Losing (My) Marbles

My AP Statistics class starts Probability sometime next week (I’ve scheduled a couple days of how-to-answer-multiple-choice in there, so I’m not precisely sure when). I’m dreading it.

I think I’m less-than-great at teaching it, but I also think I come up against a lot of baggage when we hit probability. No one thinks they know z-scores. Students readily accept that I will teach them new things about scatterplots. But probability? I’ve got that down.

Probability is easy, right? We started those problems in third grade, and for whatever reason it shows up every.single.year. Marbles? Jelly beans? Candy? Socks? Shoes? Elvis’ jumpsuits? Done ’em all.

And so I take a bunch of students who “know” probability and…it all falls apart.

I suspect the breakdown happens in between the students feeling like they’ve totally got probability (marbles) and getting at the idea of a long-run frequency of something occuring. Instead of probability as “over many tosses, about half will be heads”, it becomes “you get heads half the time, because that’s just the way it is. And since I just got tails, heads is next.”

So how do I undo that? How do I help them see probability as long-run chance, and never ever a sure thing (well, unless its 0 or 1)?

Part of me thinks I should try to teach as much probability as possible without using the word “probability”. Or maybe do some exploration of different probabilities before I start formally teaching the actual content.

Part 2 is how tricky vocabulary is around probability (especially since English isn’t my students first language). Last year I did a foldable with vocab but I’m not sure how helpful that was (if at all).

Should I have the students model the same situation several ways? Generate our own data and use that?

How do you teach probability? Any ideas of where the disconnect might be? Help!!

Number Sense: Whatever That Means…

Next up in Algebra 1 is “Number Sense”–I pushed hard for this one, and we have around three weeks. As I talked with a coworker today, he pointed out that much of number sense can’t exactly be taught–a point I only partially agree with.

Wikipedia says, The term “number sense” involves several concepts of magnitude, ranking, comparison, measurement, rounding, percents, and estimation, including: [10]
  • estimating with large numbers to provide reasonable approximations;
  • judging the degree of precision appropriate to a situation;
  • solving real-life problems involving percentages and decimal portions;
  • rounding (understanding reasons for rounding large numbers and limitations in comparisons);
  • choosing measurement units to make sense for a given situation;
  • comparing physical measurements within and between the U.S. and metric systems; and
  • comparing degrees Fahrenheit and Celsius in real-life situations.[10]

All good points, if technically stated.

I’d call number sense being able to understand relative size and equivalency of numbers, estimate both individual quantities and combinations (like products and sums) and locate numbers on a number line. I know I’m missing a lot here, and I plan on refining that definition a lot (notice something? Let me know in the comments!).

That’s all good, but I need to determine how that translates to the classroom. I talk a lot about fractions below, and have a lot more to say about them, but have been really pressed for time. I worked with my elementary school teacher/math specialist sister to develop a lot of what I did, including rethinking my OWN understanding of fractions, and I’m really excited for where my other class goes with this.

One thing for sure: I want to use Estimation 180 throughout this unit, hopefully daily (discovered through Infinite Sums).

Here’s my very work-in-progress plan (these are topics; some might be several in a day, others might take multiple days):

  • Prime Factorization
  • Place value (naming place values, building numbers, identifying place value of a specific digit and vv, naming numbers correctly)
  • Powers of 10 and equivalent forms (x 10, x 0.001 etc)–we will use the Pyramids again here
  • The Fraction Screener (to give me an idea where my students are)
  • Folding Fraction Strips & Defining Unit Fractions
  • Modeling fractions using fractions strips and number lines
  • Comparing fractions & summarizing comparison rules
  • Locating fractions on a number line and representing fractions several ways
  • Fraction equivalency (Stuck on: how to prove two fractions are equivalent)
  • Ordering fractions, then locating them on a number line, including a gallery walk style group placement activity
  • Adding, Subtracting, Multiplying and Dividing fractions (maybe. I teach 9th grade. My kids have seen this over and over and over–I don’t want to repeat the stuff they’ve already seen/heard/done, so I’m only doing this if I really think I can add value)
  • The ONE (using pattern blocks to determine the whole for different size partitions
  • Converting between fractions and decimals (use a calculator? I’m not sure I see too much value in having them convert to /10, /100, /1000 but I’m open to the idea)
  • Equivalent numbers and expressions (both 3/6 & 2/4 and 4+7 = 2*6-1)
  • Basic probability (relating it to fractions too, since who doesn’t like beating a dead horse)
  • Ordering decimals and large numbers on a # line (including a great world populations number line activity)
  • Distance on a number line (and scale? Will this help prepare for graphing?)
  • Order objects (the online game I found here via Infinite Sums)

This is where the order falls apart a little bit…

  • Classifying Numbers
  • Properties of real numbers
  • Perfect squares
  • Benchmark values (along the lines of estimation 180, the average could reasonably be which value,
  • Other number systems, like Mayan and Egyptian (honestly, because this will be on a test I have to give at the end of the quarter)
  • Perimeter and area; frequency tables (not even number sense. Just on dumb test.)

Overall ideas: Does this make sense? About how much would I expect this to be? That’s really the point of number sense, isn’t it? To understand how much it is, without going through a bunch of rules, especially rules that we understand only as rules and not as concepts. The one thing I don’t want to do is rehash the same old same old they’ve already seen year after year and never quite understood.

What does Number Sense mean to you? What am I missing? Any ideas?

Post it Planning

This is what my desk looks like right now.

Post it plans

It makes it a little hard to work on anything but my plans for AP Review. The fact that I have a month (?!?!?!) to prep for the AP is amazing. This is my third year teaching the course and by far the most time I’ve had to review with my students. Thats great, but it means that I don’t really know what to do with it all. I have plenty of random-all-over-the-place ideas, but how to know the good ones? How to decide what order, and what gets done in class, and what homework is?

I have no idea.

But I’ll get there. I’ll shift those post its all over my desk, and pair homework (the pink ones in the bottom two rows) with classwork (the green in the top three). It will come together into a schedule, and in a perfect world, every minute of time will be used efficiently and effectively and my students will be awesomely prepared. Or at least thats the goal.

Do you ever use post-its to plan? They are probably my favorite tool–I love being able to pick things up and switch them around so easily.

Binders: The Advanced Class

I’m sitting on the living room floor surrounded by paper right now. Specifically, everything I have about Producing Data, Chapter 4 in my current AP Stats text. I’ve taught Stats before, but not for the past two years. My binder organization is a post-AP two yearl old relic. “Great, hole punch everything, stick notes, everything else, then quizzes and tests. Done.”

I’m pretty sure I didn’t look at it all in the intervening two years. And while making binders perfect can seem like a waste of time, I think its about a lot more than that. I hope to be always improving and changing and growing. I get a lot of resources, I see things on blogs or pinterest or at a PD that I like. And I want to be able to use it. So I’ve been doing a lot of thinking lately about how best to set up everything I have so I might be able to use it again.

As I work with my two resident teachers this year, I am realizing all over again how hard it can be to keep track of what you’ve done so you can use it again. That’s really a shame, because I think of one of the things that contributes the most to great teaching is having more time to make things great (instead of ok) as your career progresses. The first year I teach something, I’m keeping my head above water. I don’t have the best idea how everything fits together. I’m not entirely sure where I’m going with the curriculum. I may happen upon a couple of great ideas, but there is a lot of, “I should have _____. Next time.” involved.

“Next time” is when the real fun comes in–when you get to start tweaking and changing and refining. That process is individual for everyone, so I could use someone else’s rockstar activity and need to tweak it so its a better fit with my personality, the way I’ve taught past topics, my students interests or whatever else.

Anyhow, I can’t tweak anything if I can’t find it. And I can’t use a great new idea if I no longer remember it or if its too much trouble to find once that topic rolls around.

This is a really big topic (for me at least) so I’m starting micro–with Stats. Its more of a closed system for me–most of my materials fit in two huge binders and overlap to other courses is minimal.

…and yet I haven’t broken out my binder once this year. I’m teaching the course from memory. That’s not impressive. It’s just dumb (with some disorganized mixed in). I have great resources, both my own and others–and I owe it to my students to use them.

Which is where I am now, sitting on the floor, with an open binder (just the first five sections of my master stats binder) and pages (the upcoming chapter) spread all over the rug.

Consistent order is good, although I’m not sure I like mine–the things I would look for should be in the worst spot, not the best, since I’ll look for them anyhow. Things I should try get first and last spots, where I can say, hey, whats this! And the most recent copy of that chapter’s schedule (which I revise yearly) always is the first page.

But is that enough? I think I should have some kind of a cover sheet to each chapter/section, where I can list what’s in there and also refer to other places (like blogs etc) where I saw something. If I know I pinned “Experimental Design foldable” to my Math Ideas board, I might go look for it, but if I have to sit there wondering if I’ve seen anything else good for experimental design, I might make it nowhere, even though something amazing is out there.

Stats seems like a good place to start, since some of the things I want to keep track of are done for me–like the suggested AP questions my book lists for each chapter.

Any brilliant ideas for keeping track of great teaching ideas in one manageable place?