Thursday, December 08, 2011

Triangle Quilt

Last year I realized that even though most students claimed familiarity with the types of triangles from middle school, they still didn't really know them (especially isosceles and scalene).  Plus, many were not adept at accurately constructing examples.  As a week before winter break activity I had all of my geometry classes fill a square piece of paper with examples of all the triangle vocabulary we had studied, then I took all those squares and filled a section of the hallway, making a 'quilt.'  This year I assigned the activity again, but instead of a review I used it as an introduction.  It was a great way to make sure up front that everyone had a solid experience with the vocabulary, not to mention I always enjoy the down time of a coloring activity (especially with my CP class who did this after they finished a test).

The assignment:

Triangle Quilt
The finished product:
The first round of submissions.

Final Result (Progress reports were due today
so nearly everyone has theirs in now)

Marginally related:

I love putting student artwork up in my classroom.  Whenever I see a student doodling something cool or showing off a drawing I ask them to contribute to my art gallery.  It all started last year with a centroid sailboat and has grown to take over a corner of my classroom.  I enjoy pretty things on the wall to look at, and it makes the kids feel appreciated when their work is on display.  I didn't remember to take a photo of it yet, but I do have some photos of the pieces my homeroom created after a discussion on bullying.  (These are in a separate corner.)

Aren't the birds beautiful?

The top left one says "Don't be an angry bird!"
Lots of birds because it was just before Thanksgiving and I suggested drawing hand turkeys.

Sunday, December 04, 2011

Know Your Limits

By the time Friday rolled around I was lagging, I guess it's a post-Thanksgiving phenomenon but it seemed like an endless week.  I'm not proud to admit that I yelled at one class on Friday when they were floundering.  I tried to do some open ended experimentation (which I will share once I've tried again with my other class tomorrow) and they weren't having it.  Whether I should have given more structure, support or time is yet to be determined, but getting mad is never the answer.  At least I recognized that I was getting grumpy and spent my prep block coloring bubble letters and hanging more squares in our triangle quilt (I'll share that once it's done as well).  I also forewarned my last class that the well of patience had run dry and we spent the beginning of class brainstorming what an A student looks like so they could be sure to be on their best behavior (which enabled me to be on mine).

As soon as the last student left after school (he stayed an hour on Friday, and he was one of the ones I was mad at earlier - can't stay mad at dedication like that!) I called my friend who I knew would still be in his classroom and announced it was time to leave the building.  Several hours at a coffee shop with a good friend, mint hot chocolate, crepes and parcheesi (that's a game, not a food) and I was on my way to recovery.

The rest of the weekend I did nothing.  I don't just mean no school work, but all day yesterday and today I did absolutely nothing productive.  I lounged, played games, napped and read.  I might break out a bit of grading this evening, but no guarantees.  I'm not worried, I know all the work will get done.  And I'd much rather have an hour of productive work tomorrow than 3 hours of not getting much done but feeling like I should be today.

Why am I telling you about my failures Friday and totally boring weekend?  Because I worry that everyone is running themselves into the ground.  We're not yet halfway through the year and we shouldn't be sprinting toward June with the knowledge that we can recover in the summer.  Cold and flu season is coming, for many the holiday season means extra stresses and December break is always too busy and too short.  Stop, take a break and give yourself some time off.  I always declare Saturday my school sabbath, but this weekend that needed to extend into a longer break.  You know you could teach all of your classes without any prep on any given day- sure it wouldn't be a great lesson, but your students would learn something.  So, cut yourself a break, do whatever it is that you find rejuvenating and know your limits.

Monday, November 21, 2011

Taboo Review

At the end of each chapter we spend a day making a study guide and then playing some sort of review game.  In the past this games have included BINGO (fill in laminated cards with answers, then if you solve the problem you get to cross out the square), "the points game" (jar full of cards that say +5, +10, -5, -10 and x2, correct answer means you get to pull a card to determine your points) and a simple game of solving problems in teams to see which team can solve the most before the end of class.  This year I have played these, and added in a few more thanks to the wealth of ideas on twitter.  Last week we played basketball in my fundamentals class (solve some problems on a half sheet, if they're correct crumple and take a shot at the recycling bin, bonus point if you make it in! However- if you get one wrong you have to shoot from the far line, so there's an incentive to check your work).

Today, we finally played Taboo.  I'd been hearing about the great reasons to play Taboo from lots of people, but hadn't wanted to make the cards.  Last night I sat down to do it and it wasn't actually as hard as I'd expected.  In fact, the worst part was fighting with Word to get the table to stay the way I wanted.  I started with this set (google docs link) and then added my own to get this:

Taboo Ch 1-3
It's roughly in order of how I teach them so it should be easy to add more pages as the year goes on and play again.  And I definitely will play again!  This kids were really engaged, they said they learned from it and the most telling moment was when a couple kids were hesitant to take the talking role since they knew they didn't know the words well enough.  Those two will definitely be doing some studying!  (And they did eventually take turns in the role of describer.)

These are the rules we played by:

Taboo Rules
I assume I'm not the only high school teacher whose students have selective hearing, so you do need to go around and 'buzz' kids until they start monitoring each other.  One group was just reading the words on the card!  I was impressed that they knew all the vocabulary words, but it wasn't very challenging for the describer.  They had a good laugh once they learned they were doing the exact opposite of the rules.

We didn't do a great job of forming teams but rather just grouped into clusters.  That actually worked out fine since everyone was playing an active role (describing, checking or guessing), but I think next time if we want to have opposing teams they should sit A, B, A, B, A, B in a circle so there's no need to have kids switching seats between rounds.  Finally, I didn't have enough timers for each group to have their own, so I just yelled out "Start" then when the time on my phone went off  announced "Stop! Tally up your score and switch."  And repeated until there was just enough time left in class to fix the desks.  Overall I think it was a great activity to get students talking about math, using vocabulary and stretching themselves to do something other than recite a definition they memorized.  I would highly recommend playing Taboo with your class.  Especially if you want to make cards for the next few chapters in Geometry!  Kidding, although I'd love to hear feedback on the taboo words I chose and other words to add to our deck.

Monday, November 14, 2011

I don't share well

A post on how I fail at co-teaching.

My school does an awesome job of supporting students with learning disabilities by offering courses co-taught by a content teacher and a special education teacher.  This year I have 2 co-taught Geometry courses and I have the same co-teacher for both of those.  I also have an "Algebra 1" (in quotes because we're not exactly at that level) course for students with moderate to severe learning disabilities.  That course has 2 special education teachers so we've split it into 2 groups with 1 teacher (plus several paraprofessionals) in each class and me jumping between them.

The title of this post is actually true in a far more general sense than just co-teaching.  I like to do things my way, I'm quite stubborn when I get my mind set on something and most of the time I'm rather independent.  I do enjoy collaborating and I love the support of having another teacher in the room, but I'm still stuck in the mindset of considering my co-teachers support as opposed to equal level players.  

I'd love to hear some ideas on how people have found a good balance in a shared classroom.

Some issues that have come up recently:

Grades were due last week so my Geometry co-teacher offered to do some of the grading.  Problem was, I like grading those classes better than my others since they go fast (smaller class size and my other class is working on proofs- so glad I'm not an English teacher!) so I'd already graded almost everything.  She later shared that she'd really like to do some of the grading since she wants to have a better sense of how everyone is doing.  This struck me as totally obvious yet I'd never realized it - I'd been hoarding the grading since I want to see how the kids are doing, but she should get to share those insights!  So now we're going to split it so that one of us does tests and the other does test corrections, then we both get to see.  (I know, poor me, I have to give away some of my grading.)

I talked to one teacher for "Algebra 1" and shared what I thought the kids were ready to do next.  She said that she was happy to put together a worksheet since I would be working with the other group the following class.  When I talked to some people who had been in that class later she had gone and done something totally different than what we discussed.  I was really frustrated that she didn't follow the plan that we had made, but I realized that most of the time I leave her in the dark and just show up with something to do that day.  In my head I have an arc that I'm following and it all flows, but this probably isn't clear to her (especially since math isn't her area of expertise).  I'm going to really try to work on communicating my goals and hope that she will offer me the courtesy of doing the same so when changes need to be made they aren't a surprise to either of us.

A success:

I've been using dropbox with the other teacher for "Algebra 1" so she gets real time updates as I create worksheets, write to-do lists and formulate plans.  She did her practicum in middle school math and studied computer science, so she can see the underlying structures I'm putting in place when random files pop up on her computer.  (I'm also using dropbox with some of the teachers in the math department to share everything I'm doing in my current courses and some projects I've used in the past that may apply to the courses we don't have in common.  I do at least share resources well!)

I know that part of the problem I'm having is a lack of time to sit down and discuss everything with my co-teachers.  We need to make that a priority in the future.  Otherwise, I'm having a hard time not making all the decisions and monopolizing the small amount of teacher-centered time there is in my our classroom.  Advice?  Personal anecdotes?  Articles I can share to get the conversation rolling?

Thursday, November 10, 2011

A Variety of Variables

This year I am teaching a course for students with moderate to severe learning disabilities.  We are supposed to be studying Algebra and so we are working on the concept of a variable.  I've found that many students have a really hard time understanding variables and their purpose.

"Just a darn minute! Yesterday you said x equals two!"

I can think of three different ways to interpret variables so far, and so I'm trying to provide situations that promote comprehension of variables in each context.

1.  A variable can be used to generalize, in this case it is a representation of any and all numbers.  For this situation we did number tricks:

Pick a number.  Add 6.  Multiply by two.  Subtract 4.  Divide by two.  Subtract your original number.

Students quickly realize that they keep getting 4, but in order to know it always works, they need something to hold the place of their original number.  I talk about using a variable instead of spending the rest of your life checking numbers since you can put any number in the place of the variable and it will still work.

(Side note: this is a great way to introduce proof in Geometry since they actually see why they would want to prove something- it seems clear but they don't know why it works.)

2.  A variable can be a number that changes.  It could be something that varies over time, or that is different for different people.  I came across this example rather circuitously.  I found a worksheet translating verbal expressions into algebraic ones, but I also wanted students to substitute and evaluate the expressions.  Problem was, the original author did a really awesome job of choosing different letters, so much so I didn't feel like writing in values for every variable.  Then it dawned on me, there's an easy way to assign a number to each letter- a cipher!  My non-math major friends in college all took cryptology which meant that I got to learn along with them and I've been surprised how often I've used ideas from that class in new situations.  Using a cipher to decide the numbers to substitute did a few things- first it was a cool mini history lesson on codes, second it allowed me to easily change the values and show that we could make the same expression simplify to different things depending on the "key of the day."

**Edit- read the awesome comments below, I'm leaving #3 in its original form so you know what the comments are in reference to, but I'm no longer counting this as a valid category.

3.  A variable can represent a specific number that we don't know.  This is the case for most equations that we have students solve.  We know the value of the variable, their goal is to find it.  To introduce this concept we started by solving really simple word problems (Chris has 5 apples, Josh has 3, how many do they have together?) by writing an expression equal to a variable (5+3=A).  The word problems have increased in difficulty but the idea is the same, that letter represents some specific value we are trying to determine.

I have no idea if this is a standard way of dividing up the roles variables can play, it's definitely something I'm still trying to figure out.  But my goal is for students to see many different ways to approach solving problems using variables.  And then, somehow, we need to merge all of these ideas into one concept of symbol represents number(s).

Finally, I'm hoping they will understand that all of these methods apply in any situation.  Just because you have a number to substitute for your variable doesn't mean that substituting is the best first step.  Frequently simplifying and solving before substituting can show structure (just like delayed evaluation when you only have numbers).  Conversely, even if a variable is representing a particular number you need to find, guessing random numbers isn't a bad way to start out.  For students who have no idea how to approach a problem having them try their favorite number will usually give some insight on the steps to solve a problem (which they can eventually generalize to an equation using a variable).

What misconceptions do you see when students are using variables?  What other situations can I introduce that use variables in a different way?

Monday, November 07, 2011

How to Study for Math

Last week I gave a test on proofs.  It went poorly.  As I graded them I felt badly for rushing the test to get it in before the end of the quarter.  When I returned them, I apologized for giving the test before everyone was ready but made sure to say that I was sharing the blame, they needed to take responsibility too and tell me when they didn't understand what we were doing.  I've had a better sense of what everyone knows from regular quizzes this year, but I try to make those 3 short questions while the test has multi-step and cumulative problems, which is where everyone got stuck.

All this was fine, until I started reading their test corrections.  The first question on the page asks "How did you study for the test?"  Page after page had answers such as "I didn't" or "I read my notes" or "I flipped through notes right before the test."  Now I know that most high schoolers don't know how to study for math, so from the beginning of the year I talk about how to organize notes into two columns with vocab on one side and definitions on the other so they can easily skim and quiz themselves.  We make a study guide together the class before the test (which gives them 2 nights to study thanks to block scheduling).  I make them write out the study guide even if they have nice notes because I know (and share) that the act of writing helps implant information in the brain.  I talk to them about active vs. passive methods of studying.  I specifically assign the practice test in the book.  But, after all of this I get "I looked over my notes" as the sole method of studying.  I no longer felt guilty for rushing the test, but frustrated with my students for not taking responsibility by preparing for the test.

So, I decided I must not be enough of an expert- I'd need something more official or more flashy to convince them.  So today I provided just that.  First I took this article (direct link to pdf: How to Study Math by Paul Dawkins) and broke it into 4 sections.  We did a jigsaw where each kid was assigned a page to read and annotate (underline things you currently do, circle things you could do for the next test) and compared notes with people who read the same page.  Then, they got into groups of four and shared out.  This activity made me want to be an English teacher - they read, made notes and talked to each other!  All of English must be so easy!  Then I came back to my senses, I don't envy English teachers at all, but it was fun to read and discuss something.

How to Study Math
After students shared a few of the most interesting parts of their page with the whole class I showed them this diagram:

I hope that the quote and the percentages really hit home.  Maybe now they'll start practicing vocabulary words as soon as they get them?  And do actual practice problems since the best way to learn is by doing?  Maybe?

At the very least it was a productive 30 minutes of students reflecting on how they study and being exposed to some other options from sources other than me (who they have to listen to every day).  I'll let you know how the next test goes!

Monday, October 24, 2011

Illogical Logic Units

Last year when I introduced the unit on logic I quickly realized that students were experiencing a ton of vocabulary with no context, and there was no way they would be able to "mind their p's and q's" just working with the textbook definitions.  I tried to backpedal but we'd already reached the "we're never going to need to know this" and "this isn't math" frustration level so it was only marginally successful.

This year I did things differently.  As students walked in I asked them to write a couple true sentences that fit the form "If ______, then _______."  Then we got started with this worksheet:

It went much better than last year's introduction, but I need to rewrite the questions on the second page since I ended up doing most of those with the class (there were too many questions to answer individually).  Even so, they realized that a) and d) were always true, which translates to "if a conditional statement is true, so is the contrapositive."  And most quickly saw the repeated structure once I explained exactly what I was talking about.  Best of all, only one student asked why we were studying sentences in math; she asked it genuinely and was happy with the answer I gave about precise definitions and careful explanations.  When reading the journal entries about this class period there were students who said this was fun!  Such a difference from last year!

After we went over the general form for a) through d) I gave them the names (conditional, converse, inverse, contrapositive).  Vocabulary goes over so much better when they already have a context to apply it to.  The next class we talked about biconditional statements and I used some of the examples that students had made up, which is always more fun than creating my own.

On a slightly less successful note, we're still struggling with counterexamples.  At the beginning of the year we did an activity I call "True, False, Fix" (a simplification of Prove or Disprove and Salvage if Possible from PROMYS) where students read a statement, decide if it's true or false and fix the false ones.  They keep wanting to fix when I ask for a counterexample.  We've quizzed on it twice and I hand it back with "counterexample?" and re-explain, but they still keep fixing and explaining without providing examples.  I hate to mark off for accurate statements, but they aren't answering the question I asked.

So, advice on re-wording the 2nd page of the activity?  And/or how to convince my students that counterexamples are actually examples that prove the statement is false?  Thanks!

Sunday, October 16, 2011

Organization System

It's Sunday evening and I don't feel like grading, so instead I'll tell you about how all of my piles of work are neatly organized.  Since it's systemized, when I do get some motivation I can get right to work without spending time figuring out where everything is.  That means I have extra procrastination time, great right?

In my classroom I have a magazine holder (cheap plastic thing from target that google can't find a photo of) with a bunch of folders.  It lives on a table filled with other supplies kids might need (extra paper, pencils, stapler, hole punch and sharpener) and the goal is to have students become self sufficient.  Not only do I expect them to think (and use logic! what??), but I want them to get their own supplies rather than ask me "Can I borrow ___?" or "Do you have any more ___?" every day.

First folders: Extra Copies.  I have two levels of geometry and each one has a labeled manila folder filled with extra copies of anything I hand out.  If kids were absent or lose a paper, they are learning to head to the folder to get one.  When students come in and ask what they missed, I send them to the folder.  If they lost the homework, I send them to the folder.  If they totally destroyed something, I send them to the folder.  I don't like to waste paper so I don't make many extra copies, but I know my Fundamentals class has plenty of kids who can't hold on to a single piece of paper for an entire chapter (I photocopy the review page and they do a section each night for homework- books stay in school).  

Next folders: Papers to Hand In.  This is a set of manila folders with the letter of the block (A Block is first period at my school) written on the tab.  Anything kids want to hand in must go into this folder.  I won't accept papers handed to me, but merely point at the folder.  For a class when I know I'm collecting something I will pick out the correct folder and lay it on the table ahead of time.  To reduce chaos of everyone up and crowding at the table at once we pass papers down and the kids sitting near the table put them into the folder.  If a student is handing in something late, or a correction, they find the correct folder and place the work inside.  

Last folders: Papers to Hand Back.  These are color coded pocket folders (one thing I kept from last year) with red for both fundamentals classes (matte for A and gloss for H) and blue/purple for CP classes.  Eventually I'd like to take this responsibility off of myself as well, but for now when there are papers to hand back I grab that folder and distribute them or ask for volunteers.  I like handing back papers while kids are working because it makes sure that I am moving all over the room in a rather random pattern, so I really do see what everyone is working on.  I also use it like Sarcasymptote's Ukelele Time- I tell everyone I won't answer questions about what I'm returning or the work they're doing until I'm done, so they'll have to ask their partner or look up the answer.  It's not much time, but it's a start of forcing them to talk to each other rather than come running to me.  Maybe next quarter I'll at least assign someone to look in the folders and remind me if they're full of stuff to return.

On my desk I have boxes of things everyone needs- journals, test corrections, quiz corrections and quarter sheets of scrap paper for quizzes (and every random thing I want to remind myself of).

Last year I had everything on my desk, which meant kids were in that area all the time.  When students wanted to hand work in I had them put it on my chair because I didn't trust that it would land in the right spot otherwise.  It was definitely chaotic and messy.  Now when I feel motivated to grade I just grab the manila folder of the class coming up (or really, the one filled with something easy to grade), grade and transfer to the corresponding color pocket folder.  Then I reset and I'm ready to go!  Now if only I could get started...

Sunday, October 02, 2011

Reflection and Self Assessment

This year's school-wide focus is writing.  Many math teachers groan or cringe or opt out of the reading/writing initiatives, but I've always had kids do a minimum of daily journaling; sometimes up to entire stories or paragraphs explaining projects.  Last year's school-wide focus was rubrics.  It was our NEASC evaluation and so we were supposed to all use the same rubrics so kids had continuity.  I would argue that students are more intelligent than we give them credit for and don't need that much continuity, but the idea behind the rubrics was okay and I was able to reformat them into something I find kid-friendly.  The result of these two foci is an ellipse (math joke!), okay, actually it's a double sided weekly reflection sheet.

Journal and CW Rubric

We operate on a block schedule, so if I collect these every Friday that's 5 days (barring schedule changes, which happen approximately daily, okay not really, but I do plan to count how many of the two week periods I get all 5 days filled in).  I used to carry around a clipboard all class and mark down any time a student was off task.  This, combined with attendance/tardies made up their classwork grade.  I'm still making occasional notes on my clipboard, and of course still taking attendance, but most kids are pretty honest when they fill in the rubric.  The original plan was to have them out on desks all class so every time a student was off task or doing a good job at one of the sections I (or my co-teacher) would mark that down on the rubric.  This turned out to be totally unrealistic.  If a kid is off task I don't want them to find their rubric for me to write on, I want them to get to work!  And several of them relate to behaviors when I am standing at the board.  Instead, I'm trying to use the language on the rubric when I reprimand or congratulate students on the behavior, and making a few notes so if my memory completely fails me for some reason they won't get an unreasonable grade.

The journal side looks boring now, but that's because the questions will be on the board.  Every day they will be asked "How did you meet the objective(s)?" and if they didn't to explain why.  There's also a second question that varies.  Some examples: to make a connection, to predict, to reflect (what are your goals for 2nd quarter? how should you study for the test?).  I expect a minimum of two sentences and they don't get credit otherwise.  The first week of past years I'd get quite a few "writing in math class?!?" exclamations, but this year there weren't so many.  It's a quiet way to close class and students will remind me that it's journal time if I get too caught up with a lesson.  The goal is to get students thinking about what they did in the hope that more of it will stick until next class (2-4 days away thanks to block scheduling).  The first question has changed year to year, sometimes asking what math they learned and other times about the objective.  I'm hoping that they will be more precise if they have to justify how they met the objective, although I'll miss the occasional comment about how someone did some really cool math in science class.

Thursday, September 29, 2011

Test Corrections

In an effort to encourage students to learn from their mistakes, I allow students to correct their tests (and quizzes) to earn back half credit.  I started doing this instead of retakes since many kids just want to immediately retake the test without going back and learning what they didn't understand the first time around.  I like some of what I've seen where teachers require proof of remediation in Standards Based Grading, but this works for me for now.

Originally the process was: student shows up after school, we sit down with lined paper and their test and go through the whole test, I give them some extra points.  This was fine, but not many kids were taking advantage, and it was really time consuming for me.  Then at a department meeting our head teacher shared an article about tests as part of the learning process (as opposed to coming after the learning), we shared our methods of doing re-takes/correcting tests and then came up with a template for correcting tests.  We don't all use the exact same one, but I really like this one:

Test Corrections
Reflection in actual sentences is really important in my class (students journal daily) so I have students start filling out the questions on the first page while I'm handing back the tests.  At the beginning of the year we spend quite a bit of class time correcting tests together.  I hear some good conversations between students trying to figure out the differences between their answers and I am able to circulate and check in with the students who had more striking deficiencies.  As the year goes on we won't spend quite so much class time working on corrections, but I do try to give them as much time as possible because chances are kids need some help and if we do it in class they will be more likely to analyze their answer than just take a guess and hand it back in.

Guessing won't actually get you anywhere on a correction page.  It's fine to guess on the test (I'd always rather they write something than leave a question blank) but I am quite serious about the "No explanation = No credit" statement.  They need to fill in all 3 columns- what they are correcting, why they got it wrong the first time and why their new solution is correct.  I'm not looking for an essay, since I teach mostly Geometry they can get away with a nice drawing most of the time to explain their point, but there has to be something.

So far, so good this year.  It's nice to see most of the kids trying to learn from their mistakes.  Plus, the reflection questions give me some good early insights.  They tell me who is working really hard and still struggling (I studied for hours, thought I was totally ready and then bombed!) vs. who isn't very invested (actual quote from today "I don't study") vs. who has low expectations (I'm happy that I didn't fail).  This information influences how I approach students, plus I think they like the opportunity to share their experience.

I'm also doing this with quizzes this year (I have a half sheet version) but I may only allow them to correct the following class and after that they have to retake?  Not sure yet, still in the "How do you not know all the routines and norms yet?? Oh yeah, you're all new, I forget it's only September." mode and until we have settled in I'm not sure how that new addition will play out.  To end, a cute drawing a student made who got a 100% on her quiz:

Sunday, September 25, 2011

Grading with Stamps

Alternate Title: Gold Star or the Dreaded Clock?

So you may be wondering what on earth either title means, give me a minute to explain.  If you've heard of formative assessment you have probably heard of comment only grading.  And if you heard it from someone convincing, they probably gave the statistic (which I can't find at the moment) that shows if there is a grade on the page, most students don't even bother reading all the comments and corrections you took hours to write.  So you think, "Great!  I won't give grades!"  But then you remember that you still work in a school that runs on grades.  My PD leader suggested that we give grades on resubmitted work, but not on first drafts.  Sounds doable, right?  But I worried about that disorganized kid who loses their work that they actually did pretty well on the first time around.  I want to encourage organization and independence, but I also want to give grades that reflect knowledge, not the state of someone's backpack.  So, I finally decided to record the grades in my gradebook, but not on the students paper.

Three years later and this is still working out well, with a few tweaks.  The general procedure is: Students complete an investigation (mini project), hand it in, get comments (plus a secret grade) and resubmit for more credit (plus a shared grade).  On the day of the first investigation I tell students that this is just like English Class, we do a rough draft, hand it in next class no matter what state it's in, I comment, then they edit and submit a final draft.  The reference to rough draft has been helpful since in the past I had students who were unwilling to hand something in until it was 'done' (while I really wanted to grade them all in one sitting and provide feedback sooner rather than later).

The only issue is the kids on the two ends of the spectrum.  First you have the students who always get good grades; they are super worried about that one tiny thing they did wrong and want you to discuss the entire worksheet with them immediately.  These also tend to be the kids who would correct their papers even if they got a 98% to try for the 100%.  So now, students who earned an A get a gold star stamped onto the page.  Still no grade, so it could be anywhere from a 90-100%.  This rewards the students who worked hard the first time around and calms the worriers.  At the other end you have the child who sees a couple check marks (which mean an answer is correct) and a bunch of comments, but decide that it's good enough.  These students need some extra motivation to make sure that they resubmit their papers.  So, I found a cute little alarm clock stamp saying "Take Your Time" which I stamp on papers earning a D or F.  If I manufactured stamps it would say "Take More Time" but I don't, so I'm happy to have found something cute, action oriented and hopefully motivating.  Hence the alternate title "Gold Star or the Dreaded Clock?"

I just finished grading one class's first resubmitted projects.  Everyone who resubmitted improved to at least a C (2/3 to an A!).  Only 4 didn't resubmit, and this was our very first investigation.  I gave more class time to edit than I will later in the year, but I'm thrilled with the initial results.  Plus, stamps are fun :).

Thursday, September 15, 2011

Ambiance, Atmosphere, Aura?

The only rules in my classroom (other than the school mandated ones) are: be safe and be respectful.  With each class I have a discussion of their interpretations of my rules and we establish some norms together.  It amazes me how much my classes vary in their 'personality.'  (What's the word for a group's personality?)

My first class (A Block, Fundamentals of Geometry) may quickly turn into my favorite group.  As we were discussing what to do if you need to leave the room, someone asked what to do if they get mad.  I offered the option to ask for a pass to take a walk, but then someone suggested a "happy corner" and the idea took off.  Students were excited about the concept- deciding where it should be and asking when we could start decorating it.  The next class students were still asking when we could decorate, and I promised if we finished early we could start, but by the end of class we'd forgotten and got caught up in a game instead.  Today they still remembered, and I had the perfect activity- we were learning to use the compass and the book had instructions for making a 6 pointed flower.  We practiced arcs and circles, pulled out the markers, and quickly had a nicely decorated corner.  There's a chair in that corner facing a wall full of brightly colored flowers and it's well isolated from the rest of the room by my desk and a table.  I have no idea if anyone will use it when mad or upset or if I will think to use it as a time out space, but I'm thrilled that we're all having fun.

This class also came up with:
  • instead of making fun of someone, help them to understand
  • if everyone does their homework for a month, candy for all!
  • if someone isn't respectful, call them on it
My next class (B Block, Geometry CP) is a good group, but their personalities aren't as vibrant (yet?).  They came up with some reasonable norms, but nothing particularly insightful and certainly no one is excited about their rules.  This is my biggest group, the numbers are still fluctuating but they hover around 27.  My classroom isn't very big so they just fit, with no extra space, which means I have to be more diligent about keeping the noise level down as well as somewhat restrict movement in the room.  I want them to be comfortable, to talk to each other and to go get their own paper when they need it, but when the room is packed all of those things become just a bit more difficult.  Hopefully we'll find a way to work together in the space and find a good balance without being stifling or distracting.

Their not so inspiring rules:
  • Don't talk when others are talking (if someone is, say "be quiet please")
  • No goofing around
  • Be careful with tools
  • Respect each other (if someone isn't say "be respectful!")
  • Don't shout (wait to the end of class or walk over)
  • Get a pass before leaving
Sadly I don't have the rules from C or G Blocks to compare.  C Block is the Learning Skills class and they discussed rules with my co-teacher (who they spend most of the rest of their time with).  We're still figuring each other out in that class, but today went much better and I'm feeling less overwhelmed and more "I could possibly have a chance of success with this class."  During G Block one of the students offered to type and email me the rules, so I didn't bother to copy them down and I have yet to remember to remind him to send them.  They were pretty much just like B, also a Geometry CP class but not quite so big a group.

The final class (H Block, Fundamentals of Geometry) is already high tension.  There's a group of three girls that were a major issue for the entire year last year, which I learned as soon as I mentioned the name of the loudest one to her Algebra teacher.  Other students were already frustrated by the end of the first class and my co-teacher and I discuss them after class each day.  We're making progress which I hope continues because I really can't spend the entire year like this.  The rules in this class reflect that - none of the other classes discussed consequences, but they brought up consequences almost immediately (we decided on warning, name on board, after school-time dependent on number or severity of rule(s) broken).  However, they did also set up a reward if everyone in the class earned all 3's or 4's on the classwork rubric.  I should remind them of that next week, I'm not at all above bribery!

I wonder how this happens.  When you gather a group of 20-30 kids in a room, how do you end up with such different results?  It's even the same co-teacher in both of my Fundamentals courses, so it's not about the adults.  Time of day has some effect, but not nearly enough to explain these differences.  Is it just those few strong personalities?  In A Block there are a couple sweet, genuine kids that speak up and sit right in the front.  While in H Block there's that group of 3 who are intent on loudly discussing anything other than schoolwork.  Two or three students seems to be all it takes to set the mood for a group 10 times that size.  How do we encourage those leaders to be positive influences?  To carry the class further, to grow closer, to move everyone toward success?  One of the many challenges of teaching mathematics that has little to do with math...

Sunday, September 11, 2011

Call for help

I just wrote the email below and then realized that I could ask all of you for ideas too!


This year I am teaching a new course called Learning Skills for students with significant learning disabilities.  They're mostly on the autism spectrum but some have other diagnoses.  In the past this course has been taught by a special education teacher alone, and they only did very basic math, pretty much just practicing addition.  The goal, though, is for these students to pass MCAS (but probably not until they are juniors or seniors).  I tried to google some basic math pre-tests to get a sense of what they know.  The first problem asked students to add the numbers 12, 6, 3, 8, 5, 14, 15 and 7, thinking about a way to make adding them easier.  Some were overwhelmed and skipped it, others turned to a calculator, still others added incorrectly and those who did add correctly didn't notice the pairs that add to 10 or 20.  The second problem gave data to make a bar graph from and they did that successfully.  I had anticipated using resources from when I taught pre-algebra, but I don't think we'll be able to use many of those until second semester at the earliest.  Which means I'm a bit lost.

My intuition is to focus on problem solving skills (habits of mind) and find interesting ways to drill basic computation.  For example, I remember a cool problem from one of my grad school classes that involved multiplying pairs of numbers on a number line and seeking patterns as you changed the pairs systematically. 

I would love to hear any book or resource recommendations you can offer.

Thanks so much!

Wednesday, September 07, 2011

Here we go!

The first day with students was today, it went great all considering!  We have a block schedule so today was 'Red Day' with blocks A-D, I teach A-C so it's my long day.  Normally we have 90 minute periods, but we had 2 hours of freshman orientation plus 30 minutes of homeroom (easy-peasy since I have Juniors), so I only saw each class for 45 minutes.

I had enough time to get through all the activities (find seat by matching multiplication and division flash cards, questionnaire, index card game, expanding sea creature) in both of my Geometry classes.  Those went largely as expected, the kids seem nice and were generally willing to play along with my antics.  I always spend the first week(s) overwhelmed by names, I'm not good at remembering names in the first place, so when I have over 100 to learn at once it takes some work.  Anthony and Antonio ended up next to each other in one class, in another Sara and Sarah are only 2 desks apart (randomly assigned seats).  I'll figure it out soon enough.

Learning Skills was a bit more complicated though.  That class is made up of students who aren't capable of the traditional curriculum for a variety of reasons.  They are above the life skills class, but still quite low.  One group (of 5) has Autism and the other group (of 15) is either on the spectrum or has some other type of disability (a couple have traumatic brain injuries, the rest I haven't seen the IEP's for).  The problem is, none of us know exactly what level each student is working at.  The Autistic group is all new to the high school and the rest were taught by a teacher who has now retired.  Then, the teacher who was hired to work with the Autistic kids just didn't show up to school yesterday or today.  Needless to say, things were a bit chaotic.  Math class turned out okay, there were 8 adults (between teachers and paras) so we got through my questionnaire and index card activity, but it turned out to be more than they were really ready for.  I had planned to work on logic problems next class, but I'm going to have to cut some of the wordier ones.  Since there are so many adults it's not critical that everyone can read the problems independently, but I don't know that their processing level is high enough.  A variety of pre-tests will be in order.  Turns out I didn't really know what I was getting into when I signed up for this class.  I'll figure it out, but the confusion of merging classes, a teacher not showing up and discovering that these students have trouble answering the question "What are your hobbies/interests?" left me a bit flummoxed.

At the end of the day I read through the questionnaires and found a pleasant surprise.  In response to the question "What class are you looking forward to most?" one student answered "Geometry, I heard you're a good teacher."  This year is going to be just fine.

Wednesday, August 31, 2011

First Days

Today was the first day back for teachers.  We came, we talked, we felt like we'd never really left.  There are lots of new teachers, it's hard to believe that I was there just a year ago (and there weren't nearly so many of us last year!).  But, you don't really care about the meetings or how I organized blocks this morning, what this post is actually about is the first days for students.  I've done these activities in some combination or other for the past several years and I think they all set the tone I want in my classroom.

Start of year questionnaire:  It's a fairly basic one with the focus being getting to know them a bit and having them set down some goals.  While they're filling it out, I fill one out on the projector, the message being: I'll share with you if you'll share with me.  The last question asks "Is there anything else you think I should know about you?"  I tell them that I can only hear out of my left ear (so it's a much better idea to wave than call out to get my attention) but I get a really wide variety of responses, maybe I'll share some of my favorites next week.

Index card game: As students finish I distribute index cards and instruct them NOT to put their name on it, but to write down one thing from their questionnaire and one thing they did over the summer (both that they don't mind sharing).  When everyone is done I collect and shuffle the cards, then redistribute and have them make some predictions on how many people they will need to ask to find out whose card they have.  Then, I make every single one of them get up and out of their seat!  It's a crazy thing to do on the first day, but the truth is we move around, talk to each other (teachers and students) and make a bit of noise all the time in my class.  Finally, we compare numbers and do a bit of data analysis.  If there's time I have them introduce whoever they have the card for, and they introduce whoever they have etc. Then we get to analyze the number and size of loops too.

Turtle: I have accumulated quite the variety of expanding sponge sea creatures along with packaging that makes various claims about how much it will expand.  Each class will get one to measure, interpret the claims and then predict and track its growth.  Splashing in water is fun, plus I get to see who knows how to use a ruler.  You think I'm kidding but it's really an issue.

Syllabus: On to the second class, we read the syllabus together.  Every year I try to be even more up front and clear about my expectations.  The only rules I have are be safe and be respectful, so we get to work together to interpret them.

From there in Geometry we'll head into patterns and conjectures and in Learning Skills we'll start working on some logic problems (we have no idea what level these kids are, so I'm trying to assess their thinking skills without overwhelming anyone with mathematical notation).

Wednesday, August 24, 2011

Technology for Teachers

In my Goals post I mentioned some technology that I would like my students to use, but the more frequent use of technology in my classroom is the programs/websites that I use.  As I set up for the new year I thought I'd share some of my favorites.

Dropbox:  I almost forgot to include dropbox since it's more a way of life for me than a tool I use.  No, seriously, I'm 3 referrals away from maxing out my referral bonus.  If you don't have it yet, make sure to get an invite from someone because it means extra space for both of you!  Okay, so what is this life altering item?  It's a folder.  Really, that's all it is on the surface.  Underneath though, it has hidden magic powers so that everything you put into the folder is automatically backed up online.  Then, when you open that same folder on another computer the new version is already sitting there waiting for you, no jump drive required.  But it's way better than google docs or similar sites, because it's a folder, on your computer.  You can get to it when you're offline, you can work in your favorite program and you can save all different types of files in the same place.  Plus there's the sharing and the web access and... oh just go watch the video.  Point being, it's awesome if you use more than one computer (home and school anyone?) or want to collaborate on anything.
*Free, remember more space for free if you get an invite!

PlanbookEdu: I started out with a paper planbook, then used google docs, then a word doc in dropbox and last year a co-worker told me about PlanbookEdu.  For the first time (I'm about to start my 5th year of teaching) I'm going to use the same method 2 years in a row!  The website is very simple, which is exactly what I want.  There are boxes in a weekly grid like a traditional paper book but you can customize the number and orientation, and they change size to fit the text.  You can create a template, set things up to repeat, bump lessons when you have a snow day and much more.  They are awesome about hearing feedback and accommodating requests, they're currently in process of adding tons of standards, and you can customize your own.  When I emailed to ask how to copy only some of my classes from last year to this year they responded "just let us know what you need and we'll take care of it!"  If you need to submit lesson plans there's a button to push and they're sent.  You can also share your planbook with other teachers, which is a great way to see what your co-workers are working on when you don't have much time to meet.
*Free to use, $25 for Pro version which I happily pay

Engrade: At my first school we used PowerSchool.  I loved that kids and parents could log in to see a complete progress report at any time.  When I switched schools I wanted that same access, so I did a bit of googling and ended up with Engrade.  Similar to PlanbookEdu, they're constantly adding new features (and respond quickly to emails) but the basic format remains simple.  It works with weighted categories and all that good customizability.  I'm not sure if we're going to be required to use iPass this year (that's what we use for report cards but last year they started giving 9th grade parents access) so I haven't started setting up Engrade yet.

LaTeX: When sorting through a large pile of papers last week I came upon some handwritten tests.  I forgot we didn't have computers my first couple months of teaching (we'd just moved into a new school).  I use Microsoft Word for most things, but when I taught Algebra 2 I realized how much easier it is to type in TeX (a math programming language, there's a bit of a learning curve if you've never used it but the internet is awesome and can tell you how to do anything you'd ever want and more!).  It also works much better for image placement in geometry, so now I use it for all of my tests and some other assignments.  I made the mistake of announcing that I had typeset the common midterms I was giving (the versions I got were a mess!) and then got assigned the duty of fixing the others.  At least it will make them easier to re-write this year.  Downside: you can only share documents in .pdf so they aren't editable to non-TeX-users (meaning any re-writes will be done on my computer).  At least if I'm useful I'll get to keep my job?
*Free, I use MacTeX, not sure what's the best distribution for PC

Powerpoint: I know, you all use it all the time.  But, in addition to making things nice and big so that even the kid in the back who forgot his glasses can see the assignment, it has really nice image manipulation.  It's a quick and easy way to draw a diagram and then export it as a .jpg to use in your worksheet.
*It's already on your computer (unless you're cheap like me and only have Keynote, same deal though)

Lunarpages/iWeb: I have a course webpage: (mylastname) (feel free to check it out if you know my last name, I just don't really want kids googling the course page to end up here, not that anything bad is here, but, ya know, it's mine for now at least).  I pay $0 for the domain, I paid $0 to get the domain.  That's right, a free domain of your choosing and all you have to do is mail in some school letterhead!  Any public school teacher, administrator, PTA head etc. can get a website to use for pretty much whatever you like.  Once I got the domain I thought back to the html class I took in high school, and then clicked on iWeb, no html required!  I have a page for each course that I update daily with homework and extra copies of assignments, plus a calendar (from google calendar) and some silly math comics.  Not a lot of students use it, but it's so easy to maintain that it's worth it.
*Free domains for teachers (sorry, public schools only), either you already have iWeb or you have to find some PC equivalent

What are your favorite programs and websites to make teaching just a bit easier (or at least more organized)?

If you want more information on any of these let me know.  I love them all and would be happy to expand and expound.

Monday, August 22, 2011

Goals (Post PCMI)

I found some time to go back through my notes from PCMI and write up my goals today.  Over the 3 weeks of the program I took notes from the sessions and also wrote down ideas from conversations in Notebook (a program for Mac from Circus Ponies, it's awesome and they didn't ask me to say so).  As I went I highlighted any ideas that I wanted to specifically apply in the upcoming school year.  One of the awesome features of Notebook is that it compiles all of the highlighted text onto a single page, so by the end of the program my goals list was pretty much already complete.  I took some time to decide what was doable and came up with the following:

  • Look up standards based grading (SBG)
I'd never heard of standards based grading before.  I listened to a lot of conversations, read quite a bit and decided I'm not ready for a full implementation (nor am I sure I ever will be).  However, one of my goals for 2nd semester last year was to quiz more, and I intend to continue doing that this year.  We have block scheduling so I'm aiming for a couple questions each block, but I won't be upset if it doesn't happen.  I do like the aspect of SBG that students refer to skills they struggle with rather than the generic "I don't get it" so I will name my quizzes by topic rather than section.
  • Comments only on projects 
I've done this sporadically, but now I have a system!  Last year one of my students told me that "even high schoolers like stickers."  I didn't get stickers, but instead found a star shaped stamp and a gold inkpad.  From that point forward every A was accompanied with a gold star (which that same student loved doing, I sorted and she stamped).  This summer I found a "take your time" stamp, so papers that need revision will get one of those (not sure if that will be everything below an A or just below a C). I still record grades in my gradebook in case students don't resubmit and because it makes the averages much more accurate.
  • Make classwork grade more transparent
Students get a daily classwork grade based on preparation/effort/focus but it's something I've just quietly marked on my clipboard in the past.  Sometimes I make a show of walking around to check progress, but usually that grade is a mystery to kids.  I tell them what's involved, and we read the school rubrics (new push) that they're based on at the beginning of each semester, but they quickly forget.  I'd like to use participation quizzes and also have kids self-assess on the rubrics so they get a better sense of what's needed to get full credit.  (I use classwork grades because I rarely collect any work done in class, it gets checked off as I circulate.)

  • Use geometers sketchpad
We have geometer's sketchpad in all of our classrooms and in the computer labs, but it's not used much.  After using it this summer I definitely have a better sense of when it would be useful.  We do a lot of compass and straight edge constructions, so I might use it to show how the construction works after they've each tried an example.  This way everyone gets to see all of the varieties, not just hear about them from classmates.  Some ideas (like trigonometry) require more precision than we were able to get using paper and pencil, those will be worth reserving the computer lab for.  I will also look into projects to do and use the idea of lab reports.  This idea actually came from a professor whose son took Geometry last year, we got to talking over breakfast and he shared this great idea.  I'd love to get the report format from the science department and modify it slightly to fit our needs.
  • Use Snap
I discovered Snap/BYOB (3rd or 4th generation Logo) in the spring and was able to use it for my project at PCMI.  My Merrill textbook is so old that it still has Logo activities in it, so I want to adapt those for Snap.  I'll also implement the lesson I wrote this summer on similarity.
  • Google docs
We used Google Docs a lot this summer, and I do love all things Google.  I'm not sure how often I'll be able to get into the computer lab, so they may not be as useful as I'd like.  They were great for recording and compiling ideas during group work, maybe I'll be able to share a laptop cart with another teacher?  I am also asking on the first day how many students have internet access where they do homework, perhaps I'll be able to assign something in the form of a Google form occasionally.  They integrate into my course webpage so nicely it would be a shame not to use them!

Other Quick Ideas:
  • Be silent! - to get students to use each other as instructional resources (last year I participated in the Day of Silence and it was great to see how well kids worked together once they got past the frustration of being largely on their own) 
  • Ask "how did you know that you were done?" or "how confident are you with your answer?"
  • Present a "good bad answer" to promote discussion (authentic student work)
  • Use "I observe ______ and I wonder _______" slips after investigations
  • Journal: instead of math learned, "how did you meet the objective(s)?"

Take Aways: 
(the whole post...)
Quiz regularly
Comments only on projects 
Make classwork grade more transparent
Use GSP, Snap, Google Docs

Wednesday, August 17, 2011

End of Year Reflections: Algebra II

Continuing analysis of student's reflections... (see first post for a full description)

I'm not sure I want to share this publicly. To be honest, I didn't include some quotes because they were too depressing. This class was by far my most frustrating. A lot of that was me: it was my first year in a new school and I didn't understand what was covered in Algebra I, I'd never taught Algebra II before, I got irritated when students didn't remember how to do things that they really, really should know how to do by junior year. Some of it was the kids: most didn't start coming for extra help until the last quarter, they didn't work as a cohesive class, they didn't have high expectations of themselves. Plenty of the blame can go elsewhere: some went to 3 weeks of summer school over a year ago and that meant they 'got Algebra I', many weren't ready for Algebra I so they didn't retain as much, lots didn't want to take more math beyond Algebra II and society says that's fine, society also says math is hard and it's okay to say you're bad at it.  I learned a lot from this class, but I learned it all the hard way.  It helped that the other Algebra II teacher shared my frustrations, but I wish that we'd had time to work together.  Instead, after each chapter or two we made plans for adjustments next time we teach it, which neither of us will be able to enact this year since I'm not teaching Algebra II and she's taking a year off.  However, this post isn't about all that, it's about what the kids wrote in their reflections.

Most investigations in this class were of the "graph a lot of equations to find out what the different coefficients and constants do" variety. Shockingly, those didn't make it onto the list of favorite activities. We also acted out some of those when we studied parabolas (turning the squares on the floor into a giant coordinate grid), that activity didn't make it onto the list either. Other investigations included lots of numerical examples, followed by a generalization. Still not on the list! So, which ones did make the list? Just two:

The rolling markers lab, and the interest rates activity.

The rolling markers lab was pretty cool. We set up 'ramps' of different heights (folders propped on books), rolled markers down and measured the distance traveled. It was a nice review of scatter plots, best fit lines and the different equations used to describe lines. We had some fun building crazy ramps and trying to find markers which would roll in a straight line. It was from the first quarter and they remembered it at the end so clearly it made an impression.  I'll probably try this activity with my Learning Skills class this year (math for students with disabilities who can't access the traditional high school curriculum yet).

The interest rates project was bad. A couple other teachers wrote an outline while I was in a geometry meeting. I missed the discussion, I didn't make it precise before distributing it, and none of us were really thinking about exactly how low interest rates have fallen! Students went to the bank (or internet) to get rates on savings accounts and CD's. Pairs were given a certain amount of money to invest and then compare the outcomes of different scenarios. The scenarios were too vague and the final products reflected that. The idea was cool, the kids appreciated the value of it, but it was poorly executed on my part.

The specific topics they enjoyed or found challenging weren't particularly noteworthy, as in the other classes some students listed a topic as a favorite, while others listed it as hard. The one surprise came from a student who listed the same topic (factoring) as both hard and his favorite. That kid gets brownie points in my book.

After reading this you may be surprised to hear that the kids learned anything. They did, the class wasn't awful every day, but my lasting impression was of a group of rather uninspired kids. I didn't get them excited about math. When I asked them what they needed, all they could offer was a change of scenery might help. They did get more work done when we hung out in the library, but it was a very unsatisfying class in my mind. Still, they learned, and they can tell you about it in their own words:

  • If I try my hardest I could get a good grade
  • My intelligence is not enough, I need to work and study hard too
  • I found out that I can do it
  • I learn best by doing the work by myself
  • I need to study more and make practice problems
  • Study best with flashcards
  • Staying after can help you make up a lot of points and help you understand
  • When I really want something I can achieve it
  • I learn best by doing projects
  • I can learn to solve any problem with practice
  • There are at least 2 ways to do anything in math

That was the last of the End of Year Reflections (until next year!).  Maybe by now I have some more posts written, but this daily posting thing will definitely be a rarity, so I hope you didn't get used to it ;).

Take aways:
Thank goodness you're not teaching Algebra II again!! (jk, but not really)
Do rolling markers in Learning Skills
Emphasize importance of making up work early and often.

Tuesday, August 16, 2011

End of Year Reflections: Fundamentals of Geometry

Continuing analysis of student's reflections... (see first post for a full description)

In addition to two college prep geometry courses, I also taught two fundamentals of geometry courses. Our levels are fundamentals (SPED and struggling students), college prep (aka CP, the 'regular' class) and honors. The fundamentals courses were co-taught and I got to use an amazing book: Merrill, from the 80's with only blue and black ink, filled with discoveries students should do before theorems were presented. I used many of the ideas in this book in my CP class, and I followed the ordering of each book in most cases so the two levels were taught in a slightly different order. Another thing to consider when planning for this year.

Most of the responses in the class that I had do the end of year reflection (I'm kicking myself now for forgetting in the other class) were similar to the ones in CP. The investigations were the same across the courses, but there are a few things to note.

Students in this class mentioned struggles with: algebra, formulas, measuring and square roots. Oftentimes placement is based on Algebra 1 scores, so those topics are more likely to be an issue in the fundamentals classes. Next year I might want to do some more explicit review of Algebra.

There was also one student who listed "working with others" as the hardest thing to learn to do. We discuss classroom norms a few times during the year, and I try to start the year with an activity emphasizing the importance of team work, but it's good to be reminded that it's still a struggle for many students. In truth, it's still a struggle for me! Some people I immediately click with and we're ready to share and learn together, but with others I find myself shutting down. I would like to have a better way of assessing how students are working together. The participation quiz (Sam wrote about it here) that I saw at PCMI might be a good way to do this, and I'd also like to see students discussing with each other.

In one class I gave students a daily checklist based off of our school's Habits of Mind rubric. It included points for being on time and prepared, working with others, asking questions and participating. Of course, this is the same class that I neglected to give the end of year reflection to. Maybe I can modify it from a daily list to a every 5 classes list and collect it when I collect journals... One of the best features turned out to be the "Is there anything else you'd like to share?" section where students vented frustrations, owned up to misbehavior and were generally their honest and insightful selves.

And, just because they're corny yet sincere, here's the quotes from the "What I learned about myself" section
  • If I push myself I can accomplish many things
  • I can do better work when I put my mind to it
  • I can achieve anything if I work hard for it
  • I can do things, all I need is a push
  • If I pay attention, I can learn more
  • I'm too smart for geometry
  • Homework is important
  • Geometry is easier than algebra
  • I am a lot better with geometry than algebra
  • I am good at math
  • I do well when I study
  • Studying is really important
  • If I try, I can get good grades
  • I need to be organized

Take aways:
More Algebra practice in Fundamentals
Compare the order of the levels to see if there are compelling reasons to switch either
Ways for teacher and students to report group dynamics? (rubric?)

Monday, August 15, 2011

End of Year Reflections: Geometry Investigations

Continuing analysis of student's reflections... (see first post for a full description)

Even as early as student teaching I quickly realized that working from the book day in and day out was boring. For me even more so than for the students. When life is running smoothly I do what I call investigations weekly. Block scheduling messed up my weekly routine, so last year they happened sometimes, but not at regular intervals. In geometry it's easy to do a quick investigation of "everyone draw a triangle, measure the angles, tell me a hypothesis." But those aren't the activities that kids remembered at the end of the year; they remembered the applications, the field trips to the parking lot and the ones that involved coloring. Honestly, those are my favorites as well. I get to interact with students in a different way when we're identifying trees (how do MA residents not know what a white birch looks like??) or rolling circles down the 100 foot track.

Here's what the Geometry CP students named as their favorite activities:

Expanding turtle
Measuring height with mirrors
Measuring height with shadows
Pi day (4)
Sierpinski's triangle
Comic dilation (7)
Tree activity (7)

Diameter (pi day or tree?)
Outdoor activities

I'm impressed someone remembered the expanding turtle, since we did that on the very first day of school! I presented them with a turtle, they measured whatever they wanted, predicted growth based on the package's claims and stuck it into a bucket of water. Over the following weeks students would occasionally remember the turtle was growing and poke, measure and smell it (smells like cheerios for some strange reasons). It's a nice way to get them thinking the first day, but no big deal if a kid switches in 2nd day and didn't get to see the turtle before it entered the water. Co-teachers and friends have started picking up expanding animals for me so I now have a whole crew of creatures to experiment with.

The pi day tradition started in my last school, and I've carried it with me. We gather as many circular objects as we can (wheels, jars, balls, baskets...) then students measure diameter and circumference to calculate pi. For increased accuracy on circumference (and a lot more fun!) we count the number of times it can roll down a 100 foot track. Anyone who accurately calculates pi, gets a slice of pie. I even got the grocery store to donate $25 worth of pies and the principal found funds to cover the rest!

I was happiest with the 'tree activity.' It was nearing the end of the year and I was feeling fine about where we were in the curriculum. It was hot in my classroom (no windows!) so I was looking for something to get us outside. We were studying circles and I happened upon a chart relating the circumference of a tree to its age. Each type of tree in the chart had a growth factor, so all we had to do was identify some trees and measure their circumference. In my first vision of this project we would all go out with those tree ID guides that work like choose your adventure books (if it has needles jump to page 45), but I didn't know how to find those in time. So, I gave them the identifying features of 4 common trees (dogwood, white birch, red oak and red maple) to go out and find. But, to prove to me they had the correct tree they had to draw or describe why both the leaves and bark fit the description.

I anticipated that this would be a fun, but simple activity. Oh was I wrong! Kids started by running up to any plant, plucking a leaf and presenting it to me to identify. Dear children: don't harm the tree, read the description, look at the picture, think for yourselves! They got better, but even the ones following all my advice were missing something I assumed all would have- a basic idea of what these trees looked like. One group was looking at a tree- its leaves had jagged edges like a birch and the bark was light, but it wasn't until I pointed at the tree 5 feet away for comparison that they realized a white birch is really white! It still boggles my mind that kids can live in a city filled with parks and not know the first thing about the trees that fill them. I can't blame video games or TV, those existed when I was a kid too. Is no one interested in nature? I'm ashamed of how few plants I can identify, maybe this is something that we'll all work on together next year. In fact, this just may be one of the early activities on proof that I need.

Take aways:
Prove you correctly identified tree to intro proofs.

Sunday, August 14, 2011

End of Year Reflections: Geometry Favorite vs. Hard

Continuing analysis of student's reflections... (see first post for a full description)

Geometry CP students' Favorite Topics:

Ch 1
Ch 5
Ch 10
Ch 12
Solving Triangles
Similar triangles
Trig (interesting)
Pythagorean thm
Pythagorean thm
SAS etc. Theorems

Geometry CP students' Hard Topics:

Nothing (if I paid attention)
I don't know
I don't remember
A lot
Finding lengths and angles
Area formulas

What's the most striking thing? The million Trigs!
That pattern isn't surprising to me at all. I haven't figured out yet what I will do next year (suggestions??), but Trigonometry was the only section where I had students asking "When will I ever need to know this?" We studied plenty of topics that were difficult (at best) for students to see the applications of, but they never stopped to ask that question because they were interested, involved, curious and they understood enough to be able to work toward the problem. In trig, that didn't happen. I saw confusion, frustration and kids giving up. It may have started when the first investigation we did gave data that was too far off to see real patterns (perhaps technology would be better than measuring by hand for this?) or perhaps when we started synthesizing too many ideas at once. When 'solving a right triangle' (finding all the side and angle measures given a few) we applied angle sum rule, pythagorean theorem, trig ratios and a lot of algebraic manipulation. Next year I'd like to do more problems throughout the year that synthesize topics so hopefully that won't be so overwhelming. Last, but certainly not least, trig was the first topic we did after MCAS (the state exam, required for graduation) and students feel like they should be done when they've finished that test (even though it happens mid-May and we didn't finish until June 29 this year). Overall, trigonometry got a bad deal last year. I'll try to do it more justice in the future.

Proofs are another challenge, and I believe that a lot of that is related to how they are presented. Student in my classes are accustomed to "defending their answers" and usually can do so well. However, when it comes to writing a proof they get caught up in format, and formal language. Precision is key and I certainly want my students to be able to write concise and carefully worded explanations, but I wish that they were more willing to just write something to start with. Does anyone have a method of draft proofs or easy entry formats?

Otherwise, I appreciate the overlap of favorite topics and hard topics. Different students had different preferences, and geometry has plenty of variety so most students get to experience a balance of topics they enjoy and others that they struggle with.

Take aways:
Do multi-step, synthesizing problems (before Trig)
Make proofs more 'low threshold'