Wednesday, November 16, 2016

Quizster: The Formative Assessment App

(cross-listed on medium.com)



I teach high-school math, grades 9 through 12, with classes ranging from Geometry to Calculus. In the past few years, I have found myself increasingly interested in the structures of formative assessment, because although formative assessment is something we all aim to do in our classes, its specific method of implementation can have varying degrees of effectiveness on improving student learning. During the last two years, I have implemented weekly “No Big Deal quizzes” that contain a couple of questions targeting a recent topic, but without including any scaffolding in the questions or cues hinting at specific strategies. The students tended to fall on a spectrum on these formative assessments. They would take about 15 minutes at the start of class trying the questions; I would then collect their responses and go over the answers as a class as the students took careful notes and asked questions. The next day, I would return the graded “quizzes” (usually worth only 2 to 4 points for one or two questions) and assign similar problems on the board for the students to copy down and complete, in order to make up any points missed via showing an improved understanding on those topics. For some students, just turning this new assignment in is enough to show a thorough understanding and to address previous misconceptions, but for other students in the class, remediation frequently requires a continued back-and-forth dialogue on the new questions until they finally get it and are able to demonstrate that understanding on paper. If they have trouble revising the responses, they would first go to their notes on the initial quiz and ask me clarifying questions during class. If that wasn't enough, I would offer to sit down with them to go over the process again one-on-one. What this allowed me to do was to address real-time gaps in their knowledge, so that by the time I gave a summative assessment at the end of the unit (or halfway through a long unit), I could hold all the students accountable for higher-level complexity in problem-solving. This paper-based formative assessment process worked well and was critical in advancing my students’ learning, but I found myself having trouble with effectively following up with my students regarding their assessment results. They sometimes misplaced the graded papers with my written feedback on it, or they couldn't remember whether they still needed to revise a particular quiz. When they did sit down with me, I often wished that I had a more detailed record of their processes and misconceptions, instead of just a score in my gradebook and an unreliable memory of their errors.

My husband is a software developer, always on the lookout for ways to improve the existing ways of doing things. Sensing my frustration and seeing the hours I put into sorting through paperwork, he and I sat down to hash out the design for an app that would allow me to grade formative assessments in pieces, on the go, while I am on the bus or waiting for a meeting to start. The app we built takes photos of student work and allows the teacher to dialogue with the student, updating their assignment grades incrementally and providing additional feedback until the student completely masters the desired skill. It would also provide a photo record of the students’ progress, to enable effective one-on-one conferencing. I piloted the use of this program last year with 60 of my students during a full school term, and it easily complemented the formative assessment I was already doing. To maintain their focus on the math, the students would still complete their work on paper, but instead of handing me loose sheets during class, they would simply use their phones or tablets to take a photo of their work through the app for submission, which took a matter of seconds. After class, I would sit down and open the app to find all of their submissions, already sorted by question. I would grade a single question at a time using just my fingers and a touchscreen interface on a mobile device, across all students, and upon exiting, the scores and feedback would be published to the students instantaneously. Afterwards, the students would be able to submit further revisions and to receive further feedback until both they and I felt satisfied with the results. This app quickly gained popularity with my students. They loved the camera interface, the instantaneous feedback, and the ability to pull up an entire list of assignments to see which items still needed their attention. The more organized students liked not having loose sheets of paper floating around and to be able to keep track of all of their written work sequentially in a paper notebook, which stayed in their possession. I liked the flexibility to selectively collect a single question from a homework assignment, the freedom to grade anywhere without lugging around tons of papers and notebooks, and the ability to focus on providing quality feedback in real-time without fussing with the overhead surrounding the receipt, recording, and returning of assignments, because Quizster took care of all of those logistics for me.

Quizster has helped to streamline an important part of my students’ learning. In doing so, it has made me a more effective teacher, being able to focus my energy on what matters -- identifying student needs and personalizing my responses. I look forward to reading about how other teachers will implement this app in their classroom. Following 6 months of initial prototyping and testing with a small group of teachers, the app is now ready for release to a wider audience. If you wish to be part of the testing and evolution of this product, you can find more information at http://quizster.co .

Thursday, January 7, 2016

Goal

My goal for 2016 is to always respond to a potential conflict by killing it with kindness. I had a situation in class today which I had handled calmly, but in hindsight I don't know how kindly I had come across because I was actually feeling fairly upset in the moment. This goal extends beyond professional settings, but I do want to make sure it is something that I keep striving towards in the classroom. How do I consistently show love to a kid who is misbehaving in the moment? How do I do that with the people who are closest to me? As I prepare for parenthood*, that seems like an ever-important question to explore for myself.

(*Yes, parenthood! Baby on the way, if all goes well between now and June!)

Tuesday, November 10, 2015

What it Means to Slow Down a Problem

We did a really ambitious activity early this year in Geometry. We slowed down an optimization problem for start-of-year Grade 9 students, in order to get every single kid to understand the process. It worked brilliantly, and we are trying now to help them extend the idea to other optimization problems.

I want to document and share this journey, because I think the experiment that we have started is SO challenging and SO worthwhile. We are trying to get the kids to think like mathematicians. By slowing them down.

Here was the first time we formally introduced optimization (after having the kids play around with building their own popcorn containers). If you read it carefully, you might notice that we tried to emphasize a few things: 1. Tactile learning. 2. Justifying their thoughts. 3. Understanding what x and y represent. 4. Understanding how to analyze the domain. 5. Resourceful use of technology. 6. Interpretation of results back in context.

A little while after going through this, we gave the kids an open-notes test, using a different sheet of paper to start. They did well, which showed us that they really understood the different pieces. Then, on the actual closed-notes exam, we worked backwards by giving them a factored cubic equation, and asking them some relevant questions: 1. What is the dimension of the piece of paper that we had started with? 2. What is the domain of this problem, and why? 3. What is the largest box that can be built here, and what are its dimensions? 4. How many different boxes can we build that would have a volume of _____, and what are their dimensions? Again, the kids did brilliantly!

It has been amazing and humbling to see how far along these 9th-graders have come.

The next question that we gave them, which they worked through in small groups, was an optimization problem involving a known perimeter of a rectangle and in trying to maximize its area. They needed to take the problem from start to finish, in writing a system, combining it into a single function, and doing domain and graphical analysis to find the maximum. Then, as usual, interpreting back in context.

Now, the next problem they are tackling has to do with maximizing the area of an isosceles triangle whose perimeter is 30 units. Not easy. Some kids figured out right away that this follows the patterns of other similar problems, where they will try to write an area equation. Some kids started to make tables -- another really great habit of a mathematician! The class, as a whole, needed a nudge to help them figure out how to get the height of the triangles. We stopped discussions today at writing a general height equation as a class, in terms of x, the length of the two congruent sides, and I asked the kids to keep thinking about the rest of the problem.

A worthwhile experiment, indeed! If by the end of the term, they can do even half of these problems completely independently of us, we will be so thrilled. I think the key is to slow them down. By feeding them the understanding in pieces and then giving them another similar problem, we are building the foundation that it takes to transfer the knowledge.

Stay tuned! 

Thursday, October 29, 2015

First Term Reflection

This is a rough brain dump after the recent end of school term, but I am going to try to stay coherent and helpful.


1. This past school term, I decided to be tougher-than-usual and to cut off accepting make-up work a day before the end of the term. It seems like a small change, but it really saved my sanity by so much! I got to get all of that make-up work graded and returned by the last day of the term, and to just focus on the bigger assignments (like tests) once the kids went on term break and I was working on finalizing their grades. It probably didn't save me much time, but it saved me lots in terms of sanity and focus. I wasn't trying to grade a thousand different assignments all at once while trying to re-calculate their grades.

2. Another thing that really saved me is that I created a learning rubric, asking kids to rate themselves on their growth mindset, reflectiveness, responsibility, resourcefulness, and organization on the last day of the term. It was tremendously helpful to me in writing comments for them, looking at how they rate themselves in each category of the rubric! At this point of the year, it allowed me to really incorporate their own self-assessment into their evaluation, while keeping it somewhat objective (action-based, as my rubric was formatted to be, rather than opinion-based, like it would probably be if I gave them an open-form self-reflection). Again, in the end I don't think that I necessarily saved time in writing their evaluations, but I think that I wrote really detailed and comprehensive ones, considering that it is only the first term and we have only had 6 or so weeks of school.

3. At the end of the term, I really liked ending Algebra 2 with choice assignments and ending Calculus with no-requiz-option exams. For Algebra 2, the choice assignments were all regression activities, and all groups ended up learning/practicing the same skills, but offering them the choice meant that we would potentially have richer discussions in coming weeks, and their interest level was also very high during the task. For Calculus, giving them a quiz that does not have any re-quizzing options was a great way for me to ask the students to step up to a "college-level" challenge after a term of slowly ramping them up to my expectations, and to show them that they could still do very well if they would commit to preparing and asking questions in advance. It worked! Although in general, I am a believer of re-quizzes, I think giving one no-requiz assessment every term will actually reinforce their confidence over time, even for the students who initially don't do well on them. It will also make for a more realistic preparation for college next year.

4. In Grade 9 Geometry, we had given an open-notes exam half-way through the first term, and then a closed-notes final exam at the end of the first term. These tests were super helpful, in combination. The open-notes exam was a great informal check-in on how responsible they are as learners, in asking clarifying questions in class and making sure that they had understood a quite complex task. (Their open-notes task was to take a sheet of paper and to write a cubic equation modeling the volume that could be built by folding up the corners into a box. The 9th-graders needed to do domain analysis and to use Desmos to optimize the volume, and then to construct the box accordingly, individually.) The closed-notes exam at the end of the term, then, assessed how well they are practicing/preparing for exams. I loved this combination, particularly in Grade 9. I thought it was a very developmentally appropriate way to introduce them to high-school expectations.

5. Math journals. Love them, but they're so much work! I am still looking for ways to cut down the work load that is to grade these concept journals all the time (often twice, if the kids are doing revisions on their entries). Any tips?

6. Overall, a very exciting, albeit hectic, first term!

Sunday, October 11, 2015

Wordle as a Tool to Respond to Feedback

This year, particularly after reading Thanks for the Feedback, I am making a conscious effort to gather on-going feedback from my students, in order to address them in real time and to engage my students in a two-way communication. But, let's be honest, the thing that takes the time in class is not to gather feedback, but to go over it. It always feels tedious to go over kids' concerns and appreciation bullet point by bullet point, so this year I am going to try using Wordle (or one of the alternatives) to make the discussion take up less time.

Here is an example of my Algebra 2 wordle, based on feedback for what is working well in the class thus far. I couldn't get the Java interface for Wordle creation to work either on my laptop or on the school's laptop, so I used TagXedo to make this in the end. I like TagXedo, because you have choice over both font and orientation of text. If I wanted to, I could have orthogonally-oriented text. As you can see, kids mostly thought that group work and their classmates were very helpful, as well as handouts that had some basic examples on them. Lots of kids mentioned fixing their errors as being very helpful as well, and the idea of growth mindset being weaved into that. With this picture, I can hopefully whittle down this part of the discussion into a couple of minutes, and then focus on discussing what isn't working well yet. (It didn't make sense for me to create a wordle for what isn't working well in this class, because they are only individual concerns and no real repeats.)




Incidentally, we had a great open house this week, which also weighs in as a source of feedback for me. I tried out an exercise where I asked my students' parents to write down on an index card one hope or excitement they have towards their child's math class this year, and one anxiety that they have towards the class this year. My student parents blew me away on this task! Their responses continue to reinforce my belief that our approach to teaching mathematics needs to consider, in every step, how we are impacting our students' mindset and attitude towards math.

Here are their hopes or excitement. Believe me, their concerns are equally insightful!!

I would love it if [my child] developed a sense of the Beauty of Mathematics.

I am hopeful that [my child] can regain [their] confidence and enthusiasm for math.

Feel like a mathematician and enjoy math.

Hoping that [my child] sees the beauty of method and that it becomes a great mix of method, understanding, and simplicity as a meditative experience/tool.

[My child] continues to love learning.

I hope [my child] grows [their] confidence in Math and is able to solve problems with numbers.

Confident enough to not fear mistakes and attempts and iteration.

Learn algebra

I hope for [my child] not to hate Math.

To gain confidence by asking questions and talking more in class.
 

Excited that [my child] is taking Calculus in high school.

Hope [my child] continues to enjoy math.

Deeply interested in math/Calculus both as theory and application.

I want [my child] to enjoy Calculus and math and to want to do more of it in college, to embrace quantitative theory and analysis.

Excited for [my child] to learn Calculus!!

[My child] is totally turned on by math. [They have] not expressed any anxiety.

Understanding the basics of differential equations and still keeping [their] interest/love/self-confidence in math.

Understanding the basics of Calculus.

I never took Calculus so I am excited for [my child] to learn something beyond what I took.

Glad [my child] has got classes and teachers that [they like].

I am excited that my student is in Calculus and I'm looking forward to [their] development of understanding derivatives.

Excited about [my child] building confidence with Calculus to ease the college course experience.

[My child] seems to love it.

My hope is for [my child] to appreciate that Calculus will be applied to Sciences, and necessary for [them] to succeed in.

Excited for [my child] about [their] continued exploration of new math concepts.

[My child] LOVES math and I'm excited that [they are] able to do 2 classes this year.

I am excited that no matter what [my child] learns, [they] will know more than me.

[My child] is taking charge of [their] work and meeting with you regularly.

Excited for [my child] to continue advancing in math as it is one of [their] favorite subjects.

That [they] can apply [their] learning to real life situations.

Thinking about incorporating some of this parental input into my discussion with the students about how class is going, where we are headed, and why.

How do you manage gathering and addressing feedback in your classes, on an on-going basis?

Monday, October 5, 2015

Changes to Class Structure

This year, I have made some exciting changes to my classes.

1. I thought long and hard about how I do math journals. Last year, I got raving reviews of the math journal setup from my thoughtful and reflective students, but I didn't think that the way the math journal was run actually benefited the other students. It was a hard sell. They always procrastinated at the end of the term with revising all entries, and thereby it lost its value as a reflective tool throughout the term. Also, many students complained that I was "looking for something very specific" in their revisions, so it was very stressful. This year, I decided that more than accuracy in their math journals in reflecting upon the big ideas, I just want them to engage in the process of reflection. I also decided that the stress of trying to get the most accurate answer was turning some of them off from the process of reflection, which was having the opposite effect of what I was trying to achieve. So, this year I am de-coupling feedback from their grade. The first time they turn in a journal entry, I grade them based on a simple 6-point rubric that looks like this:

So, at that point, they have some score out of 6 that I write down. I hand back their journal with both comments scribbled in the margins and a printed rubric with their score. They are then asked to revise it before I collect their journal again in a few days. (I go over in class the common errors, and I also post a couple of example entries on my wall, to help them with this revision.) The second time that they turn it in, although I still return a 6-point rubric to give them feedback, I don't penalize them for their errors. I give them full credit in my grade book for just engaging in the process of trying to revise their understanding.

I have noticed three things from this: One, that most students get the revisions correct anyhow. Two, they are proactive about revising in order to get the points back. Three, they are turning the journal entries in more or less on time each time, which allows me to dialogue with them about their misconceptions in real time. The journal is serving its purpose!!

2. Last year, I gave short one- or two-problem practice quizzes as we were learning the material, and I would grade them on a green, yellow, red sticker system. My intention was that it would be a low-pressure way to give students early feedback, without affecting their grade. But, I wasn't happy about how the kids with the red stickers would put off meeting with me, because they weren't feeling the urgency until the real, big quizzes rolled around. So, this year I still give practice quizzes, but with a few points attached. On the returned practice quizzes, I would write down a similar problem and ask all kids to show me via doing the similar problems that they now understand their error and the concept. I find that this is more productive towards encouraging improvement and a growth mindset, because in order for kids to practice a growth mindset, they have to actually do some work towards making progress!

Thus far, I like the system a lot better. It's still reasonably low stress, but the expectation is clear that kids need to work on their areas of weakness, in order to make back those lost points.

3. This year, I am working actively on building community in my classes. One thing that I did for the first few weeks was to always assign seats. Everyday, the kids would sit with a new partner. They would take the first couple of minutes of class to ask their partner for a fact that they didn't already know about that person, and they would write it down on their own name tag. This helps me to keep track of whom they have already sat with, and they started collecting lots of facts about lots of peers! I loved it! I have also started randomizing partners now that they have sat with a majority of the class. Each day, they come in and they pick a name randomly from the pile. If it's their own name, then they put it back and pick another. Otherwise, they sit with that person. (If they pick out names of people who already have picked a partner, then they give me those name tags back and pick another.) This is a low stress way of making sure that they rotate partners all the time.

4. I am using Microsoft OneNote for two of my classes! Algebra 2 and Calculus. I kind of love it. I can lesson plan very far in advance, and make modifications in real time as I see fit. The OneNote websites serve as my course webpage, where kids can look up both notes and homework assignments. (For a long time I didn't believe in posting homework assignments, but this year I am doing the opposite after reading Switch, because I want to shift the entire classroom culture towards completing homework as a norm, rather than just something that is done by already-responsible students. Thus far, it seems to be working great!) I also upload video links for the kids who just want to use additional resources. Thus far, I absolutely love it.

You can check them out, too! Please don't modify any of the content though, just look.
http://bit.ly/calcNoteboook and http://bit.ly/alg2Notebook are the two links I am using.

That's it for now. Ciao!

Thursday, October 1, 2015

The Growth Mindset Experiment

Hi, blogosphere! I thought I'd check in quickly. This school year, I really wanted to make the focus to be on helping kids to transition to my class. One of the things I wanted to teach them about is growth mindset, and at the same time to be crystal-clear about why we do the things that we do. For example, why do a pre-test? Why do we have practice tests when not everyone is ready? Why play around and intuit things before we discuss them formally?

I did a brain talk on Day 1, which had elements of the growth and fixed mindset as part of the talk, including asking the kids to practice re-framing certain negative sentiments as growth mindset statements. For homework, I asked the kids to write about an example of growth mindset in their lives, outside of math. I learned so much about their lives through this first assignment! I learned about their interests and also how they respond to setbacks. Subsequently, I have shared my own story of a growth mindset with them, and continue to think daily in terms of what I need to do or say in my class in order to generate and sustain more growth mindset. Now every time a kid asks to meet with me, I thank them for having a great growth mindset. When a kid fails an assignment, I ask them to keep working on it to revise their understanding, and I write, "Growth mindset!!" on their paper. In our Geometry class, on the day when we had individual algebra tasks, I asked the kids to write on a post-it one thing that they had learned during that class. (Some kids said, "I didn't learn anything new! I had to review..." and it was a great opportunity for us to chat about how learning new things sometimes requires re-learning old stuff first.) I am thinking about doing a growth mindset check-in, where each kid is asked to write down one thing that they recently learned or improved on and one thing that they are still working on or challenged by. This would hopefully remind them that learning is a spectrum, in order to reinforce their confidence in the process.

Anyway, all this thinking about growth mindser is directly feeding into the classroom culture, I think!! Thus far, I am loving my classes and find the kids to be actively engaged everyday.

Next time, I will talk about actual changes I have made to my classes...Some good ones, I think!