Math Hombre

All this month I'll be posting games from the Fall 2023 GAMES seminar at GVSU. This senior capstone was begun by Char Beckmann. See many of the games in this YouTube playlist. Many of the games completed in my seminar are in this playlist. In the seminar, we play lots of games and math games, the future teachers make a first video to promote a class math game that already exists, we develop a group game (a monster-themed middle school Desmos escape room and Math Heads, a number mystery game), and they develop a game of their own.

This post is sharing Corrina Campau's games - she was also the lead Desmos engineer on the escape room!

Her first video was for Jenna Laib's Number Boxes. Really an all time great classroom math game, it was extra influential to this year's seminar. Like Jordan Burnham's game Boxzee.

Corrina's original game has an original deck of cards, which would have multiple uses, but is great in her Math Spoons (Cards and Rules). What follows the video is her story of making the game, and some thoughts on why to play games in math class and which games are effective.

The Story of Algebra Spoons

Whenever I take a class at GV I am always trying to see how I can use the class to become a more effective, engaging math instructor.  In thinking about what my course content entails I became enthralled with the idea of having students differentiate between different function families.  We study linear, quadratic, exponential and logarithmic functions and so this became my starting point.  I wanted a game that would allow students to think about all of the function families as a whole.  After playing some of the games in class I decided that one of the games that could work would be to design a game like SET where students must match cards based on different attributes.  I kept thinking about SET and how I felt when I played the game.  Although I like the game, I don’t always have fun playing it because I am not necessarily the fastest player when looking at 12 cards and trying to find matching ones.  John mentioned Spoons in class one day, and I thought that was a really great idea.  I have always enjoyed playing Spoons and so decided to roll with the idea.  Thus, Algebra Spoons was born.  I began to think of the number and type of cards needed.  I decided to use linear, quadratic, and exponential function families with 4 cards in a set and 4 of each function family giving me a total of 48 cards per deck.  I knew I needed to include graphs, stories, equations, and tables, but I wasn’t sure if I should choose a theme or not.  I decided to use stories that related to GV students and even chose some stories like they had modeled in class – like the equation of the water as it comes out of the drinking water fountain.  I hoped that the stories would appear somewhat familiar to them even if the story was new.  Once the stories were written then I needed to make sure that the graphs showed the important characteristics of each story so that students would be able to determine the graphs that matched the stories with relative ease.  I also examined the tables and made sure to include the portion of the table that made the most sense when trying to match the cards.  For some of the quadratic functions I used vertex form and for some I used standard form.  In retrospect, I wish I had included factored form as well.  But making these cards took a considerable amount of time and thought, and unfortunately when I thought about factored form it was too late to change.  Having finalized the front of the cards, I decided to make something on the back to make the cards more visually interesting.  Thus, the spoons motif was added.  Ten sets of cards were printed on card stock and printed out in color.  

When I played the game with two of my MTH 109 classes, I first had them sort the cards so they could become familiar with them.  After they had a chance to match all the cards, I then passed out the spoons, and they started playing the game.  The students had so much fun!  I was overjoyed to see how they embraced this game, and this was so much more fun than doing a standard final exam review.  I would encourage all teachers to play this game as it really gives students a fun, enjoyable, and deep conceptual learning of different function families.

Why Play Games in the Math Classroom and What Makes a Game Effective?

Research shows that Games Based Learning (GBL), either digital or non-digital, in education is now one of the major learning trends of the 21st century.   So, why are teachers playing more games in the classroom, and what makes a game effective as a learning tool?  

First, for a game to be effective, a game needs to meet learning targets.  Once an instructor has decided upon what the game should help students learn then a game can be found or created that allows students to meet those goals.  In thinking about LeBlanc’s Taxonomy of Game Pleasures, we can understand the eight “primary pleasures” that arise from playing games and see how these game pleasures help to make games more enjoyable and when games are more enjoyable, they are often more effective.  

A game that requires fewer materials is typically better because there is less set-up and typically less time spent learning to play the game.  Having fewer rules or simplifying the rules is also important so students are not overwhelmed before they begin playing the game.  Games where students’ interaction with other players affects their play attract different types of players and can make the game more fun to play for all players.  A game that generates different situations or has the element of surprise can be more exciting and make players want to keep playing the game, and a game where an early advantage always causes a player to win is not as fun or effective as a game that allows all players an equal chance of winning.  

When I play games in my classroom, I look for games that yield the best results in the least amount of time.  I ask myself – what game can I play that allows students to understand, apply, analyze, evaluate, and create?  Games always make learning fun and interactive, so when I tell students we are going to play a game there is always some excitement in the atmosphere.  Games, if set up correctly, can provide low risk competition and meet learning targets in a manner that is more motivating for students.  The structure of the game allows students to engage in problem solving in a way which is typically more enjoyable and more effective.  Games create a more engaging learning environment and cause more students to pay attention to the teacher’s lessons, and they help students understand the concepts and retain the material better.  Games are also able to reach students of all levels and function as confidence builders.  In addition, game play encourages and deepens strategic mathematical thinking.  Playing games in the classroom also allows educators to easily include active learning in the classroom.  

Spending time creating games or selecting games that are already made is time well spent and worthwhile for students and a very effective way of presenting concepts, creating deep thinking, and motivating and encouraging students, and GBL should be included in every classroom.

Reference

Hui HB, Mahmud MS. Influence of game-based learning in mathematics education on the students' cognitive and affective ___domain: A systematic review. Front Psychol. 2023;14:1105806. Published 2023 Mar 28. doi:10.3389/fpsyg.2023.11058

All this month I'll be posting games from the Fall 2023 GAMES seminar at GVSU. This senior capstone was begun by Char Beckmann. See many of the games in this YouTube playlist. Many of the games completed in my seminar are in this playlist. In the seminar, we play lots of games and math games, the future teachers make a first video to promote a class math game that already exists, we develop a group game (a monster-themed middle school Desmos escape room and Math Heads, a number mystery game), and they develop a game of their own.

Jordan Burnham selected Close to Zero, and integer addition game for her first video. Handout and original blogpost.

Jordan's original game Boxzee crosses one of my favorite classroom games, Number Boxes by Jenna Laib, with the classic Yahtzee. What follows is Jordan's explanation of the game and thoughts on why play games in math class.

Boxzee

When I was first brainstorming games, I had absolutely no idea what kind of game I wanted to make. It wasn’t until one day when I was sitting on my bedroom floor that the starting ideas of Boxzee came to me.

Originally I imagined the game to have more moving parts. I first had players each being dealt 4 cards. From there they would roll a dice twice to determine a specific operation they would be using (odds = subtract, evens = add). Then after finding out those operations you would choose 3 cards from your hand to find a largest total value for that specific round. I found that this became a little confusing and players wouldn’t necessarily be able to truly “compete” if all of their rounds operations were different than each other. If one player only rolled odd values then they would be predetermined to loose solely because the other players would have a better chance of having larger numbers if they rolled more even values. 

Moving on from here, I decided to instead come up with the number box sets. Rather than using the dice to determine operations I decided this was a more structured way that players could still affect the total value by the cards they put in without having so many moving parts. I first came up with the idea to have four different rounds. The players would both have 4 cards in their hands and needed 3 to fill into the number box sets. I also decided that they would both fill in the top box row, then move downward. After playing this a couple of times I realized it could be very common to tie. So then I chose to create a number box set that would be the final round and would use all of the cards in the players hand. I liked this much more. 

Then to incorporate more of a feel of Yahtzee, I decided that players should be able to substitute their cards into any of the top 4 number box sets of their choice in any order. This gives them more of a chance to use higher cards and lower cards when they have them for specific rows that those cards would be more valuable for each round. 

Some final touches were made after play testing with Professor Golden and my classmates. These included allowing players to chance any of the cards they have in their hand. I really enjoyed this change because it gives players more risk opportunities. The queen card was introduced as being a wild card during this time as well. I appreciated this idea because I feel like it allows players to more strategic and intentional about where they substitute certain card values into the number boxes. Finally I made a coupe of variations. I came originally came up with the addition and subtraction version of the game. I then decided to toy around with the idea of multiplication and division and made the multiplication and fractions versions.

I think that teachers should play this with their students because it makes basic operations more exciting. I think that allowing students to have so much control over placing values into expressions and solving these is something they will enjoy. I also believe that it allows students to grasp where they may rather place a larger value versus a smaller value. Since the goal is to have the largest total value for each number box set, it will look different for each set. Placing a 9 in the same value that you place a 1 or a 0 has much different affects. 

I believe that this game can be adapted and used for so many reasons. The framework of the rules and rounds is something that creates such a great skeleton to then use with multiple content areas. I have thought about creating a Binomial Boxzee and think that this would be a great next step as well.

Why Play Math Games?

Math can sometimes be a very intimidating subject area for some students. Because of this, I believe that it is important to keep the classroom environment exciting and reassuring that every student has the ability to be a mathematician no matter what level of skills they may think they have. To do this, incorporating games into the classroom can be very beneficial.

Math games are a great resource for teachers to use to introduce and practice content. When playing games in the classroom in allows students to learn content in a more relaxed environment. This allows students to feel less pressure when making mistakes. This is important because students will be more likely to try and continue trying even after making mistakes which will help them master content areas. Similarly, playing these games allows students to build their strategic and problem solving skills. They want to perform their best and win, so they are able to develop strategies that can help them succeed throughout the game.

I also believe math games are beneficial in the classroom because they can be interactive. This allows students to also help each other in teaching the math skills. By not only performing the skills needed for the game, but also using their skills to help teach their classmates they develop a deeper understanding for the content. 

Finally, playing math games allow students to build a love of math. When students are engaged and having fun playing these games, this is when they will be doing the most learning. Exposing students to games that are centered around math subjects, they will be able to see that math is more than just what they may be learning to compute in class.

Now seeing some of the benefits associated with math games, it is also important to identify what makes a good game. One of the biggest things that I believe makes a good math game is having minimal time constraints. When students are practicing their math skills within a certain amount of time some may start to feel discouraged if they are not as fast as their other classmates. With this in mind, choosing games that give students the same opportunity to be successful at completing the game whether they are fast thinkers or need some extra time is very important. 

I also believe that a good math game allows for catch up. This means that even if a student is “down” in a game or is behind, there are aspects of the game that allow the players to quickly catch up and still have an opportunity to win. Since some students may not succeed right away, offering an opportunity for them to catch up and still have a chance to win this makes the game more fun for all players. This also makes students more likely to want to play and in turn allows them to practice and learn without the fear of losing. 

In conclusion, math games being incorporated into the classroom that I urge many educators to try. Not only to practice content, but also to help build up students’ love for the subject and confidence in their own skills.

All this month I'll be posting games from the Fall 2023 GAMES seminar at GVSU. This senior capstone was begun by Char Beckmann. See many of the games in this YouTube playlist. Many of the games completed in my seminar are in this playlist. In the seminar, we play lots of games and math games, the future teachers make a first video to promote a class math game that already exists, we develop a group game (a monster-themed middle school Desmos escape room and Math Heads, a number mystery game), and they develop a game of their own.

Leah Barber selected Greater Than for her first video, an integer multiplication game. (Handout)

Leah's original math game is a great spin on Uno called Geo. Cards & Handout. What follows is Leah's explanation of the game and thoughts on why play games in math class.

How Geo Came To Be

My idea of Geo came from Professor Golden mentioning Uno during one of our classes. I thought that Uno already included a lot of good components of a math game. This included number recognition, being able to categorize and identify different elements of a category, problem solving, catch-up factor, surprise elements,  etc. Since Uno already had strong components of a math game I decided to create a game that was based on it. At the start I was thinking about doing a game that had to do with geometry so I began thinking of ways students could categorize shapes. Initially I didn’t know if I wanted students to create their own connections between different shapes, so I considered doing a Guess Who style game. However, after trying out a draft version of it I thought Geo would not only be less complicated but it would still offer students the opportunity to practice identifying shapes based on properties and computing area. From here I decided that instead of colors and numbers, like regular Uno, the two categories would be shape and area. Then I went through and made a rough draft of the game that iterated through many revisions until I was happy with its final form. Throughout these iterations I changed things like what the special action cards would be, what shapes would be included, how many cards would be included, what the shapes looked like, and what information I would include on the individual shape cards. 

Why Teachers Should Play GEO:

There are many reasons why teachers should play Geo with their students. Geo covers different Michigan Math Standards such as: CCSM. 6G.1: Find the area of right triangles, other triangles, special quadrilaterals, and polygons and CCSM. 5G: Classify two-dimensional figures into categories based on their properties. Beyond letting students practice finding the area of different polygons and identifying shapes by their properties, Geo helps students practice integer multiplication, reason mathematically, and build problem solving skills. Due to Geo being a competitive game, students often become engaged doing math, checking the work of other students, and reasoning mathematically in order to win. This is another reason why teachers should play Geo with their students. Geo allows students to engage in math in a fun, interactive way. Many learners have anxiety around math or think that it is boring, hard, irrelevant, etc. Geo is a way to get learners engaged and have fun while doing math. 

Other Uses: 

The materials of Geo could be used outside of playing the game. Teachers could use the cards to create a memory style game where students try to match different areas or shapes. Other uses include going through the cards as examples of computing areas with students. Teachers could also play a Polygon Capture style game where students identify all the shapes they can that fit under the different command cards. Following playing Geo teachers could have a discussion with students about what they noticed or wondered when playing the game. This could start a good dialogue about different shape properties, how different shapes are related or different, definitions of shapes, etc. They could also have students discuss strategies and problem solving skills they used to try to win. 

Why Play Math Games? 

There are many reasons to play games in the math classroom. To start, math games allow students to engage in mathematics in a fun, interactive way. Students often think that math is boring, too analytical, irrelevant, etc. By playing games in the classroom students can experience math in a way that it often isn't presented to them. This can also dispel anxieties many students experience with math. Due to previous bad experiences with math, whether it be a harsh teacher, tough material, or overwhelming course load, students can develop anxiety surrounding math. This can also affect how students think of themselves. Bad experiences with math that cause students to do poorly can lead to them thinking they are dumb or not a “math person”. By involving games into lessons students can create positive experiences with math and start to dispel any anxiety or negative thoughts surrounding math.

Math games also allow students multiple entry points to engage in math. Oftentimes this idea of not being a “math person” is due to inaccessible lessons. By including a math game in a lesson you can create many opportunities for students to participate in math. A good math game includes some aspect of luck, strategy, catch up, or surprise that allow students who are struggling to still succeed. By creating accessible activities for students they can start to think of themselves as someone who is capable of doing math. 

Getting students to reason and express themselves mathematically can be challenging. Often students don’t want to participate in discussions in math class due to a multitude of reasons. Including a math game however is a great way to get students talking about math. Due to the competitive nature of games students are more likely to reason, argue, make conjectures, and express mathematical ideas in order to win. This creates a great dialogue where students can think through material covered in class together and come to conclusions on their own. By doing this students will continue to grow their self concept as a mathematician and be able to better communicate mathematical ideas. Math games also help students build problem solving skills. A good math game has players interacting with each other and constantly trying to figure out their next move. As stated before a good math game also includes strategy. These elements allow students to build their problem solving skills as they identify what they need to do to win, how they are going to do that, executing their plan, assessing how it worked, and what they will do next time. 

Lastly, including math games in the classroom is a great idea because it is a great way to introduce, explore, or practice mathematical concepts. Teachers or parents may feel that including a game in a lesson will distract students from their learning. This however is not the case. Math games are not something that is just filler. Instead math games are great ways to introduce new concepts by allowing students to get familiar or explore with new ideas in a low stakes, fun environment. Math games can also be used to help students review a concept they already learned by applying their knowledge in a new way. 

 So what have I been up to?

The biggest project this year has been working on Teaching Like Ted Lasso. 95% or more is Dave Coffey - inspiration, planning, and production. And I get to play along! There's a YouTube channel and the home for all the audio. We get to talk to so many interesting researchers and teachers. 

One of my favorite interviews this year was Nicora Placa:

I also get to commute with my son Xavier, a first year high school art teacher, and have an occasional low-tech, barely produced podcast with him, Background Noise. It's a little art education, a little math education, and mostly just talking teaching.

Speaking of teaching, after years of a highly variable teaching load, it has settled into a couple elementary math teacher education courses, a high school math education course, a seminar where a smaller group of students develop math games, and a math history capstone. One of the elementary courses is actually in an elementary school. The future teachers get to actually teach kids every class day, feedback from great teachers, observation by me and another student (when I can get one). The framework my colleague Esther developed for this (with others) is mediated field experience. We spoke about it at a local math teacher education conference. Here's the handout. The course page for the class is bit.ly/226-W23, and the lessons I wrote for the teaching (with a wide range of influences, colleagues, articles, curricula...) are here. 

There will soon (fingers crossed) be a series of blogposts with this year's games. We actually wound up with two seminars of five each.  Good stuff from elementary to secondary. One group developed a middle school Desmos Escape Room with a spooky monster theme. As a teaser, here's the video for one of our group games, Math Heads, which has been tested with 6th grade middle school students, algebra students and college math majors. Ryan Brummel made this video. Here's the handout with the rules and a form to support players, bit.ly/MathHeads. 

I continue to futz about with math/art. 

From one, two, three, four. The Tumblr posts have variations and links to the GeoGebra for generating them.

I cartoon when I have time or am challenged like in Mathober. They're pretty geeky. Some are college + math and some are elementary.

 Do you want to host the 13^2 Playful Math carnival in October? A month that had a Friday the 13th? 

Yes, please. Should have been on 10/13 instead of 10/31 but... apologies.

169 is a palindrome in two number bases less than 16. Which do you suppose?

It's the last square in the Pell sequence, which are connected to approximations of π. What numerator n makes n/129 an approximation of π?

Puzzling

Content

Humor

Fashion

Last Stop

Last but not least, two playful bits from my students! Corinna, Leah, Jordan, Kacy and Jill made a Spooky Monster Escape Room in Desmos Activities. Ryan, Keri, Alex, Anna, and Emma have a new headbandz inspired math game for grades 5 and up called Math Heads. And by up, we mean up to college math majors!

At the home of the Playful Math Carnival, you can find previous, like 168 at find your factors, or connect to host yourself. I'd highly recommend it! Find the next one, Nov/Dec at the Fairy Math Mother. Should be magical.

This is my stop! Hope you had fun.

P.S. This will get you to go. Ed Southall asked AI to make images of people enjoying math...

#classroommath #mtechat one of the main objectives with preservice teachers is to work on the practice of eliciting student thinking. What advice do you have for them? How did you get better at it? What are you working on now?

Lani Horn had a quick, impactful response (bsky). "I find that the work of eliciting needs to be followed with some work on listening and interpreting. i have seen some folks stop at just eliciting, and it becomes "what do you think? what do you think?" without any connections built."

Elizabeth continued: "OMG yes. Learning to listen is a challenge for many pre-service & new teachers, and I often wonder if this is because they feel so rushed/anxious themselves.

Listen, swallow, take a breath -- just because a student has spoken in response to a prompt doesn't mean I've heard them yet.

Another thought -- could we also stipulate that asking a clarifying question can also be also an essential part of teacher listening?"

Shelby Strong also responded to Lani: "YES. It's not enough just to hear a bunch of different ideas; what is similar and different about those ideas?"

Learners are definitely interested when they know you are interested. How many times have they had a teacher gloss over their answer while really just looking for what they want to hear. "Tell me more" is a phrase I try to use a lot.

Mike Steele said: "When you catch yourself thinking about what to say next when students are talking… don’t. Focus on listening. Take a beat before speaking."

Nick Smith noted: "I like the other replies here and I'll add, "Never say anything a student can say." 

I think too often I'm doing the thinking for them. The less I talk, the more I hear their thinking instead of my own." 

Good indicator. Especially tough as a novice, maybe, when you have to think more about what's next.

Shelby also said: "Get students to turn and talk and prep them that you are going to ask them to share what their partner said. It lowers the stakes because it's just one other person listening to their ideas, and it takes the pressure off of sharing their own ideas."

Karen Campe responded: "Oooh I like that... encourages careful listening to your partner!"

Coutney Flessner added: "I LOVE using this strategy. I also don’t have students share their work. They already know it! The class analyzes it and we ask the author if we missed anything. Kids are significantly more engaged with each other and math with both these instructional routines. Ryan Flessner introduced both to me!"

Your students who always talk will still try to say what they said, but I think this is a moment for them to hear what others see them as saying. 

Karen was also thinking about wait time: "An important step is to give Ss individual think time before talking to partners/groups or sharing out to class -- the T shouldn't solicit any responses until that essential time has happened. 

That way, everyone engages, & no priority to fast thinkers or those who can do it in their head. 

Then you can elicit their thinking.

I was so bad at wait time early in my career that I had to actual count on my fingers (behind my back) to be sure I gave thinking time before discussing. 

Tierney Kennedy also has a teacher hack: "My advice: take a drink bottle with you to groups. When kids ask a question or when you ask them one, take a mouthful. It builds in an automatic thinking moment. Plus sometimes they end up answering their own question." 

Trey Goesh thinking similarly: "I like to have students take 60 seconds to record their ideas silently before having them talk to a partner.

You can feel the tension ratcheting up as they collect the ideas they want to share."

Wait time is such an amazing tool. Really lets learners know you are really asking, not just checking 'any questions.' 

Dee Crescitelli has the objective in mind: "Listen to student thinking with an ear for the mathematical goal of the lesson… we should be thinking about the math story the classroom discussion is telling. How do student responses & representations connect to tell that story?"

Peg Cagle also thinking about what you're asking: "Make sure that you ask about their ideas/thinking not their “answer”, and make sure they know you are genuinely curious about & interested in what they tell you. Answers w/o thinking-worthless. Ideas w/o answers, immensely valuable…& to everyone in the room!" 

Tara Maynard: "Try to always find a positive in their thinking and then find the misconception. Ask students to write, draw, sketch how they found their solution, not just verbal interaction. Always trying to provide feedback that is helpful yet doesn’t take hours." 

This might violate Mike's advice to keep your mind where it's at, but I do this a lot, thinking about the summary/reflection for the lesson. I probably open floor question too much to summarize, but if there is an idea missing, I like knowing whom to call. 

Arika Byman said: "Model genuine curiosity every chance you get. Provide sentence/question stems to help students organize and articulate their thinking. Be patient and persistent!" 

The stems idea is another idea of which I don't do enough.  The curiosity is crucial. There are so many things I genuinely want to know about learner thinking, why not ask?

Another few people were thinking about the math about which you're asking:

Rose said: "# talks and visual patterns tell Ss you want to know what they 💭 esp bc everyone has dif ideas. Shifted my mindset too!

Working on: design small group tasks/materials that encourage Ss to share their ideas w/each other. Generally ⬆️ S talk. S talk = window into their thinking."

Sian Zelbo said: "One aspect of eliciting student thinking is asking questions that are open-ended enough that you get a range of answers.  If you ask something that is essentially procedural students can't share their thinking bc they have none."

Lastly, is sharing thinking a part of your class culture?

Susan Russo said: "One thing that helps is to model your own thought process out loud. Not: this is what I’m doing but: First I notice this, and that leads me to think it might be good to go this way so I’ll try that and see where it leads. But now I wonder… 

If you are also sharing genuine thinking it is a great model for when you ask for theirs. 

What did you notice about these responses? What would you add or emphasize? There's a comment section below just waiting for you.

I'm really grateful to all who responded. Whatever media site we wind up on, I'll be there, because talking to teachers is the best way to teach better.

OK, a book, Smarter Together, which, appropriately, was collaborative itself. 

Dave Coffey and I interviewed her for Teaching Like Ted Lasso, if you'd like to hear her for yourself.

She's leading a professional development for faculty in CI here in the math department. Small group, supported by the U and by our state AMTE chapter.

There's a few texts people have for it. Everyone has Designing Groupwork by Cohen and Lotan, 3rd edition of the seminal text. The book presents the case for why group work is helpful, and examines why it so often is not helpful in practice.

Day 1

Introductions. Why are we here?

One feature of Joy's classroom is a smartness wall.  We were each asked to write one way we are smart in math. Learners add to it throughout the year or course. Lisa Hawley, another new colleague, does one at the beginning and one at the end for them to compare. She noted that they often shift from content claims to process claims, and how many more ways they think there are to be smart at the end. The decision to use 'smart', which is loaded, is that they do already have ideas about that, and using it gives us an opportunity to intervene.

Community Agreement. What do we need to have a safe classroom, where we are free to take risks?

Groupwork norms: 

• quick start, 
• no one is done until everyone understands (each step!), 
• work the whole time, (trying this year)
• call the instructor for group questions only, 
• middle space - there was a table whiteboard in the middle of the table which we were encouraged to keep open and collaborative. 

Groupworthy tasks require multiple abilities and can't be done alone. "If it can be done alone, it will be." We did an activity with instructions for folding an open-top box (not quite this one, a little simpler) from squares of different sizes and then measured volume with beans and cubes, then had to predict the volume of a different size box. There were two copies of the task instructions, one copy of the origami instructions, a few beans, a few cubes. Plenty of interest even for mathematicians and math educators to get engaged and want to keep going. 

Afterwards, we discussed what we noticed about the task. There was a lot to notice. We really could not have done it alone in the time allotted, and there was meaningful work for everyone.

Working on the task, we had roles. I have not been able to get roles to work for me before, but I've really been thinking about how I haven't pushed for them, and never really done anything to teach how to do them. These feel less made up than some other roles, and, I think, are really another implementation of the norms.

Roles

• Team Captain - fills in missing roles, moves people along
• Resource Monitor  - call instructor, distribute supplies 
• Facilitator - task gets read, everyone understands task
• Recorder/Reporter

Individual and group accountability. Joy often follows an activity with the groups sharing results, and learners writing an individual reflection, responding to one or more prompts. In addition, while we were working, Joy did a "Participation Quiz" - teacher notes in a public space on what they observed groups doing. Great at beginning of course and when group work starts declining in quality/evidencing the norms. 

Status