An Assessment on Desmos

An Assessment on Desmos

I gave my two Algebra classes an assessment on Desmos covering linear functions. The idea started as a joke – I told a student who had found Marbleslides challenging that I’d put some on the test. As I thought about it more, though, I decided that assessing with Desmos would be a great idea.

I used Activity Builder to create the assessment. The easy-to-use, intuitive interface made creating the assessment fairly easy, but I encountered a major unexpected challenge. Designing worthwhile questions proved much more difficult. It no longer made sense to ask students to simply graph or write the equation of a line. Instead, I focused on questions that ask students to describe how to graph a line, to explain why an equation’s graph would look a certain way, and to interpret a line’s equation in the context of a problem. This is actually the type of question I always want to emphasize but rarely do.

Desmos Assessment 3

Consider the question above. If I had asked students to simply graph the line given by the equation x=5, they might have been able to do so without truly understanding the equation for a vertical line, and I never would have known.

Desmos Assessment 10

Similarly, this word problem went beyond simply asking students to write an equation to making them connect the mathematics to the situation being modeled. Each of these five students wrote a correct equation, but their understandings of the problem clearly differ. So too does their ability to express their reasoning, something seen in the following example also.

Desmos Assessment 9

Do these students understand the relationship between the graph of a line and its equation? To an extent, they certainly do, but their explanations also reveal some gaps in their understanding. What I find most interesting is how students managed to express their thinking in so many ways. Some used mathematical vocabulary; others didn’t. Some provided precise explanations that anyone could follow; others used ambiguous language that might obscure their meaning. For as much as I think I emphasize communication in my classroom, my students’ responses make me want to spend even more time refining our ability to share our thinking in a clear, concise manner. Perhaps including more problems that call for explanations on each assessment will help me move in that direction.

And that’s probably my favorite part of using Desmos for an assessment. It’s so much easier for students to explain themselves on the computer than it is with pencil and paper. Consider the following responses.

Desmos Assessment 5Desmos Assessment 6Desmos Assessment 7

I know my students, and I can say with complete certainty that they would have written much less on a paper-and-pencil test. And I would have missed out on seeing and understanding their thinking. Between this problem and the one shown in the image at the top, I developed a clear picture of what my students know and don’t know about y-intercepts, something that may not have been possible the way I typically assess.

And, of course, Marbleslides. The incomparable joy of Marbleslides.

Desmos Assessment 4Desmos Assessment 11

I don’t see a lot of students absolutely beaming during tests, but I did this time. That student I mentioned earlier – the one who found Marbleslides so challenging – successfully collected all of the stars on this assessment, and she was so incredibly happy. Seeing her smile made the entire assessment worthwhile.

I suppose it’s worth discussing the nuts and bolts. Grading wasn’t really easier or harder than a pencil-and-paper assessment. It was just different. Take a look at the dashboard below.

Desmos Assessment 1

It’s easy enough to grade a question when a student gets a check, but everything else required me to take a closer look. Sometimes, as with the following question, that was pretty easy to do.

Desmos Assessment 8

I can quickly glance through student responses and get a sense of common misconceptions. But with questions that require an explanation (or an input that doesn’t get verified), I have to take the time to look through everyone’s individual work. And that’s totally fine. That’s what grading is usually like, and I think it’s important to see and assess each student individually. Desmos actually made it easier to do this.

As far as actually tallying scores and providing feedback, I had to improvise. I used Google Sheets to create a little rubric. I included a place for a numerical score and a place for brief comments on the individual problems. I also let my brain rest and made Sheets calculate the grades for me. Here are some examples.

Desmos Assessment 12Desmos Assessment 13Desmos Assessment 14Desmos Assessment 15

I printed these little rubrics and returned them to students. Then, I un-paused the activity and allowed students to look back at their work and correct it if they so desired.

Other miscellaneous thoughts:

  • The Ohio AIR test uses the Desmos graphing calculator, so this sort of assessment should help my students prepare. It’s also easy to create AIR-type questions using Desmos.
  • There isn’t really a way for students to “turn in” the assessment. I just told them to close the tab and shut down their Chromebook when they finished. This is totally fine; it’s just something I had to tell them about a hundred times.
  • It’s relatively challenging to monitor students to make sure they’re not just using Google to search “how to write a linear equation” or using Discord to ask each other questions. I emphasized honesty and integrity at the beginning, and that seemed to do the trick.

If you’re wondering if I’d give another assessment using Desmos, the answer is a resounding yes. I’m actually designing two more assessments (one for Algebra, one for Math 8) right now. And my colleagues have agreed to try using Desmos for one of their assessments!

Thank you to Desmos for being awesome! Thank you to Julie Reulbach and Jonathan Claydon for introducing me to the idea of Desmos assessments! Thank you to my students for making my job wonderful!

Update: Wow! This post received quite a response on Twitter! Here’s the link for anyone interested: https://teacher.desmos.com/activitybuilder/custom/5bc52d70744e4b427f3ce5a6

The oldest team in the NBA?

The oldest team in the NBA?

I attended Joel Bezaire‘s Sports Analytics session at TMC18. It was awesome! Joel has done an amazing job developing a curriculum based on Sports Analytics. I decided to share a lesson I did this past year involving sports. It’s nowhere near as good as Joel’s lessons, but I think it could be something with a little work.

One storyline during the 2017-18 NBA season involved the advanced age of the Cleveland Cavaliers roster. In October, ESPN’s Brian Windhorst published the article “Cavs the oldest in a long line of old LeBron teams.” The article contained the table shown below:

ESPN Table

I presented this table and the article’s headline to my Integrated Math 1 students and asked them to Notice and Wonder. This was quite a few months ago, so I don’t really remember how the discussion went. We ended up talking about whether it made sense to use the average to determine the NBA’s oldest team. I proposed a roster consisting of three of my 14-year-old students, my pregnant colleague’s soon-to-be-born child, and one of my colleagues who I joked was 185. They quickly saw that this team’s average age would reveal very little about how old or young the team really was. We decided that we needed a better way to discuss a team’s age.

From this point, the lesson didn’t go how I had hoped. I gave every student or pair of students a team roster and told them that I wanted the class as a whole to find a way to compare team ages across the league. I provided the entire class with a single piece of poster paper that they could use to present the information using whatever representation they liked. Although I didn’t say it, my intention was for students to make a box plot for each team. If nothing else, I expected students to go beyond simply reporting an average age. The results were decidedly mixed. I think this task focused too heavily on calculation and representation, and it did not focus enough on thinking and discussion. Interestingly, several students told me then and later in the year that they really enjoyed getting to work with the NBA rosters. There’s definitely the potential for a good activity here; I just haven’t found it yet. Let me know if you have any ideas!

knowing people

July 27, 2017: The Terror of Twitter Math Camp

July 18-19, 2018: #descon18 and day one of #TMC18

Something has changed. It’s all still here – the anxiety, the relentless train of thoughts, the confusion about what to say and where to sit, the feeling that I don’t really belong. It’s all still here. But it’s better. It’s better. I know people.

When I arrived Wednesday morning, I sat at a table in the atrium to collect myself. Lisa Henry came over to welcome me. I talked with Dave Sabol, who I knew from my time student teaching at Saint Ignatius, for a few minutes, and as I sat waiting in Rade Dining Hall, Cindy Reagan, another Ignatius teacher I know, sat down and talked with me. At one point, Chris Luzniak, my TMC mentor last year, came over, gave me a hug, and asked about how my year went. I exchanged smiles with a number of people who remembered me from last year, even if they didn’t know my name or hadn’t really talked to me before. This morning, Joel Bezaire greeted me by name at his morning session. Mark Kaiser, another Ignatius teacher, sat next to me for My Favorites and the Keynote, and we chatted. When I arrived at an afternoon session, Lisa Bejarano and Kent Haines greeted me. Lisa gave me a hug and mentioned that she saw me tweeting so knew I was around somewhere. It’s an unfamiliar feeling: Someone knows I’m here.

I was never an especially social kid. I’m not sure I really knew how to be social, how to have friends, how to exist in “that” world. Two memories stand out. I recall getting together with a friend shortly after high school. “Okay, Dan, I guess I’ll see you in six months.” That’s what he said to me when we parted. It wasn’t meant in a sarcastic or cruel manner. I suppose in a sense it was almost wistful. He knew a simple truth: Even if he asked me to do something every day, it would likely be a long time before I agreed to do anything again. Whether it was shyness or laziness or anxiety or apathy or something else entirely, I simply did not spend much time being social.

The other memory involves the transition from fifth grade at an elementary school to sixth grade at the middle school. Because the middle school brought students together from four different elementary schools, the school tried to make sure that every student shared homerooms and teams with at least a few other people from elementary school. I did not. Well, that’s not exactly true. I knew Troy and Mike. They had never been what I’d call friends. They were just two boys that I knew. We got along fine; we just never had much occasion to spend time together in elementary school. But they were really the only two people I knew in sixth grade. The three of us made an odd bunch, but at least we had a group. I guess you could say we took care of each other socially. None of us were especially outgoing, and we were close to as far from popular as one could get. But we had our friendship, and I think it meant something for all of us. Although it’s been twenty years, I still remember the day I dropped my pencil box on the stairs and Troy came over and blocked the stairwell so that I could pick up my supplies. Maybe it’s not the most exciting or heartwarming childhood memory, but it has stuck with me for this long. I imagine it always will.

Marian Dingle spoke today about her children’s experiences in school. She told us how her son and daughter both had teachers with whom they formed no real connection, teachers that didn’t know them, teachers that made school a less welcoming place. For Marian’s daughter, sports, which sometimes serve to bring people closer, only seemed to exacerbate the feeling of not belonging. Despite Marian’s best efforts as team mom, her daughter did not develop the sense of kinship with her school volleyball team that is the hallmark of great youth sports programs. Fortunately, Marian’s daughter found this connection with her club volleyball team, and fortunately, Marian’s daughter had parents who strove to help her center herself in family, in community, and in her culture.

But what about the kids who don’t have this? What about the kids who walk into class and don’t know where to sit? What about the kids who hate group work because they know that no one will want to work with them? What about the kids who hope every day that they’ll be able to find an open seat in the cafeteria? What about the kids who believe that no one notices them? What about the kids who think their voices are never heard? What about the kids who feel like they just don’t belong? And maybe they don’t belong because we don’t let them belong or help them belong or provide a space for them to belong in. And maybe we don’t notice them and we don’t hear them because we don’t try to hear them or we don’t want to hear them. And maybe we just tell them to sit anywhere or to make a new friend or to just ask someone else in class because that’s what we would do and it seems so simple unless you’re 13 and you feel like you don’t belong. And maybe we send the message every single day that they really don’t belong. Intentionally or not, maybe everything we say and do sends that message. And maybe they see that message and hear that message every day at school. And we don’t do anything about it.

I teach at the middle school I attended. I’ve lived in the same community for my entire life. I don’t have any answers or at least not enough answers. All I have is the will to keep trying. To keep asking questions. To keep fighting. Because they do belong. And they deserve better.

Thank you Lisa and Dave and Cindy and Chris and Joel and Mark and Lisa and Kent and everyone else. You’ve made a difference for me. And thank you, Marian, for sharing your story and for fighting for kids.

The Marzano Tweet

What follows are my thoughts on the response to the Marzano tweet shown below. I offer these thoughts as my way of grappling with an important issue in education – the interplay between educators and non-educators. My intention is not to criticize or disparage any individual but to work toward a way for me to understand discourse about education. I hope that I at least partly achieve this goal.

Robert Marzano is an educational researcher, consultant, and chief academic officer at Marzano Research. I know him primarily from his book The Art and Science of Teaching.

I did not have the same visceral reaction to the Marzano tweet that so many others did. That’s not to say I liked it. It just didn’t upset me. I have too much on my mind to worry about what Robert Marzano thinks. But I understand why so many teachers felt compelled to criticize him. When someone shares a message about education that we know is false, misleading, or harmful, it’s important for us to dispute that message. It’s important for us to share our own knowledge and perspectives. We can’t let a false narrative dominate. So I understand the response to the Marzano tweet.

But I also don’t understand the response to the Marzano tweet. I saw quite a few comments about Marzano’s background. People criticized him for only having spent two years in the classroom and for not having been in the classroom for 30+ years. The message here seems to be “Who are you to say anything about teaching when you don’t even teach?” I find this troubling.

Are teachers the only ones with valuable insights into teaching? Is anyone else qualified to share their opinions about education? Should we reject all educational research unless it was conducted by a classroom teacher? How long can you be out of the classroom and still have a worthwhile perspective? Coaches and administrators aren’t classroom teachers – do their contributions have any value? What about counselors and school psychologists? Who do we consider close enough to the classroom to judge their ideas worth considering?

Politicians, to take one example, rarely have teaching experience. Yet politicians write every education law, and all too often, teachers have little to no input in the legislative process. It can be distressing to think that education policy has largely been crafted by people with little to no experience as educators. They rely, of course, on input from many groups – researchers, lobbyists, etc. – but ultimately, the politicians pass the laws.

Is it fair to criticize politicians for education law? I think so, but the target of the criticism matters. It’s fair to say that a law is bad policy. It’s fair to say a law is based on shoddy research. It’s fair to say a politician didn’t consult with enough people or with the right people. It’s fair to disagree with a politician’s beliefs, and it seems fair to question a politician’s knowledge and understanding of issues in education. But is it fair to criticize a politician for never having been a teacher?

Ideas should be judged based on their merit. Anyone can have a great idea. An idea isn’t great because it came from a teacher; it’s great because it’s useful somehow. Similarly, a bad idea isn’t bad because it came from a non-teacher. An idea is bad because it offers nothing useful or it’s harmful or it ignores the research or it’s based on misconceptions or for any of a number of other reasons. The idea itself must be flawed. An idea isn’t bad simply because of who offered it.

Perhaps it’s more likely for bad educational ideas to come from non-teachers and for good ones to come from teachers. But we all know that not every idea a teacher has is a good one, and I hope we’ve all heard good ideas from non-teachers.

I don’t agree with the message Marzano shared in his tweet. I don’t agree with it because it’s wrong for so many reasons that people have already shared. It’s wrong if Marzano hasn’t taught in 30 years, and it’s wrong if he went back in the classroom today. What matters is the quality of the idea itself. I worry about what happens to discourse when we reject an idea because the person who suggested it lacks a certain title, background, or experience. But I also wonder how to reconcile this worry with the reality that everyone considers themselves qualified to offer opinions on educational issues. Is there a clear line somewhere? It’s certainly not “teacher vs. non-teacher.” After all, some of the best ideas in math education right now come from Desmos and Illustrative Mathematics, and as far as I can tell, most of their employees are not currently in the classroom. I don’t have an answer. I’m not sure there is an answer. I just needed to write this all down.

What Do My Students Really Know? Part 2

During the second semester, I only assigned homework using Delta Math. This worked well for several reasons, with the most important one being that it gave me better insight into what my students actually understood than pencil-and-paper homework ever did.

The Delta Math homework I assigned surprised me right off the bat. The image below displays one student’s results on the first assignment of the second semester. Many students had similar results.

HW 1 Linear 1

This assignment consisted entirely of review material. We had assessed linear functions at least once in December, and for the most part, students did fine. I knew that students would be a bit rusty after Winter Break. That’s why we completed this assignment. The surprise came from the misconceptions I saw in student responses.

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Although I could only see their answers, I found it relatively easy to determine their misconceptions. Unsurprisingly, I saw all of the classic slope mistakes.

  • Writing slope as an ordered pair instead of a ratio
  • Subtraction errors, especially with negative numbers
  • Putting the change in x in the numerator instead of the denominator
  • Mismatching x and y
  • Forgetting to simplify (not exactly a mistake, but Delta Math marks this wrong)
  • Misinterpreting \frac{4}{0} as either 4 or as 0

These aren’t new mistakes. I’ve seen them many times, and we’ve corrected them together many times. We said “vertical divided by horizontal” at least ten times each class period every day for a month. And the students got this! Like I said, students did fine when we assessed linear functions in December.

So why did so many students continue to display these misconceptions? I’m not naive. I realize that students master the material at different rates. But how could so many of them who had mastered the material make these mistakes? Why did they return to misconceptions that they had overcome a month earlier?

One explanation is that students managed to know the material well enough to pass an assessment, but they did not develop the robust understanding necessary to maintain their skills even a month later. That’s the explanation I originally subscribed to, but I think it lacks something important. Many of my students did understand slope. Throughout the fall, they worked hard to connect proportional relationships, steepness, and lines. They built a solid conceptual foundation. They thought mathematically. They solved problems. I think what they lacked – and this is on me – was a proper emphasis on procedural fluency. Sure, we had plenty of opportunities to practice and to develop that fluency, but rarely did they have the “Uh oh, I’m wrong!” moments that Delta Math gave them. My Delta Math assignments required students to get a certain number of problems correct to get credit. You just can’t fake a right answer. That’s what I like about Delta Math – it holds them accountable.

The other major advantage of Delta Math over pencil-and-paper homework? I can look through as many assignments as I want to in a relatively short time period without having to carry papers around. I have a bit of a problem with keeping papers organized, so moving homework online and avoiding paper altogether saves me some serious time and energy. The obvious drawback is that I cannot see the work that the students did. In the examples above, it’s relatively straightforward to identify misconceptions without seeing the student’s work, but that certainly won’t always be the case. I think, though, that simply being able to see that a student struggled with a problem type may be enough, especially given that some sort of intervention would need to take place anyway.

I’m not sure yet what homework will look like in my classes this year, but it seems like I’ll want to place more emphasis on procedural fluency. Perhaps such an emphasis earlier in the year will lead to better understanding all year long. I hope 2018-19 is the year I finally figure out how to make homework work for me and for my students!

Sandra Cisneros – “One Holy Night”

Sandra Cisneros – “One Holy Night”

Last summer, I read two books with a student. We read The Awakening by Kate Chopin and Mrs. Dalloway by Virginia Woolf. Our conversations about The Awakening proved fascinating, but we didn’t have as much success reading and discussing Mrs. Dalloway. Nevertheless, I found the experience meaningful, and I think the student did too. She sent me the following Remind message before the school year ended:

Hey Carlson, are we reading this summer?

How could I say no? We haven’t yet started, but we plan to read The Piano Lesson by August Wilson. Additionally, I asked one of my students from this past year if she would like to read a book with me, and she agreed. We’ve been reading Woman Hollering Creek and Other Stories by Sandra Cisneros. The story “One Holy Night” led to an interesting discussion. Here are the highlights and my rambling commentary. To maintain her privacy, I will refer to my student simply as C.

In “One Holy Night,” an eighth-grade girl tells of how she loses her virginity to a man who calls himself Chaq Uxmal Paloquín. He claims to be descended from Mayan kings. The people in the neighborhood call him Boy Baby, and no one seems to know much about him. We find out later – after he has left town and our narrator has become pregnant – that he is actually thirty-seven years old and that he is a serial killer. The story is only nine pages long, and it focuses more on mood and feeling than on specific details.

For whatever reason, our conversation fixated on rape. C rightly pointed out that Boy Baby committed statutory rape. She expressed some discomfort with the story and mentioned that some readers might be deeply disturbed (“triggered”) by the story. We talked about the choice Cisneros made to avoid detail and use poetic language to describe the rape:

Then something inside bit me, and I gave out a cry as if the other, the one I wouldn’t be anymore, leapt out.

C was glad that there wasn’t more detail. Because rape is so disturbing, she asserted, only a bad writer would need to include more detail to bring about the desired response from the reader. This assertion seemed to extend past “One Holy Night” to all literature (and other works of art, for the matter), so I asked if there could ever be a situation in which more detail might be necessary. She said no, again emphasizing that a good writer wouldn’t need to include the details of the rape. I told C that I didn’t disagree but that I wanted to press the point further. Could there be any value in graphic description of such a violent act? And what about other violent acts like murder? C felt that rape belonged to a category of its own, that it was even worse than murder. I wondered whether a rape victim might consider it necessary to express the horror and the violence she went through. C agreed this might be possible, but she expressed her concerns about works of art that use such violence for shock or entertainment value. She talked about the show 13 Reasons Why (which I have not seen) and how she felt like it glamorized suicide. We talked about how the narrator seemed to romanticize her own rape, describing Boy Baby’s face as “the face I am in love with” even after discovering he’s a serial killer. It was a meandering conversation, but it was a meaningful one.

When I chose Woman Hollering Creek and Other Stories, I didn’t know much about its content. I didn’t intend to pick a book with a story about a young girl’s rape, so I’m glad that C and I managed to have such an interesting discussion. I’m forced to wonder where this sort of conversation takes place. Or if it even does. It’s not easy to talk about rape, but it seems important that we do. Sometimes we don’t give our students enough credit for the depth of their insights. I look forward to learning more with C as the summer continues.