Today was a mixed bag of, well, weirdness and frustration with some awesomeness.

I will start with the awesomeness. This morning at 7:15am, a learner from last year walked in and asked for help with his college math class. Loved it. I worked with him for about an hour (into the first class of the day) and he left feeling much better about his class and caught up. I felt really good about being able to continue to help my learners even after they have graduated and moved on.

The frustration was that classes can be so very very different. My one period is chatty. And by chatty I mean so talkative they actually miss out on some of the lesson because they just won’t learn to listen. They are great learners, but the social aspect is killing them. Meanwhile my other two classes have exactly the opposite problem. They are so un-chatty that they sit there in silence waiting for someone to speak up.

The classes were so polar opposite today, and I was completely flummoxed by it. I need to get the one class to talk about the math, and the other classes I need to get to talk about the math! Well, at least it is a common problem.

Finally, the weirdness. I gave my AP Stats class this lesson. Ch 4 – Tomato plant experiment But today we were learning how to calculate the fences for outliers and we applied the calculation to data set E.

The NSpire says the data point 20.2 is an outlier, as does the TI-84. But using the 5 number summary and doing 1.5(IQR) + Q3 and Q1-1.5(IQR) we get a fence of 19.95.

The value o 20.2 is not an outlier, but the graphing calculators call it an outlier. That is weird.  I used JMP hoping it would give me different values for the 5 number summary. Nope. Same as the graphing calculators.

This is some weirdness I can’t easily explain, but it did hammer home the idea we should not trust the calculator.

All models are wrong, but some are useful. George E.P. Box

AP Statistics

I was able to use this quote today in class. I was happy.

My learners were happy too, well, mostly happy. Well, okay, not happy at all at first. At first they hated me. They were struggling with learning how to do 1-variable stats, boxplots and histograms on their calculators in AP Stats. To force the issue of “you must do this, quickly and accurately” I gave them the following handout.

Ch 4 Box Plot Histogram 5 number summary INB 2013

5 data sets, all real, all crazy, none of them particularly easy. The golf data set is just weird.  These are clearly not data sets made up to look like something legit. They are data sets chosen to make them question whether or not their window is set right, whether they entered the data correctly. It forces discussion.

Then, they had this as homework.

Ch 4 – Tomato plant experiment

Yea, I am a demanding. They have until Monday, so I am not worried about the time it takes. But if they can’t make a graph, this is an impossible handout. If they try to get summary statistics by hand, they are in trouble.

I am interested to see what happens on Monday.

Algebra 2

Whew. This class started out brutal, but by the end of class they were ripping quadratic equations in standard form into (h, k) form in seconds. y=2x^2, or 3x^2, no problem. They were able to factor out the coefficient and jam on it. I was really happy about it. They struggled at first, but they were helping each other and they all had it by the end of class.

The assignment was to take 3 functions and put them all in the other two forms. Yes, the form for the second one requires the intercepts be written with complex  numbers. Are all functions factorable? Yes. Are all functions easily factorable? No.  Graphing will get them the intercepts? No. Graphing will get them the vertices at least? Yes, but (1,18) and (-3,-22) are two of the vertices. Not easy at all.

One thing I am really working on in AP Stats is the amount of notes, the lack of notes, and the engagement of my learners. AP Stats is one of those courses where the amount of vocab to assimilate is so huge, that it cannot all be done by activities. I have found that a mixture of activities and notes, and assignments and cycling back again helps tremendously.

I have the one slide from my notes today above. The literal, not figurative, brick wall between the two ideas of mean & standard deviation and median & IQR was very well communicated this year. The learners told me they understood. The formative checks I did supported that.

I still am not confident. Too many learners mess up this idea every year for me to take the face value word on it. I will be giving some questions over the next couple of days to make sure.

The re-writing of my slides to be word minimal, picture heavy, and discussion focused has changed how the class goes when I am doing notes, at least. I am happy with that aspect, and the learners I have asked directly about the notes have told me they are very useful and not boring.

That is something at least!

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PhD spillover

As an aside, the class on non-parametric statistics has taught me one thing that has impacted my AP Class. The structure I used last year as far as how I teach the content is right on the money.

In the PhD level class, we look at every problem first from the perspective of “is it categorical or quantitative” and then “how many variables”. So far, we have limited the decision to just categorical, non-normal problems (hence the non-parametric! label of the course.)

For Inference section, the course will be divided up into a. quantitative 1 sample, a1. confidence interval, a2 hypothesis testing; b. quantitative 2 sample b1. confidence interval, b2. hypothesis testing, etc. I think this structure leads better to the advanced level stats if they take a next class.

It is also the exact opposite of what our textbook does. Oh well. I didn’t use the textbook structure for 2nd semester anyway for the last 3 years. This just reinforces that decision as a good one.

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Finally, some lesson ideas I am working on.

That’s right. Funky dice!

On the left we have odd shaped, non-standard dice. Awesome. Are they fair? Not sure. On the right we have, yes, for reals, 5 sided, 7 sided and up dice. No joke. I once argued that a 5 sided fair die could not exist. Is it fair? Not sure. I am writing some lessons for expected value to take advantage of both of these.

I also received word from Robert at http://thedicelab.com/ that my order of weighted dice is coming soon.

Heh heh heh. That’s right. Real, honest to goodness (well, dishonest to goodness) weighted dice.

Expected value here we come! More later on this idea.

You are here! That is my AP Stats objectives board for the next few weeks. Today and yesterday we finished up Categorical data analysis with Relay Cards. It was very successful. I had many learners telling me they understood what they were doing, and they were saying this even though they were making mistakes in the reading of the problems.

I like the fact they were happy with the content and realize that making mistakes in reading did not mean they were not understanding. I need to figure out a way to make sure they realize that.  This is an issue I need to think on tonight and figure out a way to pull it together for them to think on as well.

I wish I had a magic phrase that everyone would hear and just go, “Aha.  I understand that making mistakes does not mean I don’t understand, it just means I made a mistake.”

I have RADICALLY revamped the notes I am doing as well.

This is the old PPT from the book. I am ashamed to say I used this for several years.

Here is my notes for this year, same topic. Yes, the quote is from Dr. Who. I will see how many learners pick that up.

Yes, there is still text on the slide, but less. And more of a story instead of regurgitating stupid words.

I am trying to do more of this type of thing with my notes instead of the “The definition of a relative frequency histogram is” blah blah blah. So far, the learners are telling me my notes are not horrible. They read less, they write less, and they are learning more and being much more quick in doing problems and asking better questions.

So far, success on that front.

Ch 3 – Relay Cards (made by Shelli Temple)

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Algebra 2

Whew, but Alg 2 is brutal.

We are working our way through a series of Quadratics. Today I introduced completing the square and justified it by needing the vertex form. All of the quadratics we have done are found here:

I started them off in vertex form, they had to provide intercept and  standard form. Now I am giving them standard form, and they provide vertex and intercept form (among all the other information found on the exploration sheet.)

They are hating me right now, but it is getting easier. The idea that ALL quadratics are factorable, is stressing them out. Some are easily factorable, some require the quadratic formula, but ALL are factorable.

Ouch.

I can’t believe I did it, but I missed a day. I did not post on Friday. I don’t have a real excuse, other than tiredness. I took a nap after school on Friday because I was running chains for the varsity football game. After doing it two games on Thursday I was beat by the end of school on Friday. That I took the nap in my classroom with the lights off just shows how tired I really was! Thankfully the custodian didn’t come in. That would have given him  a heart attack.

A quick recap from Friday to get caught up, and then today in a different post.

On Friday in AP Stats I did “bad graphs”. This is always a fun day, because we look at graphs and they learn what NOT to do. I tell them that if I ever see a graph that is 3D, or violates the Area Principle, or bad axis labels I will stop reading and return ungraded. We looked at lots of pics. Here are some examples:

And this is the assignment we did: Ch 3 – Analyzing Bad Graphs

This was fun day, but still informative and useful.

With three sections of 32, 34 and 35 in AP Stats  I am trying something different this year with teaching calculator skills. Instead of teaching the skills as I go like I did in previous years I switched it up and burned a day. It was not wasted though, it was highly productive. I have learners with Nspire’s, TI-83’s, TI-84’s, TI-89 Titaniums, and  Casio’s in my class. This variety is killer with a large class. If I had to teach how to do a 1 variable stats on all platforms as I go, class would grind to a halt pretty quickly.

With that in mind, I decided to do something radically different. I burned the day of content, and instead focused on “can you find these commands on your calculator don’t worry about what it means just find them.”

Calculator fill in blank instructions DOCX format

Calculator fill in blank instructions PDF format

I am okay with burning the day because I promised the class when one of them said, “But wait, I forgot how to do a 1 var stats!” my response would be, “Then I am here at lunch for you to show you.”  I will not spend any time in class teaching how to use the calculator, we will spend time in class USING the calculator.

There are links to video playlists, video searching, as well as some good resources for using the different calculators.

Will it work? Only some time will tell.

I know that I will be busy updating calcs over the next few weeks. That is super important.

Before I get into yesterday’s classes, because I don’t have a ton to say about them (they were a repeat of Tuesday’s classes, essentially) I learned something last night about AP Statistics in my “Applied Research Design and Analysis in Education I” also called “Non-Parametric Statistics 1” class.

What I learned is that AP Stats is absolutely a college level, advanced as heck, class. This class has two pre-reqs, neither of which I have taken. On the first day of class we did binomial stats, and last night we did Chi-Square Goodness of Fit. Next week we are doing Chi-Square test of homogeneity and independence.

That’s right. In the first three weeks of a 700 level class (that is the highest level that UNR has, I know that numbering schema’s differ from Uni to Uni) we are only covering topics that are taught in AP Stats. After 2 pre-req classes. That I didn’t take (thank you Dr. Quinn for that most excellent advice). I think the 4th week is where half of the content is new-ish.  The vocab and structure used in “Qualitative Research in Education” has also been a nice review of AP Stats vocab so far.

If you ever doubt that AP Stats is not a college level class, throw those doubts away. Bury them. Ignore them. AP Stats is absolutely a fantastic class for preparing learners for college.

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On to my classes. Just a quick update to the AP Stats exercise of “I have, Who Has” from my last post.

Three tweets radically changed how I will be teaching this and using this technique in the future:

Much better instructions, and I will be doing that in the future.

As for my Algebra Learners, who were frustrated with the whole speed dating exercise last class class? They rocked it out of the park and were excited at the end of class.

They are coming along I think.

Today was mostly successful for my learners! Yay. I am behind in the book keeping / grading department so I won’t talk about that much. This is always my downfall, and it is so easy to have a conflict of interest between grading effectively and timely, and time spent producing interesting fun lessons that teach! It is worse this year for me because of grad school on top of it.  Enough about the Failure, on to the Success!

#### AP Statistics

I did a “I have, Who Has” exercise with vocab from Experimental Design and Surveys. It was tough going at first. I screwed up the instructions and suggested they trade cards in the first period. Don’t do that. I think better instructions are:

1. You all have a card with a word, the “I have experimental design” for example.

2. Underneath that word is a definition. It is NOT the definition of the word above, but the definition to a different word.

3. Find the person who has the definition of your word, and then stand next to them.

4. When you are done, you will have a giant circle of definitions.

5. AFTER the exercise is over, I let them take the 4 pages of cards with them. Yes, I made copies for every single learner. Now they did the exercise AND there is a set for them to take with them with which to study.

The biggest problem I had when doing this is the learners looking to me for validation. One class today dove right in and struggled with it and asked me almost no questions. The other class, oh boy. They wanted me to validate every answer. Every time I tried to get them to validate the answers themselves they were frustrated and really tried to get me involved. I finally had to tell the class, “No.” Stop and think about it as a group.

In the end, both classes today were successful, but I wanted greater fluidity. One problem is neither class really had a leader who took charge. It is a work in progress for sure.

#### Algebra 2

This was a failure. I did @Cheesemonkey’s Speed Dating (and @mathymeg07 and I typeset files her files too) and was horrified by the lack of understanding of transformations of functions.

Sigh.

By the end of the period they were doing them okay. Not with any fluidity, not with any sense of understanding. I will do this exercise again. Absolutely.

They were frustrated and I was too. They wanted to do a table for every single function. Not good. By the end of class, I heard, “Aha, this is so much easier” and “Okay, I think I am getting it now.”

Next class we really need to get to, “Okay, Waddell, give me your best shot.” Eventually we will get there.

So, my lesson for tomorrow’s Alg2 class is already written. Do today over.

Time to grade more work again. Must get more things into gradebook!

#### Algebra 2:

My learners blow my mind. I assigned my Honors Algebra 2 learners to write their name.

Seriously, all they had to do was write their first name.

In Desmos. With functions.

Heh, I am evil, right? It gets worse. They had just taken a quiz, so we only had about 10 minutes left in class. I showed them how to create an account on Desmos to save their work. I showed them how to type in a function. I showed them my name in Desmos. And then I showed them that if they scrolled down on the main Desmos page, they would see, well, they would see some amazing art created by learners like themselves.

That is it. That is all the prep, instruction, training, or anything else you want to call it, that I gave them. They had to take this bare bones instruction, write your name, and run with it. I never showed them circles, ellipses, or any other function. They learned it all themselves. Here are samples of what was shared with me:

Skylar = 24 functions, Chloe = 10 functions

Janine = 35 functions and Gentry = 17 functions

Pretty representative. I did not say they had to use any special functions, just write your name. And I want to point out, I never showed them translations. They figured that out themselves by working with Desmos for ONE SINGLE DAY! Nice.

Then I started looking at the functions each person used. I noticed something very interesting that Chloe did. She only used 10 functions, but the “e” was especially interesting. You see, she did BOTH a domain restriction AND a range restriction on the same function.

See what she did there? Mind Blown. I am still stunned by the creativity she used with Desmos. When I asked her why she did both her answer was, “I was just trying stuff until it worked and looked the way I wanted it.” Genius. Necessity is the mother of invention.

Anyway, we finished up by rocking translations. They already had the main part of translations down because they played with Desmos. That was awesome. They are still trying to make things complicated, but I am almost finished breaking them of the assumption things have to be difficult.

AP Stats

I am short 40 books so far this year, so I need to do things to get my learners doing problems without the book. One way to do that is Relay Cards. This is how I play the game. I hand out problem 1. Everyone gets the same problem, so they can discuss it, but they have to write their own.  I use a magnet to hang the answer I previously made on the board. The learners can come up and read the key after they have tried it. Their answer must be the same as my key in meaning, not in words (usually. Sometimes it has to be exact, as in the probability section.)

Once card one is done, they come to me for card 2, and so on.

Having the key on the board keeps me free to answer questions and help while I hand out the new problems and double check the accuracy of the previous.

I just finished a set for Experimental Design.  I have other sets (created by Shelli Temple (@druinok) almost completely).

03 Relay Cards for Conditional Marginal Probabilities

Ch 6 – Relay Cards – normal models

These are a great way to get the learners talking about the stats, writing and working with stats, and the teacher does nothing but help, coach, and assist learners learn.

I like this activity greatly.

Some of my AP Stats learners figured out why I have been high fiving them every time they enter my room. I showed some videos about the placebo effect today, and a couple at the end of class commented on the fact that the high five is kind of like a placebo, because high fives are given for great things, and I do it on entering so it changes their mindset.

They got me. I hope they don’t spread that around, it would start ruining all my tricks.

Nothing spectacular today in class, just finishing some notes on experimental design, blocking, placebo effect and lurking variables. In Alg 2, I gave them a quiz that had them really thinking. They had to graph the 8 parent functions, and then also tell me which ones had all positive y values. Which ones were always increasing, or had a vertex at (0,0).