Saturday, March 07, 2015

Precalculus Sequences & Series

We had time for a mixed review day in Precalculus. ... As I type that, I wonder why it always seems rushed to teach this class. Last year, my colleague and I seemed to speed through things and didn't give things a fair treatment. But the flip side is, what do you leave out? There are too many cool things the students have never seen before and this class always seems like the last high school chance to showcase things. Anyway, I revived this sheet I'd made a long time ago. It has some nice challenging problems (#6 will floor you .... Hah! #clickbait) gathered from a ton of places.



I tried to make sure that the way the questions were asked forced the kids to look for efficient ways to find first terms and sums and such.

 On a "make you feel old" note, they had never heard the term "boob tube" for television. Some students thought the term referred to those tops that were elastic for girls that had no straps. Hah! So I told them to look it up.

Tuesday, March 03, 2015

Calculus Motion and Accumulation Combined

I made up a new worksheet for the students to practice straight line motion problems combined with their accumulation function knowledge for AP Calculus AB.

 I really like problems 7, 8, and 11. It's very interesting that they forget they can find the equation of a line to substitute in for the v(t) function on 7 & 8.

Sunday, March 01, 2015

Half Century

I turned 50 years old a month ago today. Probably like most people who get here, I'm still a little dazed that this number is associated with me.
I'm the young whippersnapper. I'm not the old geezer. My friend jokingly got me this shirt: 




I think it was jokingly. But I'll go with it.

I've also been teaching a long time; this is my 18th year. So in celebration (or reflection) of all this, I am challenging myself to list "50 things I've learned about teaching" ... notes from an old geezer / village elder wannabe.

(in no particular order other than what popped into my brain and when)
 

And also, obviously, these are just things that are "true" because of MY experiences and the schools I have taught in. Mileage may vary for you.

1. Enjoy the students. They're pretty amusing.
 

2. Try to separate the behavior from the kid/adult. I'm still working on this all the time (after I grumble and curse and have a pity party about what's been "done to me").
 

3. It really IS true that they will remember how you made them feel other than what you taught them.
 

4. If a kid is sleeping in my class. It's more effective to say, "___, wake up. I'm sorry you are tired, but I need you to be here." versus
    "$(&*($  ____ you will NOT sleep in my class!!!!" (though sometimes the second one feels better in the short term ... so I act it out in my head)
 

5. Just because they are staring at you while you are talking, it doesn't mean they are processing what you are saying. (I wonder what the % breakdown is ... or maybe I don't want to know.)
 

6. Every day is a fresh start and a fresh chance to do it right. (and to screw up in other ways)
 

7. Keep reflecting on what and how you are doing things. Never settle.
 

8. It's fun to learn new things along with the students. (and I am always "joyful" in my multitude of mistakes I make ....)
 

9. When I show my excitement about a topic, it adds to the lesson.
 

10. Even if I "learn something" about teaching one year ... that doesn't mean I remember it or put it into action consistently.
 

11. Just because other teachers seem to be successful doing things one way, it doesn't mean that EXACT thing will work with my students.
 

12. Even if I think something is obvious as a teaching practice, it doesn't mean it's obvious or even useful to others.
 

13. Share share share and borrow borrow borrow and adapt adapt adapt.
 

14. I teach students not subjects. 

15. I need to keep teaching learning skills along with topics.
 

16. I need to keep acknowledging to the students that learning is hard, and they should be proud of their effort.
 

17. Keep a large binder for each subject. Put copies in sheet protectors. Put the keys in there. Do it chronologically. Make sticky notes about changes for the following year.
 

18. For anything out of the ordinary in my daily schedule, make a google email reminder to help you not forget.
 

19. Humor humor humor is a nice wheel greaser.
 

20. Just because you taught it to them last year AWESOMELY, it doesn't mean they remember it instantly this year. Review, scaffold, and acknowledge that it's human. (and secretly be shocked that they don't know how to do fractions. Still.)
 

21. Teachers of non-math topics are also a source of great material to adapt to math teaching.
 

22. For big projects, I have found more success with having many stepping stone grades to ensure completion.
 

23. For big projects, I make a "contract" that has stepping stone due dates and a place for peer checking first and then my grading.
 

24. Gallery walks are great because the students get to see others' work and they also get to show off their work to more than just me.
 

25. I have been extremely fortunate in the schools I've taught in and the people I have taught with and the kids I interact with.
 

26. Even if something "bad" has happened to me in teaching/life in the past, it's great fodder for "stories" to share with the kids.
 

27. I try to do the big projects along with my students. That keeps me honest in what's involved, and I think I get more buy in from the kids.
 

28. I don't let students talk poorly about other teachers/students in my class. I try to gauge the situation to see if they can constructively resolve things.
 

29. People have to eat and go to the bathroom. I have rules that work for me and don't seem too jail-like, and then mostly everyone is happy.
 

30. Just because students are silent, it doesn't mean they are not participating.
 

31. There needs to be quiet thinking time, and students need to be reminded of it, as in, "okay, to yourself, figure this out, to yourself" .... "silently" ... "alone".
 

32. This has worked for me: "okay, now turn to someone and either give them the deer in the headlights look, or nod your understanding of what I just said". "discuss".
 

33. It's okay not to have lunch with other teachers and to just be in my room doing my thing in the middle of the day without being "on".
 

34. It's really helpful to have things to look forward to during the week. (hello Spanish lessons and breakfasts out each week)
 

35. I need to try out new ideas immediately, or else they usually don't get tried out after a conference.
 

36. For all my answer keys, I highlight the edges on both sides of the paper, so it's easy to find and identify as the key.
 

37. Answer banks are awesome. I mix up their placement, but it gives kids immediate feedback on their work.
 

38. Practice doesn't make perfect. Perfect practice makes perfect. (thank you, basketball coach, math teacher from another school)
 

39. Hurt people hurt people. Kindness rules. 

40. Make eye contact with ALL students as much as possible. It's too easy to only engage with the students that are always the contributors. I don't want anyone to feel invisible. I still need to remind myself of this when I am staring at the back of the room when I'm talking and trying to keep straight what I'm saying.
 

41. I like to exercise in the morning because I know then it will get done. It doesn't hurt that I'm a morning person. Mwa ha ha.
 

42. My clothing choices are fascinating. Apparently. New clothes? New comments!
 

43. I need to have good reasons for what I am teaching and why I am teaching something the way I am.
 

44. "When am I ever going to use this?" responses: you may not use this, but this is how it is important ..... or, you never know what you will do when you grow up, so it's nice to have options.
 

45. You are apparently never too old for stickers.
 

46. Every class has their own personality, and what works great with one may not work with another. (what's WRONG with them?????)
 

47. It takes me about 3 passes through to "perfect" a lesson so that it's actually effective in the way I want.
 

48. People Before Paper. I need to not multitask when a student is talking to me and give them my full attention.
 

49. My attitude affects the class. If I'm cranky and tired (which happens), I let the kids know, hopefully in a joking way, and I try to get over it.
 

50. Sheesh, what a wind bag .... bla bla bla .... okay, LAST ONE ... digging deep .... wise words ... stalling .... Every school has its own challenges, and parts of the grass may actually be greener elsewhere, but other parts are covered in fire ants.

Okay, look for the sequel to this in 10 years .... "60 things I've learned and maybe remember about teaching mixed in with a list of my aches and pains".

Monday, February 16, 2015

Inverse Trig Graphs Take 2

Even with what I thought were great manipulative tools (patty paper to be used to help teach inverse trig graphs), there were students that still did not grasp the overall concept when they had to put it to use. During the times that they came in for corrections on their test, this strategy SEEMED to work. I first had them sketch (say) the sine graph:

 Then I ask them to color in the restriction that will allow the function to have an inverse function (this part they remembered).


 Then we get to the part they couldn't apply successfully, so we broke it down. First I asked them to find (say) 200 degrees on their graph. This seemed a nice challenge for them and it was nice to hear their thought process.

Then I asked them to find sin(200deg) on their graph. Also, enlightening.

 Then I asked them to reason through finding arcsin(sin(200deg)), and I had them talk out their reasoning as to why it was placed where it was.



And finally, we took it to the unit circle, so they could summarize and wrap it up.

I think I may start with this technique the next time through because it shows everything on one page and they can work through the visuals of WHY even through you MAY have an angle in the first quadrant, it still is not valid for an arcsin function because the angle is more than 360 degrees (for example).

Saturday, January 31, 2015

Dear Teenager...

Dear Teenager Cashiering at the Grocery Store,

First of all, congratulations on being responsible and earning some money while you are going to school. Yay you! Second of all, you are doing a pretty good job, mostly. 

But, you are making me sad for the state of things on two counts, okay, three ... probably more, but I will stop at three. First sadness, when you are talking to the other teen that is bagging the groceries while you are "helping" me, I feel like a non-person. I am in the way of your fun chatting event with my pesky food that is sliding along and being summed up and packed. There is enough anonymity and struggles in the world without having to feel invisible during everyday chores.

Second sadness, you are giving the group that is "teens in America" a bad name or a "kids these days!" moniker. I know you're probably pretty awesome since I teach others in your group, and I enjoy them immensely. You on the other hand are not attending to your job properly, and are helping add another item to the secret adult list of "why teens are poos". 

Final sadness, for now, most of you don't know how to make change. Math! Money! Please, please, PLEASE don't look at the register screen to make change on a $16.80 bill when I give you a $20 and a nickel. Maybe my sadness is more for the managers that have (not) trained you than you. You can do it! I know you can! 

Signed, 

Former Teen Grocery Cashier,  Former Movie Theater Cashier, and Current Adult/Teacher 

p.s. Thank you Ms. Dora at AMC all those years ago for teaching me how to make change.

Tuesday, January 20, 2015

Giving Ourselves a Break

Have you ever watched a performance, music / dance / theater / gymnastics , as a non-expert in that area and just been impressed with what was appealing to you whether or not it was "hard"? Then you think about someone with lots of knowledge in that arena watching the same performance, and they are probably having a different experience. They may be thinking, "Wow! Look at that difficult move they just executed! Amazing!". You may have missed the impressiveness of it, but you knew what resonated with you. And the performer has a third version of the events thinking, "ooooh, I hope I pull off that triple-quadruple-back-slide doohicky perfectly!" and you may not even have known to be impressed with the challenge of the doohicky.

I'm thinking it's the same with our kids. We may be all impressed with our various ways of presenting/teaching a topic, but it may be hit or miss whether it works or not with the students. I'm thinking that they mostly only care about knowing that you care and that you have their backs and that if they are struggling with the learning, you will be there for them. They are not sitting back and thinking, "hmmmm, look at that student-centered stunt she just pulled off!" ... or, "wow, that's master teaching skills right there!".

So I'm thinking that, yes, we should strive to do our best with all our teaching skills, but maybe the most important thing that trumps the whizbang lessons is the fact that the kids see you caring about their learning and pausing enough and waiting for them to process and keeping your questioning and explaining processes churning to make sure they know you have a safety net for them in their learning journey.

I guess this is all to say that it's okay if I don't kill myself all the time worrying about presenting a lesson "just right" because as long as I honestly care during the lesson and am tuned in to what and how the students are learning, then I am doing fine.

Sunday, January 11, 2015

Inverse Trig Graphing

Teaching Inverse Trig Functions, Take 10 (??). Okay, patty paper to the rescue*. I'm hoping THIS year, since we are taking time to construct and ask questions and have a physical thing in our hands that we can flip over and analyze that the students will more readily be able to reconstruct their knowledge of inverse trig graphs.

We started by making an envelope for their notebooks.



 Then we SLOWLY with lots of back and forth questioning created this sheet for sine:



We had to refresh our memory on Inverse Functions in general from previous knowledge. Then we flipped the paper over (after we discussed the "x and y switch roles") by keeping our thumb (positive x) and index finger (positive y) attached to the paper:


And we had a discussion on what part we should restrict the domain of the sine graph to to make this inverse function a function. THEN we shaded the right graph part with a sharpie. 

We did the same with the cosine graph the next day. Then because of a discussion with some students AND the fact that even though we stress that ONLY ONE output is possible, they still are confused with a problem such as:

Without a calculator, find  arccos ( cos ( 200 °) ). 

So after the patty paper, I had them explore with this sheet:



 Let's see if THIS is the year the information better sticks to their brain cells.

* Funny note: when we were making the graphs and free-style drawing, a student said, "hey, they should make patty paper lined with a graph/grid". I flipped the patty paper box over and showed her that it really was paper meant to be put between meat patties or some such food.