I got to see the great Dan Meyer present today! He began with his pennies pyramid video and then we spent time talking about how many pennies were in that pyramid and how could we figure it out. It was totally engaging and I enjoyed getting to show someone at my table how to put a list of numbers into the graphing calculator to get to the answer quickly. Dan had me beat though. He showed us a cool summation calculator online that made easier work of it. I love getting new websites! I could definitely see how this approach to teaching students about summation and sigma notation could really "suck them in". A roomful of educators was totally enthralled (and no, they were not all math teachers)!

Later in the day, we looked at textbook problems and talked about how we could take information away and have the students create questions like "what is this picture about?" if we were to strip away everything except the labels on the bottom of the graph (even the graph grid taken away). I can tell you as a participant, even I (a math teacher, gasp) am less interested in the problem until you take all that "fluff" away and let me develop the questions. It became interesting then.

One of Dan's strategies when developing questions that he referred to several times is "creating a headache" that some math information will be the aspirin for. I like that analogy because it's true, in mathematics, we often try to hand out aspirin when there is no headache yet. As teachers, we need to create a headache situation for which the math is the aspirin. Dan fostered a "fight/argument" among us for which we WANTED to be able to use math to justify/support our own opinion/position. I have to say, it makes it SO MUCH MORE MEANINGFUL for students (and adults alike).

Since I have poked around on the internet looking at "good stuff", I already knew about his lengthy list of 3 Act lessons. But if you are not familiar with them, enjoy this site. There are enough to last an entire school year!!

After all that mental stimulation, I had barely enough active cells left to listen to Dr. Sherry Parrish's talk, on Global Math Dept site, about number talks. I totally HAVE to do this with my students. It is a GREAT way to see what strategies they are using and have them share. It was fascinating watching the video clip she provided and listening to the students explanations of how they multiplied 16 by 35. I was amazed at all the different ways! I always get excited when students show me a "different way"! I highly recommend Global Math Dept presentations every Tuesday at 6 p.m. Pacific Time.

Back to my students tomorrow!! Hope I'm feeling energized!! It's the day before the test and they will be stressing out (like always), and two days before the Homecoming Rally (yikes! this makes them crazy!).

P.S. I've been looking at some of the "make-up test" videos that I let my Calculus students create. I will have to create another post to talk about them! Stay tuned.....

## Tuesday, September 30, 2014

## Sunday, September 28, 2014

### What do we do if log of y doesn't straighten our data?

__Calc__
We worked more related rates problems together today. I gave them some sample problems and walked them through them as the "pre notes" before they watch their video notes tonight. What I'm finding is that either (a) I'm a much better teacher and did a much better job this year, or (b) all my students are incredibly smarter than last year's group or (c) this strategy we use in class is REALLY working. Why am I surprised? There is still the thought that it might not work as well as the old, boring, traditional way (old habits die SO hard!!). I have to say that the problems from mastermathmentor.com are extremely well done and sequenced. When the students are rushing ahead or saying "these are easy", I know I have found a useful tool!

__Saturday School__
I had approximately 18 Calc students work for FOUR hours on Calculus problems today! It was AWESOME!! They got a little "calc crazy" around 11:00 so I had them switch gears and try a Tarsia puzzle I made involving f(x) and f'(x). That really made them think, but seemed so much more fun. Great way to draw them back in! Can't wait for the next Saturday school! I think those that came got a lot of practice out of it!

__Stats__
We continued exploring regression models today. I had them practice another problem to generate an exponential model and be able to write the final equation. Then we moved on to a new data set and lo and behold, applying log to the y values was not sufficient to straighten out the data. So what do we do?

Bell rings (perfect timing AGAIN)!! Students groaned because they really want to know what to do. I LOVE creating all this anticipation!!

__Saturday School__
While the Calc students were on one side of the room the Stats students were on the other (9 in all), and they worked solid for the FOUR hours also. I had a few free response and some multiple choice problems for them. Multiple choice are challenging! I even had to think about a few of them. Think I will "reward" those that were they by throwing a couple of those questions on the next test. Hopefully they recall them.

## Thursday, September 25, 2014

### Gettin' down and dirty

__Calc__

Never expected to hear this:

Student 1: I'm getting these right?! (in their disbelief voice)

Student 2: These related rate problems are not that hard. I'm worried that it will get harder.

Student 3: I get these!! They are not that bad!

Student 4: I'm sad to leave this class (at end of period).

Today I felt like it was time to prepare them for "the worst". Of course the problems will get

*more challenging*...but at least I want them to know they__do them! So I warned them by saying: "Imagine you are playing soccer. It is raining and you are covered in mud AND sweat. This is the game that, if you win, sends you to the CIF finals. At the end of the game, it is a tie, so you are playing in overtime and you WANT THIS!! BAD!! You don't give up, even though you are tired and dirty and sweaty. You 'dig deep'. I want you to have that feeling while you are working these problems. But to get inspired, you are going to do a cheer. In your teams, you are going to put your hands in the middle and then do your cheer. You can give me a loud grizzly growl or do another animal of your choice". They really got into it and here are some of the pics!__**CAN**The best part was that after they did their cheers, I gave them the problems and they dove right in. I didn't see an idle student. And they get so excited and happy to get the problems right. If I gain nothing this year, I know it will have been worth it to have students excited to come to CALCULUS class everyday and do challenging problems together. I really believe that any of their fixed mindsets are quickly changing to growth because they are feeling empowered and that "Calculus is not so bad". When I have students tell me this is their favorite class, I know I MUST be doing something right!

**Stats**
I set the hook out today!! We have been looking at linear models for data and seeing how they fit. Today, I threw them a non-linear data set (reaped from the internet) and enter "curve ball" (perhaps pun intended). They think it's linear except for that little piece known as the Resid Plot.

Students: Hmmmm...it looks like a parabola Torres, so what should we say?

Me: It's NOT linear!! But how could we straighten the data so that r and r-squared make sense to use? Entrance logarithms!

Students:

*groan*
Me: remember, you have "hamsters" (graphing calculators) to do the work for you.

After they had checked all the model requirements, we had to figure out how to transform the equation. Dun dun dun.... (suspense music) and the bell rings.

Students: We need to know!!

Me: Tomorrow!!

Students:

*groan.*You're killing us!!
Me:

*smile*

I love my job!!

## Tuesday, September 23, 2014

### The power of a graphing calculator

__Stats__
Given that I have a set of 20 Chromebooks in my classroom that I use as often as possible, I will be the first to sing praises for having technology in the classroom. If you read most of my posts from this school year, you will know that I have used those laptops PLENTY! However, my students MUST be well skilled at using a graphing calculator for the AP Test, so I know it is important that I teach them all the tricks with that tool, and let them practice with it.

Today, we familiarized ourselves with how to get a complete analysis of a data set by looking at the scatterplot, resid plot, r, r squared and sum of resids (squared) on the calculator. One thing that I have NEVER heard former students tell me when they come back to visit is that knowing how to use the calculator was a waste of time. On the contrary, they tell me how others struggle in their classes because they don't know how to use a graphing calculator. So I figure, time well spent!! But be prepared, teaching students this soft skill takes quite a bit of time. It is through necessary repetition that they can finally remember the sequence of buttons that must be pushed in order to look at all the necessary components through which they can judge a linear/non-linear model for their data.

That took most of the period today and, no doubt, will again tomorrow.

__Calc__
Bring on the related rates!!

I tried a new strategy today and loved it!! Will continue to use it! I read off the answers to a worksheet the students had done for homework. Given that it was the first time I have used that worksheet and that there is no answer key provided (I have to work the problems out just like the students), it meant there was great potential for me to have mistakes (it happens to everyone!!! Even though the students think I am ALWAYS right, I try to tell them, I'm not....today was a perfect way to convince them!). Instead of my "old way" of asking "what problems would you like to see worked out?", I decided to tell them "if you have a question on one, put that problem up on the big whiteboard and we will see if we can find your mistake. AAAHHHMAZING!!! I had to solve literally NONE!! As students worked them, either they found their own mistake or their group pointed it out to them. And in seeing their work I was able to correct my key. But even better, I was able to show my work on the projector screen and have them tell me where I made the mistake on my paper. That was almost the best part! Having them look at other's work and find the mistakes is just as useful as them working the problem from the beginning! HMMMMM....this needs to be on the next test/quiz. Show where the mistake is and fix it! I like it!

Here are a couple students putting their work up for the class to see. After we went over HW problems, we started related rates problems. Mastermathmentor.com has some nice introductory problems to get students thinking. The students really had no problem catching on! It was exciting as I know how challenging these problems can be.

### Master Math Mentor

__Calc__
Sometimes a worksheet CAN get the job done! Enter mastermathmentor.com!! If you are a Calculus teacher and you haven't looked at this resource, you need to.....NOW! The website has so much stuff. Not all of it is free, but if you don't mind working the problems with your students, which I highly recommend, then you could consider it free. In addition to classwork and homework all neatly tied into one document, there are quizzes, powerpoint, games, projects and AP Test review. Even better, its not just for Calculus. There is material for Stats and Pre-Calculus!! Get a cup of coffee and have fun perusing all the material that is there!

I used the worksheets on Implicit Differentiation today (both Classwork and Homework). Students were so engaged working the problems on the whiteboards. Cannot say enough positive things about the power of those whiteboards! Lots of learning today! You can probably spot the "hams"!

**Stats**
Every year, at the beginning, it is a struggle to get students to stop obsessing over all the new information. It's kind of like riding a roller coaster and you are on the "up" section for a really long time (stuck there perhaps). They just want to get to that quick downhill part and I want to linger in the climb. So it's a battle between "them" and me. Today was no different. We are looking at regression analysis and some with computer output instead of having the data. I think I have made enough of a big deal about putting the prediction equation in context that it has finally stuck. But when it comes to interpretation of slope, r, r squared or the y-intercept, hair starts flying out! It's the WRITING that is the most painful because they are not used to having to describe in words. I know it will develop, but for the moment, some are struggling.

Tomorrow we look at WHY we look at residuals. Hopefully their questions get some answers because they have NOT been patient waiting.

## Wednesday, September 17, 2014

### Laptops ROCK!!

__Calc__
Today we had to take a step back from the problems I assigned for homework last night. I know that they were "killer" problems involving Chain Rule for Derivatives. I only assigned 8 and some of them they had already worked on in class. The "book" overshoots a little in what it expects, so I wanted something a little more realistic. Mooculus to the rescue!! I will continue to say how awesome that site is: IT'S AWESOME!! We are already in Week 5 of this wonderful resource!! The kids went right to work on taking the derivatives. There were mini whiteboards out everywhere and I watched and helped and answered questions. What was amusing to watch was how soon they switched to the large whiteboards because the mini ones were not big enough. I expected to quickly hear "all the work on one whiteboard for ONLY one problem", but not a single student made that remark all day. They were actually having fun!

Student 1: Why do they keep giving me the easy problems?!(they were NOT easy--it's chain rule and they all had either product or quotient involved)

Student 2: These are fun!

Student 3: It was so easy, I thought I did something wrong!

There was even a moment in every class where I "timed them out" to gather round a problem that one student had started, just so we could discuss simplifying the quotient problems. And the interesting note is that

*that one student would feel*__normally__*awkward*from having everyone watch them, but I simply said "so and so" is our recorder, so what do we want him/her to record? It was no big deal then. I LOVE how they are getting so comfortable talking about math and doing math together!!

__Stats__
Here are my THREE picks of the day for AP Stats!! First I started with a lesson from Mathalicious! If you are not familiar with this website, you should DEFINITELY check it out. We were doing a lesson designed for the common core curriculum at the Algebra 2 level, but it was very easy to use in my AP class as well. I added a bit to it, in that I used online software to help the students get to the level of thinking they need to be in AP. The lesson (called Win at any Cost) had students comparing team salaries and number of games won among four different sports (MLB, NBA, NFL and NHL). OF COURSE it generates a lot of interest and discussion as they work. To facilitate their generating lines of best fit and correlation values quickly, I put the data tables into a google spreadsheet and let them use StatKey and Interactivate. These tools are very useful and much faster than their graphing calculators, which they have been using until now. It think it's important that they know how to use other forms of technology beyond their calculators (I'm guessing in the real world they will not be carrying those around with them). This turned out to be an awesome way to discuss how we can predict for either variable. I can hardly wait until tomorrow to start talking about residuals and build on what we started today! Interactivate will show the residual graph next to the original scatterplot!!

Of course one of the best parts is how much fun they are having while being totally engaged! Again, I reiterate: I love my job!

## Monday, September 15, 2014

### Taking responsibility for learning is hard.

__Calc__
I fear that some tough lessons are going to have to be learned in Calc by several of my students. They are so used to being spoon-fed and having to take some ownership for the first time is a challenge. Prior to now they may have experienced little challenge as they were told what to memorize for a test and given review sheets that looked just like the test, but with different numbers. Now there is a lot of thought required, AFTER they read the question and figure out what it is asking. This is a new expectation entirely, and they struggle with it.

Today was a quiz on derivatives (that we have been working on for a week). I decided to try something new. There were only a few questions, but one of the questions expected them to find the slope of the tangent using the traditional formula, but I made it DEFINITELY a higher order thinking problem. We had done a somewhat similar one over a week ago in class (in their groups), so I decided to push them a little further. Here is the question:

I expected they would struggle comprehending the question, so after a specified time with the entire quiz, I made them stop and do this: take out a blue or black pen, pass the papers one turn clockwise. Now read the question (above) and make comments about the solution on the paper. Is the set up appropriate? Is there some direction you could lead them to get "unstuck"? Is there something there that you are wondering "where did THAT come from"?. But put on your teacher hat and write something on that paper. Then I had them pass again, and one more time until their own paper was back on their desk. Then I gave them 2 mins to "fix it" or "finish it" with the help of the comments. As I perused through the papers, I can say I was a little disappointed in the outcome. We will have to discuss this problem tomorrow.

As they worked on problems for the remainder of class, I had a "chat" with a few who seem to do a lot of watching. I stated that "if you only watch, you will NOT know how to do the problems. This is your chance to get help and ask questions. It's difficult to discern reticence from one being "lost" when they don't participate fully. I guess time will tell, and I will have to find ways to make them participate. I do make them change authors on their whiteboards, but with some of them, it's like pulling teeth.

More for me to contemplate.

__Stats__
Similar problem in Stats today. They had video notes last night explaining the concepts we were talking about today, and yet I found several blank papers. I did very well in containing myself. Tomorrow might not go so well. The ideas of how to "teach them a lesson about making sure HW is done" are churning in my head. I have a few.

We were working on calculating a line of best fit and we did it using StatKey and their graphing calculator. They have to do some practice using their height and shoe size data they generated in class on Friday. I pooled both classes of data together to give them more to work with. Tomorrow, we will use another website to play around with the LSRL. And they had better have homework done!!

## Friday, September 12, 2014

### Can we watch a movie?

Rally days make the students crazy!! I don't know if it is from being in a gym with everyone sitting so close and sniffing all that body sweat or the loud reverberation of noise we can't understand from the poor sound system, but something about attending those events makes them think we don't need to do math in class. That couldn't be further from the truth. I AM NOT ONE to waste any amount of time, even if it is only 40 minutes.

__Calc__
In calculus, we did LOTS of matching graphs of functions with their derivative graphs, and I even snuck in a few second derivative graphs. I feel like they are getting a better handle on what they should be looking for. I found this worksheet online that I had given them for homework last night and I like that it forces them to look at the slopes of the graph in table format. I reminded them that this can be a good strategy when you don't have a clue. After all, its how they first started graphing back in those good 'ole junior high days. They want to throw away less sophisticated techniques sometimes and those strategies can be useful. I used this worksheet page 3 (found online) for a warm-up to get them discussing in their teams. In the remaining time I gave them this worksheet to compare f, f' and f''. I really liked all of these matching activities and think the students this year will have a much better understanding of what is going on with those 3 graphs. Plus, the bonus, we are also talking about relative maximums/minimums and increasing/decreasing when those concepts haven't been introduced formally yet. I'm hoping that all this practice will help curve sketching go much better for students. I FINALLY feel like I have a better grasp of it myself after all this practice with them!

For the students who are still struggling a bit, I found this AWESOME game!! You can make it challenging for the advanced students by having them increase the number of matches required on each game, AND match 1st AND 2nd derivative to f(x), not just 1st. I put out a challenge to them (since I gave it to them to play at home): that I scored over 12,000 already and they needed to take a screenshot if they beat my score.

__Stats__
Students: Can we watch a movie?

Me: Sure! Take out a piece of paper and write down the questions you will need to answer. They are on the screen.

Students: Wait, what?! What kind of movie are we watching?

Me: Duh, a Stats video.

Students: "grumble"

Me: "laughter"!!

If you haven't seen or heard of the Against All Odds--Inside Statistics video series by Annenberg Learner, you are definitely missing out!! They provide the videos and student guides AND teacher guides for many topics in Statistics. As a matter of fact, it parallels The Practice of Statistics textbook with examples. I LOVE this series and don't get to show them as often as I like. Hopefully I will have more time this year now that I have a flipped classroom. They are extremely informative and interesting.

Now that I have a flipped model, I am trying something a little different with the Stats students that I haven't done before. Instead of me writing the notes up on the board for them to copy (verbatim), I am using a question approach. I give them a question (today it was entire class) and then we answer it. So I (mostly) tell them what they should be writing down. I am actually liking this because it forces them to put it into their OWN words and will (hopefully) be more useful as a result. At the same time, I will (hopefully) teach them how to take notes in a college level classroom (something we really don't teach them in high school because we make them copy it all down verbatim after we give it to them). I plan on collecting their notebooks to see how they are progressing with the self-note taking. I'm anxious to see!

Now that I have a flipped model, I am trying something a little different with the Stats students that I haven't done before. Instead of me writing the notes up on the board for them to copy (verbatim), I am using a question approach. I give them a question (today it was entire class) and then we answer it. So I (mostly) tell them what they should be writing down. I am actually liking this because it forces them to put it into their OWN words and will (hopefully) be more useful as a result. At the same time, I will (hopefully) teach them how to take notes in a college level classroom (something we really don't teach them in high school because we make them copy it all down verbatim after we give it to them). I plan on collecting their notebooks to see how they are progressing with the self-note taking. I'm anxious to see!

## Thursday, September 11, 2014

### So many awesome websites, so little time!

__Calc__

After having a discussion about graphs of velocity and acceleration and doing some graphing on the mini whiteboards, I had the students go to the maths online website (this is a website created at a German University for online/distant learning) that has an interactive matching activity. As a matter of fact, there are several resources on this website that are interactive for math at various levels. It was

*. The students who understood it were enjoying the fact that they could get them correct repeatedly, but I told them they needed to check on their partner to see if they were getting them correct every time as well.*__so useful__
NOTE: DO NOT let every student have a computer. It totally shuts down ALL the conversation, AND a lot of learning DOESN'T HAPPEN. In some of the classes, there are more computers available because there are fewer students. I literally have to go to them and start asking questions because they "hide" behind the computer (i.e. they just attempt to do the problems alone and don't talk). This is the "kiss of death." After today, I will make sure they HAVE to share when doing these types of activities on the laptops.

__Stats__

All I can say on test days is that I become REALLY POPULAR at lunch. There were SEVERAL in my room at lunch getting last minute help before the test. I hope it paid off for them!!

## Wednesday, September 10, 2014

### I had to stop myself!!

There have been SO MANY great days this year (25 so far) but I think today HAD to be my favorite. Many of us love being in the act of teaching, so trying to NOT teach, and instead letting "the magic" happen without being the center of it....or the lead magician is difficult. Students in Calc were working on some challenge problems that I gave them. These are the same problems that I know students skipped on the (traditional) homework last year. Now they could not avoid them! The talk and explaining was FABULOUS!! They worked so hard for all 54 minutes!! Some were even there after the bell explaining their whiteboard to me!

But as AWESOME as all of that was, the best part what what I learned. At the start of class, I read off the answers to derivative problems they had done for homework. Then I asked for questions and a few students selected a couple problems they needed to see. I was en route to a whiteboard to do my usual explanation, when "ding", the sound of an idea going off in my head, I decided to select a group to put up that problem on their whiteboard. About 4 problems were asked so I had 4 groups each responsible for a problem. And they simply got up and put the solution up. Then the students who needed that solution did a quick "gather round" for an explanation. My "tiny brain" said: "isn't this what you were planning this year? LESS OF YOU and MORE OF THEM!" It was truly magical! But wait, there's more, they are doing it on a regular basis now. Even though I REALLY WANT TO go to the board and explain, I am stopping myself and getting them to do it (while I supervise, of course). It just ROCKS!

The best part is how excited the students are about this! Smiling, high-fiving, raised fists in the air, claims of victory. It is one big Calculus work out interspersed with celebrations and encouragements! We even decided that we should have our own twitter channel today: #calculete and it is a big hit already! I posted all these photos on it right away...and it has gone crazy all day with RT's and favorites. Student didn't have this much enthusiasm last year! I don't wonder why I want to be at work so much! This enthusiasm is contagious!!

Stats was equally as "fun". Students were reviewing for a test today and after talking about their review homework, we did some white-boarding practice with the Empirical rule. Mini white boards are equally as awesome. But after they finished, we went online to the following website to review more for their test tomorrow. This website is maintained by Rice University and 2 others and is excellent for interactive feedback. If you teach AP Statistics, you should look at it. I think I might use some of those questions on their test tomorrow!!

## Tuesday, September 9, 2014

### Product and quotient rule conjoined with "are you normal?"

**Calc**

Guilty as charged...I teach tricks sometimes too. Product and quotient rules for derivatives are one of those times you just have to memorize the formulas. So here goes (for quotient):

"Lo D-Hi minus Hi D-Lo all over Lo squared"

Fortunately for my students, they attend Lo High (Los Osos High) so it helps them to remember that that part comes first (Lo High!!). But oh how the problems are challenging. Today was definitely a "whiteboard needed" day. But I love how the students jump right to it. They get so excited sometimes that they just can't help but give hints to the other groups next to them. Interestingly enough, while you might think that they potentially would look at other group's work to get hints, they really are in their own little bubbles working away. They are determined! I love it! I simply have to walk around, check for understanding, give a few hints, point out a few errors and the rest of the time, they are doing their own monitoring.

**Did I mention how much I LOVE the whiteboards?!! Most amazing thing I've ever done in my classroom. Baffled at why I never thought of it sooner...saddened that I haven't actually.**

__Stats__

We got to use our sheep data today!! Guess what...it was definitely NOT normal. But since I had peeked at it earlier, I had created another column of the difference (between 1st trial and 2nd trial for each student), and that was a little closer. Well, it was symmetric at least. We used this site to check the normal probability plot to see after we used Statkey (one of the MOST AMAZING site for stats ever!) to look at the shapes of each list of data. I love being able to expose them to different sites. Being knowledgeable about the technology available will be important to them in their futures, so it is part of my mission to give them as many opportunities now as possible.

### Tranquilizing sheep!

__Calc__

Found another awesome calc website( created by two professors at Hofstra Univeristy)! I used it yesterday to have students practice with continuity and differentiability and then today to practice matching polynomial graphs with their first derivative graphs (this was the table perspective which we did first). I hope that using these intense practice sites really gives the students a better understanding of what they are doing, thereby making it more than just "magic".

We also discussed questions they had on their homework last night and I pointed out that we were doing Algebra (the Calculus version). It's so great to poke at their brains with questions about processes they know and see if they can make the connections. Today's BIG questions were:

How do position and velocity relate to each other? At what time does the object hit the ground? When does the object reach its highest point? What is the velocity when the object is "x" feet off the ground?

Here's where I find it ironic that they are stumped. I have to ask them what the graph of position looks like. It doesn't take much to get them to see it is an upside down parabola. But then I ask them where in the graph is reaches it's highest point and how they can find it without using Calculus. I tell them they have more than one way that they knew when they started the year in the class. It takes awhile for the wheels to churn and spit out things like midpoint value of the x-intercepts, or complete the square, or -b/2a. Much discussion happens over these ideas. Then, and only then, we get to the calculus option of finding the derivative. But getting all the other ideas back in their brain and to a level of it making sense is a challenge. I marvel at how little students remember. When we discuss the -b/2a option, I ask them if they have seen that anywhere else. Someone inevitably says "quadratic formula" and I ask if we should sing. Several do. I say isn't that great, but you aren't even aware that what that formula does is generate the x-intercepts equidistant from the midpoint (and proceed to split the formula apart). They are amazed as though I just performed a magic trick. I re-emphasize the importance of graphs to help them see what is happening.

Wish graphical approach was used a lot more in the earlier classes. Seems like we teach a lot of "just memorize this formula" without the pictures to help it make sense. If we taught reading that way (no pictures), do you suppose kids would come to high school not being able to read all that well? Wonder why kids prefer "the movie" over "the book" when its available? Do you suppose we are more picture driven in our brains? I do. I tell the kids "I love pictures". I know they help. Getting them "back to basics" takes some time. It makes me sad that they have had it "beaten out of them".

I knew that once they started they would want to play it over and over, so I made sure they entered they data for only the first two trials. We'll use this data to test for normality next week. Even one of the students said "that was a great way to end class after our quiz."

I just need to find some more Stats video games!

Here's where I find it ironic that they are stumped. I have to ask them what the graph of position looks like. It doesn't take much to get them to see it is an upside down parabola. But then I ask them where in the graph is reaches it's highest point and how they can find it without using Calculus. I tell them they have more than one way that they knew when they started the year in the class. It takes awhile for the wheels to churn and spit out things like midpoint value of the x-intercepts, or complete the square, or -b/2a. Much discussion happens over these ideas. Then, and only then, we get to the calculus option of finding the derivative. But getting all the other ideas back in their brain and to a level of it making sense is a challenge. I marvel at how little students remember. When we discuss the -b/2a option, I ask them if they have seen that anywhere else. Someone inevitably says "quadratic formula" and I ask if we should sing. Several do. I say isn't that great, but you aren't even aware that what that formula does is generate the x-intercepts equidistant from the midpoint (and proceed to split the formula apart). They are amazed as though I just performed a magic trick. I re-emphasize the importance of graphs to help them see what is happening.

Wish graphical approach was used a lot more in the earlier classes. Seems like we teach a lot of "just memorize this formula" without the pictures to help it make sense. If we taught reading that way (no pictures), do you suppose kids would come to high school not being able to read all that well? Wonder why kids prefer "the movie" over "the book" when its available? Do you suppose we are more picture driven in our brains? I do. I tell the kids "I love pictures". I know they help. Getting them "back to basics" takes some time. It makes me sad that they have had it "beaten out of them".

__Stats__
What a great day....if you like a lot of quiet followed by A LOT of noise! Sheep bleating, that is! Since the kids are in groups and I didn't want to move the furniture for a quiz, I came up with (if I do say so myself) a clever idea of making 4 versions and putting them on different colors. I also gave them a divider to put up between the side-by-side students (they didn't really need it). It really was easy! Just change the numbers! Sure it meant I had to make 4 keys, but it was totally worth it! Will do that again!

We had just enough time to gather data at the end of class that I plan to use next week. We used a website that tests your reaction time. It has you tranquilizing sheep and it is SO MUCH FUN! Their expressions say it all!

I just need to find some more Stats video games!

### AP Math is HARD!!

Friday was the end of the grading quarter, and my students are definitely freaking out after their first test scores. Even though I have been working on re-wiring their brains about what really matters (their learning the material), old habits die hard. They still fall back into the old thinking of "I need to get an A." I can see their heads nod when I explain to them that the grade should correlate but that grades are a temporal thing and learning is enduring. When they are in their next math class, in college, it will be those who really applied themselves that are rising to the tops of their class. I always let them know that College math at any level will be harder in comparison so they were wise to take this course in high school. They have more time to digest the concepts in high school and more access to the instructor (ME!) for help. Plus the fact that their peer group is more accessible to them for assistance (here's where they see the benefit of the flipped classroom) is invaluable. I go on to further tell them that Calculus is a sorting hat in college. Those that can do Calc get all the "good majors"...you know the "big money maker" degrees, while those that can't compete in that arena end up in the soft majors. I want them to have their choice (it's not about the money, it's about your passion). I will have to continue this counseling all year.

But I want to make sure I'm encouraging them mostly, so I make sure I tell them these things:

1) You are talented when it comes to math! If you weren't, you wouldn't have made it this far. Look at the rest of your class (senior or junior), how many of them are here? Enough said.

2) I want to encourage you to continue pushing yourself, because you will have no regrets when you leave this class for doing that. I only have students regretting either (a) not taking this class or (b) not completing it.

(3) in Stats, I tell them: you can speak a language that most adults can't even speak! All you need to do is say 'I'm taking Statistics' and people will react with 'Whoa, you must be really smart'. So keep on pushing because you will be able to do what most can't. That will be bankable right there!

(4) I'm here for you. Come and get help

(5) I hope not all the grades I give out right now are A's. If that is the case, then why do I need to be here? What have I taught you if you have an A lock solid? I want there to be room for you to grow. I want to expand your mind, thoughts and learning. Room for growth is a good thing. Be satisfied with the fact that your brain is growing. The grade will come, so for now, just be excited about learning!!

I got a few head nods, but it will take time for all the re-wiring to happen. The affirmation is enough for now.

But I want to make sure I'm encouraging them mostly, so I make sure I tell them these things:

1) You are talented when it comes to math! If you weren't, you wouldn't have made it this far. Look at the rest of your class (senior or junior), how many of them are here? Enough said.

2) I want to encourage you to continue pushing yourself, because you will have no regrets when you leave this class for doing that. I only have students regretting either (a) not taking this class or (b) not completing it.

(3) in Stats, I tell them: you can speak a language that most adults can't even speak! All you need to do is say 'I'm taking Statistics' and people will react with 'Whoa, you must be really smart'. So keep on pushing because you will be able to do what most can't. That will be bankable right there!

(4) I'm here for you. Come and get help

*any*time. I believe in you and I want you to*get it.*Let's work through this*together*!(5) I hope not all the grades I give out right now are A's. If that is the case, then why do I need to be here? What have I taught you if you have an A lock solid? I want there to be room for you to grow. I want to expand your mind, thoughts and learning. Room for growth is a good thing. Be satisfied with the fact that your brain is growing. The grade will come, so for now, just be excited about learning!!

I got a few head nods, but it will take time for all the re-wiring to happen. The affirmation is enough for now.

## Wednesday, September 3, 2014

### This is not "hard core math"

__Calc____Best quote of the day:__"That was pretty easy. I thought it was going to be harder. It's not really hard core math. I can do this."

Let me explain what this student was doing so you can be the judge. Her English teacher thought it was (hard core math) when she stopped in after school and saw what this student was working on (across 3 whiteboards). The problem involved using the definition derivative to find the slope of the tangent line at a specific point, and then write the equation of that tangent line. Here is the student's work:

Here is the best part of this! This student has limited confidence in her abilities, so this was a huge breakthrough! I have to admit that I was so excited at her own realization that she was definitely capable and that Calculus is not so scary. I hope there are more student breakthroughs like this to follow!

__Stats__

__"Do we have to draw a bell?"__
Wish I had a quarter for every time I heard that question today. I'd be able to pay for the school lunch! Getting them to be experts on finding z-scores and areas under the normal curve requires a lot of concentrated repetition. I tell them "this is like teaching you your times tables, but statistics version. You have to do a bunch of problems all the same way so that I know you are really good at it because later, that will be a 'simple skill' to use in a larger problem." They grumble but know what I expect for their work on their next quiz. Tomorrow they will get to put these new skills to "the test" and see if I find their work up to par. Here is some of their work today:

## Tuesday, September 2, 2014

### Who wants a "do over"?!

__Calculus____:__

**Here is how I explained it to my students**
For the rest of the semester, if you have a test score that you are not particularly happy with, you may have a "get out of a bad test score for free" card to use. BUT, you can only have TWO of them, no more, so choose wisely. Here is how that "card" works: for every problem you got wrong, you are to create another question similar to it (you cannot use a question from any material I have given you, it must be YOUR creation) and then proceed to make a video of YOU explaining it to me. Since I give video notes that I have created, they know what theirs should look like. I gave them some options of how they might do the recording (Touchcast, Educreations, or use an IPhone or IPad and have it record you working on some surface). For correct explanations of similar problems, they can earn back 75% of the points they lost on the test (for those questions). It must be submitted before the next test date, and using the excuse of "my (whatever) wasn't working" because they waited until the last minute would result in my telling them NMP (not my problem)!! The whole point is that they are figuring out the concepts well before the next test so that the new material we are currently learning makes sense (something about math being sequential leads to this concept being obvious).

The best part about this: not one complaint! No whining about "my grade". AND, they really seemed to "get it". They even answered the question when I asked "what is it that

**want?" Their answer: "us learning!" Yay! we are all on the same page! So all I have to do now is create a google form for their video links and get the cameras rolling (on their time, not class time)! Can't wait to watch some really good video lessons!***I*

__Stats__

__How many kids are dumber than me?__**Me**: Isn't that really what you want to know when you look at your tests? Don't you justify your grade to your parents with "I didn't do so great, but neither did anybody else"?

**Students**: heads nodding affirmation to my questions.

**Me**: So how do we figure it out? And what information should you be asking your teacher when they return tests?

**Students**: What is the mean and standard deviation? Wait, do you figure that out Torres?

**Me**: Of course! I teach statistics! That's the information I want to know too!

We had a great time figuring out z-scores and percentiles! And all I had to do was tie it to something they already know about--test scores, SAT scores and ACT scores. Who knew that Statistics was all around us already!? Who knew it was so easy to apply?!

I cannot tell a lie! I did!

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