Useful PD!

The professional development I attended over the last few weeks was really good for a few reasons: 

1. the presenter teaches math and works with kids on a regular basis (she knows what it's like to teach math right now)

2. it was relevant (she asked what topics we were currently working on, visited our classes to see first-hand what we're working with and the whole thing was targeted to teachers of grade 9-10 "at risk" kids)

3. it was all about what to do (there were actual tasks, she gave us materials and let us try out activities)

4. the philosophy was research based (personal research in her school as well as cited articles, all of which was intermingled with the activities so every philosophical point was paired with a concrete method of applying the philosophy)

So, now that you're jealous that I got to go to 10 hours of really well planned, awesome PD, I'll share what I learned.  (If you happen to teach near Beverly, MA then you should just get someone from Landmark out to your school.  If not, my summary of what I took from the sessions will have to do.)

Sorting activities:

Jen (our presenter) is all about sorting.  She has sets of cards for a variety of topics and she has students do several things with them.  They work in groups and might sort by anything they want, or into a specified number of categories, or into the groups 'got it,' 'working on it,' and 'not yet.'  I enjoyed sorting quadrilaterals with my students earlier this year but hadn't thought to use it in other ways.  We tried sorting fractions and decimals with my self-contained SPED class and I learned so much about their understanding (and lack thereof).  Categorizing is an important skill especially when it helps streamline problem solving (this is just like ____ that I already did), students also have to practice communicating the characteristics and pay attention to detail.  When we sorted decimals the students were confusing decimal points with multiplication symbols- it's a tiny difference in placement that totally changes the problem.  Another good sort: pile problems based on what formula/method you would use to solve it, without actually solving them.  It gets kids exposed to a lot of problems and thinking about all of them, without the time it takes to actually go through the process for every question.  We did it with the state test reference sheet so it would be a great way to familiarize students with that resource if they know how to solve the problems already (or if they would, once they found the formula).

Quick practice:

We share these types of activities all the time so most were a refresher for me (good to have though, since I always forget!).  Quarter (or eighth) sheet: cut the worksheets up into individual problems with enough blank space to work the problem.  Students aren't overwhelmed by how many problems they have to do, don't feel 'done' when they finish the page and don't feel bad if they don't finish the whole page.  Put a couple stacks around the room and let them have at it.  This also works like basketball/solve-crumple-toss.  Round Robin: each student is responsible for one step, then passes the page.  We did order of operations so everyone did parentheses, passed, did exponents, passed etc.  One sheet per kid, but each kid works on several problems by the end.  Fold and Pass: In this version the goal is to go back and forth, like between factoring and expanding quadratics.  The top of the page has an equation to factor, then the original gets folded back and the next person has to expand what kid 1 just wrote, continue until the sheet runs out and hope that it matches the top!  This one was new to me, and at first I wasn't sure how to apply it in geometry.  After some thought I'm excited to try it with vocabulary where the rows will alternate between word and definition with maybe a diagram thrown in there.  I am betting it will work about as well as the game telephone does at first.  Another example of how to use it was fraction-decimal-percent-decimal (repeat).  Tic-Tac-Toe: using plastic sleeves, put 9 problems on a grid and students get to choose which to solve in dry-erase markers, putting their X or O only if the partner agrees the solution is correct.  I'm honestly more excited about the reminder that plastic sleeves work with dry-erase than playing the game, but having students think strategy is definitely a good idea.

Notebooks:

I don't require students to have a specific organization system, mostly because I'm really organized and always liked my system- I don't want kids who already have good skills to resent my imposition.  I did provide notebooks when I taught a class where we used consumable textbooks and I loved how organized everyone was.  My goal for next year is to impose a flexible system that will work for everyone.  They will need a small 3-ring binder with sections.  The thing that really swayed me toward having binders was when Jen said that students at her school clean out their notebooks at the end of every unit.  It makes so much sense but I never thought to do it!  Kids don't need to carry around all of their notes, old homework and worksheets after a unit because they should have made a study sheet with all the important information and have a test with example problems.  The old papers can be filed just in case someone wants to look back- but all of that practice and learning process should be internalized and it shouldn't take more than a good study guide and any other reference materials to recall anything they need to know.

The sections will be: Reference: including the state's sheet, study guides, tests and any other summary, maybe 'flappers' (a sheet of paper with index cards taped down so the title of the card is visible, on the card there are definitions/steps/examples or whatever other cues a student may need, mini-example below).  Notes/practice: looseleaf or spiral notebook to take notes and do classwork that isn't on a worksheet.  For students who may lose their binder: the binder would stay in class and only today's notes would go home to assist with homework. This section is cleaned out every unit.  Handouts: next year I want to type up homework problems so I can personalize them and kids don't have to carry around a ridiculously heavy textbook, plus this section would be filled with all of the photocopies I give out in class.  This section is also cleaned out every unit.

By the end of the unit the whole page would be filled.
But it would be easy to find each card!

Use the back, or don't.
Also works with printed cards (instead of index).

I'm excited to use the activities we talked about and to plan out next year's system more carefully.  It was so nice to have professional development that was immediately useful and got me thinking about my practice. 

Station Rotation

It's funny sometimes what it takes for me to try something new. Whenever I would hear people talk about doing stations I'd think "that's a good idea" but by the time I got around to planning my lessons I would forget or not see how to make it work. Until @jreulbach posted about using picture frames. Yup, all it takes to get me to do something is a trip to the craft store (or in this case the craft section of Walmart, where I bought some yarn too, of course!). Once I had the set-up it was easy to find activities among all the usual ones I do, plus all the cool stuff I've been reading about but had yet to try.

Both my fundamentals and CP geometry classes finished a unit on similarity in the past couple weeks. I set up stations for Taboo, koosh ball smart board (with kuta worksheet problems and answers hidden so they could self-check), write your own word problem, solve problems that make a sequence (answer is on the back of the next card), make a poster for a vocab word (fundamentals only), proofs framed as 'match the rule' (CP only) and converting recipes.

The students worked in self-selected groups of 3-5 and chose the stations in any order. We didn't have enough time for every group to go to every station (spent about 15 minutes at each) but there was plenty of overlap so everyone got some practice solving problems as well as doing something a bit different than the typical day.

They gravitated towards taboo and the smart board for the most part. Groups were excited for the recipes, but then discovered it was harder than they expected. That was the only station where students were not actively working the whole time so I need to skip or change it next year. One group complained about the 'match the rule' station "What's the point of being in groups if we have to do it individually?" which highlighted my concern that not all students are working when they are in groups. Allowing students to self select groups also meant that there was one group in each class who I really needed to check in on a lot, but it turned out to be easy enough to spend most of my time with them rather than having multiple groups each with one student who would be continually off task. Especially since most stations were self-checking, it was okay to spend more time with one group. This is definitely something I will do again whenever we need review. Moving around, mixing it up and having choices are all really important and this set up lets us do all three!

In case you're interested, here are the instructions for each station. I bought 5x7" frames so with a bit of folding and trimming half a sheet fits right in. These should be one set of instructions in one column, but scribd might have done something weird. Both recipe instructions were at one station.

Similarity Stations


Recipe Proportions

Area of Quadrilaterals

Last year I wanted students to discover the area formulas of quadrilaterals by breaking them down into rectangles and triangles. Except, I didn't explicitly tell them that. Instead I assigned groups different quadrilaterals, told them to find the area of a few specific examples and then come up with a formula. It didn't go so well, although a couple groups did get where I'd hoped with little to no support. The rest of them balked at my vague instructions. I constantly struggle between providing so much support that no one has to think, and so little support that everyone gets so frustrated they can't think. Ashli posted a great quote about that recently: "The clearer you are about what you want, the more likely you are to get it, but the less likely it is to mean anything" -Dylan Wiliam

This year I took an online course in Geometry, Measurement and Technology where we had to write a lesson that used technology. I chose this topic for my lesson, but I struggled to make the tech useful and to decide how much support to give. I made my own applet on GeoGebra since I couldn't find one I liked (a learning experience on its own). I'm actually rather pleased with how the applet works and think that it has added value over paper since students can see so many examples and I can give them a much more subtle nudge to be sure they see the patterns. [overall instructions] [applet instructions] Now that the constraints of the online course are over I definitely plan to re-work the handouts I give to students so that they go in order (it was surprisingly difficult to manage two handouts that jumped back and forth plus a laptop). I will also restructure it so that students experiment in class and write a lab report for homework.

Side note: I'm aiming for one lab report per quarter, full write up, following the science department's format. I like doing them, but only enough to be willing to grade them four times a year. First quarter was parallel lines and a transversal via GeoGebra, second quarter was congruent triangle rules via NCTM, third quarter will be area formulas (this year it counted as a lab, no report, in my mind) and fourth quarter is still up for grabs. Maybe something trig?

The students who carefully read the instructions and completed each step were quite successful in working independently. This was an activity where I refused to answer most questions, instead directing them back to the typed instructions, their chart or the computer for further exploration. The tricky part about this activity is that most students have seen some of these area formulas before so they know what they're "supposed to get." It was a great experience for the students who chose a trapezoid and managed to start with rectangles/triangles, factor/simplify and end up with the familiar trapezoid formula. For those who didn't reach that point it seemed more contrived than our usual discoveries since they are used to discovering ideas they'd never seen before, as opposed to proving something they knew but didn't understand.

Patterns

Yesterday during lunch duty I was talking about what I really want to teach one of my classes*.  I just introduced fractions last week and we did a lesson on ordering fractions last class.  It involved putting fractions in order and then making observations.  During the conversation I realized it is much more important to me that the students be able to recognize patterns and describe them, than to do anything more with fractions.  So, then and there I decided we would spend some time studying a variety of patterns.  Of course, I totally forgot until later that evening, but I asked twitter for ideas and they responded brilliantly to my request.  So much so that I want to share with you exactly what they said (grouped by conversation, some liberties taken with ordering).


7:16 pm: Tina asks twitter for help


@crstn85 What's your favorite pattern problem accessible to basic math kids? Decided at lunch today to study patterns tomorrow but forgot until now!

@jreulbach  Fibonacci. Or pascals triangle.
@crstn85  just searched the state test and they have pascals triangle but with 2 on the outside. We shall do both!


@Mythagon  1 11 21 1211 111221 312211 ...
@dandersod  thats a good one. Here's another: 3 3 5 4 4 3 5 5 4 3 6 ...
@johnberray Besides Fibonacci and @Mythagon's, I show harmonic sequence and perfect squares. Students find all sorts of patterns in squares.

@MathyMcMatherso Collatz Conjecture & Palindromic Numbers.  http://en.wikipedia.org/wiki/Collatz_conjecture & http://en.wikipedia.org/wiki/Lychrel_number
 @crstn85  simple but unsolved, what a cool thing to share!
@MathyMcMatherso  I know! That's why I love them

@crstn85  Thanks for all the awesome patterns! This is definitely going to be a unit not just a day before long weekend activity. You all rock.


@lmhenry9  Did someone give you the pattern with the perfect squares (1, 4, 9, 16, etc.)?
@crstn85 I'm doing that one with actual squares. I love the locker problem but one kid can't track a number line so it might be too hard...
@crstn85 oh! I just realized we could do it with pennies heads/tails. And maybe tally marks underneath? This has potential for next week.

10:01 PM : Tina goes to bed, but twitter never sleeps!


@lmhenry9  Cool! I'll be curious to hear how it turns out. I do like the locker problem as well.

@dandersod http://mathtest.idiotworld.com/
@MathyMcMatherso Bookmarked - soon to be used in math club.
@dandersod  it's a great site. Some brutal ones that high schoolers have no right getting.

@MathyMcMatherso  Just remembered: did patterns as a filler-thing to start school year. Here's the wkst I made:http://www.box.com/s/ec46ede0600ef8d1aa7f. hope it helps
@crstn85 excellent! I didn't get into visual patterns much so this is helpful.
@wahedahbug  I agree those visual patterns are GREAT!





By the time I went to bed I had Pattern Sheets A, B, C, D, E, F and G made.  The combined resources of the state test database (all the problems that I didn't type out) and online colleagues is rather astounding and I didn't use nearly all of their ideas yet!  The next morning I set up the locker problem sheet like I'd discussed with Lisa (during class, actually, when I needed a 5 minute break- they pulled it together since they knew I was mad and I calmed down and got to get the idea out of my head and onto paper where it couldn't bother me anymore).


The plan had been to give students the choice of any pattern sheet to start; everyone works at their own pace and we'd keep going until they were sick of patterns.  They had a different idea.  One person was excited about Pascal's triangle since it had a fun looking diagram, so everyone grabbed the same sheet.  Then we worked together, taking turns filling in parts on the smart board.  I was amazed that they happily spent an hour on just the first 7 rows of the triangle.  They noticed all sorts of patterns, then I had them color in multiples of 2, 3, 4 or 5 and we re-did the one on the smart board to reflect their coloring and found lots more patterns.  These are students who don't normally talk to each other so it was great to see them verbalizing so much of what they saw.  We even worked on taking jumbled ideas and forming coherent descriptions.  These kids awe me every class.   


*They're a group of 7 students who all have 'intensive' learning disabilities (a category between moderate and severe, they're in most - if not all - self-contained classes and have autism, pervasive developmental delay or some other significant cognitive impairment).  Each has a different background, but they all have had very little traditional math.  This is refreshing in some sense since I get to teach them everything: they haven't learned anything wrong and I know exactly what language to use to refresh their memory since it was my language!  But it's also overwhelming since I have to teach them everything (starting with multiples of two for some).  Two students have opted out of the state test (they're seniors) but the others have to take it even though they will never function at the level of their peers.  Administration is totally focused on passing the test, but as long as I assure them that we're studying MCAS topics (which we are!) I have pretty much free reign.  While the kids don't have a math background, these students are learning more than I thought possible, and much more than they thought they ever would.  On several occasions students have said to me "I get this!" or "I'm learning math!" or "I'm getting better at ___!" in total shock.  It gives the mantra of "high expectations" a whole new meaning.