I use Mailchimp’s “email from RSS” feature to write a blog post and then send it to people via email. It also gives one some nice tools to help manage an email list. It’s also free to use if you have fewer than 1000 people signed up to your list.

David

]]>“Hey Ben you’re basically doing guided inquiry all the time – do you disagree with cog. sci?”

I’m not exactly in the same position as Michael, I can lean on the regular Math class during school to take care of that part of learning and I’m only seeing the kids once a week not daily.

“But what’s the point of doing it even then? Are you just wasting your time on ineffective intellectual befuddling or non permanent learning?”

I don’t think so. People have different goals. Math Class is aiming at functional competence. I’m really going for first and foremost joy. I.e. I want kids to see math as fun and exciting and to understand it as a very broad subject with a lot room for creative discovery. I don’t necessarily need the kids to leave knowing a lot more material (although I certainly hope some things stick) What I want instead is for them to leave excited and interested in pursuing Math more in the long term. What I also think is valuable is experiencing struggle and problems that require more prolonged thought.

“But don’t students already experience this in class. We’re applying cog sci to make this process more efficient but it doesn’t change the overall difficulty of achieving master?”

The answer is maybe. Like all social sciences, cog sci deals in the average behavior and response of students. Its results are most true for the middle of the curve i.e. 80% of students 80% of the time. But there are outliers (one either side) Some concepts are harder than others and students aren’t always in need of a ton of DI for everything. Likewise some students have not yet hit that first wall of conceptual difficulty and really don’t have much experience of struggle yet in a math context. My aim is to push everyone I have in front of me towards that zone.

“Why not wait until H.S. then when kids are getting closer to the end of that 10 year mastery arc?”

Again not all kids are the same, a lot are ready for this process much earlier i.e. here in M.S. Its also really critical to reach some kids during this point while they are still settling their intellectual identities. Yes person X might be closer to mastery in H.S. but by then they may have written math off as boring. There’s value in showing kids the exciting horizons earlier on even if they don’t get there for a few years.

]]>Hi Rachel, mind posting a link to the blog post you wrote about some of this? I would like to add it to this meal Michael has me chewing on.

(If clicking your name here is supposed to lead me to your blog, embarrassingly I am not figuring it out)

1. How much of teaching skill is like being nicer? Do the kinds of habit-inculcating exercises in this post make sense for teacher improvement? On the other hand is learning and more knowledge-building activities, like what we do on these blogs.

2. Walking away from this post, I realized that the real place where these questions live is in fiction. I love moral fiction, where the narrative tension is generated by a kind of ethical “will they won’t they.” A few things come to mind — a lot of George Saunders’ stories, Bernard Malamud’s The Assistant, Huck Finn definitely, Chaim Grade’s The Yeshiva. I think there was also a time when people had more faith that reading literature could be morally instructive but that time may have passed, I don’t know.

]]>That’s a good point, about the difference. And truth be told I don’t *really* think about my unit as having an “application” part anyway.

Here’s how things worked out for my opening 8th Grade unit on solving equations. First, lots of worked examples (and mistaken examples and compare the strategies and faded examples and connecting representations etc.) were used throughout the unit. Frequently I would discover new types of problems that were hard for my kids as I followed my learning trajectory and then teach them explicitly with examples.

I randomly mixed in there some things that could be called “problem solving.” A few NRich activities one day. Not even that much mixed practice beyond the IM practice sets and one of your amazing shticky worksheets with a joke (the cowboy one). A DeltaMath day.

And now…we’re just moving on. We’ll have to come back to solving equations later in the year, but I was getting bored and the kids hit their skill threshold of “three-step equations” on Deltamath. The only thing is that their quizzes on Friday showed they weren’t handling parentheses particularly well, so maybe some examples/practice with those types of problems? Not sure, exactly.

]]>(I’m also trying to mentally shift, because I’ve been thinking about area and probability more than equations lately. I think equations are really interesting, but I also think they are more of a skill in their own right and there are fewer real problem-solving/application opportunities until you’re using equations to model stuff. I guess what I’m saying is that the flow of my equations unit feels different even than geometry or probability or ratios would.)

]]>1. I have to catch up on your post! Your blog is the best.

2. The middle part is the most interesting, agreed!

3. I would say what you’re saying slightly differently, maybe provocatively differently. What we don’t have enough interest in is the *learning trajectory* or a sequence of skills or (even) the actual piece of curriculum. Because I don’t exactly think of a topic like solving equations as made up of (1) worked examples at the start and (2) a middle part and (3) application problem solving at the end. I think of it as 14 different mini-skills that I’ll teach on 14 different days. And I need to keep that fresh, somehow, while also making a lot of stuff explicit along the way. I *could* do 14 days of worked examples, and I certainly do a lot of them, including erroneous examples and compare/contrast the examples and incomplete examples.

I agree that there isn’t enough interest on the middle parts. But there’s also just not that much interest in stuff that matters, in general.

]]>For one, it’s not at all clear to me exactly when “applying in a new context” is a problem-solving activity appropriate for developing independence and when it crosses the line into asking the kids to do something new–something unfamiliar enough that they’re essentially novices. If you can find the area of a whole circle, is finding the area of ¾ of the circle problem-solving in a new context, or is “finding fractional parts” a new skill entirely?

Another issue–what exactly should those worked examples look like? Should I teach kids the way I would solve the problem? Or should I have kids use a less efficient method–one I think/hope they might eventually outgrow–if I think they’ll understand it better? Lots of teachers value giving kids multiple approaches. Should I offer multiple worked examples, using different approaches? (I typically don’t, but that doesn’t mean I’m right.)

And another thing–are there activities that are “in-between” worked examples and problem-solving? For 6th and 7th, I’ve been trying some (scaffolded) writing problems in between–I think those are consistent with what I’ve read about promoting self-explanation. But while I like how they’ve worked so far. I’m not sure if they are equally effective for all ages and with all topics. And I have to believe there are other sorts of activities–maybe card sorts done well? maybe Craig Barton’s SSDD? maybe inquiry? class discussion? that could promote developing schema/metacognitive approaches… but I feel like I rarely see people from the “research” community talking about much besides worked examples or direct instruction spaced practice.

Also, I wrote about some of this week. The post got exactly one view. I’m pretty sure most people don’t share my view that the mess in the middle is the most interesting part of teaching. Oh well.

]]>I’m most interested in how to be nicer online on places like twitter since that’s where things seem to fall apart much more easily.

I notice that I most enjoy reading folks that mostly focus on their own messages and that’s what I try to model myself to greater and lesser degrees of success some days.

So I bite my tongue most of the time except where I think I have a relationship with the person or its fairly clear they want to have a discussion (or my righteous indignation is just too high but even then I rarely feel good about tweeting afterwards)

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