Sunday, April 28, 2013


The analysis of pointers is pointless.
Eckhart Tolle (at 2:12)

Yesterday, I sat with a group of concerned parents and teachers as they discussed what was happening at their children's school. They had chosen this school because it was a public (charter) school dedicated to developmentally appropriate methods of teaching and learning. But recently the school had been implementing more test-prep based on the recommendations of certain "experts" who were concerned about the school's standardized-test results.

You see, when Michigan decided to change their cut scores on the state test the school's pass rate had plummeted. I tend to think of this as a manufactured crisis meant to sell more test-prep programs but that rant may have to wait for another post. The consequences to these parents and teachers are real - and heartbreaking - and demand the attention of this post.

The parents and teachers had selected this school specifically because of its  commitment to being something other than a "factory" school; a commitment to being a school where natural learning was valued above all else. Now, however, the school seemed to be succumbing to the push to standardize teaching and learning. Parents had attempted to express their concerns to school leaders with no success. This group was now thinking about alternatives - home schooling, starting a private school, starting their own charter.

I did my best to explain what I understood to be the some of the pros and cons of each of these options, all the while empathizing with their situation. These were not people of means who could afford to stay away from a job to home school their children or pay the tuition at a private school. They wanted to know what assurances they would have that a new charter school would not result in the same heartbreak somewhere down the line. Unfortunately, I had no assurances to give.

It was energizing to find these parents so passionate about developmentally appropriate education but I left the meeting angry. I am angry that we have developed this unhealthy obsession with standardized-test results. I am angry that parents committed to learning, not test scores, find themselves looking around for alternatives and find nothing available/affordable. Pardon the violence in this video (and the earlier comic meme), but the situation has left me thinking, "What the heck!?!" and makes me want to slap someone. [Fortunately, I chose to use my words instead.]

[Important part starts at 1:15]

We need to quit focusing on the finger (test-scores) and begin looking to the moon (learning). Our current approach is shortsighted. And if we continue down this path we will not have the educated citizenry we need to survive.

Wednesday, April 24, 2013

Why didn't I think of that?

The last week of the semester we meet one-on-one with teacher assistants in what we call "exit interviews." This is an opportunity to discuss what they have accomplished over the semester and what they plan to work on during student teaching. It also provides a chance for us to learn more about these future teachers. For example, yesterday one said something like:
You might think I'm crazy but I have this big idea that I want to do in my classroom. You know how some students don't have math textbooks? Well, I want to have my students make math books to share with kids in places that don't have math books. What do you think? Crazy, right?
No. Definitely not crazy. I told her about this wonderful talk at TEDxNYED by Alan November and how it describes teachers with a similar vision. I sent her a link to the talk via Twitter and then kind of forgot about it. (The relevant part starts at about 6:00 with Learners Leaving a Legacy.)

But I included my teaching partner, @ProfJonh, in the tweet because he hadn't heard of it and later in the day I saw this:

You see, Jon and I (along with another colleague) are planning on creating materials for one of our math courses for preservice elementary teachers this summer. It never occurred to me to apply this same idea to this course. Now we are talking about having these future teachers create a text for others, perhaps around the Standards of Mathematical Practice.

It does not end there, however. This afternoon we were sharing lunch with another colleague who is scheduled to teach one of our zero-level algebra courses in the fall. She was wondering aloud about what to do with these students - many of whom had already had Algebra II but still struggled with the concepts. I brought up my concern that we sometimes address these students from a deficit perspective instead of looking to build on their strengths. Again, Jon piped in, "What if you have them make their own textbook?"

Now why didn't I think of that? Having these students write an algebra text for students back in their high schools provides both an audience and purpose for their work. They know where kids like themselves struggle in math so maybe they can come up with a book that uses a different approach. Besides, any teacher will tell you that teaching material helps you to learn it. Brilliant!

I am excited about where this is headed but mostly I am grateful: grateful that our future teacher took a risk and shared her idea; grateful that Alan November shared the idea of learners leaving a legacy; and grateful that Jon has kept reminding me of that idea. It is why I think social media outlets like Twitter and blogs are so important to improving our profession - sharing and reminding one another of the good ideas that are out there.

Keep it up people - and thanks.

Wednesday, April 17, 2013

Do the numbers matter?

One of the issues I have with some of the Khan Academy videos is how he seems to select numbers without any planning. To be fair, he is not alone in this approach of using numbers in examples without considering the impact these numbers will have on learning. Many of the novice teachers I work with struggle with the same view that any number will do. Fortunately, reading The Teaching Gap and exploring Lesson Study introduce our teachers to the importance of being thoughtful about the numbers they use throughout a lesson.

But what happens when the numbers come from a textbook? Can these numbers be trusted? During an observation, a teacher used the following problem from Holt McDougal Mathematics Course 1.

When the teacher asked students how they tried to answer the questions, they provided three different approaches.

Many of the students originally did the same thing in both cases - divided by four. One student suggested that because the area was given for the first square that they only needed to divide 81 by two. This proved to be a turning point in the discussion as many of the students backtracked on their first instinct and said they needed to find a number that multiplied by itself resulted in 81. Perhaps they had missed "an area" the first time.

Thinking that he had addressed the issue, the teacher asked, "Which figure has the longest side?" The student he called on responded that the second square had the longer side. Then the teacher asked the student, "How much longer?" to which he got the response of 0.75 feet. Clearly, this student had missed part of the discussion, but that is not what I am concerned with here.

Why had the textbook authors used 84 feet for the perimeter of the second square? Most middle school teachers could tell you that 20.25 feet would be a common mistake among their students. So why have a number (84) that makes the first part of the answer correct even when the work is done incorrectly? I would have used a perimeter of 80 feet so that both parts would have been wrong if the anticipated error had been made. Am I wrong in this choice? This is a genuine question to which I would appreciate your feedback.

Friday, April 12, 2013

Whose learning?

The following is a guest post from John Golden. Go Blue!

I was a terrible student.

I make this confession to my students all the time. When I finished undergraduate, my friends calculated whether I had attended more class, missed more class, or slept in more class. It was close. But I was a great test taker and I got good grades. I thought that class was all about what I did at home afterwards. I had no expectations of learning in class, and was delighted when I did. (From Dr. Hocking, for example.)

So I was a terrible student, but I was a good learner.

When I started teaching I focused on being entertaining and comfortable. I wanted students to enjoy being there, free to ask questions (it didn’t take too long to figure out that this was hard) and get what they wanted. But even with the ineffective assessments I was giving, it soon became clear that they weren’t understanding what I wanted them to understand.

Yesterday, I was listening to a podcast and was struck by how well the speaker captured this idea. It was Avery (@woutgeo) on Ashli’s (@Mythagon) Infinite Tangents podcast (105).

“At the beginning of my teaching I was very content focused. I need to find and create interesting content that will help the kids, that the kids will be really interested in. I had no middling success with that. I think I found some great things, and also found some other things that didn’t work and I found that teaching some of the important ideas were harder than I thought they would be.  I realized that there were plenty of ideas that I didn’t really understand myself, that I had to go back and think about a lot.  I think going back and thinking about those ideas really helped me shift a little bit to not just caring about trying to find interesting content.  But also thinking about pedagogy and how we teach things and the best ways for kids to learn.  If I had to think of an arc of my teaching career and my focus, I would say that that kind of describes my arc of going from being very content-focused to a balance between finding interesting content and also really thinking about the best way for kids to learn the content and have an experience.” – Avery

I mentioned that on Twitter and there was an interesting discussion that followed.

Shawn Urban (@stefras): Most teachers are great with content; some with relationships. The marriage of the two is often tricky.

Greg ‏(@sarcasymptote): I think the relationship piece is about trust. Young Ts fear giving up control of content to Ss

Ashli (@mythagon): I'd like to see more mentoring in teaching. Not enough time is built in for such work typically.

Shawn: I agee. Teacher prep should involve teaching & study of styles of teaching. We need models to inspire creativ

John (@mathhombre) we put a lot of effort into genuine assessment and conversation about learning. But the programming of 16 yrs...

Shawn: ... this Tweet seems incomplete. I was waiting for something mind-blowing! No pressure though.

John: we've seen so much teaching as student that we've made up what teaching is and really internalized it.

John: but it's such an incomplete picture! (And possibly not the most constructive teaching.)

Ashli:  I think it takes careful, respectful questioning to get new teachers to see beyond content.

John: @Mythagon can you say more about that questioning?

Shawn: I wonder if Ashli was refering to key questions. Why are you teaching? What do you want your students to be learning?

Ashli: I was thinking about ?s that help teachers think beyond pure delivery of content and toward formative

Ashli: + assessments, status issues. yr 1 can be a whirlwind of survival

Shawn: I thought so. Deeper, more reflective pedagogical questions.

Chris Robinson ‏(@absvalteaching): Best question any T can have while planning is "What misconceptions/mistakes will Ss have and +

Chris: + how do I plan to address these?"

Shawn: I agee. Teacher prep should involve teaching & study of styles of teaching. We need models to inspire creativ

Shawn: I think we need frequent exposure in how students learn. This is key since their learning is our job.

Shawn: When did we make teaching so complex that we forgot to teach? Even r students r distracted & forget to learn

Gary ‏(@republicofmath): IMO teaching IS very complex

Ashli: Schools can easily become a memorization gauntlet.

Great conversation about teacher learning for me.

One of the things I have grown to love about teaching is how holistic it is. When I reflect about how I learn, even learn to teach, it teaches me about how students learn. As a teacher I have to make that step to thinking about how the students learn. The kernel at the heart of this for me is a humbling one:

I can not make my students learn.

That means I can not take credit for what they understand, nor blame for what they don’t.

What can I do then? I can create the conditions of learning. I can make it as likely as possible that students will choose to learn. I can monitor what works for them and adjust. Once I care about the things I do control, I am empowered. Still frustrated at the choices some students make, but thrilled at what others do.

PS> Not that I wouldn’t be happy to have a post on the DeltaScape, but I lost a bet. I knew it was a bad bet - which of our Big Ten alma maters would go farther in the 2013 NCAA men’s basketball tournament. I didn’t think my beloved Spartans would make it past Duke. But frankly, I thought this post would be on Robert’s Casting Out Hoosiers blog. (Wait - that doesn’t sound right.) But, sadly, I haven’t learned my lesson, and would make the same bet next year.

Tuesday, April 2, 2013

What goes here?

I look forward to learning with you.

The day before a teaching observation I send out an email confirming that I have the correct details and reminding the teacher that I will need an action plan beforehand to focus my attention. I try to end each of these emails with the statement provided at the beginning of this post. It serves as a reminder that the observation will be a learning opportunity for both of us and not just a dog-and-pony show.

Sometimes, I take for granted my role as a learner in these experiences. I was reminded of this during a recent observation. The teacher wanted me to focus on whether or not she was providing adequate support to students as they were learning how to multiply and factor polynomials. This was in an eighth-grade class and they were halfway through the unit - just wrapping up multiplication of polynomials.

The lesson went well and the students were engaged in what Fisher and Frey call Collaborative work. This entailed a few items that provided students practice multiplying polynomials and a worksheet called Polynomial Puzzler that the teacher had modified from a lesson found on Illuminations. The teacher went over the instructions,
Fill in the empty spaces to complete the puzzle. In any row, the two left spaces should multiply to equal the right-hand space. In any column, the two top spaces should multiply to equal the bottom space,
 and demonstrated using the first puzzle.
As I looked through the entire worksheet, however, I identified an area I thought would give the students trouble; there were places where the four entries in the upper left were missing entries. This meant the students would need to factor some polynomials in order to complete the puzzle. The teacher had not provided the necessary support for student success. I made a note to talk about this during the debriefing.

Sure enough, after students had completed the first puzzle and multiplied what they could in the second puzzle, many started to ask, "What goes here?"

The teacher responded with something like, "That's a great question. I guess I didn't give you enough support." She pointed to the upper right corner and said, "We want to find out what goes here. In other words, what times this {pointing at (-15x+3)} will equal this {pointing to the lower right corner}? Okay?"

I thought to myself, "No. Not okay. They need to know how to factor." But the students seemed satisfied and went on about their work. And the surprising thing was that they were okay. In fact, they were better than okay. They were amazing.

The students at the table nearest me began looking back at the work they had already done and sharing what they noticed. "Look. -4x+10 divided by 2 is this one {pointing at -2x+5}," one of the girls exclaimed with more enthusiasm than I usually see in math class. The group then began talking about dividing the polynomials to find the missing entries. Sometimes they tried using guess-and-check to identify what was missing. The main point for me was that they did not just give up.

They seemed to be embracing the struggle that so many students in math class are determined to avoid. And they weren't alone. I heard several ahas from students seated in different groups around the classroom. I do not know why this class acted so differently than others I have seen. The cooperating teacher is a former GVSU graduate, so I would like to think that the learning environment had something to do with it. Or maybe it was the fact that it was a puzzle and not homeWORK.

After the lesson, I asked the teacher if she had anticipated any problems. She had thought that the instruction might be confusing. When I pressed about the factoring, she acknowledge that it could have been a problem but that she thought it was actually good that they did not know exactly how to do the puzzle our way because then they would obsess about doing it right. "Besides," she said, "I just wanted it to foreshadow factoring. Now they're ready for the next lesson."

I love my job. I learn something everyday. Even on those days when I think I'm the teacher.