Jumping in the Pool Dogpaddling!

This year I am coaching an FTC Robotics team for the first time (for me and our school). Here are some of my students at our first scrimmage. We were so nervous and being all "girly" and judging ourselves harshly, me included.

Things going through our minds:

* We'll embarrass ourselves.

* Everyone else is better.

* We won't know what we're doing.

* We're nervous.

* We don't know the process and aren't ready.

* Our robot is not finished yet.

But that (obviously) is ridiculous, even though it still streams through our thoughts. STILL. If we stifle ourselves with self doubt and angst, we'll never try anything new, and we'll never improve, and we'll never have the thrill of learning and experiencing new things.

Thoughts that got us through:

* Everyone has to start somewhere.

* We're a rookie team. Other teams have had more years of experience.

* Let's give ourselves a break, we're WAY further than we were in September.

* People are here to help us.

* This is a learning experience. 

* We can do it.

Ultimately, we had a blast, though we were super tired from the adrenaline and stress and lack of sleep and worry. We learned a ton. We met nice people. We can make progress. We had cool t-shirts. We're on our way to more robotics challenges. Our pit area rocked:

 

Yay! End of the Six Weeks ... And We Know What That Means.

The joys of students scrambling to take care of business on the LAST minute of the LAST day of the LAST week of the grading term. What's that? You say ... why didn't they do things the other 4 to 5 weeks? Good Question.

I just had a math student literally wait until AFTER the last minute to try to turn things in. For any other student who I'd seen trying throughout the grading period, YES I would have accepted the work. For this student who has not turned in 7 of 10 homework assignments and has come in maybe 10% of the available time for help? Not so much.

Yes, I know it's for the student's own good. Yes, I know that they won't step it up until they don't get any free rides any more. But yes I also know that it scrambles up my insides and I'm having angry conversations with the kid in my mind.

To maybe detox, I just sent this e-mail to her and cc-ed the counselor and her mom. I am crossing my fingers that she figures things out.

Dear You,

I'm concerned about your work ethic this year in math. As it stands, there have been 10 homework assignments on the grade book. I see that you have not turned in 7 of them. That is part of the reason you are failing, but it is not the whole picture. Because you do not do the homework, you then do poorly on the Section Quizzes (based on homework). It also seems that you don't do the rote memorization skills necessary for the IR quizzes.

There have been 5 weeks of time for you to come in and reconcile your misunderstandings. I have barely seen you for tutoring. I am available every morning from 7am until 9:15. I am in my room at lunch every day. I am there after school M-Th. You have come in for a scattered amount of tutoring, but not enough to take care of business. I frequently see you in the halls talking with friends, and I have to bite my tongue when I want to ask you why you are not doing make up work. Yes, friends and socializing ARE important, and they are a vital part of life. However, there has to be a balance of taking care of business, and enjoying your free time.

In advisory, which is a prime time to seek help ... a FREE 30 minutes at least 3 times a week in MY advisory, with me willing to answer your questions, you have not been doing any calculus work.

It worries me that you scramble at the last minute and try to turn in extremely late work, and it is still not on time, and yet you say that it is.

More importantly, I see you being exposed to challenging work and then not stepping up to the plate. You say you don't want to turn in the homework because you don't understand it. Great. And yet I do not see you taking the necessary steps to make progress. I do not see you putting in the brain work and the hard work and the thinking work to make it happen.

I'm wondering how you are watching the flipped videos. Are you just going through the motions when you do watch them, or are you taking the required (at least) 40 minutes of time to absorb and think?

I have been filling out college recommendations this year for seniors, and these are some of the questions asked by the colleges (i.e. things they want to see in prospective students):

* How does this student behave when faced with challenges?

* How does this student react when confronted by setbacks?

* What are this student's "disciplined habits"?

* How is this student's initiative?

This is the 3rd math class I have had you in. I know you have a very capable brain. I am wondering if you will rise to the work necessary to comprehend topics that don't come easily to you.

I care about you and your school experience, and I hope you don't squander it away because it requires work you are not willing to do.

Ms. D

Big Sighs

Just a reminder to myself and others about the various EXTRA things kids may be going through in addition to doing/not-doing my math homework (taken from separate things I've heard lately in my town/school, but I'm guessing could be just about anywhere):


* Parents just divorced last month. Student still angry at absent parent and not fully functioning yet.
* Thrown out of the house and now scrambling to keep it together.
* Single parent too poor to pay bills. Kid must find other means of functioning for studying purposes.
* Came out to parents. Got kicked out of the house.
* Temporary housing due to recent weather occurrence.
* Clinically depressed.
* Health issues due to poverty and lack of proper nutrition.

Lately, I think that we just need a big daily hug fest to let kids know we love them and are rooting for them.

Related Rates and Crowd Sourcing

Year Six of teaching this pickle of a topic in Calculus. I keep changing it up hoping I'll happen upon the magic elixir that will allow students to eagerly gobble up the problems and spit out the correct answers with joy and understanding oozing out of their pores.

Issues:
* Finding problems that aren't the Wisconsin of all Cheese Balls.
* Reading and interpreting the problem.
* Being able to translate known information and subtly given information into Math Speak.
* Finding the right equation that links all the variables together.
* Navigating the Dangerous Path of Implicit Differentiation.
* Plugging back in at JUST the right time.
* Finishing things up with a tidy bow.

I have a good feeling about this year! And yes, I say and mean that every year, so I am allowing my bubble to remain floating blissfully in the air yet again.

First of all, cheesy problems: ladders sliding down walls, circles mysteriously expanding and contracting, lots of liquids being poured into and leaked out of cylinders/cones/prisms, cars passing in the night at some perpendicular intersection.

I started off this year's spiel with just a blathering of why this topic is important:

BP oil spill, how fast is it spreading? How will they know how much resources to devote to the problem?

The rain recently in Austin, TX, people's houses were ruined, water was rising at various rates, what could that mean for drainage capabilities and emergency personnel?

Fires in Bastrop, containment, speed of spreading vs speed of dousing ....

The amusement park problem on some previous AP exam about rates of people in park and number of employees needed ...

But then alas, we had to start on the cheeseball problems. But I prefaced it with, "no one really cares about a balloon being expanded or contracted, but as with all math modeling, we may have to start with a simplified version of reality just so we can gain understanding and maybe add difficulty and more accuracy later. Think about some real life things that could be modeled by a malleable sphere."

That was about as far as I got on that THEN. Wait for it .....

Also, I spent a class period JUST setting up problems with the students, and their homework was to differentiate and solve. I found Bowman's set up with the table for variables very nice and tidy and useful. I'm a convert. In the past, I just set the students on their merry ways to attempting each problem on their own. This year I was uber bossy and said I wanted things set up in a specific way - enter the drawing and table and something new I added: a highlighted box or equation that I labeled SUBTLE information. There are some things that are not specifically mentioned in the problem, but you can figure needed information out like a detective. I wanted the students to be on the lookout for such things and to know that they exist.

I think this is the NEW component I'm adding to the homework next time. They will get the goofy circle/square/car problems, but with EACH problem or maybe just one, they have to do extra. This is where my crowd surfing comes in. I want them to think of a NEW specific real life situation that (say) could be modeled by this simplified version or expanded upon, and discuss what rates are needed and why anyone would care.

I'm looking forward to seeing their responses.

CS and Algorithms

Last year I knew I did a subpar job on teaching students how to write algorithms to prep their code. How do I know? Thanks for asking. I know because one of my top coding students mentioned after that year something about someone talking about this weird word, "algorithms", and she didn't know what it meant. Who was HER poopy teacher? ME!

So this year in my CS1 class, for their programs they are writing, I have made 3 extra slots on the sheet under each code:

Algorithm (signed off by Ms. D) ____________________
Code (checked by another student) _________________
Code (checked by Ms. D) ________________________

I also had a discussion about the code-checking by someone. I mentioned that if I was ultimately asked to sign off on a code, and it wasn't working, then the "signer offer" would get the BIG FROWNY FACE OF DISAPPROVAL.

Their algorithms are getting better. They started out just regurgitating my words. This allowed for discussions of algorithms being like "steps in a recipe". You wouldn't say: walk to the fridge to get the eggs to crack 2 open into the mixture. You would say: beat in 2 eggs.

I also like the fact that their code has to be checked by someone else. They then get to talk with others and see others' code and practice the art of checking code for bugs and direction following.

Teacher Mistakes and Teacher Voice

I make a lot of my own materials, and though I check things, I am human and make mistakes on keys and answer banks and such. Now I'm not saying that it's 50 bazillion mistakes on every assignment, but still.

I've just realized this year that that could be thought of as a good thing. My kids now know to be skeptical if their answer doesn't match mine. I hope that lots of them stop and think and redo their work and then in their mind if they can convince themselves that they have done no wrong, then they ask me to check things. This way: they gain confidence in their abilities, they learn to trust themselves, they don't always take the printed word at face value, they practice polite conversation in the how they approach me. Sometimes I'm NOT wrong even if they've done all this, but I use this as an opportunity to thank them for checking and to say that THIS TIME I was not wrong.

In a related type of situation, at various times when I ask questions of kids in class, and they answer, and the answer is correct, I put on a scrunched, disbelieving face and ask if they're sure or if that seems like the right answer. I've done this often enough that they stop and redo their thinking in their heads, and MOST times they go against the "ADULT" voice and say YES, that is the correct answer. Again hopefully they're being trained to stand up for themselves and their thinking.

Okay, ending with a silly joke that made all of us laugh on a much needed stressful day last week:
Q: What's brown and sticky?
A: A stick.

Calculus Practice

I'm trying to incorporate more AP Calculus multiple choice style questions throughout the year this year. I've scanned for various released documents and then changed them up with different problems but same intent. I guess this is kosher. We are not supposed to publish secure documents or let the kids take them home. I have not done that, but then I still am feeling antsy because the kernel of the ideas came from secure documents. Anyone have an opinion on that?

Here is what we/they had for homework recently. I like my last question (not from another source). I realized that the students were still not clear on the distinction between the derivative being the GENERAL tangent slope equation for ANY x versus a SPECIFIC slope at a SPECIFIC x using the general equation.

 

 

"Baby" Applications of Trig Functions

We just finished learning how to solve all sorts of basic trig equations (cos ___ = #, cos # = ____). We'll get to equations soon, but we wanted the students to see some applications right away. I didn't want the standard: Billy is standing 5 feet away from a tree and how tall is the tree problems from geometry.

I searched in my favorite precalculus textbooks for some ideas, and found some applications under the GRAPHING and TRANSFORMING of sine wave functions/equation section. With a bit of fiddling, I adjusted the problems, so that the students could just find the angle or plug in the angle.

We first had a discussion on the cyclic behavior of sine. Then we brainstormed as to what in real life gets bigger then smaller then bigger and on and on. Then I showed them this sheet. We made sure to discuss how in algebra when you are solving for a variable you have to isolate it by undoing what's being done to it. Then I mentioned that this is JUST like solving for "x" in algebra, but on "steroids".

Voila! New problems for the kidlets to tackle:

Trigonometry on the Calculator

I came up with a memory tool that I hope will help the kids remember which process to use when solving/evaluating on the calculator:

csc ____ = 5    versus     csc 25 =____

It all seems to get jumbled up together in their heads after they learn various equations on the calculator.

Entering either one on the calculator involves a reciprocal somehow, and they mix up when to reciprocate. For the first one:

 csc ____ = 5     you enter:   sin ^-1 (1/5)

For the second one:

 csc 25 =____     you enter:   1 / sin (25)

Here's what I hope will stick:

For the first one:

csc ____ = 5     the BLANK is in the MIDDLE,
so the RECIPROCAL is in the MIDDLE   sin ^-1 (1/5)

For the second one:

 csc 25 =____     the BLANK is on the OUTSIDE,
so the RECIPROCAL is on the OUTSIDE   1 / sin (25)

Many more ways to mess up, but maybe this will fix one problem.

A Nice Reminder

For the past few years, I knew which semester the students were taking P.E. For several months, they would waddle slowly into class and groan as they tried to sit down. "My butt hurts" ... "Ow" ... "50 burpees!" ... "walking lunges!" They'd seemingly "complain" about the PE teacher, and in a wide-eyed manner, regale others with astonishment at what difficult physical feats they were required to perform. This would happen basically all semester, whichever kid, whichever semester they had P.E.

Fast forward to this year. That teacher is still around, but some of the students now have a new P.E. teacher. This is what one kid told me after a few weeks had passed: We've asked her to work us harder. We want her to be tough like Coach C. She DID ramp it up a bit, but it's still not as challenging.

Huh.

Maybe what we hear as complaints is just a badge of honor that the kids are touting as they process in wonder at what hard things they can do when they are "forced" to. They are saying it out loud as sort of a "go me" type of conversational pat on the back. They complain, because they are humans and teens, but secretly they crave the challenge.

So maybe when we hear that they have SO much homework and the problems are SO hard, then we should reply, "yes, and look at how great you are doing by struggling and keeping at it". Work those brain muscles!

Correcting HWK

I'm trying something new this year both in AP Calculus and in Precalculus when the students go over their homework, and I think it's a win for me/my class/my students.

For the past several years in precalculus, I would work out the homework, place the key on the document camera, and we would painfully and slowly go over the answers while the students corrected in a different colored pen. I grade on completion since I think homework should be a time to practice. I understand (obviously) there are different philosophies on this, but I feel this works in my situation. I do watch for kids sneakily copying things in pencil and passing it off as their own. I do look over the homework later to see if they attempted all problems.

Anyway, this always took way too much class time, and most likely, students were probably not looking as closely as possible to solutions, and everyone most likely had different problems they were confused about, so some were sitting around needlessly while they waited for their particular problem to be shown on the document camera.

This year, I take my key and make enough copies for 1 per 2 kids. They silently glance over the key and correct their work. This has gone MUCH faster than before. Also, kids can see how I lay out my work and have the time to concentrate on the particular problems they need to see and have good examples of process and thoroughness (or maybe I'm just being idealistic).

I've also done this in calculus. I used to just collect the homework, then put the worked out key on the LMS site for them to check later. I'm guessing that by the time they got back the homework by the following class and had more homework to deal with, they never checked the old homework. This year in my flipped class, they have the key on their table and can carefully go over it and ask questions right when it is still fresh in their minds. Again I like the fact that they have constant reminders of how the work should look if it's thoroughly done.

Brought to you by the letter, "V"

Apparently, for now, there are only 24 letters that are "safe" in the alphabet as it is used in a high school setting. I used to toss about all 26 freely as I broke my bonds from the variable "x". X is overdone, I thought! Who made "x" the boss? Let's start sprinkling the other 25 neglected letters, I blithely demanded.

Well, starting last year, the letter "D" brought some giggles. As in, "okay students, find the "d" in this equation." TEE HEE HEE! Ms. _____ is looking for "d"! Oh my word, REALLY. THAT'S a thing now? When did that become a thing?

So this year, I stepped lightly around the "d" landmine so far. Go me! Successfully navigating the other 25 letters. No problem. ... Update: Problem.

Today in Digital Electronics, we started talking about Ohm's Law ... V = I*R. There's a nice helping tool where you put the 3 letters in a triangle and cover up the letter you are solving for, and the remaining visual tells you whether to multiply or divide to find your solution.

First problem, let's solve for voltage. "Okay kidlets, cover up the V ..."

Tee HEE HEE HEE.

What?! Oh my God people! Okay, is there a sexual reference for I? For R? Are there other taboo letters no one has told me about yet? Should I assign that as a homework assignment: free association of making EACH letter a "thing"?

Precalculus Matching Game...

Today my precalculus students were starting their journey of being able to quickly visualize the "special triangle" standard angles by matching 3 sets of things: angles in radians, angles in degrees, and graphical representation of the angle in standard position.

About 7 years ago or so I first did this activity. And in my most-likely last-minute planning that year, I didn't have baggies to store the 36 cards, so I made up something like this:

Okay, exactly this, because this is the actual "envelope" where the students would store their cards. I folded up a piece of scratch paper and bent in the sides and shoved the 36 colored cards in the packet. That year and that school I thought that kids would try to be "funny" and maybe take out one of the cards, so that the next class would not have a matching set. Who's the jerk cynical teacher that doesn't trust their students? ME!

Anyway, then it became a thing year to year and class period to class period that they would sign their name to the envelope. It was kind of fun to read over the names each year and see if I remembered the students.

Anyway, flash forward to this year. Different school from that first year, and about 7 or so years later. One student when she was signing the envelope said, "hey, my step-aunt's name is on here". I asked if she went to that school I taught at (since maybe it was just a similar name), and she said she did. Fun Coincidence! Or a case of .... look how old you are, you taught my aunt!

Reference Triangles

I had this idea to use string, masking tape, and dry erase markers so the students could explore reference triangles for the first time. I had a bunch of embroidery thread left over, so I gathered supplies:

I had my kids rip off a piece of masking tape and poke a hole through it to thread the string through then tape it to the desk. We discussed spacing issues and such, and they drew circles (eventually they were happy with them after a few erasings).

Then they drew the xy-plane with the origin at the center of the circle. (OCD note: do you SEEEEEE the pen with the cap off! It's drying out, people. CAP THE PEN!)

Then I had them get out their scientific calculators that I had them buy, and we explored sin(20), sin(380), sin(-340) and they noticed things. We then did (on the calculator) sin(160) and sin(-200). They discussed why the values were the same. Then they started moving the string around the circle.

We talked about how it didn't matter how you got there, you still got the same reference triangle (which I kept defining and bringing up) .... no notes yet. We talked about x, y, and r. We explored when the sine/cosine may be negative. I had them draw some more using their fingers and string and dropping of the perpendicular as references for their pens:

We explored when the sine value would get bigger and why.

THEN we went to notes:

I think they liked the novelty of drawing on the desks. Hopefully, the tactile aspect of creating the reference triangles will stick in their heads.

"MTBoS"

Oy! I've kept my thoughts to myself, but I've been conflicted EVERY TIME I "hear" this term come up in various posts and tweets and such. But today I just read a post claiming certain group think, and it has prompted me to post.

Maybe I'm not part of this MTBoS. Maybe I am. I don't even know. I blog. I teach math. I share resources. I find resources. I look at tweets. Here are the thoughts that go through my stubborn, ornery, contrary head every time I see those 5 letters:

* Don't tell me what to think.
* Don't speak for me.
* I don't feel that way.
* I feel excluded.
* Am I missing something.
* Am I not part of the cool kids skipping around enjoying their time on the Internet.
* No one invited me.
* Why is there a need to yell "YIPPEE" look at us so often.
* This is having the opposite effect I think it's intended to have.
* I want some chocolate.
* No. Wine. I want wine.

Maybe I'm in the minority. Maybe people didn't invite me to parties as a child, and these are the after effects. Maybe I feel awkward in a large group. Maybe I need to mull things over myself, and keep my mouth shut.

I guess mainly, I'm thrilled that there are so many teachers that are willing to allow me to peek into their classrooms and thinking and teaching journey. That's enough. Anything more, to me, is just drawing a line in the sand and potentially making people feel excluded whether that intention was there or not.

Or maybe I have no idea what I'm talking about, and I'm the only one that scrunches her face at such a "thing". Anyway, here's a sweet picture to calm me down.

Teaching Radians

Since I was testing in another class the other day and was BORED from not chatting with kids and teaching, I had some time to prepare more than an hour in advance for teaching precalculus. I tried 2 new things this year to teach radians, and I think they're keepers for me.

First I had compasses and protractors and had them make 3 different circles in their notebooks. Then they measured the radius of each and recorded it. Then they "carefully" used a ruler (my compasses are the orange cool ones with a ruler on them) to "wrap around the circle" one radius length. Then they measured the angles.

We talked about how we're human, and it will be off, but we noticed the numbers were similar. Here's the page of my notes.

The next thing that worked was a table. I made them create a table with 3 columns, angle in standard position, degree measure, radian measure. One row at a time, I would give them one of the values, and they had to figure out the other two, and then we'd discuss it and their strategies. The highlighted portion is what was given to them.

  

I liked this because it's all ordered in one table, and they can absorb it and see connections and such as opposed to my last year's notes where I sloppily just did a few around the page and put all the information on the graph.

CS First Assignment

This year I have a stacked class of CS1 (11 kids) and CS3 (4 kids) students. In CS1 I did the same first assignment as I did last year (a packet that walks them through graphics and has them create their own original picture). I basically only help them when they get stuck or when they want to do specific things NOT explored in my packet (like various colors or polygons).

This year, after being inspired by our art teacher who hangs up the kids' work around campus and most times has an "artist's statement" to go along with the picture, I decided to do the same thing. After my students finished their assignment, I asked them to type up an artist's statement about their experience and challenges and such. Loved their responses. Here are 3 samples.

Also, here is a disclaimer about my school. I teach at a public school. We are roughly 60% F.and.RL, 60% Hisp (not necessarily from the same pool). There is a strong culture of working hard and doing your best. It is a small school, so no one is invisible (for the most part). I teach girls. I mention all this so that when I show samples of my students' work you can understand what background they have that allows them to do things.

You Know You Need More Sleep When ...

... you think of something you MUST do and CAN'T forget, so you decided to send yourself an e-mail to remind you to do this tomorrow. As you are writing the e-mail (and list some other things to do), ..... you forget the original thing you needed to remember to write down so you could remember to do it later!

Oy!Okay, I finally remembered after I walked around, but seriously folks.

In other news, I'm coaching an FTC team this year for the 1st time (for me). Woot! Do I know anything about robots? Not yet. We had our "sort of 3rd" meeting today, and the students are eager, so I'm thrilled about our upcoming adventure. There is a nice, seasoned coach from another school that's being very generous with tips and guidance and such, so that will be of great help.

In other, other news. I actually signed up to run a February Marathon. Have I mentioned that? Well, I have to people at school. Several Times. Hah! I've caused them to take up running ... away from me when they see me walking towards them to mention THE MARATHON I am training for. Sounds all fancy and such ... but really, I'm only still doing a 5k and building up my time so I can do a 10minute run / 1 minute rest. I'm currently at 5:1. I guess you have to start somewhere.

First Day Report

In my Precalculus class, I did end up using the activity mentioned here. I decided to have 2 different pictures for my 2 different periods, the ISS and another cool one of a bridge. I had them spend some time wondering and such, and then I had them write one of their comments on a sticky note and we posted them in the hallway around the pictures.

Some of their comments were goofy, but I did hear some intelligent ones. If I do this again, I'll give them more time and mention at the outset that once they start thinking more and more about the pictures, they may develop more intricate wonderings. As it is, I don't think I gave them enough time or direction to get to the potentially cool thinking.

Here are some sample responses for the ISS picture:
* The ISS is a place where astronauts of different nationalities collaborate and study in space together.
* The ISS was engineered using math.
* On the ISS, astronauts suffer severe weight and muscle loss.
* Has anyone died in attempting to live out in space?
* I know that astronauts line in the ISS.
* Do you have to stay in your jumpsuit throughout your stay at the ISS?
* There are clouds.
* How many mathematicians were involved in creating the ISS?
* How much energy is required to run the ISS?
* How often do they see the sunrise or sunset?
* How exactly was this assembled?
* Does the ISS orbit Earth in a circle or ellipse?
* What happens if someone dies while they are in the ISS?
* Will they build more?

Okay, now that I read them again, there are some cool questions and wonderings. I guess if I did this again, I may on the SECOND pass have the class explore their thinking on some of the questions and get MORE questions from them.

Here are some sample responses for the BRIDGE picture:
* What is the bridge's purpose being under water?
* Does the highway ever flood? What happens then?
* What prevents water from overflowing onto the road?
* How much math was used to make this bridge to keep back the water?
* Underpass slants down towards middle of bridge. Water needs to be level to stay in one place, but bridge looks higher than grass and trees.
* How did they hold the water back when building the bridge?
* Why is the white structure almond-shaped? Why not rectangular?
* Did the builders drain the water in order to build this?
* Is there animal and water life safety nets under water in a safe distance from the bridge?
* How did the idea of the bridge start and what was the first step to build it?

Piecewise Functions...

Hello School! We meet again!

I did the first day activity previously mentioned, and I will blog about it, but I'm more excited about how we did piecewise functions today in precalculus. During the previous class we walked through an IRS example and discussed how taxes were calculated and what the graph may look like, and we did a simplified version of it and ended up with a step function for the rates. I went online to find current information.

Today, we learned 3 skills, and I think the color coding went really well. I could refer back to it for each skill, and they could see what parts went where.

Here's what the notes looked like.