AP Calculus AB

The Adventure Continues ...

2006-06-29T15:49:00.000-05:00

Our adventures in blogging continue....

Watch for 3 new blogs going live September 6, 2006 ...

Pre-Cal 30S (Fall '06) (Grade 11)
Pre-Cal 40S (Fall '06) (Grade 12)
AP Calculus AB 2006-07 (Grade 12)

So Long ...

2006-06-28T18:15:00.000-05:00

We had our graduation exercises today. A gentle push into the world for all of you. I hope you're leaving with the keys to your future in your hand.

I'm so glad we've had this time together,

Just to have a laugh or learn some math,

Seems we've just got started and before you know it,

Comes the time we have to say, "So Long!"

So long everybody! Watch this space in the fall for pointers to new blogs for each of my classes.

Farewell, Auf Wiedersehen, Adieu, and all those good bye things. ;-)

Student Survey Results

2006-06-28T18:02:00.000-05:00

The exam is long over and we did a little survey in class. The results are below; 4 students participated. Here are the result. Please share your thoughts by commenting (anonymously if you wish) below .....

How prepared were you to write this exam? (Average score out of 100)

75%

How much effort did you put into preparing for this exam? (Average score out of 100)

67.5%

How good a job did your teacher do preparing you for this exam? (Average score out of 100)

92.5%

Did you have enough preparation using your calculator?

Yes 100% No 0%

Did you have enough preparation without using your calculator?

Yes 50% No 25% Middle 25%

Was I too hard or too easy on you??

Semester 1 was easy. Semester 2 was really hard for me. It killed me actually.
Just right.
Too easy.
Too hard.

What was the best learning experience you had in this class?

Blogging (2)
Mini exams (2)
Group Work
Wiki
Pre-Tests
Teaching and explanations were very clear and easy to understand

What was the worst learning experience you had in this class?

Homework (2)
None
Blogging On Blogging before tests

What suggestions can you share for next year?

More wiki assignments from past exams.
More exam-like long answer questions in class.
Have students doing boardwork in class.
The blog didn;t help me that much.

It's interesting to compare the items that were considered both the worst and best learning experiences. Also, take a look at the list of worst learning experiences compared to suggestions for next year. Help me do a better job next year by commenting on what you see here ....

The Places You'll Go!

2006-06-09T19:09:00.000-05:00

You have brains in your head.
You have feet in your shoes.
You can steer yourself
Any direction you choose. --Dr. Suess, Places You'll Go

It's almost graduation--what direction are you choosing?

Passing it forward--

2006-05-29T20:09:00.000-05:00

Some 43 years ago, when I was about your age, my father who used to travel a lot, wrote me a letter enclosing a small article clipped from a magazine. In that letter, he wished for me a life of purpose and joy. He shared with me the clipping which described such a life and quoted George Bernard Shaw whose words you can read above.

I carried that article with me for years; unfortunately, somewhere in the many moves, it was lost. But not the thought and the power of those words. They have become a part of who I am. I know that my career as a teacher, and the mentoring I do now for teachers seeking National Board Certification are but "drops in the ocean" in this often violent, globalized world of ours but my life has been filled with joy, happiness and love.

I'm sure that my father writing and sharing those thoughts adds to their meaning for me, especially now that Alzheimer's prevents him from recalling what occurred. But his belief in me, in mankind in general, shaped my world. I'm passing that forward --my belief in you, my belief in mankind, and my wish that you find the real joy in life!

Wishing you success ahead!

2006-05-26T18:58:00.000-05:00

I am thinking that these days each of you, your family, and your friends are looking to your future and wishing you success. I'd like to do that too!! To wish for you all that Emerson describes-- Would this meaning of success be one you'd be willing to adopt?

Two roads diverged in a wood---

2006-05-18T19:25:00.000-05:00

THE ROAD NOT TAKEN by Robert Frost

Two roads diverged in a yellow wood,
And sorry I could not travel both
And be one traveler, long I stood
And looked down one as far as I could
To where it bent in the undergrowth;
Then took the other, as just as fair,
And having perhaps the better claim,
Because it was grassy and wanted wear;
Though as for that the passing there
Had worn them really about the same,
And both that morning equally lay
In leaves no step had trodden black.
Oh, I kept the first for another day!
Yet knowing how way leads on to way,
I doubted if I should ever come back.
I shall be telling this with a sigh
Somewhere ages and ages hence:
Two roads diverged in a wood, and I-
I took the one less traveled by,
And that has made all the difference.

This has always been one of my favorites as I've found myself faced with those "two roads diverged" so many times in my life. I'm thinking you may now be viewing "two roads diverged" now as you are about to graduate and I know you will be many other times in your lives.

My choosing ( It wasn't necessarily an easy choice.) Earlham College was one of those times I "took the road less traveled" and it has made "all the difference" in my life. My years at Earlham have had a profound impact on who I am today, how I see the world, and what I believe.

Have you taken/will you be taking a road "less traveled by" and has it/will it made/make "all the difference"? Or does it matter?

Congratulations-- What's next?

2006-05-09T07:24:00.000-05:00

Congratulations on completing your AP Calculus exam!! That is quite an accomplishment!!! When you look back on the process, did you surprise yourself? Did you take some time to celebrate?

After celebrating, was your first thought "What's next?"

What will be the next immediate challenge? Isn't that the incredible part of living? That once you complete one challenge, another awaits. More hard work, more frustration, more hard work, always something.

Below is one of my favorite quotes (when I was teaching, we began each class with a quote; often ones that my students suggested; we felt each one captured something essential about living and life) ; Ara shared some of hers and since I've lived my life by a quote as you'll find in a future posting, I'll continue with this one here:

"Every day you may make progress. Every step may be fruitful. Yet there will stretch out before you an ever-lengthening, ever-ascending, ever-improving path. You know you will never get to the end of the journey. But this, so far from discouraging, only adds to the joy and glory of the climb." --Sir Winston Churchill

Your climb has just begun! Your AP exam was one great step!! What's next?

Kakuro Sunday

2006-05-07T11:12:00.000-05:00

'A Kakuro consists of a playing area of filled and empty cells similar to a crossword puzzle. Some black cells contain a diagonal slash from top left to bottom right with numbers in them, called “the clues”. A number in the top right corner relates to an “across” clue and one in the bottom left a “down” clue.

The object of a Kakuro is to insert digits from 1-9 into the white cells to total the clue associated with it. However no digit can be duplicated in an entry. For example the total 6 you could have 1 & 5, 2 & 4 but not 3 & 3. Sound simple? Be warned it gets hard and is as addictive as Sudoku.'

Click here for more Kakuros.

(Thanks again to Think Again!)

Running Up That Hill

2006-05-02T22:29:00.000-05:00

Take a look at this:

You're not the only ones using our blog to get ready for tomorrow. ;-)

If you're an AP Calculus student reading this now ... go to bed! You've got to be ready for tomorrow. Your brain is an organ; take good care of it. It needs sleep, a good breakfast tomorrow (like cheese, fruit, eggs and juice) and lots of water. Don't forget to do some exercise when they give you breaks so you can get the blood from your bottom into your brain. ;-)

Lastly, remember that luck has nothing to do with it. It's all about doing your best ... Learn Hard!

Answers to Mini-Exam #6

2006-05-02T09:45:00.000-05:00

(1) D
(2) D
(3) A
(4) B
(5) A

free response question

(a) Because g is the derivative of the function ƒ, ƒ will attain a relative minimum at ta point where g=0 and where g is negative to the left of that point and positive to the right of it. This occurs at x=6.

(b) Bcause g is the derivative of the function ƒ, ƒ will attain a relative amximum at a point where g=0 and where g is positive to the left of that point and negative to the right of it. This occurs at x=3.

(c) We are trying to find the area between the graph and the x-axis from x=-3 to x=6. From x=-3 to x=3, the region is a semicircle of radius 3, so the area is 9π/2.
From x=3 to x=6, the region is a semicircle of radius 3/2, so the area is 9π/8.
We substract the latter region from the former to obtain: (9π/2) - (9π/8) = (27π/8)

(d) Because ƒ''(x) = g'(x), we are looking for points where the derivative of g is zero. This occurs at the horizontal tangent lines at x=0, x=4.5, and x=7.5.

Just do it!!!!

2006-05-01T18:35:00.000-05:00

On the day that I was to take my "big" test, I was just about to leave for the testing center when I asked my husband to wish me luck. "No," he said, "I won't do that." I was crestfallen. I felt like I needed one last boost before the "big" one.

Then he continued, "You don't need luck. You're smart. You're prepared. You're good. I believe in you. Go out there and just do it!!!! I'll be here when you get back."

It's time for me to pass that forward to you! You don't need luck. You're smart. You're good. You're well prepared (thanks to your hard work and Mr. K). I believe in you. Go out there and just do it!!!!

Your second wind--

2006-04-30T18:20:00.000-05:00

Most people never run far enough on their first wind to find out they've got a second. Give your dreams all you've got and you'll be amazed at the energy that comes out of you. --William James

I wonder, would this apply to calculus too?

From ZZZZZ's to A's

2006-04-28T18:38:00.000-05:00

The bottom line: Teens need 9.25 hours of sleep per night

from Do Teens Get Enough Sleep?

In experiments done at Harvard Medical School and Trent University in Canada, students go through a battery of tests and then sleep various lengths of time to determine how sleep affects learning. What these tests show is that the brain consolidates and practices what is learned during the day after the students (or adults, for that matter) go to sleep. Parents always intuitively knew that sleep helped learning, but few knew that learning actually continues to take place while a person is asleep. That means sleep after a lesson is learned is as important as getting a good night's rest before a test or exam.
from Adolescents and Sleep

At the risk of sounding "mom-ish", have you taken this into consideration in your preparation for your upcoming test? I saw in a scribe that Mr. K had mentioned it!

Asking only because, when I was sleep deprived, I know I wasn't fully aware of how much more difficult problem solving and remembering was. I never fully realized how sleep deprivation changed my abilities and me until after I started getting adequate sleep.

Another factor in your preparation to be your very best for your test??

Your self portrait!

2006-04-26T18:46:00.000-05:00

How is your self portrait coming?

Visualizing excellence in calculus!

2006-04-24T19:48:00.000-05:00

"Almost all of the world-class athletes and other peak performers are visualizers. They see it; they feel it; they experience it before they actually do it. They began with the end in mind. You can do it in every area of your life. Before performance, a sales presentation, a difficult confrontation, or the daily challenge of meeting a goal, see it clearly, vividly, relentlessly, over and over again. Create an internal "comfort zone." Then, when you get into the situation, it isn't foreign." --Steven Covey

Are you an athlete? Do you visualize already? Maybe you've already thought about this before--

I wanted to share because I think that with your success on your mini exam (saw that in one of Sarah's comments! Congratulations to you all!) and all that you are sharing, and reading, and problem solving on this blog, you really can visualize excellence for May 3! You are doing everything the quote from Stephen Covey suggests! Now with visualization for May 3, you'll be in your comfort zone and on your way to a peak performance.

I had mentioned earlier in an earlier post that I had been faced with a major 3 hour assessment. I sense that I prepped in some of the same ways that you are. I "relentlessly" researched and reviewed all I could find that could help me with the six test questions. The organization provided generic test questions and scoring guides for each question. I practiced answering the question within the half hour framework. I practiced with the software that I would be using in the testing center. I visualized how each question might be phrased and how I would respond. I can't honestly say I was in a comfort zone when I entered the testing center, but I know that when I took a deep breath and began, all that I had visualized and practiced seemed to flow from my brain, through my fingers and into the testing software.

Do you think visualizing could be helpful to you too?

The Da Vinci Code Quest Sunday

2006-04-23T15:34:00.000-05:00

It started last week. Google releases one puzzle each day for 24 days until the movie "The Da Vinci Code" is released in May. So far 7 puzzles have been released. You have to solve the puzzle to reveal a clue. Then you have to answer the clue question(s) to advance to the next puzzle. You can win a prize for solving all 24 puzzles. Now I realize this is all about marketing and they're really just trying to get as many of us as possible to go see the movie but the puzzles are really cool! Google searching often helps to find the answers. One of the puzzle questions can be answered using The Fundamental Principle of Counting and the very first (sudoku-like) puzzle uses a couple of mathematical symbols.

Challenge 1: What is the question that can be solved using The Fundamental Principle of Counting and how do you use the counting principle to find the answer?

Challenge 2: What mathematical symbol is used in the very first puzzle and what number does it represent? (Not the "delta," in a later puzzle it has a different meaning.)

You have to sign up for a Google Homepage in order to play, but that's a free and very useful service. After that you can begin the game. Click on the US button to start 24 days of fun! (Actually, 17 because you could work through the first eight today.) Don't forget to also find the answers to the Challenge Questions above!. ;-)

The Main Thing

2006-04-19T19:40:00.000-05:00

Spring has sprung in Chardon, Ohio! Yes! We get lots of snow and winter seems so long that when the daffies bloom and the forsythia bursts forth with yellow, I'm estatic. (Last year this time, a late storm dumped 15 inches of snow on us) Is Winnipeg the same?

With spring, I'm finding that it is more difficult to stay with the course I'm designing for superintendents and principals now. I'd much rather be walking in the park, or out in the garden-- And so I've been using the thought above to help keep me focused.

What about you? What helps keep you focused?

endings-- beginnings--

2006-04-13T18:44:00.000-05:00

Ara's post really hit a spot with me. This entire notion of an end to something or not---
Do you think this quote applies as you work toward to your graduation?

A New Feed Window

2006-04-09T23:08:00.000-05:00

There is another Winnipeg AP Calculus class sharing their learning on a blog. You can peek in on what they're learning by checking out the new feed window way down there at the bottom of the side bar underneath the del.icio.us box. Take a look at their blog. Are they publishing anything that you find helpful? If so share it with us in the comments to this post.

I'll bet you like getting comments on our blog. Be a good netizen; drop in on them and leave them a positive comment too. ;-)

Four Colour Sunday

2006-04-09T14:01:00.000-05:00

You may have heard that any map can be coloured with four colours in such a way that neighbouring countries receive different colours. That it can be always done is one thing. How to do it is another. Are you ready to start colouring?

(Thanks again to Think Again!)

Roboclaw Sunday!

2006-04-02T14:40:00.000-05:00

Move the robot arm to pick up the ball. Clean, simple design. I got to level 19. I died. It's a doozy!

Synergize? in calculus??

2006-04-02T12:31:00.000-05:00

I really liked Ara’s quotes and intro in her scribe! And wonder if there is any relationship between our willingness to embrace the “pain of a new idea” (step outside our comfort zone), and the habits we develop? Do you think these last four habits (that round out the 7 habits from Sean Covey’s book) have anything to do with willingness to embrace something new?

Habit 4: Think Win Win
How might this attitude help Goldilocks and/or affect your life?
Habit 5: Seek First to Understand, Then to be Understood.
Does Covey sum it all up with? “You Have Two Ears and One Mouth… Hello!
Habit 6: Synergize
I mentioned the lesson from the geese in a comment on Sarah’s blog. If I bring it here, does this suggest a strategy for success?
Habit 7: Sharpen the Saw
Subtitle—“It’s me time!” I’m the first to admit I’m not good at this. How can taking time for you really be important??

Of these 4, I have two favorites. What do you think? Are these habits of value? And if they are not new to you, then which of these helps you the most and how? Is it time for some synergy here?
Best,
Lani

You guys need to see this ....

2006-03-30T15:06:00.000-06:00

This is a video recording of a presentation called: "From Smart Toilets to Smart Schools." It was given by a world class educational technologist named Alan November. He travels all over the world teaching teachers about powerful uses of technology for their classrooms. He's been talking about us all over the world. In the video he talks about our whole class, and Ara, he mentions you by name. (How cool is that?) This particular presentation was given in Ohio on February 14th. If you didn't really believe me when I said you had a world wide audience reading and learning from your work, well, ..... watch the video.

Start watching the video at the 38 minute mark. I think it will go offline on April 14th so don't put off watching it. You'll need to have realPlayer media player installed on your computer (it's free). Just click on the link to [RealPlayer - Free]. Here's the video! You should be very proud of yourselves ... I'm proud of you. ;-)

Urgent, Important? First things first!

2006-03-29T18:41:00.000-06:00

I can certainly relate to Sarah’s feeling that there are too many big rocks for the bucket of our life, as she mentioned in a comment. In early 2003, my bucket seemed to overflow. I felt then that I had to find a way to make it all work. Achieving my goals was too important to me and my test (which if I passed would lead to a national teacher certification; only 40% of test takers passed) was only one of many goals. I was really trying to be superwoman—just as I imagine many of you work at being superteens. I thought I was prioritizing but ooohh---a to-do list with 20 items all the time!!!

What I struck me one day when I found myself in tears because I had not met a school deadline, was that I was not always prioritizing by what would help me meet my goals. Urgent “stuff” kept happening and I was always responding to that. Does that sound familiar?

That night I sat down and broke my test review into manageable chunks (I had 2 months until the test; I divided the topics into sessions for those two months) and put them into my planner. I did that first because the goal to pass the test was so important. And I planned to turn off instant message, not answer the phone, or have the TV on during the review sessions. I had tried to plan before but was always interrupted by the phone or my students on instant message with questions about our studies and I found that I didn’t accomplish half as much then.

Then I looked at my other rocks, and categorized them: vital, important, or nice. Then I took the vital rocks and categorized them again: vital, important, or nice. So my house wasn’t very clean during the process, and we didn’t have gourmet dinners. But the laundry was done and we had quickie suppers. My student’s work was graded but I didn’t plan any big field trips or projects during that time. I set aside a time every second night to evaluate their work. As I look back now, I prioritized, and then prioritized again. I did a mental daily check of my goals and made every effort not to be dragged down by urgent if it didn’t help me achieve my goals.

Of course, I had to be flexible at times. I couldn’t always follow the plan exactly. But since I knew where I was going and I had planned for time to get there, my review was accomplished by “the day”.

I truly believe, that with good preparation and putting first things first, you'll too feel that great rush of a job well done, and a goal achieved when you learn your scores. I share these experiences, knowing that you are planning and reviewing, but wondering is there one little piece here you could use to help you on your way? Or can you point us to some tips that are really helping you manage the rocks and put first things first?