Do we have to speak English?

Calc class today

 This was SO AWESOME!!
 I gave the kids the following problem.

First "funny conversation":

Student: What does it say in the upper right? (student was on opposite side of room from whiteboard where this was displayed).
Me:  You realize you can get up and go see, right?
Student: Oh.
Me:  Time out class!  In case you haven't figured it out, this is a non-stationary class.  If you can't see something, get up and move so that you can!  If you don't want to sit in your desk at all this period, I won't care!  As a matter of fact, I think next year, I'm asking for just benches.  It will look like a sports field sideline with nothing but benches for the players to throw their "stuff" on.  Oh the assistant principal is going to hate me!  Who wants to sit in these hard desks anyway!  Not me!

It's taking a little bit of time, but more and more students are buying into this idea of working on the whiteboards.  I love it! And having them wrestle with this problem was great!  They did all get to the answer (at different times) and I was then able to show them the lesson on Mooculus that will require their understanding of the slope formula for finding slopes of tangents.  NOW, they will have no problem with the practice problems. Still in love with that website!

Second "funny conversation":
Student 1:  Do we have to speak English when we discuss this?
Me: As opposed to what else?
Student 1: Togala!  3 of us can speak that to each other.
Student 2: Except for me.
Me: You can speak anything you want, but remember, you want everyone to be able to participate.  So, I guess you will need to make sure you write down ALL your work so "he" can follow what you are doing.
Student 3:  Yes, math is a universal language!

It was just so enjoyable that they were so excited to talk about the problem and it made it easier for them to speak in "their" language.  I would never have known that in my old classroom setting. This new work space is so AMAZING for getting to know the students (on their level(s)).

After we did that warm-up exercise, I made them create a folder on Google Drive and share it with me.  Inside that folder, they were to write me a Friday letter.  I got this idea from Twitter Math Camp via Rebecka Peterson (@RebeckaMozdeh).  I told the students that I wanted them to write about how they felt being in this classroom/Calc class.  I know this was a huge mind shift.  When has any teacher cared about that?!  Least of all a math teacher!!  I cannot wait to read them!  If kids were not on a laptop, they could write me an old fashioned letter (yes on paper with ink) and hand deliver it to me.  I also said if any parent had an old mailbox in the garage that they were never going to use again, I would love having as the "old fashioned mail" depository.

If students finished early, I had a puzzle for them up on the screen.  It was trivia questions from this fantastic site. The students were going crazy trying to answer them (or be the first to answer them). All of a sudden, I notice a student trying to look something up on his cell phone (answer to a question).  Keep in mind that he still had a laptop sitting on the desk in front of him.

Me:  "student", you realize that you have a laptop in front of you, right?
Student: oh yeah!
Class: (laughing!!)

Stats class

This is the problem of the day today for stats.  I did another (easier) version with them to get them started.  I asked them how they were going to prove the y-values that they needed to find lengths of vertical heights/bases.  This took some serious thinking on their part.  Eventually they led me to similar triangles or using slope and equation of a line. Awesome!  This problem really made them "up their game"! Some still have to finish over the weekend.  It's so wonderful to hear all the explaining that goes on amongst them. NOT me doing it, THEM doing it while I listen.  I only interject if I need to.  How empowering for them!

Kids say the BEST things!

Calc class today:

They changed seats today:

Student 1: I have a hard time figuring out where I sit because I can't tell on the seating chart where the front of the room is.
Student 2: Um, I mean where's the front of this classroom? There's boards everywhere.

That was the best compliment I've gotten this year!  Exactly what I want my students to think: there is NO front of the room.  This is their LEARNING environment.  I think it's actually working.  I'm now called "the spotter" because while they "work out", I spot them. I had a student call me over today to "spot him" because he was stuck and needed help.  I love when my analogies actually stick!  I heard a student say (when his group called me over to assist) that they were trying "something" and it didn't seem to be working, could I help? Wait, is that music I hear? Well, at least music to my ears.  Kids working and asking for help only when they got stuck (and had a lot of work already shown).  It was JUST SO AWESOME today!! It felt like that scene in Good Will Hunting when Matt Damon is working on the board in the hallway and the professor comes along and looks at it (only to find it is correct)!

Let me tell you what we were actually doing:  finding the slope of a tangent line using the definition.  The problems were HARD and the kids were just eating it up.  I had to pinch myself! They even were enjoying the challenge because I had warned them that we would be "bench pressing 300 lbs today". To see them all get up and work together on THEIR board (reminder: no front of the room) was another BEST DAY EVER!

Stats class today

Student: I don't guess and check in this class because it's too hard to do that in here.

That put a smile on my face.  While guess and check in (math) class can be a viable option for getting to a correct solution, it is true that guessing and checking is a useless strategy in Stats.  You actually have to know what you are doing.  It kind of fits the old adage: you can't BS a BSer!  The students do quickly figure that out (no use trying to fool Mrs. Torres because she can tell that I didn't know it).

Let's start by saying that if you had walked into my room during the first 10 minutes, you would have wondered what was going on.  Students were (mostly) in a state of confusion trying to figure out what they were supposed to be turning in today (Chapter 1 assignment packet) because this is the first time they have done this (probably ever).  After resolving everyone's "issues" we moved on to talking about what it was that they read. I made a worksheet to guide their thinking and for them to respond to in their notes.  I've never done this before and I REALLY LIKED IT!  Normally I would write down the notes on the board and they would (take their sweet time) copy them down.  This was a complete twist.  Now the notes would be in their own words, but in reference to questions I present them with.  I'm going to try this for a bit to see how it works out.  I'm being optimistic!  We'll see how they do on the problems I assigned tonight.  That will help me decide how the first day of that went.

I will end by saying that I had a GREAT discussion with one of the "overachievers" after class.  When he saw his test, he almost passed out from shock.  But I did get to thinking that he did in fact know a lot of "stuff" that we had talked about, but my points were assigned to other more specific things.  Sometimes it is so difficult grading with objective mindset as opposed to subjective.  However, I know what the AP test is looking for.  So I think I have a solution that I am going to try...here comes my thoughts about SBG.  I'm going to let them "do over" the free response portion and see if they can write better.  After-all, that is exactly what I am after (making them good technical writers).  This solves my dilemma of getting them to LEARN and their dilemma of improving a grade when they feel like they really did know it.  If I want to get them to keep trying, I have to provide them the feedback and another opportunity, right?

Is it possible for standard deviation to equal zero?

Such a great question: Select only four numbers from the numbers 1 through 10, such that the standard deviation is the smallest.  Repeat to find a standard deviation that is the largest.  Is there more than one choice for each set?

I love this question.  It gives the students a real chance to experiment to see what happens.  They were all positive about the fact that there were multiple solutions to the first part, but we had to experiment to determine the second.  Then they explained "WHY?" to me.  Hopefully that is all the explanation they will ever need to have that concept.

I felt like I was getting more correct responses as we reviewed material today.  I had assigned a problem set  before giving them formal definitions about resistance or how mean compares to median in skewed graphs.  So as they read off their answers I heard some say, "well I know that answer is wrong now, so I'm changing my answer".  I like that!  Although I would love to think that they are doing some extra research on their own, outside of class, in order to get the right answer, at least they can spot right away that their answer is wrong after the class discussion.  They are spotting their own mistakes.  Can't ask for more than that!

In Calc today we went over a problem that I gave them that was a real "brain buster".  I explained that mathematicians are still alive (no they are not all dead) and that we don't wake up and know all the answers.  Sometimes we have to explore and look for patterns, and this problem would be a good example of how I could do that.  So we went on an exploration of what happens with limits if you get 1/0 or 0/0.  No formal definition, just an exploration.  I want them to know how exploration works and can lead us to discovery (even in math)!  I was expecting to hear "is this going to be on the test" and I was shocked, but I didn't!  Maybe I am going to be able to turn them all into Christoper Columbuses or Ferdinand Magellans!

Whiteboarding works!

Well, I had an epiphany over the weekend about using my whiteboards.  So I had it all planned out for Calc.  Today I gave them problems from each problem set (the old HW pages that we now do in class) and had them put them up on their whiteboards.  I loved all the working and  talking.  Most of the groups were up and standing at the board in order to discuss and write out their work. It's interesting when they don't use that approach.  A few groups are still tied to paper and pencil (that may take a long time to train away) without chatting much.  Eventually they put it up, but it's like they are worried about not having the correct answer to display right away. The one good thing about changing their groups frequently is that they will eventually work with others who are quick to jump up and get started.  Hopefully then it rubs off.  I definitely liked this workflow.

One idea that I had was to have them write a problem (for me to do) similar to the ones I had them work first.  The reward was that whichever group wrote a really good one, I would put it on the test.  This was the first place winner.

 Statistics students sometimes struggle in the beginning of the year with problems that require that they use "outside knowledge" from the real world.  Today was one of those days "I don't know anything about pregnancy".  I have to remind them that I'm fairly sure they know enough to reason out the answer to the matching question.  Then they "pop the question": "so you mean we are supposed to use what we know from outside of this class?".  Novel idea isn't it?  Always cracks me up.  Imagine finding out that knowledge is connected and not segmented into 6 periods per day.  Crazy that anyone should expect you to put together what you know from other experiences and classes!  It makes me challenge them when they complain "this isn't English class" because I tell them that I'm going to pick apart what they write and look for grammar and spelling and all those "other English things".  They groan and think it's preposterous.  I say "if you speak English, then I expect you to write it.  The discussion ends there.  They will take their first test this week, so they will soon see what I mean by their grades!  First test is always an eye-opener.

How I spend my Saturdays

Some might think I'm a little crazy with all the ideas that I am already employing.  So the fact that I spend Saturdays traipsing around Southern California attending conferences to learn even more stuff is simply insanity.  Let's face it: I probably passed insanity awhile ago! We've only been in school for 2 1/2 weeks and 2 of the 3 Saturdays I have been to conferences trying to gather more ideas for improving what I do with students.  And it has been AWESOME, so much so that I thought I should include it as a blog post.

August 9th, I went to Playdate LA (free), as you can probably guess, in LA.  It was fabulous, not because I learned so much, but because I ended up sharing so much.  This was the part I was NOT expecting.  I still think of myself as a "newbie" in the world of technology (and change), but apparently my lurking for the past 6 months (on twitter and blogs) and reading (for endless hours) other's ideas online, as well as attending a few other conferences has REALLY paid off.  I actually know some "stuff" now! The feeling I get from sharing what I have learned was really exhilarating!  I was finding others who were at the place I was 6 months ago, and helping to "fill up their cup" of knowledge was gratifying and at the same I affirmed my confidence in what I have learned.  By putting my students in teams and expecting them to work together EVERY day, they are having the same experiences.  And I can tell how good they feel when they get to contribute to their peer's understanding of a concept we are talking about. Learning is great, but sharing what you learned is SO MUCH MORE!!

August 23rd, I went to EdCamp605 (also free).  The first awesome part was that now that I have a been to enough of these that I actually KNOW people.  I shared a few hugs with people that I had met at Playdate LA and CueRockstar (attended back in July).  In addition, I was able to connect two people that I know, who were both at Twitter Math Camp with me, who did not know each other (it was perfect because they are both in a TOA position and I knew they would enjoy exchanging information.) I sat in some good sessions, and got some good ideas, but I've figured out that it's just not mentally possible to hold onto everything that gets thrown into my brain.  Unless I'm really able to apply it, create something before I leave,  or use it immediately when I get home, it just falls away.  I overheard people talking about Doctopus (a google add-on) and while I participated in a great presentation by @jstevens009  at CueRockstar, I don't remember much about it. Somedays, all that knowledge is just too overwhelming.  You really have to pick and choose and not try to use all of it (at least right away).  I even had @EdtechBUSD amazed at how much change I've already done and that I'm considering using Standards Based Grading.  The more I've pondered our conversation in the past 24 hours, the more I realize that's going to have to wait for a 2015-16 iteration.  There really are not enough hours in my day/week to do all the ideas I have gathered.

While I strongly encourage teachers to attend these wonderful conferences, know that you will need to pause for moments of reflection and your brain will need time to process and USE the information (in order for it to stick).  Keep in mind that this is what our students experience EVERY day when they are in our classes.  We don't often give them reflection time (because we are trying to cover the content so fast).  Students (of all ages) need time to process, and use what they have just learned.  It is essential for growth.  There is a substantial amount of content that falls out of their brains (just like mine) because they don't get to apply, create or use it immediately.  This is the reason why common core is being pushed.  We need students engaging with content at those higher levels if it is going to "stick".

I look forward to the next Saturday session. The networking has been one of the best parts!  I have created a wider circle of colleagues and they are just a tweet away, waiting to help with their resources, experiences, advice or whatever else I need. I've enjoyed every conversation and words of wisdom that have so willingly offered!  I hope that it is all transferring back to my students so that they too look forward to every "session", and that they are encouraged by the work with their peers. That is the "stuff" that will definitely stick!

"We are learning!"

It doesn't get any better than that!  Students yelled out in AP Stats today, "we are learning!" If it weren't for the fact that that only drives me to push myself (and them) to new levels of success, I think I'd pack up, turn in my keys and leave for retirement on that note! I suppose there is the fact that I am still too young to consider that also.  And to think that I kept "wrecking their thinking".  I have 4 different worksheets that contain either box plots with histograms, or partial numerical summaries with box plots, or the summaries with histograms and they have to match them.  We do one page at a time, they get to discuss among their teams, and then I ask for their answers.  They love shouting out what they think is correct, that is until they get one wrong.  After I have read all the answers, we then go over why the pairs are matched that way.  On to the next worksheet, repeat.  What is always funny is there are students who get them correct and yet their team convinces them they are wrong.  So there is a lot of "I said that!" and "I told you!" going on as I read the correct answers.  The part I love is the retooling that goes on in their brains before they get to the next set.  By the 3rd worksheet, they were excited that they were getting pairs matched correctly.  This is my version of "try a few, get feedback, repeat" until they hit success. The students love all the "haggling".

Calculus was equally as engaging today.  The students had all kinds of questions about problems they worked on last night, and were eager to ask them.  Some were just how to put the information into their calculator to get the right information back out.  I explained that this was their new cell phone and if they currently use IPhone, this was an Android and vice versa.  I told them "you know what I mean, you go crazy punching buttons saying 'no that's not it, [punch another button], no that's not it, [punch another button], AGGGHHHH!'"  They laughed.  I explained we would all be learning how to use our "new cell phones" [aka graphing calculators] together until they got used to them.  I also told them that the first step to breakthrough in Calc was admitting that "we" have an Algebra problem.  My students who were able to admit this early last year had breakthrough much sooner because they learned to be more careful on the Algebra steps within their Calc problems.  I expect we'll be having a lot more breakthroughs earlier this year!  What was really awesome was when one student announced today "I feel like a lot of solving these problems it just cleverness".  I responded with "you are absolutely correct!", and he stated, "I'm not that clever".  I retorted with, "you just got me through this solution, so apparently you are!".  It was great listening to the "ooohs" and "aaaahs" as they watched magic unfold when I wrote out what they told me to do next.  I hope that my simply following the directions they give me eventually gives them the confidence they need to get themselves from beginning to end of every problem (okay, well at least MOST of them).

One last thing: it is always a great day when I get to start out showing colleagues new websites.  This morning I worked with the Algebra 1 & 2 teams and showed them Desmos Central Park, Robert Kaplinsky's website chocked full of cool lessons, and Nora Oswald's (@NoraOswald) games on her blog Simplify with Me (Line Game, Parabola Game, Sine Game and Domain Ranger game). I found these when she shared them via a webinar sponsored by Global Math Dept and I thought they were super!  In addition, I introduced them to Game About Squares and 2048. That will definitely keep them busy looking at cool stuff for their classes for a few weeks.  I'm getting excited to hear how some of the lessons they plan on trying work out....call it living vicariously through them!

I love the Aha! moments

Statistics today was filled with several aha's! I can almost hear all the cogs clicking in their brains.  I gave them three data sets and had them make a box plot for each as well as find the mean and median.  Then I asked them about the shapes and the comparison of the mean to the median.  The first example I gave them was clearly symmetric with mean = median (always start with the easy ones first!)  Then they had to decide between skewed left/right for the next two.  There was a lot of shouting going on as each student thought they were right.  Then the "why that?" explanations.  I love these moments.  In some brains, you can tell there is a backflip happening as they have to redirect some previous thoughts.  It's as though they are re-categorizing their thoughts, while some are glib about their correct choice the first time.  So, of course I have to challenge their thinking some more.  I offered them 4 histograms with 4 box plots.  They have to match them, and it's NOT EASY.  While two of them are actually fairly obvious, the other two are difficult to match.  There was SO MUCH discussion.  I can't wait for tomorrow!  Just when they think they have it right, I will challenge their thinking AGAIN!  I have to enjoy this now, because once we get past this unit, they are smarter and it is more difficult to get them.  Boy, do they grow SO MUCH!

Continuity and limits to infinity were the two topics today.  Mooculus helped them look at graphs of infinite limits.  But when they went to paper problems, their struggle increased.  Deciding continuity and how to fix removable continuities is pretty abstract at the moment.  This will take another day for sure.  Especially because we don't offer piece-wise functions too much in Pre-Calc.  Even remembering graphs of rational polynomial functions, radical functions and logarithmic functions has gotten lost in the recesses of their brain. Note to self: the summer assignment needs to contain more graphing of all types of functions, including piecewise.  This needs to get lodged back in their brains before school starts. I'm looking forward to "the workout" tomorrow!

Histograms and stem plots and box plots (OH MY!)

It is amazing what the internet world can bring into the classroom!  This week we have used a program made by Ohio State University (Mooculus), a practice set made by Cal State LA (National Curve Bank) and a practice set made by UC Davis (Limits of a function). I really think this has helped the students understand the concept of limits so much better than last year.  They really struggled with it last year, but I think all the "hands on learning" by practicing and practicing and practicing with the instant feedback and help from me and their teammates (groups of 4) really helped.  I think the lessons had that real element of "stickiness" that we all hope for as teachers.  I know some of the students actually went online at home and played with it some more!  It doesn't get any better than that!  I've realized that the biggest bonus to being able to access all the college materials is that my students are now getting exposed to COLLEGE material while they are still in high school!  I'm expecting to hear great stories, after they head off to respective colleges, about how overly prepared they were, both mathematically and technologically for their college math courses. 

Statistics students did a practice set online at (ck12.org) today.  Some of the problems had errors in the answers and the students quickly found them.  They wrestled with the graphics not being perfect so we had a chat about how to compare "bad graphics" in order to select a correct answer.  These types of  problems will exist in the real world for them (can you say..."I never get to speak to a human when I call.....".  Technology sometimes causes more problems for us doesn't it?)  I love listening to all the "buzzing" while they are working together to convince each other that there answer is correct.  Just when they think they know everything about graphs and graphing, I throw them a curve ball and they have to readjust their thinking.  I love expanding their minds!!

What to expect, when you are expecting

Interesting question for myself today.  I expect the students to learn about limits and derivatives and integrals (OH MY!) this year, but trying to flip 2 different AP classes is definitely a bit daunting.  I will definitely need to keep track of my receipts for the coffee (is that tax deductible?)!  And if someone asks again "how do you have time to do all that?!", I might not be able to resist the urge to punch them!

I have decided that I don't think it is possible to do a superstar job at both courses.  One always falls backseat to the other.  At least I'm getting my head wrapped around that idea that I simply do not have enough hours in the day/week to do all I WANT to do.  Not that that stops me from trying, mind you!  I'm a tad on the stubborn side, so I can't "let it go". I think I can, I think I can, I think I can!

But the bigger question, is "what am I expecting from my students?"  I hate having to decide "x" number of points for this and "y" number of points for that...and extra credit for this (just to get them to REALLY do something I want).  As a matter of fact, I have to STILL figure out just how much time I expect them to spend learning my subject each day.  Now they have about 25 mins of videos to watch and then another 15 mins of "easy" problems to do.  In class, I try to find computer practice for them that reinforces what they learned, and then its on to the worksheets (that were the outside HW last year).  I know those problems took at least an hour most nights because that is how long they took me sometimes (and we know the kids take longer). I also know that many times they skipped problems on those HW sets, so I'm hoping that I can force them to ponder those types of problems while they are in class.

Don't get me wrong, the work/learning that happened today was AWESOME! I'm really happy to see that they practiced on some questions online and quickly got through them, and moved on to the paper version.  Many asked questions of either me, or their teammates.  I listened in on great explanations and provided a few of my own.  It was rewarding to hear students say "Oh, I get it, I've never had anyone explain it like that before".  It felt good hearing the students talk math amongst themselves.  But eventually the question will have to be asked.....and answered "what's my grade?" It simply seems like it inhibits what I'm really aiming for...LEARNING!!!  I always tell them "I don't care about your grade, I care about what you actually learn because I know that will be way more important to you later on."

So, I still have to figure out: what am I expecting?  And the students will wrestle with the same question of me (so they can accumulate their points).  I'm expecting them to learn!  But how do I put points on that?  Currently, it appears to be happening to all of them.  Each day I tell them "you are smarter than you were yesterday", and it's true.  I know they can find limits (in Calc) and they can make/read a graph like a pro (in Stats), but beyond, I am still in a quandary about how I'm going to explain their point value based on my expectations.  I wish there were a meter stick to measure the growth of their mind after I have stretched it everyday.

MOOCulus!

If you are reading this as a Calculus teacher, and you don't understand the title of this post, let me be the first to introduce you to the wonderful world of MOOCulus!!  It is the most amazing website I have found thus far for using in my AP Calc class.  Since it is a creative commons website, and a creation by some fabulous people at Ohio State University, it is all free to play around with and explore.  This is exactly what we did today in Calc.

My students had taken their first set of notes on Limits.  Now, I create my own notes and videos because I like to have that "relationship" with my students, and have them know that I am equally invested in what we are doing.  My videos might not be as entertaining as those on MOOCulus, but my students enjoy them.  After watching the notes, I wanted the students to practice what they had learned.  So I had them enter the MOOCulus exercises on limits. You know you have scored a great day when the students say "that was fun!"  I love it when my plan actually works.  Actually I think the best quote all day was "why don't these laptops have a caps lock button so I can type in DNE?" and then followed up with their own response "first world problems".  This practice set had students typing in x-values in order to see the limits of a function graph from both the left and right of a given value.  It made them write their answers in 3 decimal places so we had to discuss how they could get their answers in that form (rounding).  One remarkable note: Calculus students may still have trouble rounding correctly to 3 decimal places.  HOWEVER, they figure it out real quick when they can't get the computer to say "that is correct".  They will not quit until they have gotten "that is correct. next problem" and then see their progress bar increase.  It was as though they were playing a math video game.  They were upset if their progress bar didn't go up enough.  This made me laugh inside.  (insert evil voice in head): I have them doing limits and being competitive about it....a new subject that they really don't have conceptually in their head, but they are working like crazy to get the problems correct!  AWESOME!!  When they finished "playing", what I really mean is learning, I then led them to another Limits website (created at Cal State LA) to complete the problems using drop down boxes.  I liked the practice in this order because completing the 1st set made the 2nd set easier.  They had developed a decent understanding by then.  When they were finished, I had them switch to a "paper version" (aka their worksheets) to do some more limits solving.  It was a perfect blend and I was pleased with the use of class time today!  I plan on using more of MOOCulus this week to reinforce more about limits.  Some days the lesson is so fun that I wish I were a student in my class...today was one of those days!

AP Statistics:  I have realized that much of what I have always done in stats is non-lecture based.  It's just not possible (in my humble opinion).  And the technology component has ALWAYS been there because we rely on the graphing calculator so much.  It was fun today to "mess with their heads" by making them create a named list in the calculator, transfer data into it and then seemingly erase ALL of the data before we got to graph it (especially because they had just entered all 30 data values by hand).  When you show them that the named list is still in their calculator, they are amazed. I'm going to believe that the quote "that is SO SICK" is a good one!  SO MANY things to learn about this technology tool.  I LOVE this time of year, where they know so little about this tool and I get to teach them.  Later, they become so expert with it, that I only get to laugh at how fast they all enter data and I just hear buttons being pushed rapidly.  For now, it's gasps at what the calculator just did (as I lead them through the button pushing) that makes me smile.  I enjoy listening to them and hearing things like "how do you....?" and "I always forget that".  I even have to lecture them about taking the calculator away from their neighbor and simply pushing the buttons for them (pet peeve of mine).  People only learn when THEY do the button pushing.  I enjoy making that point with them.  It's fun teaching them to THINK about what the graph should/does look like. Weaning them off "what does your window look like?" and telling them that they HAVE TO become expert "hamster trainers" (a name I give to their calculators--"the hamsters").  I even tell them that they can add hamster trainer on their resume' after this year (would definitely generate a funny discussion in an interview!).

It's days like today that I think I would probably show up and do this "job" even if I didn't get paid!

Calculus around the room and "the Statistics talk"

I cannot express enough how awesome it is to have the whiteboards (mounted all the way around) in my room this year. Ask me again in a few months when I have possibly had to purchase the markers (although I am making that a requirement for every student in their school supplies).  Today I put up one question on every board (9 total).  I told the students that there was a problem on "their" whiteboard that they had to solve and that I was giving them 2 minutes to work it.  After that they were rotating and solving the next problem. WOW!!  You should have seen them working.  Sometimes they were so quite that I had to interject "you know you can talk, right?".  They responded with "we are working!"  That made me chuckle inside!  At the end I asked if they felt rushed and they responded with "only on a couple of them."  I said they would have plenty of time tomorrow to do the same quantity and caliber of problems, and they seemed relieved.  Sometimes I like to push them a little harder in training because then during the test, it doesn't seem as difficult.  I liken it to training for any sport.  Train harder so that the actual race/competition seems less challenging.

I also like to surprise them.  I asked if anyone was interested in having a copy of the problems to practice again at home. Several hands went up.  Then I asked if they'd like a worked out solutions guide. Several hands up again.  I followed up with "is anyone interested in a different set to practice on?" A lot of "yeses", to which I asked would you like solutions for those as well?  Of course that was a no-brainer.  So I gave them the questions and the extra set on a worksheet and told them the solutions that I worked myself would be posted online.  They think it's Christmas because I'm supplying "the toys" and I think it's Christmas because I get kids doing more math!  WIN WIN!

THE TALK
I gave "the talk" today.  "If you are feeling confused, you are not alone".  I keep this on a post-it to remind myself that I will have to give this talk to the AP Stats students near the beginning of school.  I could hear some huge sighs of relief.  Graphing and analyzing graphs is a lot harder than they thought and many of the "overachievers" are starting to feel "the pinch".  Should I stay in the class? is becoming a non-ignorable thought.  I always tell them that this class is different from every other math class.  We will not be doing number crunching.  We will use the calculators (another piece they have to learn...and it takes time) to do the calculations for us, we have to know how to explain our findings.  It's fun though to bring up things like "this data proves sexism in the ____________ industry" and then let them discuss.  It's a challenge for them to use DATA to support their opinions instead of their "feelings". This is one of the qualities of Stats that I love (something completely new that they do not have refined skills in).  I know because I have taught it for so long that they will be completely different people after learning statistics for a year.  It's fun to watch the fledglings in the beginning.  They try to start jumping from the nest, only to find out that they are not anywhere near being ready yet.  You have to love that confidence they have in themselves as evidenced by their trying.  But now they are starting to realize that they aren't able to catch the updraft yet...back into the nest for a few weeks more.  My poor little birds!

Graphs are too easy....er, maybe not!

Today was a great day.  The Calculus students were busy working on a review that I gave them for the end of the Preview chapter (a review chapter of all the math they learned in the past 3-4 years.  There were A LOT of cobwebs needing to be cleaned out in their brains. Things like where are the principal values for sin, cos and tan located?;  how do we solve a trigonometric equation?; and what does arcsin mean? I nicknamed someone Captain Jack Sparrow because he had found the buried treasure (after solving a problem) and then I made his group the class experts for explaining it to others when they got stuck.  In one class period we had a "gather round" to see the work of 3 separate groups on a tricky problem and I explained how mathematicians try something with new problems, not just stare at it and complain this is too hard, or I don't know how to do this!  I stated that there were going to be lots of problems they wouldn't know how to do this year, but that these "giving up" approaches were not progress toward learning.  I explained that the groups I had nudged had come up with those processes on their own, I had simply asked a few questions.  SUCCESS!!

One of the district tech coaches came out to meet with me today (thereby definition of a good day...I always love that I get to learn new things in tech). I got lots of tricks, tools and good info to keep me busy for a few weeks.  But the best part is that I actually got to share something with him that he didn't know. SUCCESS for me!  I am enjoying my moments where I get to give back to others and share something!

Now on to the AP Stats class. At the beginning of the year we are looking at all the different ways we can graph data.  At first students think "this is gonna be easy" and then the questions come with all the different types of graphs: frequency graphs, cumulative frequency, relative frequency and cumulative relative frequency graphs are the "killers".  And then the questions switch up which version of graph is the most useful for reading...or even worse, there is no choice.  The graph is given to you and the questions require thinking....DEEP thinking.  Sometimes backward thinking.  "Dope, I think I just felt an aneurism!"  This is where the students start to come "unglued".  This is a new experience!  And they start to think "I don't know what I'm doing and I'm not going to be successful in this class". That was plank we were walking out on today.  I can feel it and I expect it.  So, tomorrow is "the talk".  Their stress level is getting a little high and I have to calm them back down, give them a pep talk and let them know "it's gonna be okay".  It's always funny at the end of the year when they write their suggestions to me for next year and many say "go faster in the beginning".  They forget that "the beginning" was a struggle too.  But as we progress, so much of what they learn becomes part of their "fabric" as though it has always been a part of them and they can't remember not knowing it, or struggling with it.  Happens EVERY year!

Overshooting a little

Trying to adjust my lessons and plans to this flipped classroom approach is taking a bit of time to wrap my brain around.  I spent all summer gathering materials (thank you to all the people who post on twitter and their blogs, and those at Twitter Math Camp who are willing to share for free....YOU ALL ROCK!) and reading blog ideas and simply gleaning content and materials from anywhere I was able.  I printed out several notebooks worth of stuff.  I was able to even get it organized by chapter.  Now moving on to the next step...using it.  The videos (although time consuming like I knew they would be) are covering what goes on at home, but I want "stuff" that is going to cause engagement while the students are in class.  I had decided that there needed to be much more discussion amongst students with the explanations about their thoughts/process, and my asking kids "why does that work?", "is there another way?", "how do you know?" and so forth.  While I knew that this is the quality thinking that takes time, I guess I didn't anticipate how much longer it really does take.  I've taught for 29 years with the "hurry up and get through HW so you have time to deliver some lecture notes" method that it never dawned on me just how much I was going to have to slow down.  So while I'm planning all these activities that we can get through each day, only to realize that there is NO WAY I can get the students through ALL THAT if I want them to have that deeper understanding that I'm hoping to get this year.  Thus the justification of my title:  I have definitely been overshooting on my lesson plans.  In some way this is actually a relief, because it means I won't have to use EVERY SINGLE THING that I found this summer...and then some!  It means I'll be able to pace all the "good stuff" and I will probably be able to pick and choose which ones I want to use this year, with leftover materials for changes next year if I need to.  HALLELUJAH!  I have been really worried about filling 180 days with awesomeness!  I wasn't sure I'd have enough.  It's so nice to let groups finish a task they are working on, and at the same time, give those who are done something more as a challenge.  That turned out to be easier to come up with (off the top of my head) than I expected.  The challenge now will be to keep track of every extra thing I generate spur of the moment.  I don't want to have to create everything again next year.

Today was a good example of how this played out.  In Calculus they have been working on a set of 15 multiple choice review problems in their groups over the past 3 days.  Some groups were done, so I posted challenge questions on the board for them to work on while the other groups finished.  In addition, they had to post their proof (trig identity) and graph (trig graph) on their vertical whiteboards.  I  overhead students asking their teammates "can I put my answer up?"  How exciting that students WANT to put up their work for everyone to see!  I'm bummed that I have been missing out on this for so long!  I liked this asynchronous workflow because it kept everyone engaged so there wasn't wasted time waiting for all groups to finish.  Sure, not all groups did the same amount of problems and, OF COURSE I would like for every student to complete ALL the problems I gave, but if I rush them, then those that need to discuss a few minutes longer don't get the time (nor understanding) they need.  Over time, I know there will be a payoff for every student. I think inevitably they will all do more problems as a result of the groupwork than they would have done solo.

In stats, I sometimes forget how many iterations it takes on the graphing calculator before students understand the steps for doing things like graphing histograms and copy the results onto their paper.  Every student was working away trying to get "the hamsters" to give them the correct graph that they had already described to me.  Although some of them helped their teammates, most of the time they were intent on working to get the desired results.  I had to MAKE THEM STOP, and claimed their brain needed a commercial break, so that I could show them another graphing calculator tip.  Can I ask for anything greater?  I think not!

The wonder of Desmos

My calculus students were reviewing graphing concepts today: find the points of intersection, find the intercepts, transformations on parent graphs.  We were using the graphing calculators and I was making them explain to me how to do each of these processes.  Some of them were feeling quite proud of themselves because they remembered and were able to shout out the steps and buttons that I should push.  Enter Desmos!!  They have never seen this operating platform before.  We have Chromebooks in the class, enough for two people to share.  I started with a "find the intersection points" problem and they were in awe.  Then we moved on to finding all the intercepts.  Excitement continued as some of them were discovering new things about it.  That's what I love, you do the introduction to something on the computer and they RUN with it!  No nudging required!!  Then we went to the transformation with sliders!  Their graphing calculators can't do this!!  They were having SO MUCH FUN!  Some of them zoomed so far out it was as though there were looking at the graph from an airplane at 30,000 feet.  Should I reiterate: their graphing calculators can't do this!!  But when they figured out that you could hit the "play" buttons on the sliders and watch the transformation animate, there were mesmerized!  When I hear "I can't focus because I'm too busy graphing", you know it's a GREAT DAY!  When I made them pick back up their calculator and do it "old school", they grumbled that using that piece of technology "sucked".  I had to agree!  And I have been the biggest salesman of graphing calculators to my students.  Now I am encouraging someone to step up and manufacture a hand-held Desmos calculator....I think it's been done...called an IPhone or IPad!  But the problem is: they can't use these on the AP test, so we have to keep using the slide rule, er, I mean the graphing calculator!  How long until the world of education (and testing) catches up to the "real world"?  I hope I get to see it!

In AP Stats, I gave the students 10 different data sets.  They had to select 5 and make 1 bar graph, 1 dot plot, 1 pie graph, 1 stem plot and 1 back-to-back stem plot and show me the graphs on their whiteboards.  These were some of their results.  There is so much discussion! I love it!  And students can even spot mistakes in others work on the other side of the room!  Then when I asked them questions like "was there anther data set that could have been used for this type of graph?" and said discuss in your group, they were all on task DOING THAT!!  Can I just say how much I LOVE this new set up?!!  (groups of 4 and vertical whiteboards).  Even though I'm giving them the lesson via video notes as homework, the group work is SO POWERFUL!  It really is like me getting to double my time with my students! And the students are so excited to be a part of this! Why did it take me so long to get to this place?

Playdate LA 2014

I hadn't intended to blog about my "excursions" to professional development conferences, but I definitely want to be able to view my own posts later so that I can see my growth and how the twitterverse has grown me in SO MANY unexpected ways, both with my students and apart from them.

I attended Playdate LA this morning.  It was my first time and I was excited to attend after looking at the scheduled sessions.  I thought it was like an EdCamp, but then I saw the schedule and expected something more like the annual CUE conference.  It was like the conference in that the titles/topics of the sessions were already chosen, but like EdCamp in that there were no scheduled presenters.

We had a few minutes to mingle after all the housekeeping information was given out, and it was suggested that if anyone in the room was not on twitter, that they find someone to help them accomplish that task.  Helena (last name unknown) was standing next to me and said "I don't know what to do with twitter, do you?" Well that was all I needed.  I had her signed in and downloading tweetdeck in a flash.  We were fixing her channels and getting #playdatela on it immediately so she could view the tweets all morning.  We got so into it, that we didn't notice it was time to go until one of the organizers interrupted us to ask if we planned on attending the first session.  I felt successful for helping one other person!

So off I went to the first session about non-clicker student response systems.  There was only one other person in the room to start, but after a few minutes a 3rd person joined us.  None of us had any experiences to share, so we all decided to go to our second choice which was screencasting.  Now, I have been doing my videos for a little while and can teach others, but I don't consider myself and expert.  Couple that with the fact that I use Touchcast and I have met no one yet who uses that app.  So I was looking forward to learning about something new.  I was surprised that I turned out to the the "expert" and I did all the talking/describing/answering of other's questions!!  Actually, shocked would be a better description.

Second session, I went to presentation tools.  Someone was taking charge in there and started by asking what presentation tools we each used.  I stated that I used none of the ones listed on the program.  Many of the others had little experience either, but a few had played with Haiku Deck.  I was interested in that one and was hoping we would go in that direction.  It seemed to for a little while, but then took a turn when I said "well I have used Voki and Go Animate to present information to students and they are both REALLY SIMPLE".  This immediately  caused others to say "can you show us?".  So once again, I became the "expert".  I was having so much fun that the time flew by.

Session 3: Using Social Media with students.  A few teachers were already in the room and talking when I got there.  I eagerly listened to the ideas that were being thrown around, hoping we would land on one and I would have something concrete to use when I left.  Well, after participating in the discussion, I finally got into the small group that was looking at "Today'sMeet".  It works like twitter but is self contained and expires after a given time.  So you could use it for a class period and then it would be gone.  Great way to engage students in a discussion though!  I will definitely try it out!

We went back to a large room for closing session and people were encouraged to stand up and share what they learned.  Helena stood up and said "I got so much information from Paula Torres and everyone should be following her!"  I was NOT expecting THAT!!  Now my twitter is "blowing up" with new followers!  I also had earned enough "stars" from everyone that gave me one that it got me a prize for having the most in the room.  HOW DID THIS HAPPEN?!!!  I consider myself to be a beginner!  I guess I have learned/absorbed a LOT more than I even noticed! It was great affirmation!  And I loved being on the helping side!  I hope to get to do more of this in the future!

Convince me!!

Today was another good day.  Calc students had problems that they were working on in groups as I circled around and eavesdropped on conversations.  I LOVE listening to them talk math!  The competition consisted of multiple choice questions and I sit with each group and randomly select students in that group to tell me answers...picking a new person (or sometimes the same person) from the group each time to give me the next answer. This way they all HAVE to work together because they don't know who I will call on for each answer.  They worked the entire time.  What I really love is with whiteboards on the wall for every group, we could have discussions with diagrams to help them see concepts that aren't currently clear to them.  I also have mini whiteboards with graph grid on them and I noticed students reaching for those to draw a graph in order to choose the correct domain and range.  Such SIMPLE tools that kids now have quick access to by being placed in groups around the perimeter of the room.  I LOVE THIS NEW SET UP!

In Stats today, I made them answer questions to the Fruit Loop Activity.  They had to convince me about whether the mean and/or median would change if another data value was added.  What was "cool" was 5th and 6th period classes had different data that led to different rationale.  So my plan for Monday is to switch their data and see if they can answer the questions correctly with the other list.  Then I'll know whether or not they really have the concept.  But the discussions were SO POWERFUL!!  And I found out who could explain really well on paper (whiteboard).  We also had the discussion that it is not enough (in Stats) to say "he's guilty" and then just sit down.  There needs to be some evidence.  This was taking me back to the great presentation by Chris Luzniak (@plspeak) at TMC14 on arguments (argument = claim + warrant)!  I am definitely working this strategy into Stats this year!  Using that analogy was a quick way to get them to understand how much more they need top put into their explanations.

Here is what I noticed.  Some students were struggling with the concept of how the mean changed based on adding another data value until I said "so your test average is 80, what happens when you get a 60 on the next test?  Or a 95?  Or an 80?"  They could tell me the answer right away.  Interesting that it needs a certain context for them to have it conceptually, and when you use a different context (# of fruit loops in a handful), they don't get it so easily.  Perhaps we rely on the same contexts too often.  There definitely needs to be more real life brought into math lessons.  There next task is to select from 10 different data sets that I gave them to create 1 bar graph, 1 dotplot, 1 pie graph, 1 stemplot and 1 back-to-back stemplot.  It was fun to watch them start to discuss which data would be best choice for each graph.  I can't wait until Monday!!  I also can't wait to start using google forms with them and have them create their own surveys to collect their own data and then graph it and analyze it.  Laptops in the classroom open up so many opportunities!!

On another side-note, I got to share the awesomeness of Mathalicious (@mathalicious) with my department this morning!  I took them through about 3 lessons so they could see how useful they would be to our math teams.  In addition, I showed them the fantastic-ness (a new word) of Desmos (@desmos) and the 4 lessons in teacher.desmos.com.  So stellar!  I love opening up the world of technology for others they way it has been opened up to me!  It's so fun to share that wealth! I have gotten some colleagues to join twitter this week!! YAY!!

They won't fall asleep this year!

Well, it might be the year that I need to retire my spray bottle of water.  In the past when students fall asleep, they get a squirt to the face.  Once the students realize this, they tattle on whoever is sleeping just so they can see them get sprayed.  It always warrants a few good laughs, even from the person getting squirted.  But now that I have whiteboards all around and laptops out every period, the students are BUSY!!  After having to sit in student desks for the last 2 weeks of summer, I definitely realized how uncomfortable they must be for 7 hours (glad I got to walk around all the time)!

In all classes, today's technology piece was how to get to their locker, google drive and class page on School Loop.  It took very little time as most students already had a google account.  Those that didn't made one with some help from me, but more help from their partner.  Students know so much about navigating that I learn from them (I LOVE THIS!).  I already announced (the first day) that while they would be learning Calculus or Statistics, I too would be learning how to use the technology that we ALL need to know to live in this technological world.  It's surprising to find out that as tech savvy as we think they are, there still are lots of things they don't know.  I want to help them learn how to use the tech more effectively and efficiently.

In Calc, we finished with web navigation and moved on to back-to-back graphing.  I found this activity on Study of Change (by Becky Hart Lyon) and I modified it a bit.  I had students facing each other, one looking at the projector screen and the other with their back to the screen. Students who can see the screen have to explain to the other how to draw what they see. They begin easy and get more "math like". Students drew on mini whiteboards and then held them up when they thought the drawing was correct.  They switched positions after each drawing.  I heard so many great comments!  And they were so busy explaining, drawing and switching, the time flew.  We would discuss some characteristics about the graphs after everyone got it correct to help them improve their explanations. Will definitely use this next year!

In Statistics, we were finishing up the Fruit Loop Activity from yesterday (see yesterday's post). Students were using the data and making box-whisker plots.  First they had to do it by hand on their whiteboards.  Then I showed them how to do it on their graphing calculators and finally we copied the data into Stat Key to do the same thing.  We found an "error" on Stat Key and had to decide what the program was doing.  It was great that they even asked the question!  The minute I said I want box plots on your boards, they were so quickly up out of their desks and talking was happening!  I love it!  I think the best part was when students asked "simple" questions, I got to say "What would you do if you were at home right now with that question?" and when they responded with "google it", I pointed to their laptops and walked away.  It is a mindshift when I don't give them the immediate answer, and I got the usual "but you're the teacher".  It will take awhile to get the spoons out of some mouths, but I have nothing but time to teach them how to be learners and use resources!  It's gonna be an AWESOME year!  I may have to change my blog to "180 days of best day ever!"