The Week Ahead: Master Designer & MVP 1.6

Monday: Master Designer (an activity to promote group work)

9.25 Master Designer Group Work Norms

Some of my classes have been working great together at their #VNPS, and others less so. There’s one class in particular that has a lot of built-up animosity among students dating back many years (to middle and even elementary school).

In an effort to promote positive group interactions, I will be doing Master Designer on Monday. This activity is from Designing Groupwork: Strategies for the Heterogeneous Classroom.

Basically, each kid gets a collection of cut-out shapes (9.25 Master Designer Shapes). The “Master Designer” arranges the shapes into whatever sort of beautiful/creative design they want. Each kid, including the Master Designer, has their binder set up on their desk creating a “privacy cubicle” so that no one else can see their shapes. The Master Designer has to leave their shapes on the table and communicate through words and/or gestures how the shapes are arranged so that the other group members get their shapes to match the Master Designer’s design.

One student sits out each round and checks off when they observe positive group behaviors, such as giving clear explanations or when someone other than the Master Designer helps explain the arrangement to another group member. When someone thinks their design matches the Master Designer’s, they can ask the observer whether they are finished, but the observer can only answer with a simple “yes” or “no”. If they designs don’t match 100%, the observer can NOT say what needs to change – rather, the student who thought they were done needs to ask clarifying questions of the Master Designer to figure it out.

After each round, you rotate who is the Master Designer and who is the observer. For the first round, you can have a particularly loud and distractible student (or a shy and introverted student) be the Master Designer for each group. This forces that student to actively participate because the entire group relies on them!

The Warm Up for this lesson has two purposes:

  1. Have the students suggest the positive behaviors that the Master Designer activity reinforces. It’s important to have leading questions ready to make sure the target behaviors are identified “organically” from the discussion.
  2. Demonstrate that you can describe characteristics of shapes without fancy vocabulary. For example, if you don’t know the word “square”, you can still describe a square. You can also gesture. I’ve done this activity successfully with newcomer ELLs, and this point is important to make in the Warm Up.

Depending on how much time it takes to go over the directions for the activity, this might be the whole period, or we might have a bit of time to kill at the end. If there’s some extra time, we’ll work on practicing function notation for recursive functions: 9.25 Recursive Functions.

Tuesday and Wednesday (and maybe Thursday): MVP Lesson 1.6.

9.26 MVP 1.6 Day 1

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We’ll start with a #noticewonder of this scenario. A key thing students need to do early on in this lesson is to realize that the total amount of candy is (15 lbs)(180 candies/lb) = 2700 pieces of candy. I’m hoping that this comes out of the notice/wonder conversation, but if it doesn’t, I think I’m still going to release kids to groupwork. We spent so much time talking about the context of lesson 1.5 as a class that they really didn’t start working on the problems until day 2. I don’t want this to happen with 1.6, particularly because even if they start off thinking that the machine begins with 180 pieces of candy, they’ll still be able to grapple with the mathematics behind a decreasing arithmetic sequence.

I want the debrief to this task to bring out a lot of important mathematics:

  • recognizing that an arithmetic sequence can decrease
  • understanding that multiplying neg*pos is repeated subtraction the way pos*pos is repeated addition
  • comparing the graphs of increasing and decreasing sequences
  • writing explicit and recursive equations using function notation

As such, I expect this lesson to go at least into Wednesday, possibly Thursday with groups making summarizing posters.

If everything happens to be amazing on Tuesday and Wednesday and I feel like they really don’t need another day on this lesson, I’m planning to use Thursday to review multiplying negatives by introducing the students to Desmos with this Desmos activity.

Building this familiarity with Desmos will be particularly helpful since I’d like students to use Desmos when working on lesson 1.7 the following week. In fact, I’m even considering turning lesson 1.7 into a Desmos activity…

Friday is a Professional Development day, so the kiddos get a long weekend.

Happy teaching, everyone!

Shuffle Tests: An Alternative Assessment to Combat Status (Part 2 of 2)

This is the second post in a two-part series about shuffle tests. In the first post, I discussed what a shuffle test is, as well as some of the successes and failures I experienced implementing a shuffle test in my classroom.

In this post, I will discuss some objections to the very notion of a shuffle test. I will also go into greater depth as to why this alternative assessment is a powerful tool to promote equity and combat status in the classroom.

Objections to the Concept of a Shuffle Test

In implementing a shuffle test in my classroom, I encountered two objections. One came from a student, one from a teacher.

A few of my higher-achieving students objected to the fact that their oral exam grade on a shuffle test would be dependent upon whether or not a classmate understands the material. My response to this was two-fold:

  1. Communicating clearly is an important part of doing mathematics, so part of what I’m assessing with this test is the ability of everyone in the group to explain math clearly to their classmates.
  2. My goal is for you to succeed, and the oral exam is not a “gotcha” test. If someone in a group isn’t able to explain a problem or answer my questions, I will simply say, without judgment, “it looks like this group isn’t ready yet,” and walk away to give you more time to discuss the problem. I’ll return again when you’re ready.

This response satisfied students’ initial concerns, and I didn’t hear any other complaints.

The objection from the teacher standpoint is that a shuffle test is not as rigorous an assessment as a traditional test. Here are my thoughts on that:

  1. The oral exam component provides accountability to ensure that students aren’t just mindlessly copying from the “smart” kid in the group.
  2. This test serves a dual purpose: it is a test, but it is also a status intervention. Thus, you cannot look at its benefit to the classroom purely through the lens of its ability to measure student understanding. It is also a profound way to get ALL students collaborating on and persevering through challenging problems.

This is Deeper than Just an Alternative Assessment

It’s worth exploring a bit more that second point above: a shuffle test is fundamentally a status intervention.

If you’re unfamiliar with the notion of status, I highly recommend reading everything that Ilana (Lani) Horn has ever written. Lani is a researcher at Vanderbilt who studies equitable teaching. She identifies a key problem that hinders student learning: status, which she defines as, “the perception of students’ academic capability and social desirability.”

As Lani notes, “The word perception is key to this definition.” Students who perceive themselves as “good at math” don’t always want to listen to or value ideas from their peers whom they perceive as being “bad at math”. Similarly, students who have struggled for years in math often don’t feel like they have anything valuable to add to the conversation.

Lani has discussed many status interventions, such as establishing and maintaining norms, assigning competence, broadening students’ definition of “smartness” in math class, and visibly random groupings. I have also written on the importance and ease of using visibly random groups.

The status interventions listed above are primarily focused on the culture around everyday classroom tasks and activities. As wonderful as it is to promote positive interdependence among students during class with these status interventions, these interventions should not just be relegated to classroom activities, but should also include assessments. As Lani points out, “Assessment is one of the most powerful ways teachers communicate their values to students” (Strength in Numbers, p. 56).

Lani discusses shuffle quizzes as an example of what “Paul Black and Dylan Wiliam and their colleagues refer to … as assessment for learning“. That is, the primary purpose of the assessment is not to evaluate students, but rather, to promote their learning (Strength in Numbers, p. 56).

This was definitely the case in my classroom. This was the first question on my shuffle test:

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We had worked with composite figures before, but I had never given students a question in which “cutting out” part of a shape decreased its area but increased its perimeter.

Some groups were able to handle this entirely on their own, but I noticed others in which all of the students were leaving incorrect answers to the perimeter and moving on to the next question. There were two ways this was happening:

  1. They only added the straight parts of the shaded region’s perimeter.
  2. They treated perimeter like area: they found the total perimeter of the rectangle, then subtracted away 14 cm for the dotted lines.

For these groups, I intervened by asking the following two questions:

  1. What does perimeter mean?
  2. Trace for me with your pencil or finger the perimeter of the shaded region.

These two questions were enough to trigger a lightbulb moment in at least one student in each group. Additionally, I think that every student’s memory of that lightbulb moment will be much stronger than it would have been if I had “taught” them how to do this type of problem through direct instruction, since they struggled and thought about this funky perimeter for a significant and sustained period of time before finally seeing how the perimeter needs to be treated as fundamentally different than the area.

When Lani discusses assessments for learning and the research behind them by Black, Wiliam, et al., it is primarily in the context of formative assessments that will guide the teacher’s future instruction.

I used my shuffle test as an end-of-unit summative assessment, and I was very happy with its ability to serve that purpose. That being said, after seeing the incredibly rich mathematical thinking and discussion that my students engaged in during the shuffle test, I definitely want to try to incorporate this more frequently as a formative tool in my classroom.

Shuffle Tests: An Alternative Assessment to Combat Status (Part 1 of 2)

Screen Shot 2017-03-28 at 8.39.13 PMI have often found that many students underperform on traditional tests. They may know the material, they may work hard and be able to explain things in class, and they may even study, but when faced with a traditional, individual, silent testing environment, their stress and anxiety get the better of them and they freeze up.

As a result, I’ve been looking for alternative ways to have students demonstrate mastery, especially for my English Language Learner class, because they seem to particularly struggle with traditional tests.

This post is the first in a two-part series about an extremely exciting and positive experience I had while implementing one type of alternative assessment: the shuffle test. Not only is a shuffle test a great way for all students to access and demonstrate mastery of challenging content, it also has the added benefit of being a very effective status intervention.

In this post, I’ll discuss the mechanics of a shuffle test and talk about my experience implementing it. In the next post, I’ll go more into the pedagogy of why this is a powerful tool to promote equity in the classroom.

What is a Shuffle Test?

  • Students are randomly assigned to groups
  • The test itself consists of a small number of rich, challenging problems
  • Each student submits their own written solutions for an individual grade
  • Each group receives a collective group grade for an oral exam in which students explain the group’s solution to one of the questions

Some Important Points

Because the students are working in groups, the questions can and should be more difficult than those you would give to students on an individual test.

A key part of the shuffle test is the group grade for the oral exam. Traditionally, for the oral exam portion of a shuffle test you randomly choose one student to explain the group’s solution to one of the test’s questions. This means that all students need to ensure that all group members understand each problem on the test fully. This forces them to work together and support each other.

I actually did the oral exam portion of the shuffle test a little bit differently than the “one student at random answers for the group” model that I originally learned about. When I first learned about shuffle tests, I saw a video of an oral exam. In the video, after one student in the group was randomly selected to explain the group’s solution, one of the other group members pretty much checked out since they were now “off the hook”.

To mitigate this, I had students take turns explaining their group’s solution. I used equity cards to randomly select who would start explaining. When a student was selected, they were the only one in the group allowed to talk. After they had talked for a bit, I would use the cards to randomly select another group member to pick up the explanation where their colleague had left off. This forced all students to pay careful attention during the oral exam because they knew that they would be the one explaining at any minute.

My Experience: What Went Well

Really, the impetus to write this blog post was that I needed to share how shockingly sublime my classroom was during the shuffle test. I have developed a pretty decent culture of collaboration and group work in my classes, but it (like most things) is imperfect – a perpetual work in progress that requires constant vigilance and upkeep on my part.

The day of the shuffle test, however, was truly a dream come true: after I reviewed the procedure and expectations for the shuffle test, kids got into their groups and immediately started working together. They found the questions to be really challenging, but they just buckled down on working through them together rather than asking me anything. I think that by calling it a “test”, they more easily internalized the notion that they should rely on each other rather than me. 

I spent a significant amount of time casually milling about the room, subtly eavesdropping on their phenomenal discussions and making mental notes to myself, but really, my presence was not necessary for the excellent math thinking and learning that they were doing.

In one of my classes, I had been worried because a student who is a bit of a … *character* … had been absent for several preceding classes and had missed some of the key material on the test. I was worried that this student might act out as a defense mechanism (as was often the case), and that their group members would get frustrated and turn on them.

What actually happened was the exact opposite: this student was the most engaged I’ve seen all year, and worked really hard to pull their weight in the group. The other group members – including a super high-achieving, high-status student who always needs everyone to know that they’re right – responded by helping this student with the material they had missed, and welcoming them into the group.

My Experience: What Could Have Gone Better

The test that I gave was too long for one period. While some groups almost finished on day one, others were only about halfway done. I had suspected that I might need to budget two days for this, but there were some definite downsides to continuing into a second day.

The most fundamental downside was that students lost a sense of momentum and focus that they had had on day one. While the class still went well on the second day, with kids mostly on-task and working together on the math, that idyllic classroom utopia that I described above had returned a bit to its normal, human (and thus flawed) state.

Additionally, I had several kids who were out on a field trip, which messed up the groups. Even worse, my Geometry classes are at the end of the day, so as the field trip ended and students started to arrive back at school (at different times depending on the metro train their field trip group had caught), they trickled back into the class, forcing me to rearrange the groups several times.

My goal for the next shuffle test is to have it be short enough that every group at least finishes their written solutions in one class period. While it would be ideal to do all of the oral exams in the period as well, I think that as long as students have answered every question and written up all of their solutions, it wouldn’t be too hard to have groups come after school or at lunch to complete their oral exam.

I would like to give a special shout-out and thank you to Bill Day and Julia Penn, who led the Math for America DC session that first introduced me to the concept of a shuffle test.

In my second post on shuffle tests, I discuss some objections to using shuffle tests (from both students and teachers), as well as more of the pedagogical theory behind why shuffle tests are a powerful way to promote equity in the classroom.

Visibly Random Groupings: Why an Initially Terrifying Prospect Turns Out to be My Favorite Way to Promote Equity

Summer is often a time of reflection and change. We teachers make our New Year’s resolutions in August, not January. So as you think about the coming school year, and what small steps (or giant leaps) you’d like to take to do things differently, let me make an easy suggestion that changed my life this past school year: group students randomly.

Wait! Don’t go! Before you stop reading because, “that’s just crazy!” or “that’ll never work in my classroom” or “what about these ten problems with implementing random groupings that I immediately thought of?!”, allow me the time to argue that random groupings (1) are good for students, and (2) make your life easier. And yes, I promise to address your concerns about why this is the craziest thing you’ve ever heard of.

Good for Students: How Random Groupings Send Subtle Yet Important Messages that Promote Equity

In my opinion, the single most important reason to group students randomly is the fact that when we don’t, students will try to read into the groups we assign and the roles they should fill within those groups.

If we group homogeneously, they might think, “Yep, I’m in the dumb kids’ group. No surprises there. I’ll just pray I can make it through this class without looking like an idiot,” or alternatively, “I’m in the smart kids’ group! That means my ideas matter the most when we discuss things as a class.”

If we group heterogeneously, they might think, “I’m the smart one in this group; these other kids are not going to be able to keep up with my genius or help me solve this problem,” or alternatively, “I’m clearly the dumb one here. I’ll just copy down whatever the smart kid says.”

Even if students aren’t conscientiously narrating these thoughts to themselves, they are certainly internalizing the subtext of the group they have been placed in and their “role” with that group.

Furthermore, these unproductive thoughts are often filtered through the lens of race and gender and any other way that students can feel marginalized in a math class. Whether we like it or not, students carry the baggage of cultural norms and biases, social expectations, and status into the classroom.

Random groupings therefore send a powerful message: everyone is equal, everyone’s ideas are valid and deserve to be heard.

Before learning about random groupings, I used to make groups by trying to “spread out” the strong and weak students, i.e. I’d make sure that my strong students weren’t too clustered, and that the weaker students always had someone who could support them. While I did this with the best of intentions, this approach is problematic:

  • I was assigning “strong” and “weak” classifications to students based on prior achievement. Despite the cumulative nature of much of mathematics, a quality math task will invite innovative and creative ideas that can come from anyone, even a student who struggles with some basic skills.
  • There are many ways to be “smart” in math class. Most people tend to assume that being “good at math” means being able to do basic arithmetic computations quickly and accurately. While that’s a great skill to have, most mathematicians (myself included!) will readily admit to struggling with that particular skill. When we assign groups based on prior achievement, we’re only validating a narrow definition of what constitutes being “good at math”.

By grouping students randomly, we send the message that there are multiple ways to be smart at math (seeing patterns and connections, drawing a graph or diagram to visualize a problem, communicating ideas clearly, etc.).

Obviously your students won’t fully internalize the idea that there are lots of ways to be smart at math simply from random groupings alone; this message needs to be explicitly reinforced many times over. But random groupings are a powerful way to put your money where your mouth is. This can start to chip away at the status barriers preventing full participation and engagement.

If we truly believe that all students can be successful in mathematics (and if you don’t, why on earth are you teaching?), then visibly random groupings are the only way to organize the classroom.

For more about why random groupings are essential, listen to this tumblr post from Ilana Horn, check out her blog Teaching Math Culture, or read her book, Strength in Numbers: Collaborative Learning in Secondary Mathematics.

But What About…? Calming Your Fears

I will be honest: even after reading enough to be convinced that visibly random groupings are a good idea in theory, I was terrified of actually implementing them. What if the random groups create nightmarish social dynamics? What if all the weak kids get put into one group and completely flounder?

To that second concern, I’ll note that if a bunch of “low” students end up in one group together, oftentimes they will realize that there are no “strong” students to hide behind, and they will rise to the challenge. And if they don’t, then at least they’ll be concentrated and you can spend extra time with their group!

But back to the broader concern that randomization can create bad social dynamics. This is obviously true, and you don’t have to live with those bad dynamics. Supporting randomized groupings doesn’t mean you have to blindly accept a group that you know won’t work together well. The key is that you change groups based on social, not academic considerations. For example, you could say, “I know you two always get chatty together, so I’m going to switch you to another group.” Or, as was the case in one of my classes last year, if two students have associations with rival gangs, they should definitely not be seated together!

As long as the groups are visibly randomized from an academic standpoint, with any conscientious tweaks occurring for purely social reasons, your classroom will still get the positive benefits outlined above.


So how can you actually implement this in your classroom? Ilana Horn shows an example of a chart you could hang in your room with different group roles. Simply shuffle cards with students’ names on them and place them randomly into the slots. Screen Shot 2016-07-06 at 11.00.15 PM

That’s way more sophisticated than what I did! At the beginning of this past school year, I was so nervous about random groupings that I decided to start out simple: I only did random groupings for a few specific, group-work tasks. I would visibly shuffle cards with students’ names, then put them down four at a time on desks to create the groups, saying the students’ names as I went.

Later in the year, I realized that random groupings are actually the greatest thing ever and I started using randomization to create my general seating chart. I would shuffle the cards, then have a student read them to me in order as I wrote students’ names on a blank seating chart. I would then allow students to silently raise their hands to request to move closer to the front if they had bad eyesight and had been placed too far back.

This whole process took about five minutes, and created a visibly randomized seating chart with student input. I found it was generally best to do this at the end of class and then have the new seating chart posted as students came in the next day.

Good for Teachers: How Random Groupings are Actually the Greatest Thing Ever from a Selfish Point of View

I hope that I’ve convinced you that random groupings are both good for your students and logistically feasible. But now for the selfish part: they will make your life as a teacher significantly easier.

Creating seating charts randomly has freed up soooooo much time! I cannot even begin to describe how much time I wasted two years ago trying in vain to balance the delicate Rubik’s Cube of student personalities and abilities, only to have each new seating chart seem even worse than the previous one. By making my seating charts randomly, I essentially gave myself hours of extra time to devote to lesson planning and grading.

Additionally, students used to feel personally insulted if I made a new seating chart that separated them from their friends, and they would lobby incessantly for specific seating arrangements. When students get a new seat that they don’t like but understand that it arose from a visibly randomized process, they complain less and for a shorter amount of time.

I also think that using randomization has made me a better teacher. It’s a great reminder to view all students as having the potential to make meaningful contributions, and it helps me avoid deficit thinking. When I began using random groupings this past school year, I found myself expecting more from the students who struggled the most, and as a result, they rose to higher challenges. (Mostly. Ish. Depending on the kid. This is education after all; silver bullets don’t exist!)

On the opposite end of the spectrum, random groupings are a good reminder that we can’t always tell who is going to struggle with a given task and who is going to need support. I had a student in my Geometry class this past year who demonstrated very early on that she was incredibly strong with the procedural skill of solving algebraic equations and was also quite adept at correctly setting up equations from geometric situations. I therefore thought of this student as one of my “stronger” students. When we started working on proofs, a lot of kids needed support and feedback, and I found myself being spread quite thin around the room. I ended up not checking in on this student (or the group she was working with) because I thought that she was one of my highest flyers and would be fine without me. It wasn’t until I read her proofs that I saw she was grasping at straws trying to form a coherent and logical argument.

I had let my preconceived notions of this student’s intelligence get in the way of recognizing that she needed more guidance and support to complete the task at hand. Random groupings can be a helpful reminder that we can’t necessarily judge future success from prior achievement in a subject as complicated, disparate, and interconnected as mathematics.

Concluding Thoughts

If you’re not already using random groupings, I hope you’ll consider this for next school year. It has the advantage of being good for students’ conceptions of themselves and others in math class, and also making your life easier. Furthermore, this is a fairly easy and straightforward new strategy to implement.

If you already use random groups, what have your experiences been? Do you have other ways that you put students into groups randomly? Please share!

Will random groupings magically solve all status issues in your classroom? Of course not. But it is one powerful piece of the puzzle that can help all students recognize that they have valuable ideas to contribute to the class.

Thoughts? Questions? Concerns? Please let me know!