Friday, April 18, 2014

Do you have a boring worksheet that you want to make more interesting?

Yesterday, I shared a worksheet I was using in my math course for preservice elementary teachers on Twitter. It got enough of a positive response that I thought I would share it here with a bit more context. Here is the Tweet:

I made the point that this combined two worksheets. The original worksheet came from This one reminded a lot of the future teachers of worksheets they did in elementary school. Some of the teachers had bad memories about those times. I told them they were not alone. A lot of students become disenchanted with mathematics once they encounter the way we teach fractions - rules without reasons. 

We also talked about how pointless it seemed to do all the problems. How much practice did they really need? How much proof did the teacher need in order to know whether the kids could follow the procedure? I shared (confessions of a bad math teacher) that sometimes I might only assign the odds or evens. Still, the only choice I was offering students was the choice to do it or not do it. And many chose the latter.

Fortunately, I learned from Brian Cambourne the importance of providing learners with choice.
Learners need to make their own decisions about when, how, and what "bits" to learn in any learning task. Learners who lose the ability to make decisions are disempowered. p. 187
This lead me to begin altering my approach to assigning work, which is evident in the second worksheet. I began adding a line or two asking the learners to pick the problems they did or did not want to do and why.

There was nothing special about the first worksheet. It could be on just about any topic. But the extra instructions, the two sentences asking learners to make choices and explain those choice, seemed to make the task much more engaging. And not just for the learners. I found reading their rationale behind their selections much more interesting than simply checking their answers.

Finally, teachers could have fun with the extra instructions. A group of student teachers came up with the idea of asking their high school students, "What items would you assign your best friend? Your worst enemy? Why?" So what questions might you add and why?

Tuesday, April 15, 2014

When should we intervene?

More on the session
During our session at NCTMNOLA, participants explored several games that offer opportunities to encounter mathematical content and processes associated with the Common Core State Standards for grades K-2.

As the teachers played the games, or observed as others played, we asked them to keep an eye out for meaningful mathematical moments that might be shared with the entire group.

One of the games introduced many of the teachers to a new manipulative - a rekenrek
A teacher in this group anticipated that students might have a hard time following the directions for this game and treat each row as a separate roll. She wondered when to intervene if a student did this. 

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I am sure I gave her a very unsatisfying answer, "It depends."

It depends on my goal for the lesson. If the lesson is about using the structure of the rekenrek to help students visualize groups of tens and fives in regards to place value understanding, then I might intervene. However, if I want the lesson to focus on decomposing numbers in order to make groups of ten, then I might wait until the whole class discussion (reflecting on the learning); this choice allows us to talk about it as a group.

It also depends on whether or not everyone is exhibiting the same issue. I hate putting out a lot of little fires. If I saw everyone doing this, then I might intervene with the entire group since there would be a lack of diversity in what students could share during the reflection. However, if it was a single student, then I could decide whether or not to select this approach for the reflection and where in the sequence (see Orchestrating Discussions).

So let's assume that my goal was about making tens and only Patsy played the game in this way. After having a few students who followed the directions as written share, I would move our attention to her "game board."
I want to share Patsy's work because she played a slightly different game. She answered a different question. If I wanted to know what Patsy rolled during each turn, I could find out from her rekenrek: 10 the first roll; 7 on the second; on the third a 3 (coincidence there, eh?); 9 on the fourth; 1 on the fifth; and 4 on the sixth roll. But the game wants us to say how many beads we have total and how many we need to get to 100. So with an elbow partner, I want you to devise a plan for finding these two numbers, the total and what's left to get to 100, but don't find them - yet. Ready? Go.
Although it is not what I expected (probably because it is not what I expected), I really like what Patsy's new game does for the lesson. In fact, I might tuck this example away for another time when we play the game. Then, if no one else plays it this way, I can still use it in our discussion because the game provides a shared context. This context, at least once, created an interesting problem for students to solve. And that was the main point of the session:

Tuesday, April 1, 2014

Do you need some ideas for a sub plan?

The 2014 Annual Meeting & Exposition of the National Council of Teachers of Mathematics (NCTM) is being held in New Orleans this year. I am taking a group of preservice math educators to the conference, as well as co-leading a workshop on Playing with the Common Core with my wife. This means that I (like many other teachers attending a conference that meets during the school-week) will be away for several classes and in need of sub plans. Fortunately, for me, I teach teachers and they have several projects they can work on for the two class periods that I will miss - no sub needed, just plans. But I remember being a middle school math teacher in need of plans that could be "sub-proof" while I was away facilitating professional development at other districts. My favorite activity to assign was "Rewrite the Text."

Now it might be called "Math Book Makeover" in homage to Dan Meyer's TEDxNYED (see below). In fact, there are a lot of things I would change, given what I know now. If you are looking for some sub plans, here is a workshop I might use.

Math Book Makeover Workshop
My thoughts are in blue.

Schema Activation: (Done before I leave) Chair-Pair-Share
  • What would you expect to see in a math book?
  • Which of these things helps you learn math?
  • Are there any things you think are missing?
  • Are there any things you would get rid of and why?
Focus: (Watch before I leave) Math Class Needs a Makeover

We are going to watch a former math teacher talk about some ways we might change math class. I want you to pay particular attention to ideas associated with changing math books and how we might apply these ideas to our textbooks. Please keep a record of these ideas so we can talk about it later.

I know that much of this might go beyond a middle school learner's current level of understanding, but I believe he or she can get a sense of some ideas of things to do to change the text. The goal is to immerse the learner while focusing on what is important.

Whole class discussion: What were some of the ideas you might consider applying to a makeover of our math book?

I hope they will notice that we need to change the text so it:

  • Supports reasoning;
  • Promotes problem solving;
  • Matters; and
  • Incorporates dynamic resources (video, technology, ...)

Activity: (While I am gone) The Makeover

Depending on the number of days I was going to miss, I might assign a section for each day. I know this would probably not be enough time for my learners, but I am in the habit of giving learners too much to do because it forces them to make choices about what is really important to accomplish. For each section, they would need to identify what part of the lesson would go, what would stay, and what they would add. I could require particular features (practice problems, assignments, technology, assessments, rubrics, teacher notes, ...) if it made sense given where my learners were in their understanding of math books.

The level of polish would depend on my audience and purpose. If I am the audience and the purpose is to simply to see how they thought about revising the text, then sticky notes might be all I needed to see. But if the purpose is to really revise the sections and perhaps use some of the ideas with future learners (leaving a legacy - another good TEDxNYED Talk), then I might want something more substantial. This might require giving them more time and feedback. And, if I want to avoid checking their Google Docs at the hotel after attending a day full of sessions, some time in class after I get back.

Reflection: (At the end of each period when I am gone) Glows and Grows
  • Glows: What are the two parts of the revision that you are most proud of and would want to share with others? What makes them so good?
  • Grows: What are the two parts of the revision that you believe still need some work before they are ready to share with others? What work do they need?
These questions put the learners' work into perspective. I can spend more time evaluating the Glows, because they are presumably the best work, and allow for some approximation in the Grows. The learners can also use this reflection to make a plan for what comes next.


If you are looking for sub plan ideas, I hope this helps. As a middle school teacher, one of the reasons I liked this plan was because it was so adaptable to whatever content we were currently exploring. I did not need a special project that addressed some specific content. I could also avoid using a plan that was disconnected from our current work. It seemed like an approach that could be used with any section in any middle or high school text.

So what do you think? Would a workshop like this work as a sub plan for you? Why or why not? Please leave your thoughts in the comments.

P.S. If this doesn't work for you, then check out these sub plan ideas from Julie Reulbach.

Saturday, March 22, 2014

Don't you want math to be better for your kids?

That's not the way I learned it! And if it was good enough for me, then it's good enough for my kid! (Along with either: "I was bad at math." or "I was good at math.")
That's how I interpret some of the posts trying to pass themselves off as examples of "bad Common Core math problems" (Google it and take a look at some of the images). Justin Aion has a great post that points out the problem with associating these examples with the Common Core State Standards in Mathematics (CCSSM). However, even if these examples are decoupled from the CCSSM, there's still the sentiment that these new math approaches are flawed.

Take this post, for example. The parent's letter says it all:

From Jeff Severt (some context)

"simplification is valued over complication" writes the Frustrated Parent. But is the parent's approach the simplest way to compute the difference between 4,000,002 and 3,999,999? As math educators, we encourage young mathematicians to build up a variety of computational tools so that they can attack any problem with confidence and phronesis.

Recently, my class explored the thinking inherent in the work of these third grade girls.

From The Big Dinner 
This was a Big Idea on the Multiplication and Division Landscape, Proportional Reasoning, that was new to nearly all of my preservice elementary teachers. Consequently, I followed up with a Think Aloud to reinforce the Big Idea and connected it to the CCSSM 3.OA.B.5.

Afterwards, one of the preservice teachers said, "I've never seen this before. Why?" Why, indeed. 

Wednesday, March 12, 2014

How is it different in March?

Winter returned last night. It wasn't too bad here but around Michigan the temperatures fell (along with some significant snow in the southeast part of the state). The reaction on Twitter and Facebook made me wonder how we go from having fun playing in the snow
to wanting to commit snowman murder in less than three months. 
It's probably related to perspective. When the snow is fresh and new, it's easy to get excited about the change in season. But after a few months of bundling up and shoveling snow, we can't wait for warmer weather.

Unfortunately, complaining about the weather does nothing but put me in a bad mood. So we try to make the best of it by staying active
Kathy skiing from our cabin in the UP
and exploring new places created by the very cold we wish would go away.
Eben Ice Caves
What does this have to do with education? I think the same thing happens in a lot of our classes. While there is initial excitement about a new school year, students and teachers quickly get stuck in a rut of doing the same thing day-after-day. I once heard Debbie Miller say (in regards to the Gradual Release of Responsibility), "If you're doing the same thing in February and March that you were doing in September and October, you're doing it wrong." As teachers, we need to find ways to keep everyone active and explore new ideas and making the best of it.

Before Spring Break, I asked my students what was working and what they wanted me to change. I used their suggestions to make adjustments to the upcoming unit. They had some really good ideas about combining some assignments and addressing new areas. One group wants cookies.

Nice try.

Friday, March 7, 2014

Which character are you?

WARNING The following post contains incomplete thoughts that might be uncomfortable to some readers. The author is simply attempting to write his way to understanding. Readers looking for coherent thoughts about teaching are encouraged to seek elsewhere. Possible Side Effects: head shaking, eye rolling, and muttering.
Some stories are meant to be told, not just read. Fred Stella reminded me of this as he recited the first chapter of the Bhagavad Gita. The translation by Edwin Arnold helped, but it was Fred who brought the text to life. His inflection and gestures helped to give the sense that we were a part of the scene being described.

And according to Fred, that was the point of the Bhagavad Gita. He explained, "In myths, like dreams, we ought to be able to see ourselves in all of the characters." Consequently we are able to identify with everyone in the story, regardless of whether the character is good or bad.

Maybe that's why those Which Character Are You? tests bother me so much. In good storytelling, I can see myself as being anyone in the story - not just Aberforth Dumbledore.
What does this have to do with teaching? I'm not sure. However, I am convinced that good teaching is related to good storytelling. Therefore, I wonder how the "story" we are telling in our lessons is inviting learners to relate to all the "characters." The open questions described by Marian Small come to mind, but I think there's more to it than that.

I'm still thinking about this, but I wanted to get this out there in case anyone else had some wisdom about it. I'll get back to you if anything more comes to me. And don't blame me if this post left you wanting more - you were warned.

Wednesday, February 26, 2014

When's the last time ... ?

I am so angry.

I just got done reading this piece by Michigan Radio's Jack Lessenberry about plans for making up school days missed this year in Michigan because of snow, ice, and cold. Some politicians want to extend the contact hours each day instead of adding days into summer vacation. This is in spite of direct opposition to the idea by the entire State Board of Education, especially by the State Superintendent of Schools, Mike Flanagan.

Here is the response one of the politician pushing for extending the school day gave regarding the opposition:
When asked about the state superintendent’s views ... Potvin said: “He hasn’t signed any checks lately for transportation,” apparently meaning the cost of school buses.
Forget that Rep. Potvin is putting money before learning (Lessenberry addresses this in his piece). I am more angry with how Rep. Potvin seems to believe his business experience trumps Superintendent Flanagan's educational perspective when it comes to running schools. It makes me want to scream.

But instead, I decided to use my words. Therefore, I wrote this post and used this meme to appropriately express my anger.
Ah, that's better.