Author Archives: Michael Pershan

“Whole-class discussions. How hard you are for me to lead!”

Cool post.

Day 1: We started by challenging the students to find a Eulerian path and circuit through the basement (we didn’t use that language). And then took them to the basement.


Good struggle:

What I still need to work on

Ohhhh whole-class discussions. How hard you are for me to lead! How to balance argument/excited participation with listening? How to balance desire to go to lunch with listening? Discussions, I aspire to be best buddies with you one day in the near future. Please be open to our future, awesome relationship. Love, Sarah.

How do you structure a good conversation? 5 Practices, anyone?

“The two main areas I want to and need to work on are student engagement and differentiation.”

The two main areas I want to and need to work on are student engagement and differentiation. What do you do in your classes to have students doing most of the “work” if you will and you, as teacher, not being the one up in front of the class? How do you structure your lessons to accomplish this? I realize that not every concept will lend itself to some of these strategies, but any guidance you can give will help. John Scammell shared what he did with multiplying radicals earlier and I am using that here in the near future. How do you create these kinds of materials? How do you set up the worksheet for them to discover the rules? What other strategies do you have to share?

Go forth and comment.

Michael Fenton is a boss.

This is the most terrifying thing that I’ve read in a while:

If the lesson was a train, then it pulled slowly out of the station, flew off the rails, crashed into something big and destructive and flammable, and burst into flames. At least there was no ambiguity. It was undeniably horrible.

When I realized the depravity of our situation, I called for everyone’s attention in order to make an announcement:

Hey guys, this isn’t going well, and it’s my fault. I didn’t prepare for this lesson as well as I should have. I want everyone to stop working on the handout and find something else to do. You can work on something from another class or just relax and chat with your friends. I’m going to sit down to rewrite the handout. If I can fix what’s broken in 5 or 10 minutes, we may resume. If not, we’ll pick things up tomorrow.

At the center of Michael’s post is a redesign that turned this into this.

What changed?

For one, it’s certainly clear that he lightened the tone in his new version, adding a bit more expository support and generally giving kids a bit more space to work. The instructions are dished out in smaller chunks. He also added a whole prequel to the Key Curriculum worksheet that checks in on their ability to solve systems graphically in Cartesian coordinates. He also added support questions to flesh out the original handout.

What are Michael’s assumptions? What were the curriculum developer’s assumptions? Why did they diverge?

I think that I’ve been planning ahead all wrong

In the past, I’ve planned ahead by trying to outline lessons several days, or weeks in advance. That’s never worked for me. I still find myself planning for Day x+1’s lesson on Day x.

It’s time to kick some long-term planning ass.

Since I’m so bad at putting together long-term plans, I’m going to do the exact opposite of what I do now. I’m going to start planning for the end of the year, and go backwards from there.

My thought is that by planning for the medium-term future, I’ll have to work efficiently and wisely. (After all, today’s lesson is still right around the corner.) At the same time, those are investments that will start to accrue as time passes, and I’ll find myself with solider lessons and more time to think about the current day’s stuff.

So the plan, in short, is to really skimp on short-term planning, and go all-in on the medium-term future.

Thoughts? How do you plan ahead?

“I have no idea why they would do this”

In the midst of a very good post, Julie writes:

They also distributed the exponent to both numbers inside the parenthesis.  I have no idea why they would do this, because I don’t even teach them the power to a power exponent rule.  I have them expand any set of parenthesis with an exponent.  They do love the distributive property, but we-e have never, ever, ever, distributed an exponent.  Sigh.  I failed.

There are a lot of wonderful reflective moments in that post, but I find the above fascinating. Kids are distributing exponents inside the parentheses.  You might be tempted to explain this mistake as confusion between the power rule for exponents and the distributive property, but seeing as the kids haven’t yet learned the power rule that explanation seems false, at least for Julie’s kids.

Distributing exponents is tempting for kids. Why?

Julie has a strategy for helping her kids move past these sorts of mistakes:

So, starting Monday, I am going to have one problem of the day for both classes posted on the board.  It will look like a variation of this.  Evaluate  -3x^2 – 2x + 5 when x = -2.  I’ll throw in fractions, decimals, and any other basic, easily forgettable concept.  This should help them quickly practice evaluating algebraic expressions, exponents, and the order of operations, EVERYDAY.  And we will go over it, together, everyday.

Will repetition work? Will she need something else? Here’s hoping that there’s a follow up post from Julie letting us know how her experiment goes. The question for me is, what are the returns on any given genre of problem? Do they diminish with repetition? How different does a problem need to be in order to promote real learning?

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“Being an SBG teacher in a non-SBG world”

The struggle is just seeping out of Sam Shah’s really terrific post about Standards-Based Grading and student motivation. (And I’m not just saying that because he gave us a huge shout out on his blog recently.) Check this out:

The thing is, though, I started to worry that SBG wasn’t serving the purposes I adopted it for:

1) Independence and Responsibility

2) Students learning about their learning process

3) Clarity about what students know and what they don’t know

4) Making mistakes, but learning from them

I was having, and still sort of am, having a true crisis of faith. Because if SBG didn’t address these things, what’s the point? And clearly much of this is on me. Because careful implementation is crucial and that is my responsibility. I’ve seen it be wildly successful with students since starting, students who wouldn’t have a chance in hell in a traditional class to learn and be awesome at calculus. And for those kids, the kids SBG really works for, it’s enough to keep me invested and wanting to continue. 

If you’re ever wondering whether a post is a good fit for our blog, check to see if it ends with a question. Sam’s post ends with 3 killers:

1) What concrete things do you do to keep the philosophy, spirit, understanding of SBG alive… so that it doesn’t become a mechanized system by the third quarter?

2) If you are in a school that isn’t SBG, have you found any ways to combat the notion “SBG class can come last”?

3) If you are teaching SBG in any school, what mechanisms/procedures do you have to help kids individually understand how they learn, and how SBG can help them learn how to learn better? Do any of you have individual conferences with your kids or anything? Do you have them reflect about what they’re learning (or not) through SBG regularly, and do you respond to those reflections?

It’s a great post, with probing questions and you should go to his place to check it out.

Though Sam is thinking about SBG in his post, I’m wondering whether he’s just having trouble about reassessments. Though he also talks about homework, I don’t really think of that as part of SBG. But I also think that SBG isn’t particularly helpful language right now, because it’s being used as a catch-all for at least four separate things:

  • Standards versus Assessements: Determining one’s grade by averaging scores on a list of standards rather than by averaging one’s scores on a list of assessments
  • Reassessments: Determining a kid’s grade on a standard through multiple assessments
  • Student-initiated reassessments: Allowing kids to initiate a reassessment
  • Homework Policy: Refusing to grade homework for correctness, and often refusing to grade homework at all.

As annoying as it is to urge a change in language usage, Imma go ahead and urge it. Let’s try to limit SBG to the simple grade-book change of keeping track of standards instead of assessments.

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“What does it mean to earn an 80% in a Geometry class?”

Brandon’s got a problem:

My school has recently begun an inquiry about how we assess. I have been struggling through the process for a number of reasons. I struggle most with trying to break away from assessing how I’ve been assessed.


He considers the possibility of grading based entirely on knowledge, but struggles with it:

And what of work ethic? If a student is really trying, improving, busting her ass on every assignment but still only masters 79% of the material, we give her a C. That somehow feels cold and unfair. But standards/objectives-based grading would imply that she earned exactly that grade.

He concludes:

I’m still at a loss for how I want to approach grading philosophically. I had a great professor at Baylor tell me that he did not want to give out any grades, but write two sentences about each student. I think that mindset is powerful, but rarely feasible. Maybe I’m approaching this the wrong way and equivocating grading with assessment. I would love to know some other math teachers’ (or just teachers) thoughts on this particular model.

Go leave your thoughts here.


“An excuse to make my students do algebra”

Last year, at any given time, about one-third of my tests were old skills ‘wrapped’ in a new geometry context. .. the assumption was always: These problems are an excuse to make my students do algebra because they still need to learn it and these problems will force them to do so.

Reflection 1: This is fundamentally dishonest – I’m ‘tricking’ my students into learning algebra by making it reappear throughout the whole year.

Reflection 2: This practice kept the cognitive demand of my classroom at a continually low level.

Another great post from Dan Schneider over at MathyMcMatherson. Visit the post for interesting questions about the relationship between teaching and assessment. I think that I would challenge his take on curriculum — he writes that curriculum is “the order that I present mathematical ideas” — but he’s got great thoughts about the ways that assessment decisions can drive daily decision-making. If you’re part of the SBG crowd, you’ll want to check this post out.

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Honest, critical feedback from kids

Over at my place I wrote about a really raw conversation I had with a kid. He told me everything that was bugging him about class:

He thought that class was kinda boring and awfully repetitive. He wasn’t a fan of the worksheets that I give out on most days, and he thought that the Warm Up was becoming a distraction. He wanted more notes, because they keep kids from just being spoon-fed information. He wants the notes to be more step-by-step. He’s willing to stop by during lunch to show me what he means. He’s worried that we’re not going to be prepared for the Regents.

And there’s actually way more that from the kid. My conclusion is that I need more conversations like this, with my least happy students. Head over to the post to drop a thought about the value and limitations of these sorts of conversations.

“I need some help vision casting”

The graphic above is fantastic, and the rest of the post doesn’t disappoint, as Michael Fenton cuts deep into his own classroom style and offers an incredibly articulate explanation of what it is that he’s looking for. It’s hard to imagine that he won’t find it before long if he keeps up this sort of careful self-analysis:

As you can sense, there’s some more bad news: Even though I’ve identified what I want to change (my teaching style) I don’t know how to get from here (“conversational direct instruction”) to there (something better than what I’m doing now), or really even where “there” is.

So here’s what I need from you. I need some help vision casting (what could my classroom look like). And maybe more importantly, I need some advice on how to get there.

And the comments are just fantastic. Here’s a brief selection:

Dan Anderson: “A small change that I’ve made that seems like it makes a big difference is the grouping of students, and me moving myself physically to the back of the room.”

Reilly: “I think that just like its easy to inflate your sense of awesomeness with honors classes, it’s also easy to inflate your sense of awfulness with regular-to-low or remedial classes.”

Gregory Taylor: “As a whole, I feel I still do a “direct instruction” style (real world activities almost make me physically uncomfortable) but where I can, I reverse it. Instead of ‘here’s the topic, here’s some examples’, start with the examples. Walk around, see how they tackle them. (I’m not necessarily at the back, but I float a lot more than I used to.) Answer questions individually rather than as a whole. Then present the topic partway through the period, referencing what you saw students do (or having them reference it themselves). This might allow you to transition your lessons to something more open without feeling you need to totally reinvent yourself.”

More good stuff over at the blog.