Tuesday, September 12, 2017

What's your vision?

After the long winter of waiting, it was my first duty to go out lamenting. So after the first rain storm I began to get ready.
I recently heard Kent Dobson talk about this idea of "lamenting" - what is often thought of as a "vision quest." [I apologize in advance if I get some of the details wrong in this post. A lot of what I'm writing is a combination of my memory of and the connections made during his talk. Please let me know in the comments if anything needs correcting.] 

In the Lakota tradition, when a seeker comes of age, he or she goes off with an elder to "cry for a vision." After some preparation, the seeker is left alone to lament the current state of the community and seek answers in the form of a vision. From time to time, the elder looks in on the lamenting to advise and support the seeker. When the lamenting is complete, the seeker returns to the community and shares the vision. This is an important rite for the community because without new ideas, a community withers and dies.

As I begin a new year of supervising student teaching, I want this ritual to inform my work. I hope to play the role of the elder supporting coming-of-age teachers as they experience (and lament) the current circumstances in math education and seek new answers. I will listen to those answers and take them seriously because in many ways our profession is withering. And I will help the student teachers to share their visions with the larger math education community, so that these seekers might contribute to the development of our profession.

Thank you in advance for welcoming these seekers and helping to interpret and implement their visions.

Monday, June 5, 2017

What needs changing?

The Michigan Department of Education is considering changes to Michigan teacher certification and asking for feedback. Here is more information about their proposed certification structure.

Feedback is due today. (Sorry, I'm still a bit of a procrastinator.) However, if you consider yourself as having any stake in education, I encourage you to complete the survey, as soon as possible. It'll take maybe 45 minutes to watch the video and answer some questions.

For what it's worth, here's my response. (And, yes, I know I am biased.)
My issue with the structure being proposed is that it seems to presume that new teachers ought to be completely prepared upon certification. Even if we focused on giving specific grade-level certification, there is no way to address all the issues (textbooks, culture, community, resources, …) new teachers might encounter across the state (or country). Furthermore, this structure will limit the options available to teachers and potentially restrict administrators' ability to fill positions. I can imagine school districts asking for waivers to put PK-3 certified teachers in 4th grade because of a lack of options - a teacher that may have no training at that level.
I encourage that the state look at the Grand Valley State University teacher certification program as a model. We support the development of teacher-leaders in content areas by requiring even pre-service elementary teachers to get a subject major. Local districts regularly call us looking for recent majors because they know they will be content experts who can also integrate other subjects into their practice.
Also, the MDE needs to rethink professional development for inservice teachers. Because no teacher is truly finished learning, we must return to a robust professional development process that helps teachers build on current education experiences to deepen their pedagogical content knowledge in all discipline they might be teaching. Such a system is especially important now because we have so many new, inexperienced teachers entering the profession.
This professional development ought to be in partnership with accredited bodies responsible for initial teacher certification. These institutions are aware of the training new teachers bring to the profession and can provide meaningful experiences that can expand teachers’ current abilities. The experiences would be the result of the institutions and inservice teachers collaborating on areas needing improvement.
In my discipline, we often hold up Dr. Deborah Ball (former dean of the University of Michigan’s School of Education) as the model elementary math teacher. However, we fail to recognize that Dr. Ball rose to this level after identifying this as an area of weakness in her teaching – after being a certified, inservice teacher (see p. 9). She decided to do something about it by going back to school and learning more about the subject and its teaching. We need to allow all inservice teachers to follow the path from awareness to adjustment without fear of being labeled unprepared or ineffective. 
While teacher preparation institution must make changes to better prepare teacher-leaders, teacher certification is not the primary problem. A lack of opportunities for meaningful professional development is the issue. Changing teacher certification to try to address a broken inservice support system focuses our efforts in the wrong direction and may do further damage to education in Michigan.
Thank you, in advance, for your attention to this issue.

Tuesday, May 9, 2017

Wanna Play?

Grand Valley's College of Liberal Arts and Sciences has a policy that all courses must meet and have a culminating experience during finals week. Typically, I try to do something other than a traditional exam during these meetings. Most of my students are preservice teachers, and I want to offer them an alternative way to "show what they know" and reflect on the semester; this often entails presentations. But this year we decided to throw a party.

I got the idea when I attended a session at the NCTM 2017 Annual Meeting and Exposition that was led by Kassia Omohundro Wedekind and Mary Beth Dillane - "We are Mathematicians": Building Mathematical Communities Based in Sense Making, Agency, and Joy. During the session, they talked about kids at their school hosting a math party for their peer, teachers, and parents. At the party, the kids shared some of their favorite math activities. I decided this would be a great way to wrap up the semester.

We started the celebration with a popular party game: The Marshmallow Challenge.

Then the pre-service elementary teachers started developing their Math Teaching Vision Boards. I got the idea from this podcast that discusses the role instructional vision has on math teachers' instructional practice.

After about 20 minutes, we were ready to share our visions. We didn't have peers, teachers, or parents at our party, so we set up a series of viewing venues arranged by group.

The sharing looked a like this:

At the end of the party, the preservice teachers gave me some feedback. One said, "That was 2 hours of reflection disguised as fun."

Another complained that they didn't get to go to the viewing parties of their table-mates. I told them that was too bad but maybe they could connect with those peers after class to talk about their visions. Then I wondered out loud, "Do you think I did that on purpose?"

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."