June 21, 2012

Welcome to Teaching

Math bloggers from all over have joined forces to greet new teachers with our best nuggets of wisdom. Check out the ever growing #matheme page to see them all.

Hello, and welcome to teaching!

Congratulations on deciding to step into the classroom.  Teaching is a wonderful profession and we are so thrilled to have you.  It is a challenging but rewarding job that will take over your life (in the best way, we'll try to make sure you still get to have a life outside of it though).  You may think you have all the answers, and you're right.  Whether you've completed a full teaching program with hundreds of hours of observations or are jumping in with your memories of being a student, you know enough to get through today.  And if you're here reading this letter you know to seek advice.  So, you know everything you need to right now and you are able to find all the answers you might want later.  Be confident, if you chose to teach you know what you're doing enough to get started.

To become a great teacher you absolutely must be flexible: things won't go as expected, sometimes better and sometimes worse than anticipated, either way you have to have to have to be able to go with the flow.  Flexibility is my number one characteristic of a good teacher- figure out what gets you frazzled and then figure out how to keep it together.  When you're teaching you are usually the only one in charge in a room of up to 30 teenagers; you have to know now that things won't go as you expected and make your peace with that.  If you can be flexible - adjust in the moment or announce that you need a moment - then everything else will come in time.  

To keep yourself sane: Get out of your classroom at lunch- unless the faculty room is filled with grumpy complainers, avoid them when they're venting but don't write them off as bad teachers.  I always take Saturdays off from all school work, come up with a schedule that works for you.  Try to go out with friends after school on Friday (form a new teacher crew during orientation and trade phone numbers immediately, you might not see each other in school for the next several months!) but Friday nights feel free to go to bed early.  Sometimes it's better to just sit down quietly at your desk when class is totally out of control- either the kids will realize they're being insane, the few who are with you will come get any help they need or you'll lose the rest of the period.  No matter what happens, if you sit down you aren't yelling, saying something you'll regret or making rash decisions- next class you will come in with a plan and the students will recognize that they weren't with you and the vast majority will feel bad about it if you've built any sort of relationship with the class.  Certainly try other strategies first, but when you reach that point- sitting down isn't admitting failure, it's giving yourself the opportunity to regroup.

Put up some positive reminders: I keep a quote in my desk drawer that I only find when I'm digging through the drawer for something I can't find, I leave a few positive emails in my inbox and I put up these fan posters right next to my desk.  Do whatever works for you, but find ways to give yourself a boost when you're drained (you will be- teaching is tiring!).

I give you permission to work all the time: you'll be thinking about your lesson plan in the shower, re-hashing that conversation with a kid while driving, and writing emails mentally while you search for groceries.  It's okay, you'll know when it's not and find a way to not think about work (for me it takes crocheting and an engaging TV show - eyes, hands and ears busy - to get my brain fully shut off).

Talk to people: whine to friends about your crazy situation, find a mentor with the same prep as you (my first year I spent one prep every day in my unofficial mentor's classroom- bless him for giving up that precious time to talk to me!), talk to twitter, read blogs and comment, write your own blog and ask for comments.

SMILE.  As soon as I walk into the building I plaster a smile onto my face.  If I'm not quite awake enough to be thrilled to be there, the act of smiling sends feedback to my brain which concludes I must be happy (based on actual scientific research as well as personal experience).  Your students may not get a lot of genuine "good to see you"s outside of school- try your hardest to look happy to have them in your classroom or glad to pass them in the hallway.  This also works well for discipline- if I'm always smiling, students know something is really wrong when the smile has been wiped off my face.  I can't solve all problems with a look, but it really helps when your stern look is dramatically different from your usual facial expression!  The "no smiling until Thanksgiving" rule is bogus (but the underlying intention of being stricter at the start of the year is valid).

A few more practical thoughts: reflect on every aspect of your day and take notes on those reflections (I need to do this, if you find a good format for it please let me in on the secret!).  Read the archives of a blog of someone who teaches your course and ask people for resources (I've taught nearly all the standard high school courses and have a neatly organized dropbox folder for each one- if you ask for something I will send you the link, but I probably won't send unsolicited documents in the way I'm giving out unsolicited advice!).

But most of all, have fun! Be silly, enthusiastic, sarcastic- whatever your personality is, let it shine through.  When the kids see you being honest with them they are much more willing to go out on a limb for you or admit they don't get it.  No need to do a song and dance every day, make sure to let the kids do the brunt of the work - teaching is, after all, about them, not you - but share a bit of yourself with them.  If nothing else, it will make you smile when at the end of the year a student asks "do you even watch TV?" and a voice from the back of the room pipes in with "she only watches Netflix and Hulu." They are listening, always, even with their heads down, headphones in or eyes rolling.  You matter to them, let them matter to you and you'll reap great rewards.

Good luck and I can't wait to hear what you learn along this exciting journey!


June 16, 2012

Classroom Layout

As the school year ends I want to record what I liked and didn't about the layout of my classroom.  I'm also moving to the room next door (it's so much bigger!!) so I have to re-organize whether I want to or not.

Left side:

The agenda for each course I teach is on the board.  I use this much more than the students do- I do all my planning online (planbookedu) and my memory is terrible so I need my outline somewhere easy to glance at during class.  Some students look it over when they arrive, but most just wait for me to direct them to the next task when I write our current activity on the front board.  A few students will write in their journal before the end of class (which is counter to the purpose of reflection after doing the day's work) and do their homework when they are supposed to be doing classwork (which makes me grumpy) so I am considering leaving those off and putting them on a slide at the very end of class.

File cabinet: The top two drawers are for students- I keep extra folders in there for students with organizational challenges.  Some students take a folder for their backpack, others leave a folder in the top drawer with their work.  Next year we are moving to a binder system- I think I will have Fundamentals of Geometry keep their binder in class and just take home the day's notes and the homework worksheet in a folder.  Luckily my new room has two filing cabinets so they can have one just filled with binders.  The bottom drawers are for me- I started organizing all of the cut up problems, class sets of packets and great examples of projects in hanging files.  The teachers who are leaving have 3 million hanging file folders so I will be able to get things really well set up next year.  I don't want to save extra copies of most handouts since this year I made edits on the computer, but then made copies from an old sheet I found - which of course still had the typo or unclear question.  Everything that's leftover becomes scrap paper or recycling.

Table: pencils (usually golf pencils- cheap, pre-sharpened and the kids hate them enough to leave them behind), paper, pencil sharpener, calculators, tissues, stapler and hole punch all live here.  When students ask me for anything I just point.  Rulers, scissors and toolkits may be added to this area next year.  Tape will stay hidden away- I don't understand the temptation to use an entire roll of tape to fix something, but when the tape is out it disappears astonishingly fast.  This year I had a system of folders that worked great, except that kids weren't always clear about which folders were in vs. out vs. extra copies.  Next year I will put those into separate stands and label them better.


We are supposed to have a word wall.  I have done this in various ways over the year and have yet to find one I like.  One year I made pages with the word, definition and an example for all the types of quadrilaterals.  They look really nice but aren't easily visible from the back of the room.  Other years I've had students make mini-posters.  Those don't look as nice and still aren't super legible from afar.  Next year I think I'll just print the words with no other information in some huge font- maybe I'll print outlines and have kids color them, then laminate.  I do like the idea of having words up so that students have somewhere to look when they are searching for the precise term to describe a situation (although it took me 4 years of people mandating word walls for me to reach the point of admitting they might be useful).

The left side of my white board has the basics (name, room #, date) and a place for me to record students who participate or disrupt and to tally extra homework when the whole class won't settle down (I forget whose awesome idea this was, but thanks! Comment if you know and I'll give credit where it's due).  I did this for a while, but then didn't need to as much, and finally got a smart board so I don't usually have a dry erase marker in hand.  I record tally marks in my gradebook each day of who participated and disrupted during our class discussions, but students do sometimes need to see that I'm recording it, which is the purpose of having it on the board.  If I need these boxes next year I may do the split screen method on the smart board and make one page with just those 3 boxes.

My desk has boxes with: journal/CW sheets, scrap paper for quizzes, quiz/test corrections and MCAS reference sheets.  It may make more sense to put these papers with the extra copies of class activities.  But, students generally didn't make a mess of my desk this year since everything had a place to go and keeping papers in boxes meant the piles couldn't fall over!

Student desks are usually in pairs, which I like.  I'm excited for the possibility of extra space next year to have a place for groups to work without needing to rearrange the chairs.  They are currently as spread out as I can get them for exams (this room was not meant for 30 wide desks!).

Right side:

Random announcements and schedules fill these boards.  I have far more board space than I need so some get used as bulletin boards.  Next year I'd like to leave some of the extra boards blank and encourage kids to use the boards to work together.  This is also where the student art gallery is (hidden by the cabinet).  My cabinet has stayed organized since I cleaned it out at midterms.  Success!

June 12, 2012

Aging Trees Lab

As a way to encourage scientific writing (which I would distinguish from writing about math/science) I've been doing quarterly lab reports.  Students experiment in geometry all the time: we make hypotheses, try them out, evaluate our data and come to conclusions.  Four times a year I'd like them to write up that process a bit more formally.  This was the first year I've done this and I'm still learning what the expectations are in the science department and how to translate that into math class.  For this last report I went with a fill in the blank format; next year I will probably start with this type of handout and hope that they can write their own report without the structuring by the end of the year.  Sometimes I have to work backwards to find the right amount of support, but we got there!

This lab was originally inspired by a heat wave and a never ending school year- we were studying circles and I needed a good reason to go outside.  Well, outside there are trees, which have roughly circular trunks.  I did some googling and discovered some wonderful scientists had done the research that would let us determine the age of several types of trees knowing only their circumference!  The biggest obstacle in this lesson turns out to be identifying the trees, not the math involved.  I narrowed the list down to 4 trees that grow along the path behind our school and provided detailed descriptions for identification.  Even when I started the class talking about how we were going to determine the age without hurting the tree, there would still be one kid who would run over to me with a leaf saying "What tree is this?!"  But I think that learning about nature, while out in nature, is really important.  So they examine the tree with the light bark and the toothed leaves, and then I give them a hint to look a few feet away to find the tree that has white bark and doubly toothed leaves.  Because yes, the white birch really is white!

Worksheet we use outside: (one per group)

Aging Trees by Circumference

Scaffolded lab report: (one per person)

Aging Trees Lab Report

Many thanks to Journey North for the original lesson, they provide more growth factors if the 4 I chose don't grow on your school grounds.  Note the comment on forest growth vs. pampered plants; that is what I was hoping students would think of when I asked for sources of error, but most everyone just said that maybe they measured wrong (the more experienced report writers attributed it to rounding error which sounds far more sophisticated).

June 10, 2012

Summer Assignment

I'm in the middle of writing a summer assignment for Honors Pre-Calculus students and I need your help! I haven't taught this course before, and the only Algebra 2 I've taught was a CP class that struggled.  The current summer assignment is a random assortment of problems that neither of us who will be teaching the course next year want to assign, let alone grade!  So, here is what I have so far, major inspiration taken from @mgolding's project: Function Family Album.  Feel free to skim or skip right to my questions at the bottom to see what I'm requesting feedback on.

Summer Assignment
Your mission is to create a resource which summarizes the types of functions you learned about in Algebra II.  This assignment will give you an opportunity to showcase your creativity, but will also be an excellent reference for you to use throughout the course; so be sure to include enough information to refresh your memory on all the topics included.
You may choose any format you like to present this information (poster, pamphlet, scrapbook or anything else you can think of) so long as it includes all the required aspects.

Families of Functions:
Linear, Absolute Value, Quadratic, Cubic, Exponential, Radical, Logarithmic, Rational

For each family you will provide the following information:
  • Parent Function graph (ex: f(x)=x^2)
  • One shift (horizontal or vertical)
  • One stretch or shrink

When you have completed this section you will have 18 graphs all labeled with a title, an equation in function notation and a description.  Be sure to have at least one of each type of transformation (horizontal and vertical shifts, stretch and shrink) among all the graphs.

Choose one of the following:
*Coming soon* (equations for cubic that’s increasing and decreasing, quadratic with x intercepts, radical with x and y intercepts etc.)

For this function you will provide more detail:
  • Graph and table of values
  • Domain and range
  • Intercepts (x and y)
  • Intervals of increasing and decreasing
  • Maxima and minima (local and/or global)
  • End behavior
  • Whether or not each of the following points is on your curve *coming soon* (list points where at least one is on each option)
  • Value of function at x=__ and y=__ *coming soon*
  • Make up a situation that this graph might describe (feel free to be as silly or serious as you like; if your function looks like someone’s velocity as they fly to the moon write that! Just provide enough detail to match parts of the story to parts of the graph)

Does this seem like too much?  Do I encourage technology or require them to graph by hand?  I obviously need to fill in some functions and other details.  Do you have a favorite function that would work well for the last section?  Is this enough detail if I provide an example on my course webpage?  We will also be available via email and have a few summer sessions at the coffee shop in town.

June 9, 2012

Trig Intro: An Applet!

I made my second GeoGebra Applet and this time I included a slider.  I'm so fancy, I know.  But, for trigonometry the technology really is a huge help.  Last year I had students draw triangles, measure sides, compute the ratios and make observations.  The problem was, all the ratios are supposed to be between 0 and 1 which leaves them with very little room for error if we want to get nice patterns.  Needless to say, last year's lesson left most students bewildered and me frustrated that we spent a lot of time to get results that weren't useable.  This year, GeoGebra draws the angles precisely and computes the distance down to the hundredths place.

Everyone gets the chance to see all the triangles (no need to divide and conquer), calculate all the ratios and get a really nice table.  Changing the triangle to see what is an invariant (the ratio!) is as simple as dragging a point and then re-calculating ratios.  Everyone who was paying any attention easily worked through this lesson and made some good observations.  It took a lot more to fully understand trigonometry (I can't tell you how many "aha!" moments there were where students finally realized that all this crazy vocabulary really just means those ratios that we started with), and then still more to grasp inverses.  However, I liked this introductory lesson and loved the addition of GeoGebra to achieve the necessary precision.

That said, I will never eliminate paper and pencil activities from our explorations.  We started similar triangles with protractors and rulers- filling posters with triangles (some which were similar, others which weren't) and we continued on to special right triangles using Mathy McMatherson's awesome worksheets (first two links).  The technology made sense for us because students understood triangles and similarity, what we were focused on was a new type of ratio that required exact measurements.

The rest of my trig unit was okay, but still needs work.  However, at this point it looks like I won't be teaching any triangle trig next year so I hope someone else will use this intro and build a better unit off of it.

Trig Intro

June 6, 2012

How to Draw a Crowd

I stay after school to offer extra help most days each week, and I nearly always have students in my room.  Teachers who walk by will say "You're so lucky!  I never have kids stay after." but we all know it isn't luck.  There are a few key ingredients in the recipe of great after-school attendance.

First, students need to have something they can work on.  SBG means they can re-assess (I'm almost there, aiming to do at least partial implementation next year), doing rough drafts with feedback and allowing students to resubmit gives them concrete goals, even just letting them do old homework for half credit gets them in the door and working on math.  I allow students to improve their grade on every assignment through the end of the quarter (for teachers who worry about kids learning how deadlines work, there are 8 per year for progress reports and report cards, plus I grade in batches so if they want prompt feedback they know to hand assignments in on time for the first due date).

Second, students must understand that they will gain something from attending extra help.  For some it's all about the grade, but since I think my grades reflect understanding fairly well we're using different words to say almost the same thing.  For others they will gain confidence, study tips, deeper understanding or just a good space to do their homework filled with resources and their peers.  However, most students aren't convinced by the idea that this might happen, so we have to start in class.  The first test of the year I give everyone plenty of time to correct the exam in class (next year this will translate to time to correct one day, time to re-assess another day).  As the year goes on I give less and less class time with more emphatic reminders that I'm available after school to help them finish their corrections.  That first experience in class helps encourage them to come after- they know what to expect.

Third, students have to know that they're welcome.  My door is always open after school, I announce my availability regularly (that's one of the end of class announcements) and I greet everyone with a smile and "Do you know what you want to work on?"  For many that's still not enough though, they need a personal invitation. It was my goal this year to invite students based on different categories each week.  Sometimes I printed out a list of students with missing assignments, other weeks I listed students who had failed a test, and other times students who were failing for the quarter.  While everyone was working I would circulate the room and inform the student that they ____ (category of the week) and could they come after school this week?  Other weeks I print progress reports for everyone and emphasize when I'm available after school.  The best is when one student comes to class and shares how much they got done in one afternoon- first hand stories are the most influential (students have gotten help with that vs. I accomplished all of this!).

Sadly, this still isn't enough for everyone to pull their act together.  I can offer as many opportunities as I want, but that doesn't mean students will take them.  Last week I gave every student with less than a 65% average for the year a note with their average informing them that they were at risk of failing, they needed to have over a 60% to get credit and there wouldn't be an opportunity to correct the final so make sure you have a cushion!  I also wrote a postcard* to the parent(s) of every child who had a grade between 55 and 60 (there's still time to pull it together!).  I've seen some new faces after school lately, so never stop asking, one day they just might be ready to respond.

I'm excited to be able to talk more about standards next year and less about averages (although those certainly will still play a major role considering our current report card system), though all the principles will remain the same: give students a taste of what extra help looks like, reward them for it (assuming they are productive and have actually improved their understanding) and invite students personally.

*I did a great job of writing these in March, it was kind of what I did for Lent, and then vacation happened and life got in the way.  Goal for next year!

Motivating the unmotivated seems to be the most recent #matheme.  Write something or look up an old post on the topic and share!

June 3, 2012

A Simple Visit

What re-energizes you when your energy is lagging? For me it's students who come back to visit. When I taught in Lawrence I had an awesome calculus class and several of them would stop by my classroom sporadically during the year, even after they graduated. Most things that interrupt my teaching flow annoy me, but past students are definitely an exception. Most of the time these visits don't include any explicit statement of "you made a difference in my life, thank you" but just the fact that they want to stop by implicitly states "you are important to me" Sometimes, though, past students would talk to my present students (freshmen usually) to say something along the lines of "Ms. Cardone is the best, you better be good to her!" which always put a huge smile on my face.

Since moving to Salem I don't get to see those students, and I have had very few students graduate since I'm teaching mostly sophomores. But, past students do still visit.

Last week I was feeling unmotivated during my prep so I decided to clean my classroom and do all the little things that didn't really need to get done. But then, one of my students from geometry last year appeared at the door! At first I thought she was just checking in to see if I'd successfully built the fan I was putting together last time she walked by (which I did, it creates a wonderful breeze); but instead she asked if I could help her with Algebra 2. This isn't the first time she's come to me for homework help this year and I love that a former student is comfortable enough to show up and ask for help in a class I'm not even teaching. This student does an awesome job of verbalizing her thought process so I was able to finish cleaning while she worked out problems. She interspersed the tutoring session with random comments- how she misses my class and wished there was a geometry 2* so she could take that. When she expressed concern over taking pre calculus next year, I shared that I will be teaching a section of the course- she was so excited about the possibility of being in my class!

This encounter was exactly what I needed to jump start my day. Most students don't share their appreciation for what you've taught them (both mathematically and otherwise), in fact many won't come to realize it until much later, or may not trace that understanding or character trait back to you at all. But, those few instances when students do display trust, gratitude, or even a genuine smile remind me of all the reasons I love to teach (my original typo "live to teach" may be just as true!) and that even in June, when I had to buy a fan for my classroom because with 3 weeks left the heat is already stifling, everything I do has meaning and value. I can't wait to do it all again tomorrow, and next year, and for many more to come!

*I am actually developing a proposal for geometry 2 to start running fall of 2013 since we increased the math graduation requirement. I'd love ideas on what to include in the course: it should be accessible to most but include topics beyond the traditional high school curriculum.

June 1, 2012


My last post was inspired by a trend.  I've seen people blog lately based on requests of other people; not to mention everyone who has finished the year trying to get all of their reflecting done, quick, before they forget!  This made me think that a blog carnival would be fun- different prompts to encourage us to write those posts that have been lingering in the back of our minds, but haven't quite formulated yet.  It would also be a more permanent way to share some conversations (like homework) that apparently happen yearly.  However, no one really wanted to organize a formal carnival.  Then, @druinok had the great idea of a twitter hashtag to share posts on a theme more informally.  Thus was born #matheme- it's a math themed meme.  Our first topic is Writing in Math, I've built a #matheme page on this blog to keep track of posts and potential future prompts (which I promise to maintain diligently until I get distracted, and then feel free to remind me!).

So, write about writing, then let me/the world know (tag a tweet #matheme, comment here, email me, whatever).  If you've already written about writing, share that link too!  Let's keep this conversation going until we're excited about something else.

Some possible future prompts (totally off the top of my head when I couldn't fall asleep last night):

A day in the life (I arrive late, stay late, leave work at school, except on Sunday...)
GoalsGrading (SBG, hybrid, traditional, other?)
Standards list if you do SBG, course overview or major themes
A great problem for habits of mind
Biggest success/Worst failure
Today at math camp I learned. (definite prompt in July!)
Your primary role (I don't think my job is to teach kids the definition of circumcenter, but what is it?)
An awesome story that makes me want to teach (even in June when my classroom is 80 and humid)

I hope you'll join in to force all of us to think a little harder, reflect a bit more deeply and learn so much from each other.