Whew!

Hello vacation. I have a love/hate thing going with time off. 
* Love the 9 hours of sleep each night. 
* Hate not having so many people to interact with. 
* Love being able to read good books. 
* Hate that at the end of a day I sat too much ("worse than smoking" is now a thing). 
* Love that I have time to cook non-frozen things. 
* Hate that the refrigerator is right there. All the time. Waiting. Calling.

Last week of school. There is a student that hangs out in my room before school starts each day (to talk with her other friends who I actually have in class). I was chatting with the kid, and she was groaning, "I shouldn't have come today. It's going to be so boring. We're watching movies all day." It reminds me of a great piece of advice I got from my math supervisor in NJ long ago, "you need to give students a reason to be here. Otherwise, who could blame them for staying home." She mentioned this around vacation times, and it always stuck with me. Even when the kids groan, "what?! you're making us work?" I think they're just yapping and are secretly glad to have something productive to do. That's what I tell myself anyway. 

Goals for break:
* Map out how I'm going to use my SparkFun Redboards in CS and DE. 
* Try acupuncture. Have always been curious, and I saw a discount for teachers.
* Do yoga daily.
* Not sit all day.
* Be a movie matinee glutton.
* Continue drinking my 16 glasses of water a day. (link to what got me)

Crack Kids....

I was not in my classroom some time two weeks ago, and for whatever reason, I had various kids come up to me that I had to record their names. It was a mix of kids I teach and don't teach. I don't know about you, but in those situations, I panic and for the QUIET kids in my class, those who NEVER speak or never engage me in side conversations or never disrupt class or never cause a ripple and fall through the cracks of my attention, I feel time pressured and blank and either can't remember if they look familiar because I've seen them in the halls or if I actually teach them.

I mean, sure, if they are in my class, and quietly in their seats, and in a context my mind links with their names, GREAT! I remember their names. Otherwise, it's a 50-50 shot.

So I was recording names after looking at their faces, and for the ones I didn't know who were just standing there, I said, "who are you?". Well, of course, this one student got all wide-eyed, and her friend who I also taught looked at me, and there was red egg on my face as I slowly realized who she was. I made a joke about it, "well, you are SO quiet! Your homework is now to talk to me in class."

But then I festered on this situation later. Here is what I did in my classes this past week (when I remembered). If time and lessons allowed, I walked up to the ripple-free student in my class and said, "tell me 3 Laura facts" .... or "tell me a Judy fact". That opened up a short conversation and I actually heard their voices that I would not recognize ... yet.

 

Calculus f and f Prime graph information

Surprise! This is a hard topic for my students. I have adjusted some things and through various conversations I've had and pondering I've done, I came up with this activity that I tried today. This is after a couple of days of activity and discussions and problems related to:

If you see THIS on ____ graph, what does it mean about ______ function?

Here's what we did today for a while. I took it problem by problem and then we discussed it and for each problem I had them draw the "eggnog height vs time" graph after they had ruminated for a while. I also then introduced up and down arrows under the curve to represent "magnitude of rate of change".

In one class, we had a heated discussion about whether when you start or stop pouring, if it's an immediate leap to some rate of change or gradual.

End of the Semester

I'm loving the switch over I've made from doing a paper copy to a GoogleDocs Form of student surveys for my classes. Now all the survey responses are online and easily searchable/readable without having to find the papers and remember them from years past. 

I also have them do this in class after I discuss "constructive criticism" and "helpful comments" and the fact that I have found previous comments very useful and have even changed how I run class because of some comments. I think that if I didn't have them do this in class, many would forget to do the survey, and I wouldn't have enough information.

Here are the questions I ask:

Useful feedback so far. For example, I recently started uploading my flipped class videos a different way, and I wouldn't have known it was not as helpful if it were not for some comments kids made. I also try to keep my videos short, but some comments asked for my creating extra "showing examples" videos that would be optional. I think that is a useful comment.

And because I just copied this form from the year past and changed the name, I have last year's comments to refer back to to refresh my memory. Win. Win.

Sine Graphs and desmos.com

We have finished all of the transformations for sine and cosine graphs, and soon I want to have an application day where they can write models for various data: blood pressure, tides, weather, oscilloscope readings.... but first I assigned them the following homework:

Think of a city in the world, maybe you want to visit, or it's exotic, or it's far away, or it's a place you have never heard of but searched for online. Then find weather data for a 12 month period for your city. We quickly logged onto desmos.com and they got accounts and we practiced making/plotting table data and changing window settings and such. They were to come back with their city weather data entered and saved.

The next class, we practiced on paper with "weird data":

I made them just draw a generic sine graph with no axes or numbers around it. I then prompted them for numbers, and then got (say) the "28" for the top x value and the max (71) and min (-31) y values. I made sure to wait until I heard things I wanted before I committed them to the paper.

Then they had to find the amplitude/vertical shift/horizontal shift/period. We talked it through and then got an equation. We did it again for a cosine graph. 

Then we went on the laptops and they brought up their weather data. I asked them to do what we just did to find an equation that would model their weather data. Most importantly, YES they could guess and check, but it would be WAY better to think things through and come up with an equation first and some justification for the 4 key values as we practiced and then play around.

It made for some interesting conversations about "not normal" data points (I picked Timbuktu, Mali, and the year's data had a cold snap for 4 months that should have been hot) .... and about north of the equator and south of the equator cities (one student's data was warm in January and cold in August) ... and cities that were near the equator (all the temperatures stayed basically the same all year). 

My Prague data worked out better than my Timbuktu data:

 

Hello (mid) November

I have nothing to blog about, so here I go blogging. Isn't that how it works? Is there a point in every year/blog/person where you start to think of something to expand on and then go, eh, been done, not interesting, navel gazing, ....

Some things I've learned so far this year:

* My "if you want help, you need to ask for it" policy was NOT working for all kids. Shocker! In my mind, I was all, "You're 11th and 12th graders! Ask for help!" But in reality, for whatever reason (apparently, I'm scary??), there were kids that were just fine with sitting there in class or after school and being stuck but not asking for assistance. When I finally picked the brains of some kids, I got various responses: well, I don't know how to phrase the question specifically .... well, you were busy .... well, I feel you judge me .... etc. This has caused me to reevaluate how I run class. Now I purposely stop at each table and kid and ask how it's going. It seems that if I'm the initiator, then I get more responses.

* For precalculus, I have a 100% or 0% quiz I give to the students so they learn the values of sine/cosine/tangent of special angles in the 1st 2 quadrants. They initially have 2 minutes and 10 questions, and if they get any wrong it's 0%. They can take the quiz as many times as they want in a grading period. Usually, this is enough of a motivator for my groups of kids to study. This year, not so much. I had the idea of having MANDATORY 15 minute conferences with me about 2 weeks into the grading period. I made a sign up sheet that basically said: morning, lunch, after school with 3 name slots for each and told the kids they HAD to come in at some point in their time frame. I loved it. This allowed me to talk to kids that would NEVER come in for help. I could see how they were tackling the problems and give tips on speed and patterns and strategies. Of course some kids were already fine, so I could just validate their awesomeness in this arena and move on. I'm thinking of having such a mandatory conference for all my classes (on what?) and all my kids at some point in the year. Am I the only one that hasn't ever done this? Some things I like about it are that I talk to kids I may never talk to in class. I also get to see their thinking and pick their brains one on one on how they are doing. I also get reminded that they are humans and not math-receiving vessels.

* In AP Calculus AB, the learning opportunities NEVER stop. I hear my kids learning AFTER an exam when I make them come in to do corrections one on one. I see them learning when they go through my detailed answer key where I give them extra tips on how to do things and what to watch out for. I sense them learning when they are helping each other through hard problems. Yay math.

* Humans are prone to be happy AFTER something is over and they realize it was not so bad after all. I saw some kids that were in calculus last year, and they are unsettled with the math they are learning this year. They said they "missed calculus" and they were surprised. Hah. I take this more as, now that calculus is over and they saw they were successful, they want that comfort level again because they know how it turns out. Now they are in a new situation with a new teacher and it's an unknown, which everyone knows equals SCARY. I'm guessing next year, they'll be all, "oh, I miss last year's math class!".

* I'm turning 50 this school year. Oy! So that's occupying a large space in my mind. I've decided to make this a year of "trying new things". So far that has entailed going out to eat at DIFFERENT restaurants, ordering a DIFFERENT smoothie than usual, cutting all my hair off into a short cut not seen since 1985, .... that's it so far: food and hair. Go me. 

Okay, maybe I did have some things to blather on and on about.

Fraction Remix...

I had about 20 minutes after a test today, and RIGHT before the test, a high school student in precalculus was confused about how to divide 2 fractions, and she couldn't remember the method: "do you multiply the top and bottom?" were words that came out of her mouth.

So. I thought I'd give the following short lesson on why the "flip and multiply" that they seem to spout works.

First I asked them the following questions:

Simplify:   (7/3) / (4/5)

Then after they did that and checked, I asked them to discuss WHY it worked, and "my teacher said so" or some such thing wasn't an option.

Then we walked through the following 4 scenarios:

 So to recap, it basically boils down to seeing how many groups of the denominator fit into 1 unit (that's where the "flip" comes from), and then how many 1's fit into the numerator, and then you combine the 2 numbers and MATH.
 

Boring Ceiling. Fixed That For You.

Something needed to change. I could no longer stand the travesty that was my ceiling. How could we spend day in and day out under such a boring mess? How was learning taking place? How did we all not just fall asleep under the endless white scandal that was looming over our heads?

After searching the internet for ideas and finding an art teacher that had her kids paint black and white designs ON the tiles and realizing I didn't want to go THAT far, I came up with:

 I am happy with the results. I still need more, as not all kids chose the opportunity. And as a side note ... for all the questions I get about bonus points, you'd think I'd be drowning under a pile of drawings, but, nope. Nada. I am not one for bonus points, and this was a rare instance, but, hah, go figure.

 

Intermediate Value Theorem

I have never liked my unit as a whole for the Intermediate Value Theorem in Calculus. My explanations, I like, my homework and the time the kids spend thinking about it and then quickly forgetting it, I don't like.

Attempt this year:

 I like this first page because the kids have to stop and process the whole IVTh and think about the parts and then analyze the parts and see what goes wrong. I heard some good discussion.

I like this second page because for 5 and 6 they then have to start the thinking process graphically on how to apply the IVTh. Then problems 7-9 are what I just used to do by themselves. Hopefully, this year after they've processed things, then 7-9 should go better. We will see.

In other news, apparently I make kids feel dumb - based on a conversation I had with a parent. Oy! They interpret how I talk to them as just expecting them to know things already. Of course it's an obvious logical conclusion on my part that "one kid" implies THE WHOLE CLASS. Go me! Because of this, I made the following handout, and we had a discussion, and I asked them to tape this in their notebooks (or staple it to their hearts) to remember:

Trig Identity Match Up Activity

I'm on my quest to try different things for the Trigonometric Identities unit. They explored last class, and today I wanted to get them started on simplifying various trig expressions using identities. Here's what I did. I made this set of 2 sheets for every student, put it on colored paper, and then made them cut them up (my first class) when they started.

They're mixed up on the sheets, and there are FOUR total problems that start with the "squiggly" boxes, but I didn't tell them that first. I said they should look for 2 cards that pair up in such a way that they are ONE step away from each other either by an algebra law or by an identity. I did one example with them and took questions. Then they were on their way.

Since they sit at tables, and I didn't want to do different colors of sheets of paper (though I guess I could have), I had them draw dots in different colored pens (one per set) at the bottom right corner of their cards to avoid mix up.

Once they got as many pairs as they could, and I mentioned that depending on a variety of things they may not get pairs. Then I said they could try to find a "triple" pair for their remaining lone cards. After some time for this, then I asked if they can "pair up" the pairs to get a set of four .... Ultimately, I then said, or they noticed the "squiggle" cards, and we got to the point that there are FOUR separate problems, that each start with a squiggle card, so see if you can set up 4 different strings of "one steppers".

 

During all this they had their "notes" on pink paper that they were going to eventually tape in their notebooks.

This all took about an hour or so to give them think time, and not everyone was successful with all of them, but we came together as a class and talked it out and got the 4 sets of problems, and celebrated any successes they had. Some problems had 7 steps, some 6, some 4. Then students taped the notes in their books, and we copied down 2 of the problems into their notes with "reasons". Hopefully, this will aid in their homework tonight where they have to do a string of one steps for each problem.

Trig Identities

We have started our unit on Trigonometric Identities in precalculus. Every year is going to be THE YEAR where it all comes together nicely, and the sun comes out and the birdies chirp and the kids embrace their Identities. Yes. It will happen. Chirp. Chirp.

I took some extra time at the start of the unit this year for them to explore instead of me walking them through things and them nodding their heads pretending to understand.

This took most of a block period (2 pages), and it was a nice refresher of a few things: 

* proof rules from geometry

* fraction rules for adding/dividing

* exponent rules

Hopefully, the extra time we spent will be worth it in the end as we skip and hop through solving/simplifying various equations/expressions involving trig.

Learning is Hard

Students are learning to solder in Digital Electronics. I let them tinker and figure a lot out for themselves. I do give them tips, and we had a safety discussion, and we saw a soldering video and we talked some more. But basically, once they have the kits, they have to jump right in to something they are not comfortable with. 

There are casualties. 

Hopefully, this is not a symbol on how they feel inside.
 

Basic Derivative Rules

Last year our school got "schooled" on Kagan strategies, and one I liked was "Quiz Quiz Trade". I used that today for about 10 minutes for my calculus students to help each other learn some basic derivative strategies for monomials.

They always struggle if there are radicals or x's in the denominator or fractional exponents. I have tried in the past to get them to rewrite the f(x) first as ax^b. But after they nod their heads "yea yea", they go back to messing up.  

Quiz Quiz Trade to the rescue. They get practice, and they have to explain, and they have another student helping them, and they want to understand. I think it helped this year, since I had less questions when they started their homework.

Here is my template for cards that looked like this:

Quiz Quiz Trade Rules:

You have to model this and keep an eye on them and move them along.

1. You raise your hand high when you need a new partner and you search for 

    another hand and you pair off.

2. You greet each other with eye contact (social skills)

3. One person holds their card, question side facing partner.

4. The quiz-ee tries to answer it.

5. If correct, you praise the quiz-ee (social skill).

6. If wrong, you give hints on how to get to answer .... until answer correct, 

    then praise.

7. The quiz-ee is now the quiz-or and does 3-6.

8. When both done, TRADE. and go to 1.

Back to School Night

It's that time again: Back to School Night. Our school is following the "no schedule" rule, so that after a brief overview in the "cafetorium", the parents can wander the halls and pop in on various teachers at their convenience as opposed to rushing from class to class and being talked to for about 5 minutes before they zip off to another class.

Because it's not always possible to talk with every parent for as long as they would like, I have made up a half-sheet hand out that sums up why the courses their kids take from me may be useful or interesting. I didn't list everything, obviously, but just enough for "dinner party" conversation.

I'll also have some projects laying around and our notebook of things learned so far (or maybe last year's notebooks).

Stolen Ideas....

I found a "study sheet" of one of my Calculus students practicing for their trig quizzes, and I totally stole her idea for today's trig lesson.

(excuse the sideways issue!) I feel it will be a great visual resource when they do these special radians in their heads.

Templates HERE.

Unit Circle and Radians

Breaking News: Kids struggle with fractions!
Alert: Kids can't describe how 3π/4 relates to π.
News at 11: Radians? What new torture is THIS?!

I tried something new today in precalculus to help cement the "special angles" around the unit circle. Based on the spontaneous comment of one of my students ("this REALLY helped."), I am hoping for greater and sooner fraction success this year.

First I made templates and printed them on various colors of papers (one color for each special "radian"):

Each student trimmed the circles and pasted the yellow "unit circle" in their notebooks along with a blue slot to store wedges:

 

We then had a discussion about π/6 and I had them place various radians in standard position and we discussed reference triangles and values around the sides:

I made sure to do some negative angles:

We finally discussed the π/6 angles and worked through a problem:

 Now I sit back and wait to see if THIS year they are fraction geniuses!

Function Notation Error

No matter how clearly I think I explain that f(x + Δx) ≠ f(x) + f(Δx), I still have the "believers".

Yesterday, I drew a graph to explain it to a student, and she had the big, "OH!" moment, so hopefully, THIS will work. Here's a short video of what I did:

Yearly Goal

Aaaaaannnd we're back into the swing of things at school: frenzied hamster on the wheel looking over her shoulder while madly scrambling faster, so that the big boulder does not plow into her because she did not complete a task.

Fun things for the 1 week of school so far:

* Love my students.  Because I haven't taught all the geometry kids now for a couple of years, I have tons of new student (to me) in precalculus.

* My advisory students are just funny and sweet.

* I've purged a bunch of things I've basically never used but felt I needed or "would use someday" from my classroom, including the teacher desk, and now it feels more roomy.

* I keep thinking of this quote, and it gets me through just about everything.

* I think my operating theme for THIS year is: take care of each other above all else.

It's more important to have kids feel heard and valued and loved than to "get through my to-do list". People before paper! Be present! Enjoy the little whipper-snappers.

School School School

Back to school on Monday for the start of PD week. Our fun admin has decided to "flip our lessons" for the week, so that we have more time to chat and plan together. That should be new and intriguing. 

And we have 2.5 new math teachers to show all the ropes to. Yay for new blood and new ideas. Boo for sleep deprivation. Yay for getting back to more people to talk to than just my mirror's image, so I can alleviate the loneliness of summer isolation. Boo for sleep deprivation. Yay for actually moving around to justify eating calories. Yay for goofy kids and spontaneous laughter.

This year (don't have the official word yet, though, you know, since it's more than a handful of days before school starts), I will be teaching Precalculus, AP Calculus AB, Digital Electronics, and Computer Science 1. A nice mix to keep me from getting bored. 

I'm working on doing some form of SBG in DE and CS1. I had grandiose plans of mapping it all out during the summer. Yea, about that ..... apparently, it will be business as usual, and I'll think about to and from work and in between and map it out as the year goes on. I don't know why I'm so continually deluded into thinking that I'm a different person than I really am.

Other than that, hopefully it's another epic year in the making. Good luck and good math to everyone else who is starting or has already started school. Go Us!
 

In Class 1st Day Activity

Okay, after 17 years of teaching, maybe I WON'T leave everything until the last minute, because I think I've just finished all my 1st day things. Hah! Who am I fooling. This is a fluke. Soon it will be back to business as usual. This year is different, though, because I think I'm going to fly out for the weekend before school starts to see my turning-80-years-old dad, so I won't have those 2 days to get ready.

I did just remake my 1st day in-class activity for precalculus. It really has nothing to do with precal, but that's the class I'll use it in. I like my calculus activity from last year and will do it again, and for digital electronics, I'm going to have them do a DE thing, and for CS, they will be coding independently from day 1.

I was inspired by this activity from KFouss. Woot! Internet Searches! 

Here is my version:

These will be done by the kids in class while I'm snapping pictures and calling roll and passing out a seating chart and passing out more information.
 

Who Vacuumed Up All the Summer?

Sheesh! I just realized that I only have 2 unstructured-ish weeks left of summer. Must. Soak. Up. Fun.

I did enjoy doing a crafty thing by knitting and felting a "bowl" for a friend (just look away from the glaring error that SOMEONE was too "zen" to fix):

And I have revised my first-day homework assignment:

And I'm trying to sit less by sprinkling exercise in throughout the day via a checklist:

 Other than that ....

Studying Tips for Students

I recently attended a CS workshop for teachers, and if you live in TX, I highly recommend it for next summer. We learned a variety of things, and though some topics were not immediately adaptable to taking back to the classroom, they still were fascinating things you could mention to your students or adapt in some way to your population. Example, did you know that your brain doesn't have to process how to walk (for the most part), the mechanics of the motion are stored in your spinal cord.

One of the talks was on effective teaching, and the presenter mentioned VARK, which I had never heard of. This stands for visual/aural/read-write/kinesthetic, and, of course, refers to learning styles. What I found useful in the talk was actual suggestions on how students could study for and take exams more effectively than they may be doing currently. The hand out was not in a form I would hand out, so I made my own version on half pages for the students to tape in their composition notebooks on the first day of class for future reference. I culled from the VARK website and others that offered tangible ideas.

Online they have a questionnaire for the kids to take to determine which type they are (yay, first night's homework!). I like that you can choose more than one answer for each question and that you could be a "multi-modal" learner. There are different versions of the questionnaire for adults and such (do a search on VARK).

I want the students to tape in ALL four styles into their notebooks because they may find helpful ideas from a mix of strategies.

Geometry Idea

Next year will be the 2nd year in a row I haven't taught geometry, but I had an inkling of an unformed idea for a possible exploratory activity. Whoa! Doesn't that sound like you just want to jump on it and use it the FIRST day of school (far far away from now).

I was in an Airport Shuttle and staring mindlessly out the window and saw a building wall made up of tessellated hexagons. Then I remembered how learned about angle sums of polygons in class by separating various polygons into triangles from one vertex and noticing a pattern [(#vertices - 2)*180]. 

Let's use the pentagon for an example of my future I-can't-use-it idea. Kids most likely don't know that there are 3*180 or 540 total degrees in all the interior angles of a pentagon. I was thinking of (for the pentagon group) having the kids use 10 pieces of spaghetti taped on 5 different scraps of paper to form 5 different angles. Then they would measure the angles and get a total sum of the 5 angles. Then they would try to manipulate the 5 taped down "2 sides and a vertex" scraps of paper to try to form a pentagon. 

I'm thinking there would be 4 or so people in a group, and they would each have a different sum they would most likely come up with. Most likely a pentagon won't be able to be formed unless they happen upon a 540 degree sum.

Then maybe they could try again. Then maybe they could see what works and get that sum (having a human error discussion at some point for measuring mistakes). I'm also thinking there would be different groups with 4 sides and 6 sides (3, too??).  In this way, they can see the tactical things that go wrong with angles that don't "fit". Then there would be a follow up summary and pattern.

Next post: things I could teach in 6th grade math ..... KIDDING

Playing with Math

I just finished a nonfictional Romance Book called "Playing with Math", edited by Sue VanHattum. It's filled with passion (for math), joy (of games and puzzles), good-looking heroes and heroines (math makes you sexy), conflict and tension (hello math haters and standardized tests), and a warm and fuzzy resolution (math conquers all). Okay, it's not really a romance novel, but the passion about math is threaded throughout the whole book. There's basically something for everyone, whether you are a math teacher of any sort, a parent, or a math enthusiast.

I teach in a public school to goofy high school students, so I can only give my perspective as a non-mother, non-math-circle-participant, non-unschooler, non-homeschooler. But just like in math, where you see patterns in one problem and can then extrapolate to solve OTHER problems, in this book, I could read about the variety of settings, and always find something that I can either take back to my classroom or take back to my mind to work on. 

Every other chapter is a math problem of some sort. These range in levels of difficulty and variety of math concepts. Many times I found myself putting the book down and pondering the cool problems and figuring them out. There are also a ton of resources listed, from books, to online options, to people you could e-mail and start a discussion with. This wealth of goodies in itself is a reason to read "Playing with Math".

Before I read this book, I only had my biased, public-school-teacher opinion of homeschooling and had never heard of unschooling. Through the various sections and vignettes shown, my opinions were swayed with an understanding of how such situations could be in the best interest of different students, and how kids could thrive. And even if I won't rush out and un-enroll my non-existent offspring and start unschooling their imaginary selves, I did find myself taking notes on each chapter to remember great quotes and philosophies and teaching techniques that I'd like to remember and adapt to my classroom.

I also enjoyed to peek into things I didn't know existed. There is a section on taking a math circle to a prison, and the nonthreatening and successful way the teachers engaged with the men. There is a section about the nonlinearity of learning math, written in a nonlinear and creative fashion, and it's filled with words I want to mull over and process. And these are just a few examples.

Whether you want to have a new source of good math puzzles, or find out how to start a math circle, or re-engage your love of math, or find more things/thoughts/techniques to bring back to your class this coming fall, or simply to stay awhile in the company of others that love math as much as you do, I think you can't go wrong with this book.

Binary Addition

I would like to move towards SBG for various basic topics in my Digital Electronics class next year. To that end, I will spend this summer creating and/or finding online practice tools for my students to hone their skills. 

One of the topics they learn is Binary Addition. After searching for "just the thing" online and coming up short, I created a Scratch program for them:
 

I think I'll leave it as such, but if you have any suggestions for improvement that can easily be done by a summer teacher, thanks for sharing.

Also, I had originally created this program with Java with the intention of making an applet to put on our school website. This turned out to be a pain full of "security issues" ... "bad!" .... "don't even think you can open or share this applet". Don't know if I'm doing something wrong, or if that's the way of applets these days, and I have to pay money or some such to be able to have that message not come up. Does anyone know?

Viva La "Inflated Sense of Self"

And by the way, Viva La End of the School Year.

This week our school got together as a team and discussed children and things that may benefit them next year and what resources they may need that we should provide. Threaded through the conversation a handful of times was that so-and-so had an "inflated sense of self" with the meaning that the kid may be in for some wake up call in terms of college applications and acceptances. I nodded my head in agreement because I knew the kid(s), but then later I started to wonder if we have it all wrong.

I think back to my childhood, and alternately absent and alcoholic and human and goofy as my parents were, they ALWAYS made us feel like we could do anything and why shouldn't we and of course it's possible. Maybe we were living in a (champagne) bubble and other adults were going around tsking and shaking their heads and wondering when our big fall would come. I know my 6th grade teacher despised me and thought I scraped the bottom of the barrel, and I know a few HS teachers and college professors that would scrunch their faces if they knew what I accomplished, but being "bubble girl" (and I now realize "inflated sense of self girl") I still plowed on. 

Maybe that's one of the important things we can provide for the kids we teach, "of course you can do it" ... "why not you" ... "don't be silly, it's totally within your reach". This, obviously, has to be sprinkled with lessons on hard work and persistence and grit and the power of failing and getting back up and such. But how sad the alternative would be, a kid looking at you and your shaking head and attitude of "bless your heart" and taking that to heart and giving up on whatever before they even put out their whole effort into the endeavor.

There are students I have who I don't know if they'll "do it", but who am I to decide. And mostly, I hope what comes out of my mouth and heart is, "DO IT" "you can do it" "obviously it's within your reach". I just do this without thinking all year long, but I'm reminded of the power of this when I get a smattering of end-of-the-year cards that state, "thank you for believing in my and not giving up on me". I am also reminded of this when a student, just by happenstance, gets put into a position to shine, and they soar way beyond what we've seen of them before. These may not necessarily be the kids that think they are all that, but whatever "that" is, hopefully I don't, as a teacher, contribute to snuffing it out before it has a chance.

Post Calculus Exam: Sonic Boom

I spent 2 of the class periods after the AP Exam exploring and expanding on a cool problem I found in Smith and Minton. The problem is about what a sonic boom is, and how you can visualize it graphically.

The first day we had to refresh our memories on parametric equations and graphing. Then the students looked up various things on the internet and wrote it in their notebooks as such:

We had some good discussion on the various speeds and if they are "exact" and what could change the values. Then I made sure they got what a Mach number is by the following "quiz" in their notebooks:

I had them look up the speeds of various vehicles and we tried to get a wide range of numbers and then they had to figure out the Mach numbers based on their speed of sound.

On the 2nd day we then read over the "yellow" paper from page one, and I had to make sure they understood what a unit on the graph was. That was fascinating. It was more of a struggle for them than I would have thought, but we eventually got to it, and again, good discussion.

Then the actual graphing began. We had to take it slowly and keep talking about what the units meant and how you made decisions and such. Here is the graph for a jet going Mach 0.8. We had to keep stressing that the "arcs" were at time 5 seconds after "start" of the 5 noises the jet made at various times:

 

Then we graphed the "same thing" but for the jet moving at Mach 1:

 

 The students were excitedly asking me question upon question, because really it is cool and wonder-ful ... and I kept mentioning that I'm not an expert, but that we should write their questions down to think about for later.

Then finally we did the same process for a jet moving FASTER than the speed of sound ... Mach 1.4:

 

We had to be cautious with scales and such and all sorts of great mathy things came up. Then class was over. 

I loved their enthusiasm and questions and wonderment at this actual topic.  

 

GrumpyCrabbyNess

Why are all these teenagers acting like ..... teenagers?! How old ARE you anyway? Behave and fly right!

Excuse me while I detox:

Our principal some time earlier in the year did away with bells for whatever reason. You were still required to show up to class on time, but you had to rely on yourself and your handy dandy watch/clock/cell phone. I let a ton of things slide in general (lie, but ...), but one thing I do not like is kids sauntering to class late. They started being 15 seconds late, then maybe a minute, then consistently 3 or so minutes. It got to be too much. So I instituted a "be in the room or get a demerit" policy last week. I hate giving demerits. Boo on being the bad guy. I know it's ultimately good for them, and I know I have to be consistent, and I know I still have a grumpy knot in my stomach for the about a bazillion demerits I have given out in the last several days. Kids have started coming to class on time. Shocker. I still have a grumpy teen that is consistently late. Yay! Have her for 2 classes. Twice the demerit fun.

AP Calculus Exam Studying. Hmmmmm. I think a good chunk of the kids are studying the way I think they should be studying. The rest are being, well, teens. I have carved out time in class to do released exams and have them discuss things. In my mind that's going to help the most. We will see in July when the scores come out.

AP Exams start this week. So do EOCs. And thus, so do tons of kids being gone from class in a sporadic fashion. Yay for being flexible and being able to roll with it. Or at least putting on my game face.

Good things: 

My CS class and I are going on a field trip to an apparently well-known local game developing business. We have spent some time playing their games and researching them and creating questions for the field trip.

The NHS group of kids I co-sponsor have done an amazing job this year with doing service and getting fund-raising ideas and actively participating.

My precal students are just a hoot, and even the not-so-strong-mathematically students are a treat to talk with.

Ice Cream.
 
 

What?!?! Me Study?!?!?

AP Calculus Exam coming up. Let's have the kids create a study calendar! That's the ticket. Because you know, if you fail to plan, you plan to fail.

I fell into the old Geometry Logic trap. Just because ~p --> q is true, it DOES NOT say anything about what p implies. Silly me. About a week after they all made their calendars, I checked in with about 3 or 4 of them. Sheepishly, they admitted that they were not adhering to their study calendars ... their beautiful calendars they set up.

We had a class powwow. We brainstormed. We came up with ideas. Who knows what will work.

Things I need to think about changing/adding next year: a part of the homework for the calendar that mentions what incentives they'll give themselves for studying ... maybe some strategies they need to write up for the times they DON'T feel like studying ... other?

I checked around with other AP teachers. Yup, their students (we all share) basically admitted to not doing extra studying outside of class ... much.

Okay.

Well, I've instituted some other motivations. Don't know what will work, so I'll do multiple ones of them. Here's one I thought of today after seeing something similar on Pinterest.

Today, I had them start a foldable that is due next class. I prepped for the insides by listing various things they need to memorize:

 

Then I made one myself (sort of) and made a flipped video for them to watch to see what goes on the inside. Here are the flaps:

 

 Here's a wee look on the inside. I didn't just want formulas, I wanted examples:

I'm SURE this will be the ticket. Girls LOVE pretty colorful things, right? They won't be able to tear their eyes away from it. They'll study daily.  

Making a Graph Updated...

A while ago, I used to make graphs for my worksheets in a way that, at the time, seemed reasonable. Hah! and Double Hah! I have seen the light. I don't know where I heard about this technique, but I am using it now, and just today, I enhanced it to be easier for me. 

Here is a finished graph that took about 4 minutes to make from a blank space:

I like this process because I can never seem to find my old "made" graphs, and if I do, they are never the right size.

Also, I used to make a similar grid using "tables", but then I would go and insert shapes with textboxes to do the scale. Tedious. I just realized today how I could do it all with tables. Viva la tables!

Here are instructions in case you are in need of graphs.

Quick PSA for Precalculus

We are now into our Logarithms and E Unit, but before that I wanted to review exponent rules and manipulations for a day. We did that, but I showed my students THIS Public Service Announcement. To set the stage for their project.

We went over 6 different exponent rules, and I mentioned that if everyone remembered them really well just from taking notes and practicing them, then we wouldn't need this review. I said that they each were assigned one of the 6 rules, and they had to make a PSA for that rule. 

We discussed that JUST restating the rule was not effective and sort of besides the point. We discussed that humor or shock value is effective. We discussed linking new things to things you know. We also discussed that the thinking of the actual content was the hardest part, and then you had to ink it out, so just use your "pockets of time" in the next 2 days to brainstorm through some creative ideas.

I also only gave them until the NEXT class to do it (8.5" x 11" paper, colored, correct, effective...). I also joked with them that if I had given them a week, they would have left it until the last minute anyway, so just pretend I assigned it last week.

Don't know if this will be effective or not, but I liked the project, and I liked seeing the wittiness and creativity of kids that I may not otherwise talk to that much because they're not the yappers in class. Here are some samples.