Week 1 in Review

Year two is off to a great start. So far I feel I’ve done a pretty good job of meeting my goals of being prepared and being present. I have actually felt like I’m in the moment in all of my classes. Looking back, I was spending quite of bit of energy last year worrying about how things were going. Now I’m in the flow.

I’m teaching two sections of IMP1 again and teaching a class for the second time is… I actually don’t know how to describe it… a joy?  It is so much less stressful.  I’m trying to not to assume that this year’s students will be exactly like last year’s, but it is nice to know where the potential road bumps are in the curriculum. I also feel more comfortable in making pacing adjustments. Now I actually have time to polish opening PowerPoints – I know the questions I want to ask, this year’s task is to refine the wording¹.

I have three sections of IMP4. This is a new prep for me (and for our school). So far I LOVE IT. Honestly, I was a bit worried about how my students would do with attempting to solve this problem:

Image source: High Dive Teacher's Guide, Key Curriculum Press

The unit problem is to determine when to release the person from the platform so (s)he lands in the water. So far my classes have managed to extend the sine function beyond the first quadrant, determine an equation that models the height of the platform as a function of time, and accurately predict what this graph would look like. I’m not sure if I was more impressed with their development of reference triangles or of the periodic nature of the sine function.

Besides being impressed by their willingness ability to develop and share these mathematical ideas, I am completely blown away by the way they are working in class.  Sharing their thinking, proposing alternate methods, trying things and not getting stuck when they don’t work, helping each other in an appropriate manner, saying “slow down, I don’t understand”, having discussions, … my seniors rock!²

Next week things get a bit more complicated, but I am not nearly as anxious about their ability to handle it. I also need to do a bit more checking to make sure that everyone has fully grasped these concepts.

Also coming up next week is preparation for homecoming activities (I’m the sophomore class sponsor and we’re in charge of planning the PowderPuff game – we’ve also got the usual decorating that goes along with that) and the first practice for math team³. Grad school starts the week after that. I’m hoping to get the rest of my grading and planning done tonight so I can spend the rest of the weekend relaxing.

¹I’m also working on the design, but I don’t think I’ll ever be happy with that.

² I have actually heard things like, “Well, I’m not going to tell you the answer. Explain what you understand about the problem and what you’ve tried”.

³ Hey, does anyone have any really good competition problems on the geometry of right triangles including trig?

And so it begins

Tomorrow is the first day of school. I’ve been thinking about my goals for the year. In doing so, I realized those two statements I posted are actually my goals for the year – be prepared & be present. For me being prepared means knowing the mathematical goals of each lesson – crafting the right questions, designing meaningful activities, structuring the class to allow each student access to the concepts, … Being present to me means to be totally focused in the moment and what is going on in the classroom – despite what else may be going on in my life. The students deserve my full attention, so when I walk through those doors and the bell for each period rings – everything else fades away.

I’ve also been contemplating Bud Hunt’s “Open Letter to Teachers”. I’ve read it a few times now. What struck me most was his line, “Try very hard not to work all the time.” I don’t think I did a very good job of that last year. So I’m extending my “be present” goal to my time away from school. I’m starting a grad school program next month, so I know finding a balance will be vital. I need to create a time each day to turn off Jackie the teacher and Jackie the student and just be. I think my husband will thank me too.

Lastly, I just ran across these 10 Commandments for Teachers written by Pólya:

1. Be interested in your subject.
2. Know your subject.
3. Know about the ways of learning: The best way to learn anything is to discover it by yourself.
4. Try to read the faces of your students, try to see their expectations and difficulties, put yourself in their place.
5. Give them not only information, but “know-how,” attitudes of mind, the habit of methodical work.
6. Let them learn guessing.
7. Let them learn proving.
8. Look out for such features of the problem at hand as may be useful in solving the problems to come – try to disclose the general pattern that lies behind the present concrete situation.
9. Do not give away your whole secret at once – let the students guess before you tell it – let them find out by themselves as much as is feasible.
10. Suggest it, do not force it down their throats.

I really like the part about “give them habits of mind”. That is such an important piece, the ability to think about one’s thinking.

And thus the year begins. I’m looking forward to it.

One Graph, So Many Questions

I’m not sure where I first saw these types of questions. It was either at  Dan Greene’s¹ or the Pre-AP Mathematics site². Sadly, it was not in a textbook.

Here³ is one I made last week.

I plan on using this with my freshmen sometime early first semester. There are a plethora of questions that can be asked, depending upon the concepts your students have learned. Some examples are:

• What is the midpoint of segment AB?
• What is the length of segment BC?
• What is the distance from A to C?
• What three dimensional figure is created when AB is rotated around the y-axis?
• Draw a segment from point B to point D. What is the area of triangle BDC?
• Draw the graph of f(x) + 2.
• What are the zeros of f(x)?
• What is the domain of f(x)?
• What is the range of f(x)?

So, you get the idea. What other questions can you come up with?

¹ Dan Greene has some of the best stuff out there when it comes to multiple representations. I’ve used this on composite functions and this on transformations. Good stuff.
² There are some nice activities at the Pre-AP site. I really like the idea of adapting released free-response questions too.
³ Here is the worksheet .doc or .pdf Only want the graph? Here you go .png

NotK12Online

Bud Hunt has asked me to join the NotK12Online planning committee. What is NotK12Online? Great question. That’s one we’ve been trying to figure out. Bud has the introductory podcast up here.

The committee is made up of a great group of people, with whom I’m looking forward to working:

Bill Bass
Twitter: wbass3
Email: bbass3(at)gmail(dot)com

Marcie T. Hull
Twitter: ecram3
Email: ecram3(at)gmail(dot)com

Bud Hunt
Twitter: budtheteacher
Email: budtheteacher(at)gmail(dot)com

and me:
Twitter: jackieb
Email: jackie(dot)ballarini(at)gmail(dot)com

What is NotK12Online? To quote Bud, “It’s new.  It’s different.  It’s a walking contradictory paradox.” Listen to Bud’s podcast. Please contact me or any of the other members with your ideas and input.