I have been working through the lessons for one of my new preps next year. I am working day by day through each activity/assignment – as both a student and a teacher.

First I “just do” the assignment as a student would. However as I’m doing this, I’m not only doing the math, but making notes to myself regarding the wording of questions, how long each problem takes, what is needed to do the homework (graph paper, calculator, … ), and misconceptions students may have.

Next I’m switching into teacher mode. I’m asking myself questions about goals:

- What is the mathematical goal of the lesson? What idea/concept/skill is this addressing? At what level… exposure, mastery, or extension?
- Is it a worthwhile goal?
- Is this the best way to meet the goal?
- How does each activity contribute to the overall goals of the unit?
- Will supplemental activities be needed? (
*I have a hard time with this one – how am I supposed to know now, what my future students will need?*)
- What is the process goal? How will the students develop the mathematical goal?
- How will I know if the goal is met?
- What will I do if it isn’t?

I’m open to suggestions, thoughts, ideas, … is there anything I’m missing? A better way to do this?

So far I’ve worked through one of the five units. I’ll be posting my reflections on the first unit soon.

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This is one of those questions that’s probably painfully obvious to people with more/better resources. How are you able to do the student perspective first? Where are you getting your assignments?

(I’m getting motivated to go through my preps and I know backwards planning says to get the assignment out of the way early. I just don’t think I can do that before figuring out what my goal is, looking through the sample textbooks that I do have, searching online, and then coming up with the assignment.)

Ah, good question Sarah. To summarize a very long story, we use Interactive Mathematics Program. Next year is our first year in rolling out the fourth year of the program. So, everything is there for us – in class activities and homework. Do we use it “exactly” as dictated? No – hence the summer work. We’re each (the four of us teaching it next year) going through it and meeting periodically over the summer to discuss what we like/don’t like.

You’re prepping already! Noooo…I’m going to pretend I never saw that π

Granted, my new prep is just math 7. Doesn’t require a whole lot of math thought on my part, just instructional thought. This can happen in August, right? (just nod along)

Ahhh. I have IMP year one in my pile of books to sort through…

My mom was on the textbook committee for new math books when I was in high school. She really liked the books from Key Press, but the teachers were reluctant to transition to the discovery curriculum. Only after teaching do I understand why (though I still don’t appreciate it). Anyway, she’s amused that their books are currently covering the dining room table.

I’d add a question that has helped out my prepping considerably: Given that you now have a well-defined and worthwhile goal, is the lesson that you have planned the simplest possible way to get students to that goal?

That is, have you overcomplicated or overthought the lesson? Could you make a shorter, briefer, simpler lesson that has the same amount of instructional value as the one you have?

It’s amazing how much junk and fluff my lessons have before I start editing.

Oh man, I’ll bet you’re working through the ferris wheel problem, huh? Have fun with that one π

Jackie, when I work through a new unit in IMP, I do pretty much what you’re doing. We do tend to alter a few things after a year or so of teaching the units, but before that I always try to give the writer of IMP (and CMP) the benefit of the doubt and stick as closely as possible to what they intended. Sometimes I’ve underestimated how students will be able to handle a certain topic in the curriculum, only to find that indeed they were ready for it at that point in the master plan.

I’ll only be teaching IMP2 this next year, along with a bunch of computer programming classes. Kristi Julien, however, will be doing level 4 again and is happy to give advice if you have questions. She may be hard to reach over summer, though, so if you have specific questions, send them to me and I’ll get them to her somehow–maybe via bike messenger or something!

Richard

JackieB,

You deserve a massive pat on the back for being so deeply toughtful and reflective about your instruction. What you’re doing is very similar to some protocols we use with teachers to get them to collaborate with one another regarding instruction. It seems to me you’re at the beginning phase of this (troubleshooting and examining each lesson/activity). Sometimes being able to have a colleague (perhaps one who is not a math teacher) experience pieces of your work can provide you with another perspective.

As a staff developer, one of the programs I’m involved with is Schools Attuned. One of the processes in that training is to look at your strengths and reflect on how often you teach to your strengths. The next step is to say, “knowing that I probably teach to my strengths, how can I provide opportunities for students with opposite strengths to succeed in learning what I’m teaching?” It’s a very powerful look at differentiation and strength-based learning.

Reading your post MADE MY DAY.

JenI’m here nodding. August is fine, really…SarahDo you get to choose your own textbooks? Every year?That’s a great question

Robert, thank you! I’ll keep that in mind as I’m making the supplemental activities.I

lovedthe Ferris wheel unitRichard. I thought it did a nice job of developing the sine function. I like that graphing the functions isn’t treated as a separate concept. Right now, I’m working through the programming unit. I appreciate what you said about not making too many changes during the first year of implementation. We are still debating our plan for the year (there are three others teaching Year 4). Thanks for the offer for help. I think I’ll be taking you up on that!That is an interesting point about teaching to

mystrenghtsTim. I hadn’t (actively) thought about that before. I do try to stress multiple methods in my classes, but I wonder if I overly stress the method that makes the most sense to me. Excellent reminder. Thank you!Jackie,

Came across this today and thought you may want to consider vodcasting as they describe in this video as an instructional method. At the end, they mention students would love a similar approach in their math classes.

http://educationalvodcasting.com/samplepodcast.asp

What do you think?

karenjan, I don’t know about younger (read: k-8 ) students, but I can definitively say that I would not have liked vodcasting in math (or any of my classes) in high school (and possibly before, though I can only make that claim for the past few years). If I’m learning something (and therefore don’t really know what I’m talking about), I’m certainly not interested in recording something in a one-shot recording that will be available to dozens (if it’s limited to the school) to millions (if it’s public) of other people. If I already know what I’m doing, I have little interest in doing a vodcast to prove I knew it. (On the other hand, if I thought it would help other people understand, I’d be willing to try, though I’d still prefer something that wasn’t one-shot.)I see that as a bit different than a blog post or such, where I could feel free to edit, go back and change something I realized was wrong, or ask a question without being incredibly obvious / disruptive (as it would be with a vodcast, in most cases, lacking proper editing equipment).

(Obviously those are just my thoughts, which don’t really apply to anyone but me, and could very well not apply to me in a few days. But they’re valid at the moment..)

That is an interesting approach. I might consider it if I actually lectured in class. However it is rare for me to be at the front of the class explaining anything. The classes I will be teaching next year are have a focus of the

the studentsexplaining the methods they used to solve the problems. Then we have discussions and compare solutions. There is a combination of individual work, small group work, and whole class discussion.One of my goals (and my department’s goals) is creating an environment where there is shared mathematical authority. The activities are designed so that each lesson builds upon the previous and students are able to develop the ideas with very little direct instruction from me.

…and it appears that my last comment entirely missed the point. Whoops, sorry. When the teacher does it, there are a slightly different set of issues: It can take away from the time the teacher has to prepare for the rest of the class, though it may make the presentation more well thought-out. If the teachers don’t later teach exactly off the same notes they used for their vodcast, things can work out well, but not being able to be flexible from there (as the teachers have apparently gotten comfortable with their presentation without an actual audience) could be dangerous.

However, I will agree that that could be valuable for, as

Jackiepoints out, lessons that are almost entirely lectures. (Though I might question the value of that over a well-presented blog post / webpage / whatever, as it’s far easier to view the plain website than a video, both from the bandwidth/hardware perspective and the fact that it’s easier to skim text than audio.)“itβs easier to skim text than audio” perhaps for you

Andy, but there are students who struggle with reading for whom the auditory approach would allow them to have access to the material.Jackie,

So glad you mentioned that last point, which is ultimately the point anyway. Different students learn best with a variety of instructional methods and strategies. Understanding the educational rationale for the methods we choose is vital. And considering and adapting to the different learning styles of the students in our classrooms is essential as well.

Many teachers still rely predominantly on a lecture/textbook/print approach which is not helpful for many students (as you know).

(I find it fascinating that you rarely lecture in class. That was the approach that was used by all my own kids HS math teachers. I often heard, “mom, i understand it in class: I don’t get it now. Wish you could have taught my kids!)

Ah, not quite the choose-your-own textbook.

My school’s a mess at times. (If you want an expanded story, I can e-mail it.) For now suffice to say that the books on the table are truly sample textbooks and that the textbook the school has was not included in the materials I brought with me for the summer. Hence the ever-present need to try to plan ahead now, rather than sort through everything as I’m doing it.

Work, self, work. (Sorry Jen.)

Karen– thank you. I try to have the students actually doing the math in class – then I can see what they’re thinking and on what we need to work. Watching math done is very easy. However, as you know math is not a spectator sport!SarahSounds, uhm, interesting. Yep, plan ahead… that’s what I keep telling myself. (ignore thisJen).Be careful what you offer

Richard. I’ve got a running list of questions about As the Cube Turns (mostly logistical). I’ll be sending that in a few days. Any help is greatly appreciated. Seriously, sheets of Plexiglas? Did you find an easier way? Oy.Well, mostly what I offer is access to Kristi’s expertise! Some of the students in my programming club, however, just finished IMP4 (with Kristie) last year, so they could maybe help out too, with a student’s perspective.

I always get distracted with the Cube unit, as I don’t do the programming on the TI calculators. Kristie does, though, and likes that unit. I know that the lessons learned are very useful for any students considering 3D game programming. Last year one student told me that it would be easy to program the unit challenges using Python and Pygame.

Kristie is wonderful, though, so as soon as she’s back from vacation I’ll mention this to her. She’s a real advocate for IMP with a long history of teaching math in many different schools. She’d love to help out.

Richard