## Carl's Teaching Blog

#### Category: Improving Teaching (Page 2 of 2)

In my last class I focused a lot on proportional reasoning, and at the end of March I wanted to give the kids a project that would be rich with a lot of different examples of the topic.  My original idea was to do a theme based on turning a beat into a song, but it seemed contrived.  Frustrated, I headed down the street to the only empty grocery store, and thought about how all the prices there were really high.  Suddenly a flash of insight hit.

The students can take down their expensive local grocery store!

Kids can imagine a product that they like to sell, and then look up how much cheaper it would be at a warehouse store, and compare the difference in prices.  Then students can use evidence from their local store to estimate how much money they would make from a day of selling the products, and then scale what the products would make over a month.  I went back home and scribbled a bunch of notes about the idea with a Doc-Brown-Esque level of enthusiasm, but I didn’t really put together a polished task until last week.

Here is what I gave kids, although I really wish I could have made it better.

• It is a pretty straightforward task whose end goal makes enough students that all students can really understand what their end product should mean.
• Students need to use proportional reasoning in so many different places that there are countless numbers of places to discuss it.
• Since all students can do different products at different stores, the entire class can come up with different project results so there is no copying fear.

• As a project to help kids express their proportional reasoning, should I have asked them to explicitly demonstrate two or three different ways of finding a number that would proportional to some other set of numbers?  If so, which ways should they all HAVE to know how to do?
• How could this be better?

IF you can give me any feedback about the project, I’d appreciate it if you mentioned it by commenting on the google doc of this here.

3/30

When schools from Boston to Texas are missing school,teachers may start thinking about how to tune up the tasks they give their students.  Some recent blog posts, and one from the past, can show different ways to think about the tasks that we assign our students.

In Andrew Gael‘s blog there was an interesting post about describing a number of ways to present students with a task that asks them about area while keeping in mind each of his students’ “mathematical strengths, goals and cognitive pathways your students use to access the content.”  In “There’s More Than One Way to Skin a Task” he effectively makes a framework for thinking about task in terms of the kinds of thinking students would use to finish the task.

#### What do you want your students to do?

Kate Nowak described a framework which explores another way to improve a task in her January post “On Making Them Figure Something Out.”  When teaching a concept to a student, Kate implies that in the worst scenario you could “Tell Them Something.” Better than that, you could “Make Them Practice Something”, and perhaps even “Make Them Notice Something” or “Make Them Do Something”.  “But lots of times, the learning that comes out of MTDS and MTNS doesn’t really stick that great.” Kate writes, “They can maybe do an exit ticket, but ask them a question that relies on The Thing in a week, and you just get a bunch of blank stares.”  In this post she explains how she turned a MTDS task about the discriminant into the penultimate type MTFSO, “Make them figure something out”.

How Mathematically Complex Is The Task?
If you want one more way to look at tasks, and don’t mind looking at a post from 2009, Mr. Vasicek wrote about the “Task Analysis Guide” which was originally published in a mathematics journal and looks at problems in terms of cognitive complexity.  The different scales in this guide include “Memorization”, “Procedures without Connections”, “Procedures with Connections”, and “Doing Mathematics”.

If you want to give some of your tasks an upgrade, all of these teachers give you ways to think about tasks that can help illustrate tangible next steps to improve student learning.

October is the month where teaching starts to get real.  By now the school has sorted through all of the beginning of the year hiccups, and your kids have all gotten comfortable in the room.  This time of year, October, is where it starts to become about you. Right now if it might feel like you are having problems or your plans from the summer are falling apart, and it’s easy to get frustrated with yourself.  Don’t get too down on yourself at this point of the year.  Now is the time to take a positive look at yourself to remind yourself how silly it is to get down on yourself so early in the year.

#### This is why I’m hot

First thing you should do is look at all things that are ‘hot’.  On a sheet of paper, or in your evernote, or even on your blog list out all of the things going well.  Here are some prompts to think about:

• What systems are functioning?

Looking at the goings on around your classroom, what things are working so well that you take them for granted.  Some days I think back to the first October of my teaching and I had to change my entire system for pretty much everything (how they entered the class, how they took notes, what should happen when they throw broken crayons across the room, etc.).  I persisted through the world falling apart around me only 10 years ago, yet now I act as though it’s bedlam when it takes more than a minute to transition to group work.  Give yourself some credit, and think through all of the things that are going well.  If you can’t think of anything, ask a colleague to come in and write down what they notice.

• What students are responding?

In your room there might be 1 or 2, kids who are not getting it, and seeing them struggle can’t help but get to you.  You’ve pulled them aside, rearranged the seats, and even worked their names into a worksheet but you still can’t make any progress with them.  Well what about the kids who are responding?  What is working for them?  If you don’t have any idea what will work, maybe gather some information with exit tickets.  You’re better off improving the overall experience for all your students than targeting just the one or two trouble spots.  That’s like the guy who wants to cut down his gut, but instead of getting a better diet, doing all around cardio, and purusing a more active lifestyle, they strap on a slendertone ab flexing belt and curls up on the couch with a pillow and a pint of ice cream.

• What extremes have you been able to navigate?

Teaching is a constant dance between extremes.  First you want a loud, energetic discussion, then you want a quiet, focused independent work time.  Maybe your students will be thinking through all the ways to challenge an idea, and next they’ll want to think of all the ways to support some other idea.  You probably begin most lessons wanting students to be in their comfort zone, only by the end of it, have them grappling with something completely new.  Swinging from one extreme to other, whether it be in content, or classroom layout, or interaction style, is a difficult and important task.  Before you worry about how far forward you wanted them to go, give yourself credit about how much lateral progress you were able to make along the way.

• Other reasons you’re awesome

There are lots of things you have to write down.  You just aren’t doing it because you’re modest.  Come on, if you’re going to get down on yourself, you owe it to yourself to brag a little bit first.  Write down all the reasons you’re awesome and some of the positive things going on in your class.

#### This why I’m not

Next, after you’re done with the positive list, and hopefully shifted your perspective, list out all the things aren’t working well. As you write, you need to think about the next steps.  Don’t think that once your list of things are finished you can just curl up on the coach with the Triple-P (Pillow, Pajamas, Pint of Ben & Jerry’s) and feel sorry for your self.  You’ll have to get your growth mindset in gear, and make plans to have growth in those areas that aren’t working.  Make plans to address them so next time you can say: “Well this isn’t working, but I am on the way to fixing it.  Some general plans to getting things fixed could include:

• Asking for help from colleagues, friends, or other people
• Trying a new technique to see if it works
• Reading more resources for teaching
• Looking around the #MTBOS for ideas
• Sitting down with people in your class and getting to the root of the issue
• Sticking with what you’ve been doing, but with more preparation, more planning, and broken up into different chunks.

Hopefully this helps out, I’m only a little ways into teaching, but I’m going to explain why I’m hot, and why I’m not in a few weeks.

If teaching is improved, the improvement is the result of a teacher making changes in the classroom.  Perhaps policy, professional development, or standards inspired that change, but what matters is what happens in the classroom.  There are a number of levers that can be pulled to change what goes on in the classroom, and a quick list could include the following:

• Content of printed or electronic teaching materials
• Way the teaching materials are introduced and explored with students
• Relationships the teacher has with students, and the students have between each other
• The conversational norms  among students and the teacher about the material
• The methods of formal and informal assessment
• The messages students receive about assessment, learning and mathematics as a discipline

A teacher could come in to work and tweak any of those things tomorrow, and notice a difference with their students.  The next day the teacher can take the change they made yesterday, and how it differed from previous classes, and try another tweak.  Over a school year of tweaking their teaching, as well as noticing, and responding to the differences, the teacher could improve at teaching.  Teachers making adjustments in their class and learning from what changes is perhaps the only way changes in teaching practice.

#### Traditional ways of changing teacher practice

The traditional methods of changing teaching, such as PD,  attempt to create the catalyst that starts the teacher along a chain of reactions of tweaks that will lead to changed practice.  A one day PD gives teachers 3 examples of new lessons with the expectation that teachers will take those 3 lessons, use them, and question their current practices in positive ways.  The PD would then be a one-time catalyst of future growth.  Of course if the chain reaction dies out before the teachers leave the conference hall, then it will never have any intended effect, even if the teachers pantomime the 3 lessons and go back to business as usual next week.  This may not be the fault of the PD either, the teacher may be in the middle of working on some other part of their teaching, or have a different adult learning style.

In this traditional model, those in charge of improving teaching can only worry about the clarity and power of PD’s ability to inspire a change in the teacher, but cannot support the continual process of experimentation and noticing the difference.  What could be a new way to do it?

#### Supporting The Process

Blogging sounds like a perfect method towards supporting the process that teachers start in their own classroom. It provides a place to document the little changes they make  and also get feedback about those changes.  They can read about things that other people are doing in their classrooms they can learn new things to try in their room.  Thus, the blogosphere serves as a 24/7/365 set of ideas that can catalyze a chain reaction of teacher growth whenever the teacher needs it (as opposed to the 3 designated days on the district calendar).

There are certainly other ways to spark, support, and push the on-going teacher development process taking place inside their classrooms.  For people who aren’t interested in typing, there is a lot of value in talking about teaching with your peers.  A structured way to do this would be in a professional learning community and looking at different products of student learning through protocols.

Teachers reflections about their teaching are only as good as the information they have about it.  Having clear formal and informal assessment practices would allow them to have more information to base their next decisions on.  Other teachers have learned from having student surveys and feedback forms about their teaching.

Nothing is more important than doing something. There are also a number of specific technical things that can be done by teachers to improve a specific facet of their teaching.  I think part of what you’re asking in your tweet is how do we get people to improve their teaching when they might not want to otherwise.  We can package up a bundle of practices and air drop them into teachers lounges across the country, but it won’t make a difference unless teachers are actually trying them.  Actually trying means accepting the fact that constant change and growth in your practice is as much a part of a teacher’s life as having summers off.  (It’s not just teacher’s.  Surgeons, artists, scientists and many other professions have to hone their methods and explore new procedures

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