I’ve been trying to blog about this NBCT portfolio for two reasons. First, because there is not a ton of information out in public about what goes into these portfolios. Second, the actual write-up of the portfolio requires a careful eye for concision, brevity, and more generally for careful consideration in your lexical choices, an ability to get the point across in as few words as possible and to make painful — but necessary — cuts from your prose in order to maximize the evidence/word ratio, avoiding at all costs writing that is overstuffed, repetitive, repetitive and indulgent.

But here, I write how I like.

## FEEDBACK WELCOME AND ACTIVELY DESIRED FOR ANY AND ALL ASPECTS OF THIS POST FOR THE EXPRESS PURPOSE OF HELPING ME IMPROVE THIS SUBMISSION. THANKING YOU IN ADVANCE.

There are three sections of this NBCT portfolio:

- Knowledge of Students
- Generation and Use of Assessment Data
- Participation in Learning Communities

I’ve been spending the last month doing the legwork for the “Knowledge of Students” piece. This involves three little sub-tasks:

- Making sure you’ve got good sources for your knowledge
- Synthesizing what you gather into a profile of the kids
- The meta-task: justifying/explaining your sourcing and synthesizing process

## Sources

I like to think of myself as someone that knows his students well. I have relatively small classes, I like talking to kids and they tell me stuff about themselves. I also think of myself as someone who is pretty good at snuffing out what they’re good at and where they flop.

This is not what NBCT is interested in. They want an *investigation* — an active effort to gather information about kids from people who aren’t you. You need sources for the knowledge of students you profess to have. This is probably a good requirement, and it’s one that I enjoyed trying to fulfill.

Here are people I ended up talking to about the kids in my class:

- Other math teachers who taught my kids in previous years
- Learning specialists at my school who work with the kids in my class with learning disabilities
- A guy who tutors one of my kids
- Someone who observed this class for me after I reached out to them
- Parents

(To give you a sense of the NBCT expectations, my conversations with parents are actually the *weakest *source for my submission, since I’m just reporting what we talked about during parent-teacher conferences. I didn’t especially arrange those conversations.)

How did I do, by the standards of NBCT? Here is what NBCT calls for on the section on sources:

I did a good job of talking to a lot of the “school or professional personnel” about my kids, and I also talked to families. My case would probably be stronger if I could support if with something that isn’t a conversation. My school doesn’t keep assessment data from previous years around, but we do have anecdotal reports for every kid going way back. It would probably be good for me to take a look at them…and I just got in touch with my department chair to make this happen. If I add anecdotal reports to the mix, I think I’ll be pretty solid on my sourcing.

## Synthesis

Besides for parents, I ended up having serious conversations with about eight colleagues about the kids in my class. What did I learn? And — NBCT emphasizes — how will this affect my teaching choices?

I think my class is roughly made up of three types of kid: high-flying, seriously struggling while learning disabled, and academically serious but historically struggling students. What makes this class special, I think, is that, even though this isn’t always the case, in this class *each of these sub-groups prefer and naturally seek skill-development as the primary activity in class.*

High-fliers often love problem solving, or working hard on tricky situations, asking wild questions, working their way around new and sophisticated ideas. This is not what colleagues tell me about the strongest math students in my class, though:

- “Empowered by her toolkit being filled, liked getting right answers, not so much into big problem solving without clear path forward. She likes getting techniques down.”
- “Thrived in algebra, applied it everywhere. Not motivated by optional work, preferred to work independently unless she was well-matched mathematically and personally; not a mathematical risk-taker.”
- “She enjoyed solving equations and ‘getting into the groove.'”

So the high-fliers in my class happen to love to chase skills.

About a third of the students in my class have been evaluated for a learning disability. Their issues cluster around attention and reading comprehension, and their best successes in math have come when they have a particular type of problem they can get good at solving:

- “____ enjoys feelings of mastery, will even enjoy 10 identical problems; has one of the most serious math disabilities the school has seen, has reading difficulties too, he’s almost never giving full attention, is anxious about math.”
- “She loves mastering techniques. Worked with learning specialist on study techniques, implemented them and really loves them.”
- “He worked well with a partner on a skill-practice assignment…has reading difficulties. Enjoys getting right answers.”

And many of my students come with disclaimers about their past academic lives, even though they’re academically serious.

- “Father says: Likes math, but if you ask her if she’s good at it she would say ‘no.'”
- “Low-processing speed.”
- “Disliked and did poorly in math in previous years.”
- “Has geometry under control despite struggles in previous years.”

In a lot of classes these kids would be checked-out of math, but they aren’t in my class. They take school seriously, and they want to succeed. And if you’ve struggled in math in the past but are seeking ways to be successful? Skill-mastery came up again and again in my conversations about these kids. This *totally fits what I’ve seen in class*. A kid recently told me that she never gets bored by repetitive worksheets. She’s right — she doesn’t. She loves it, and to the extent that it makes sense to talk about the preferences of a collective, this entire group of kids loves it too.

The big question: how does this affect my teaching?

## How does this affect my teaching?

On the one hand, you can get decently far in math by just learning skills. There’s no such thing as *just *learning skills, of course, if you’re really learning them. To really be able to solve a type of problem is to combine conceptual and procedural knowledge, and (if you do it right) to apply that knowledge in creative ways to new scenarios.

And experience has shown me, over and over again, that this group most naturally hums along when we’re working on skills and problem types. It’s when things just *work* with this class. And this fits perfectly with the picture of the kids I gathered from my conversations.

But math is more than just mastering types of skills. It’s also about trying stuff when you have *no *clue what to do. It’s about inventing new words or concepts to describe mathematical phenomena. It’s about mathematical modeling, which inherently involves putting out ideas for revision’s sake.

This stuff is harder for my kids; it’s not natural for the group. It takes careful planning to pull off, and even then it often flops.

NBCT wants to know how my knowledge of kids affects my teaching. For this group of kids, I know that learning will happen if we’re working on getting better at solving a particular type of problem. But the wider vocabulary of mathematics is harder to bring to this class, and I have to think very carefully when I try to share it with this group.

So, NBCT: how did I do on this one?

I’m doing OK, I think, though I haven’t yet identified an area for future information gathering. Since the growth area I’m looking at is sharing non-skill development math with this group, that would be a good place to gather more info. (And maybe it involves talking to people from beyond my school who might have smart things to say about this — there’s room for that in NBCT’s world.)

## Reflecting on All This

NBCT gives you reflection prompts for the written commentary.

*Q: What guided you in selecting those particular sources of information?*

A: Things were going ok for this class, but I wanted to know what made them hum. The kids seemed generally content, but I wanted to know what about math got them excited. So I sought out people who knew them well — their past teachers, tutors and the learning specialists who worked them regularly. The sources were appropriate for helping me figure out what these kids enjoyed about math.

I also had a bunch of kids with learning disabilities, so the learning specialists (and the kids special out-of-school tutors) were a no-brainer, source-wise.

*Q: How did you determine the relative importance of the different kids of information you gathered?*

A: This is a tough question for me to answer, and I’m not exactly sure how to go about it.

The learning specialists provided a really important perspective, but sometimes they were talking more about what they saw working one-on-one with a kid instead of the fuller, social situation. For one kid they said that the enjoys working on a lot of problems that are nearly identical — this surprised me, because he does *not *seem to enjoy this in class. My interpretation is that the social situation is different for him, mathematically. He worries a lot about doing math in the presence of others. He still might enjoy working on a lot of similar problems, but around other people he gets self-conscious about looking stupid by not knowing how to do a problem, and chooses to just opt-out of the whole game.

Sometimes people would tell me various instructional techniques that worked well for various kids, getting close to making recommendations. Example: he likes moving, he likes having very clear examples, he likes touching things. I rated this information as interesting, but non-crucial. Instructional techniques are my job. I wanted information about what kids were like in other settings, what they enjoyed. That’s what I listened for, even while people were recommending teaching moves to me.

I might end up with some surprises when I look through old anecdotal reports. I’ll have to decide how to situate those to the conversations that I’ve had with others.

When parents tell me what their kids are like in math, I take that as data, but I treat it as tentative. A few sets of parents told me that their kid historically struggled, but a few others told me that their kids were looking for more of a challenge. This was helpful, but not as important to me as knowing the specifics of *what their kids enjoyed doing*. Knowing that a kid likes math or doesn’t, that they want more challenges or they don’t — these aren’t exactly easy to act on. I needed more specifics, so the specifics I gathered from colleagues helped me figure out what to actually do. So I guess that makes them more important, though this whole investigation started from the comments I got from parents at conferences, so it’s not like they were unimportant comments. I don’t know.

*Q: What are some of the trends you identified?*

A: That several kids have diagnosed learning stuff that makes it harder for them to understand new contexts and problems, and as a result they tend to really like when there are a series of questions of a similar problem-type.

That a bunch of kids have baggage from previous math experiences, but they have found success with developing their skills. Even the kids who don’t have math-baggage prefer not to take big mathematical risks, and this is something that their previous teachers noted to me too.

In terms of pair/individual preferences, my class is mixed. Some kids *really *prefer working alone, others prefer working with partners. No consistent trend here, which is sort of a trend itself.

*Q: How did you identify or confirm the trends?*

A: I asked one person, but then I waited to see if others brought it up. And the skill-development theme just piled-on with each successive conversation and observation. We’ll see what happens when I go through anecdotal reports. (My answer here seems thin, and I’m not entirely sure how to beef it up.)

The observation was really helpful in firming up what I thought I was seeing with my kids.

*Q: What other factors did you take into account when analyzing and reflecting on the various sources of information and why?*

A: My first reaction: I have no idea what this question is getting at. That’s my second reaction too. Anyone think they know what this question is all about?

One thing I took into account is that my class — high school geometry — might be different than kid’s previous experiences in math class. Like a lot of geometry teachers, I’ve noticed that kids sometimes love or hate it because it feels different from their other experiences. And part of your job in geometry, I think, is to help kids learn that this is also math. You want to teach them that geometry isn’t so different, and hopefully use that to help everybody come to like math a bit more.

I also didn’t want to assume that any of the things that people were telling me about kids were stable. So if a kid enjoys skills work? That doesn’t make them a *skills-lover. *It’s good knowledge to have, but even if that’s true there’s no reason to think that’s fixed. The mathematical experiences that a kid has had impacts their preferences — those can change.

I don’t know if that response makes any sense.

*Q: What are the needs of this group of students and what kind of supports to you anticipate providing in order to meet those needs in fair and equitable ways?*

A: All the above leads to some clear moves I can make:

- I’ve got 1/3 of my class with diagnosed learning disabilities. These kids need lots of processing time, they need the context and scenarios of problems to be carefully developed for them, to reduce their reading load.
- About 1/2 of my class has had difficulties with math in the past, and that impacts their ability to take academic risks in class. They don’t want to look dumb. They need to feel safe that they won’t feel dumb to do math that goes beyond skills-development work.
- That means that, if I’m going to help them try more mathematically adventurous things, they’ll need lots of time to understand the problem, and the problem will need to be non-text heavy.

I think that’s a perfectly fine answer, though I feel like maybe I’ll think of a way to go deeper. If you’ve got ideas, I’d love to hear them!

*Q: What other educators, professionals, family members, or community members will you need to collaborate with to meet these students’ needs and why?*

A: I’ll need to talk to some people who work with kids with learning disabilities similar to the ones my kids have.

I’ll need to collaborate with tutors and anyone else who meets with a kid out of class.

Hmm. Again, I’m not exactly sure.

## Next Steps

To finish off my source-gathering, I want to look at anecdotal reports for my students from previous years. I feel good about the trends that I’ve identified and the way I’ve synthesized what I’ve learned about the kids. When it comes to the written commentary, though, there are a few questions where I’m giving answers that don’t feel like they go so deep. I need to think more about those.

I’m ready to try writing this up for submission, though. And then I need to figure out what unit I’m going to plan, and what I’m going to assess my kids’ ability to handle.

I think a good goal would be for my kids to engage more seriously in non-skills math in this next unit. A formative assessment might help all of us figure out how to do this in a non-threatening, non-text heavy way.