Sunday, February 26, 2017

What's your next move?

Our presentation from Math in Action 2017

Games are an effective way to engage students in learning. Participants will experience how to support the development of pre-adolescent mathematicians through purposeful play. [Grades 3-5]

Consider what you think it means to effectively teach mathematics. Now take the Simile Survey provided below. What are the characteristics of your simile selection that relate to good mathematics teaching?
A while back, Dr. Doug Fisher introduced me to another teaching simile: Teaching is like being an expert commentator. During the lesson, the teacher highlights important aspects of the "routine" that the student might otherwise overlook. In cases where the action moves too quick, the teacher might need to "rewind and show it in slow motion" in order to clarify some move. Here is an example from the 2016 U.S. Olympic Trials that demonstrates these characteristics. So what does this look like in math class?

Imagine we are in a 3rd-grade class playing BINGO. If the students are fluent in reading number symbols, there's not much to the game. So let's break it - add another dimension by allowing players to decompose the number that's called.
If you were in a 5th-grade class, they might ask why they can't decompose the called number into more than two addends ... or use operations other than addition. Then the challenge might be, "Can I get a BINGO with just one number called?"

After (or during the game), what sorts of things would you want the students to notice? What would you highlight and maybe have to slow down? It depends on the game and our players.
  • If I was playing the regular game of BINGO with young kids still struggling with number recognition, I might be sure to call "thirteen" and highlight ways to tell the difference between 13 and 31.
  • If we are decomposing, I might want kids to recognize that 38 can be decomposed into 30+8 or 31+7 and highlight the concept of compensation.
  • For 5th graders, I might show how "thirteen" can be written as 13+8/(9-7)-4 and highlight an important property of zero in our number system. [To demonstrate another important property of zero, ask students if they could cover the entire board if "thirteen" was called.]

It is important that teachers have the opportunity to play games before using them with their students. That way the teachers can consider possible modifications (ways to "break" the game) that would meet their students' needs. It also gives them experience playing the games that can lead to insights into important mathematical aspects encountered while playing that the teachers might want to highlight for their students.

Game Centers 
Number and Operations - Fractions 
Grades 3-5 

Other Game Resources

After playing the games, we reflect on our experiences using Math Teacher Chair:
  • What games did you play?
  • So what mathematical ideas would you want to highlight?
  • Now what would you do to break the game or slow down the play so students would benefit mathematically from playing?

Thanks for your participation. You can reach us using the following contact information. 

"Rocket science is child's play compared to understanding child's play."

~ Unknown

If you are attending the upcoming 2017 NCTM Annual Meeting and Exposition in San Antonio, we will be presenting this session again. 
We promise it will be better next time thanks to the feedback you've provided on your session evaluations (or in the comments below).

Friday, February 10, 2017

Can we have five more minutes?

Excuse the pun, but it was like clockwork. I would assign a group project (something like making a concept map), give them 20 minutes, and set the classroom timer. The timer would go off and nearly all the groups would ask for more time - usually about five minutes. It got to the point where I would just add five minutes into the plan but then they'd still want more time. 

It wasn't as if they hadn't been working the entire time; they were just really invested in getting it perfect. Even the smallest detail, like the use of colors, had to be debated. I explained that these details didn't matter as much as the connections they were making, but somewhere they got the notion that the presentation of their ideas was paramount.

Then I was introduced to Design Thinking and the principles of bias to action and prototyping to a solution. I decided to apply these principles to the problem of students attempting to create the perfect poster. I went back to giving groups only twenty minutes but I broke it up into smaller intervals - each with a defined purpose.

First three minutes: organize the concepts in a way that reflects how you see them related and glue them on the paper.

I knew if I simply moved on to the next phase nothing would change; they would get stuck in the same old debates. Therefore, I had the groups rotate clockwise around the room. They were now looking at another group's vision of how the concepts might be arranged. 

Next three minutes: consider the previous group's arrangement, talk through what the arrangement might represent, and add connections (nothing more).

During this time, I kept reminding them that the previous group had only spent three minutes coming up with the configuration of concepts upon which they were working. There was nothing they could do to ruin it. This was simply a prototype and they had limited time to add their contributions. After three minutes, they rotated clockwise to a new group's poster.

Third interval of three minutes: consider the work of the previous groups, talk through what the work represents, and add descriptions to the connections.

I reminded them that only six minutes of work had gone into poster. The previous groups didn't really have anything invested in what was already done. So they shouldn't worry about doing anything that might change the poster. I even encouraged them to add new connections if they thought it made sense. After three minutes, they rotated clockwise to another new poster.

Fourth, fifth, and sixth intervals of three minutes: repeated the previous intervals - add more concepts, add more connections, and add more descriptions.

Each time, I repeated the mantra: "The other groups only spent three minutes on the poster. You can't ruin it. Just get to work." 

After 18 minutes, each group returned to their original poster. There were some audible gasps and laughs. Rarely had the poster turned out as expected but each group could infer the intent behind the decisions other groups had made. They spent the last two minutes creating an artist statement for their concept map - something they thought an observer ought to notice.

None of the groups asked for more time. They were satisfied that the posters were prototypes - works in progress that allowed viewers to add their own perspective. We used the "extra" five minutes to do a gallery walk and see how our work turned out.

Thursday, December 1, 2016

What's the deal?

Over the past two years, #M323 teacher-leaders have designed several centers associated with Common Core State Standard 6.SPA.3. Below is one of my favorites, which I am attempting to revise for my #M221 pre-service teachers. Any feedback you are willing to provide would be appreciated.

Data Set Deal
  • Remove all the face cards and Jokers from a deck of cards;
  • Deal out five cards, face down, to each player;
  • Turn over exactly three cards;
  • Determine the mode (color), median (number), and range (number) of the three cards;
  • Other players check to see that your answers are correct [1 point per correct answer];
  • Predict the mode (color), median (number), and range (number) of all five cards;
  • Turn over another card;
  • Determine the mode (color), median (number), and range (number) of the four cards;
  • Other players check to see that your answers are correct [1 point per correct answer];
  • Predict the mode (color), median (number), and range (number) of all five cards;
  • Turn over the last card;
  • Determine the mode (color), median (number), and range (number) of all five cards;
  • Other players check to see that your answers are correct [1 point per correct answer];
  • Check to see which of your predictions were correct [2 points per correct answer]; and
  • The winner is the first one to 21 points.

Score Sheet
Please leave any questions or suggestions in the comments. Thanks!

Friday, November 25, 2016

We're really going to get to do it, aren't we?

One of the projects the pre-service elementary teachers (math majors) that I teach worked on this semester was designing a 4th-grade statistics lesson to address 4.MD.B.4.

The teachers went through a design cycle to make the lesson. They ... 

  • Built empathy by observing two fourth-grade classes;
  • Defined the problem by developing a User/Needs/Insight statement;
  • Brainstormed a variety of possible activities;
  • Developed a prototype SAFARI Lesson;
  • Tested the lesson by sharing it with the classroom teacher; and
  • Revised it based on her feedback.
Three teachers co-taught the lesson in two different fourth-grade STEM classes. They made adjustment between the lessons based on what worked and what didn't. Afterwards, they reflected on the experience and shared the lesson with me. The lesson was so cool, I decided to make a few adjustments and use it in another class for pre-service elementary teachers (mostly non-math majors) that I teach. Here is the SAFARI Lesson that I taught.

Schema Activation - Prediction
Directions: "You have two sticky notes. On the green sticky, I want you to predict the number of seconds you think it would take you to write the alphabet from A to Z. On the purple sticky, I want you to predict how long it would take you to write the alphabet in reverse order from Z to A. You have a quarter of a minute. Go!"

Focus - 5.MD.B.2
Share lesson target: "We are going to make line plots to display data sets of measurements in fractions of a unit."

[Anticipated learner responses are in brackets.]

"Who thinks they can write the alphabet forward the fastest? [13 seconds or 2 letters per second] Who thinks they will take the most time to write the alphabet forward? [52 seconds or 1 letter every 2 seconds] Alright, let's get up and stand in order from fastest predicted time to slowest predicted time."

Learners order themselves

"As I listened in, it became apparent that several of you made similar predictions. It would be interesting to see how the predictions cluster. But we could potentially have a lot of unique guesses. In order to gather those guesses, let's round our predictions to the nearest quarter-of-a-minute. For example, Sam guessed 20 seconds forward and 55 seconds backwards. He would round to 1/4 of a minute for forward and one minute, four-fourths, backwards. Work with your neighbors to round your predictions to the nearest quarter-of-a-minute and then post them on the board - forward at the front and backwards at the back."

Learners post rounded predictions

"What do you notice about the data sets?" [The writing in reverse predictions are "higher" and more spread out than the forward predictions.] 

"Why?" [We are familiar with writing the alphabet forwards so we think we can do it faster and know more what to expect.]

Activity - Writing the Alphabet in Reverse Order

Directions: "I am going to give you three pieces of paper."
At this point in my lesson, one of the pre-service teachers asked, "We're really going to get to do it, aren't we? We're really going to find out how long it takes us to write the alphabet from Z to A? Is it weird that I am so excited about this?" I reassured her that it wasn't weird - that my other pre-service teachers had designed a pretty cool lesson.

Directions continued: "You have a choice. On the yellow paper, you may write the alphabet forward on one side and use it to help you to write it from Z to A on the other side. You'll see the second sheet has the alphabet already on the back in the form of classic blocks, like the ones my grandson plays with. If you choose that one, you will incur a 1/2 minute penalty, which means you will add 30 seconds to your time. The last piece is simply scrap paper; use it if you want to try to write the alphabet from Z to A without any other support.

"A few more things: 

  • You must start at Z and write the letters in reverse order to A. You can't cheat and start at A on the right-side of your paper. 
  • The letters must be legible. Your table-mates will decide if they can read your letters, and you will earn a 5 second penalty for each letter they can't read.
  • When you finish, check the timer on the front board, record your time, and round it to the nearest quarter-of-a-minute.
At this point, a student rose his hand to ask a question. The girl who was so excited blurted out, "I just want to get started!" The other student asked if the letters had to be upper or lower case. I said it didn't matter to me.

Set the online stopwatch and say, "Go!"

When everyone is finish, have learners trade papers check letters for legibility.

Reflection - Noticing and Naming
Directions: "If you used the yellow paper (wrote A to Z on the back), write your result, to the nearest quarter-of-a-minute, on the yellow sticky note. If you used the blocks, and added 30 seconds to your time, write your rounded result on the blue sticky note. If you did it without any support, write your rounded result on the pink sticky note. Your rounded results go on the line plot on the back board underneath your predictions."

"What do you notice?" [Look for opportunities to introduce terminology related to measures of center and spread, like median, mode, and range]

I want to ... - Choice
Directions: "What do you want to do now? Here are some ideas:
  • Try it again using a different level of support and add it to the line plot;
  • See if there is a difference between writing in upper and lower case;
  • Try it forward and compare it with your prediction;
  • Gather more data from your friends and family over Thanksgiving;
  • Consider other activities that ask people to do familiar things in unfamiliar ways and what the data might show; or
  • Come up with your own idea to extend your learning."

Wednesday, November 23, 2016

What's the hurry?

The moment you (some of you) have been waiting for [insert drumroll] ... the Carousel Lesson Design process. Previously, we learned about SAFARI lessons and prototyping. In this post, I share how to encourage teachers to embrace creativity and connectivity while collaborating on a week long unit design.

First, you need some ingredients. It's best if you have: 
Investigations Curriculum

  • 5 willing teachers;
  • 1 set of targets;
  • 1 rich curriculum;
  • 5 pieces of easel paper;
  • Various scented (optional), colored markers;
  • Multiple sticky notes;
  • 1 lesson design framework; and
  • 1 timer
Each teacher is assigned one of five sequential lessons and given 5 minutes (no more, no less) to look through the lesson in order to determine what is important.  At the end of this time, they use another 2 minutes to set up the SAFARI lesson framework on their easel paper and write down some of the most important ideas from the lesson they were assigned.

After 2 minutes the teachers rotate (like a Carousel) to the next lesson. Day 1 goes to Day 2 ... and Day 5 goes to Day 1. They use what they know from their own lesson and the important points the previous teacher wrote down to inform them about the lesson. They also have exactly 2 minutes to add to the lesson. I am constantly reminding them, "Don't worry about designing it perfectly. You don't even know for sure what the lesson is about. Don't worry about offending the teacher that started the lesson. They spent all of 2 minutes on it so far."

The teachers aren't always crazy about the artificial time crunch. However, it helps to contribute to their creativity (think MacGyverMath) while ensuring progress. It keeps them from letting their perfectionism get in the way.

Rotate! And repeat ... three more times (Note: only two interactions shown below) at 2 minutes a piece.

The teachers are now back at their original lessons. They take 1 minute to read through what has been added to their initial ideas. The sticky notes are used to identify questions for the author or indicate likes (thumbs up). The teachers can also continue to add new ideas based on what they have seen in the other lessons. After 1 minute the teachers rotate again and again and again and again and again. At each lesson they answer questions, add stickies, or contribute ideas.

At the end, the teachers have spent 20 minutes to design a five-day unit.

Yes, there is still some work to do to sift out the essential elements of the lesson. These will be written in the SAFARI format and then shared with their peers for feedback. Finally, the lessons are tested out in the classroom. The next post is about one of those lessons.

Tuesday, November 22, 2016

Where are we in the SA F A R I?

I might have gotten a bit ahead of myself in the last post (or perhaps I am building suspense - you decide). Before I introduce you to the Carousel Lesson Design process, let me explain a bit more about the SAFARI prototypes. This should put the framework into a clearer context.

As I said, SAFARI is based on an instructional approach called the workshop model. SAFARI is an acronym for the components of the model [Schema Activation, Focus, Activity, Reflection, and "I want to ..."], and in Swahili it means journey. So in designing a lesson, we are thinking about it as a journey from the known to the new.

One thing that design thinking has shown me, is that this journey also reflects the flair and focus necessary for innovative thinking.
The Schema Activation begins with a flair. Sometimes referred to as the anticipatory set, it ought to be an open-ended invitation for everyone to join the journey. Next, the lesson quite literally Focuses the learners' attention on what to look for during the journey; this might be a "think aloud" in typical workshop lessons. Entering the Activity portion, the lesson once again flairs - allowing each learner room to roam. Here you might encounter what Dr. Jo Boaler refers to as a "low floor, high ceiling" task. After a set amount of time exploring, we refocus by Reflecting on what was important during the activity. We should not wait until everyone is finished before making time to consolidate our thinking. In fact, we want students to cry out for more time; it's what Ellin Keene calls fostering learning lust. Finally, we ask learners to consider what comes next by brainstorming "I want to ..." statements related to the lesson. Perhaps they want to spend more time exploring the task they didn't finish. This represents the final flair until tomorrow when the journey starts all over again.

After explaining the components to my teachers, I give them 10 minutes to develop three different SAFARI lessons related to some topic.
At the end of the 10 minutes, I ask the teachers to share their prototypes with a peer for feedback. The teachers are often resistant to share unfinished products because of the implicit need for perfection usually associated with typical lesson plans. I remind them, however, that they had, on average, three-and-a-third minutes on each prototype. So no one expects their lessons to be perfect.

Afterwards, the teachers express appreciation for the process. Not only have they outlined three possible lessons that they could use in their classrooms, but because the lessons were incomplete their peers were able to add innovative ideas in the blank-spaces. "I wouldn' have thought of doing it that way," one teacher admitted. She continued, "And if I had created a full-blown lesson plan, I don't think [the other teacher] would have been able to see and share this amazing idea."

It's a good reminder that the creative process is often about finding and cultivating the cracks that allow new ideas to grow. So how does this get any better? Here's what you've been waiting for - the Carousel Lesson Design ... in the next post.