceptions stand out.

I know that the students prefer the social aspects of the classroom. Whatever our next step is, it should involve coming together and acknowledging and appreciating we are in a room of people learning together.

We need to make sure that we are social when being social is productive to learning.

We need to make sure students have time to learn and think on their own.

We need to make sure students can also learn what they need to know in the hands of an experienced guide.

All of these are crucial. Any one channel we use loses its effectiveness to learning when it becomes routine. I think this is especially the case when that routine involves staring at an entity that can't talk or laugh back.

Building Up or Breaking Down: Creating States-n-Plates

In piecing together States-n-Plates, I wanted to learn more about React, a web application library created by Facebook. In the process, I found myself finding parallels in how I go about learning anything.

Before I describe the details, I'll give a (hopefully brief) description of what React does.

An HTML page normally consists of HTML tags that tell the browser what to display, with other rules that also describe how the HTML should look. A page created through React reframes that page as a series of components that each serve a different function. The image components need to have the ability to be dragged onto the targets. The targets need to be able to accept a dragged image, and need to be able to indicate whether the image dragged onto the target corresponds with the correct plate. The scoreboard needs to know how many states have been correctly matched at any given time. The components also have the ability to respond when a user clicks, types, or drags other components into them.

In a well designed React application, each component uses information from the component that contains it in order to behave (or, um, react) as the application is used. Building the pathways for how this information flows from one component into another is deliberately designed so that each component can act independently from another.

When I first started working on creating States and Plates, I started with a fully formed webpage that looked much like the final product above. I followed the React documents that then suggested breaking the page down into components, one by one. I did this without really understanding in detail what I was doing, but was able to get the components to each have the appearance of the original web page, which felt like real progress. Eventually, my progress was halted when I reached the limits of what I understood. I needed help.

It was at this point when I picked up a book on React and started working through the basics. I began to understand better what the guiding philosophies of React were - the design decisions, the behaviors that one component had in response to another, and how to think through an application the React way. This was where it was helpful to read the perspectives of some people much more experienced then me - I understood the vocabulary they used and could make the connections I needed to make progress.

With some of the basics figured out, I rethought the application from scratch. Rather than starting with the webpage as a whole, I started creating components and making sure each one worked as expected before moving on.

By the end, I felt comfortable thinking about my application both from a bird's eye view and on an individual component level. I needed to have the experience of breaking the idea down into individual pieces and seeing how they interacted with each other to produce the whole. I needed to take time seeing what rules guided the function of one component in order to understand the whole. If I had started by reading the documentation as my step one, I would not have had the context that the big picture view of the application yielded for when I actually did so in my learning. Both views were important, and neither view was sufficient on its own to lead to full understanding or transfer.

We need to give our students opportunities to have both views of the content we teach. Insisting that student mastery of the basics is a necessary gatekeeper to higher levels of thought misses opportunities to understand the context of that basic knowledge. Student exploration of concepts through Desmos or Geogebra or problem solving is a great way to engage with the standards of mathematical practice, but without discussion, review of underlying concepts, or (gasp!) direct instruction where needed, opportunities for growth might be limited.

Let's make sure, as a team, that we are attacking this problem from both ends.

Zack Miller and his PBL/PBL Merger

I've been skeptical about Project Based Learning (PBL) for a while, despite many people trying to sell me on it as being a step up from more traditional instruction. I like the concept, but I have too many reservations with veto-power to keep me from jumping in completely. These are my main issues:

  • While PBL provides a rich environment for learning, it doesn't work as an effective means for assessment.
  • The idea presumes that every mathematical topic has a problem that forms a solid context for a project. In the recent past, I've made a commitment to my students to not force a context on them if it doesn't actually fit, and to tell them outright when I've artificially created one. There are many rich applications for many topics, but this is not generally the case.
  • I have never seen a project based rubric that I really like, even (and especially) ones that I've created myself. Something ends up being incentivized unintentionally, or students focus on the wrong elements despite my best efforts to prevent this. This is my fault though, not PBL.

All of that said, I'm really enjoying Zach Miller's ongoing series on combining Project Based Learning with elements of Problem Based Learning, which I also like, but also with reservations.

His posts are pushing my thinking a bit, and I'm liking how it's getting me to adjust some plans for this semester. Check out his blog when you can.

More of What Matters

Just over a year ago, my first daughter was born. Like most newborns, she couldn't hold her head up. Yesterday I watched her pick up her pacifier from a table and plop it in her mouth.

It made me realize that I've witnessed the entire progression of skill development that made that happen. She developed an awareness of the muscles needed to grip, lift, and rotate. She learned to use visual feedback to move her stubby fingers to the right location in her field of view, close them, and then move the pacifier to her mouth, which she could not see. This learning was all hers - nobody had to tell her what to do, or why she needed to go through the steps. My daughter's skills will continue to develop as she grows and encounters the great variety of people and places in this beautiful world we all inhabit together. I've made more of an effort this school year to be present for these moments, and it has been among the best decisions of my life.

There have been times in my teaching career when I've thought about how nice it would be to be able to start completely from scratch with students. With no misconceptions, bad habits, or fear of failing like the time before, maybe I could help them be more successful. I quickly stop myself. First of all, my own instruction is not perfect, and in all likelihood, the students would still discover shortcuts that might work in my class, but be detrimental to their success in the next. Second, and more importantly, our students are not computers to be programmed. The experiences they bring to our classrooms is what makes this job what it is. As rewarding as it might be for us as teachers to see students make all of the progress we want for them, teaching is not about us.

Our students have all walked their brains through a unique path that passes through our classrooms, and that path certainly doesn't end within them. The knowledge and skills that our students take from our classrooms are also not under our control. Our students' lives will hopefully be a long series of meaningful moments of discovery and excitement, and the reality is that those moments that will last are likely not the ones that transpire in our classrooms. That said, the time we all have together is precious and always decreasing.

As we start a new year today, let us remind ourselves to work to make the important things matter. This takes work because of the noise of distractions that surrounds us. Build opportunities to grow instead of dig in to old habits. Make a deliberate effort to express gratitude to the people that you are with. Recognize the value in being at this place, at this time. We will not always be successful, but accepting this is part of becoming more successful on the next attempt.

Be well, everyone.

Acting Upon One's Beliefs

Suppose you know in your heart that what you believe is right, and others disagree.

If you are in control, do you charge on ahead and act upon your beliefs?

Do you frame this as merely a communication problem, or is it something bigger?

What is your responsibility to...

  • ...those who agree with you?
  • ...those who disagree with you?
  • ...those who are impacted most by what happens next?

How do your answers to these questions change if you are not the one in control?

How do your answers to these questions change if you are in the minority?

These questions have bounced around in my head since last week, and not just in relation to the U.S. election. It bothers me a lot that I can't answer my own questions with any certainty right now.

Class Notes and Workflow (On The Other Side of the Wall)

I've struggled in the past with the role of class notes. I wrote more than a year ago about my solution using Microsoft OneNote. Since moving out of China, I've realized just how far behind I am in just awareness of what Google Docs are capable of doing. My new school uses them extensively for all sorts of organizational and administrative purposes, not to mention applications in the classroom. I decided to upgrade my class notebook system this year to make better use of these tools. Now that we're approaching three months in, I'm feeling pretty happy about my system thus far.

I now make all my handouts on Google Docs. The bandwidth and lack of a Great Firewall make it a reliable way to have access to files both at school and at home, which means that I'm not dragging my computer back and forth anymore. There's something to be said for carrying a minimalist backpack, especially given the temperatures here. I relied on iCloud Drive last year which worked well enough, but the fact that I'm not worrying about files syncing between home and school is a clear change for the better. These files are titled U3D02 - CW - Title of Day's Lesson to signify 'Unit 3, Day 2' for ease of identifying files and their order. These are starting points for class activities, resources to use during class such as Desmos activities, videos, or other parts of what might be useful to students learning a given topic.

screen-shot-2016-10-31-at-8-16-35-pm

Each handout is shared with the class through Hapara teacher dashboard and Google Drive, and I give students read access on each file. Two students are randomly picked to be responsible for class notes. These two students make a copy of this handout during class, name it with the same title and unit/day designation, and then change CW (class work) to NB (notebook) file to indicate the purpose of this file.

I take notes during class using Notability and my Wacom tablet. It's easy to copy and paste images from the digital handout into the notes, and then annotate them as needed. I take photos of student work with my phone and use Airdrop to get them to my classroom laptop. At the end of the class, I paste images of the notes I take during class into the relevant part of the notes. The two students are responsible for solving problems from the class handout and from homework, taking pictures, and putting them into the notes file on Google Docs. Links to these files are then shared on the course website with the rest of the class.

My class handouts are still printed on A5 paper as an analog backup, and quizzes are usually still on paper as well. I still insist on students doing problems by hand since that's ultimately how they will be assessed. The computer is there for access to Desmos, Geogebra, and the digital handout.

The most satisfying part of all of this is that students are being remarkably proactive about asking for materials to be shared, letting me know when they think something should be added to a handout, or adding it themselves when they have editing access to the file. There is also a flow of suggestions and comments to the students that are responsible for each day's lesson.

It's pretty amazing what is possible when a major world power isn't disrupting the technology you want to use in the classroom (or for whatever) on a regular basis.