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.

Today was my quiet day, only two classes. But, I was busy all lunch upgrading my learners calculators!

Yes, that is the pile I have done today at lunch. About 5 learners have already come in and picked their calculator up, thank goodness. I am a bit nervous having \$1200 of calculators sitting on my shelf, especially when they are not mine!

This is one of the things that we don’t often realize takes up a ton of time. The learners don’t realize that these things have operating systems, and that the operating systems change from time to time. When learners are buying calcs on eBay (which I always encourage because TI=ripoff) the calcs often come with out of date OS’s and are lacking functions that truly make the calc useful.

For example, look at the following two prompts, both come directly off of the TI-84:

vs.

Which one of these screens would you rather see when typing in information?  Me too. The left one is much more friendly.  I say at the beginning of my class, every day for the next two weeks, “You want me to make sure your calculator is updated. Please come see me.” We had a 2 minute discussion of what the current versions were the other day when we were talking calculators too.

I think this is the biggest change so far this year on the calculator front. Last year, I had 5% of my learners ask me to update their calcs. This year, I am up to around 40% already. That is worth it. I am really annoyed in May when someone says, “Yea, I knew there was something about updating, but I never bothered.” That person probably is not trying for a 5.

How to make this process easy? For the NSpires, have 2 4 port hubs with cables plugged in. This allows you to shove out updates to 8 similar calcs all at once using the Teacher Software.

For the TI-83 and 84’s you have to update one at a time, but it is fairly quick using TI-Connect.

Oh, and it helps if you have a directory that looks like this:

All the current OS update files, old update files (bcs the NSpire must be updated to 1.7 before you can take it to 3.9), 83, 84, 84C images, etc. I download all the new files when they update (2 times a year for the NSpires, really TI?)

What a pain in the butt. But it helps my learners.

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AP Stats:

Not much happened today. It was a continuation of yesterday (same content, different period). Tomorrow is my 3 in a row stats day.  I am going to challenge them with some bad graphs and another short relay card race on contingency tables. Then, moving on to 1 variable quantitative stats. Yay!

Alg 2 Honors:

It was an AMAZEBALLS Day.  We did this exercise with one quadratic function. Just one. But the conversation we had was so amazing. I gave then one, factorable function in Vertex form. Then we started going to town. The “wow, look at the connection here” and “oh, I get it why it was this!” and “wow, this is all the same stuff!” was terrific.

The homework was to do one more.  The future of this looks like doing another one. Then, I will give one in standard form, and we will have to teach completing the square. And they will get one that has imaginary roots, and I will discuss imaginary numbers. This one page will get used 200 times throughout the year to deeply understand the functions and the connections between functions.

And the day was awesome because I said about 20 words, and my learners said about 200. I am shooting for a 5% ratio tomorrow.

I want to do these in order of their occurrence today because it set the tone for me. I was giving an exam in AP Stats (hence no new info about AP Stats) and at the end the exam a learner handed me a note. It was very personal, but it essentially said “please forgive me if I seem out of it this week, a person close to me passed away this week a couple of years ago and I always have a bad week around now.”

Wow.

I sat there thinking about the struggle this learner has this week, the memory of the passing, and the fact that teaching is not about content but about the relationships. This is a concept that I did not have 8 years ago. I jumped into teaching thinking I could teach math and rock the content like no one else.

Today I know better. Today I know I know content; I am confident in my content; but I KNOW for a fact that all of that knowledge is useless if my learners do not trust me and I don’t trust them. I have not always had that knowledge. I have made mistakes on this issue in the past.

By the way, I thanked that learner for communicating with me. I will watch this person closely to make sure there are no problems. I owe  that much for sure.

Alg 2

Then I introduced rational exponents later. I put one question on the board.

“Given that you know what 8^(1/3) means. Given that you know what 8^2 means. What do you think 8^(2/3) means?”

I let them think about it for several minutes.

Eventually, one learner broke it down into two parts, cube root of 8 is two; two squared is 4.

Excellent. We discussed why that works, we discussed what happens if the order is reversed.

Then we rocked some complicated problems I put on the board.

Yes, they made mistakes, but the mistakes made were procedural mistakes. Mistakes about not distributing to all terms, or multiplying fractions wrong, or moving all terms instead of only the term with negative exponent.

I am telling you, this was absolutely successful. I did not approach rational exponents like this last year, but it works. Let them create the meaning.

Never say something a learner can say.

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.

Every single day since the beginning of school I have stood at my door and high-fived every single learner who has walked into my room. No joke. If I miss one because I was talking to someone, I go back and find them. Well, all except for one learner who gave me a funny look and said “no”. She has told me “no” every day since the beginning of school. That is okay. She told me today there is a chance I might earn a high five from her; just a chance. That will be a good day when that happens. I am looking forward to it.

Why do I do it? Last year I did it for a week to one class. One day I didn’t. I heard from several learners that they felt I had let them down because I didn’t give them that five.

I really want to make my class special. They should NOT walk into my classroom like they walk into everyone else’s room. Coming into my room should be something special, something unique, and something to be looked forward to, not despite the fact it is math, but BECAUSE it is math. High fives are one way I can make that happen.

#### AP Stats

I was asked on the twitters what I do for warmups in Stats. I use the Barron’s MC AP Flashcards as my warmup. Everyday the learners come in and there is a question on the board. I use my Elmo to project it, all large and in charge, and they have to come up with a solution.

One idea I stress is that these ARE the MC questions review for the AP exam. From Day 2 of the year, we ARE prepping for the AP exam and they need to focus like a laser on these question. Every learner must commit to an answer, every learner must decide why it is that answer and be able to defend and convince. It has worked well for me. They take it seriously, we have discussions about strategy on questions they don’t know, and we construct knowledge using them. I am happy with that.

#### Algebra 2

We are doing parent functions right now. But not in any way most people do, I think. Every function we go through this page and answer all the questions, even the ones that have no answer.

We are going through all the parent functions and detailing all the info. Then, after that, we will extend the understanding and go deeper with this document:

By the time they go through and can do all of this for every function on my wall, they are golden in almost all the algebra they need.

This connection between topics, is crucial, and I am excited to start doing some modeling with them. I will have the time because of the time I get back later.

Want to watch an ap stats classes eyes glaze over? Start talking to them about stratified vs. cluster vs simple random sample vs judgement sampling.

photo via

Really. Pull the powerpoint from the book, throw it on the screen, and watch the light dim from their eyes.

I didn’t do that. …. This year. I didn’t do it last year either, but I was not totally successful in this endeavor. Last year I did some activities AND showed the powerpoint. Not this year at all.

Last week on Thursday and Friday I showed the powerpoint I created that had the theory, the background and the why we are learning the vocab, then they looked up the words themselves.

Today we did the Jelly Blubbers activity. Jelly Blubbers teacher handout and the Learner Notes and a   stratified blubber page I don’t hand out.

It drove the point home that judgment sampling is wrong because it creates bias, and that for certain things, stratified is terrific! We had a short discussion of why we need different ways to do the sampling, and what benefits are achieved by sampling.

This was the progression and order we did it in. The bias in the judgement sample is clear. They really liked the larger blubbers over the smaller ones.

All in all, it was a great day in AP Stats.

Algebra 2 was more … difficult.

There is a lot of vocab to go through, ie. Domain, Range, function notation, set notation and interval notation, etc etc etc.

We spent the entire period learning those. I really feel like it was not successful, HOWEVER, they were involved and active in the discussion about what the different ways of representing domain, range and the other ideas were. I think they learned useful things today, it just was not as an active day as I would want.

I will work on that tomorrow.

Can I tell you how much I love my learners! A sophomore girl walked into my classroom this week with these shoes and and said, “Mr. Waddell! Look what I found this summer!”

How awesome are Calculus Toms. If you know or have any influence at Toms, tell them to make them again! I am so bummed that they are not for sale anymore. This learner found them in a used clothing store and was completely excited that she found math shoes. I must be doing something positive in the classroom if my learners from last year are this excited about shoes.

As far as my classes at the end of the week, they went well. The first week of school was successful. My algebra 2 learners are crushing the rules and can solve any literal equation I through at them. This means that they CAN solve any equation they need to all year long. Tuesday, I connect those dots with them and then move into parent functions.

One thing I am very proud of is my syllabus this year. I completely redesigned it, and I incorporated Remind into it in an important way.

These are pages 1 and 3 of my syllabi, with page 2 being the signup sheet that Remind prints out. I have almost every single learner signed up for Remind in my classes, and even some parents. I am really excited by that level of commitment. What makes me even happier is that I heard from one learner that every single teacher she has is using Remind.

At that point the teachers are being consistent and even in their approach to communication and usage of the tools for communication.

One thing that I have done this week is record one of my classes. It wasn’t hard. I took my old cell phone (a Motorola Mini) and created a super high tech platform for holding it.

No, really. Super High Tech

That is it. Just a paper cup, cut with a slit and room for a power cord if necessary. I recorded a class on 720px and got 50 minutes of video in a 4gig micro SD card. I will move it to the laptop, delete, and be ready for the next recording.

One thing I want to do is regularly record and observe my classroom. This will give me a way to observe my class as an observer would. What will I see? Not sure yet. But I will be using those videos as part of my reflections. I can not show the videos online, but I can describe and use them to change my teaching.

All in all, a great first week, some very positive response to the syllabus, to the lessons so far, and the development of the classes.

Excellent.

My 3 rules for Algebra. Meg Craig made them pretty, I framed them, and went over them in Alg 2 Honors class last period.  Today we moved into Literal Equations. That is how I teach the rules and reinforce the rules, with literals.

Typically, these are one of the hardest things learners to grasp and wrap their head around. I am taking my physics book from college to the board and writing down formulas from it and from chemistry. Go.

And it was tough. Learners who can tell you that 25-25 is zero in a heartbeat will balk at v – v is zero. So there is a lot of coaching an patience as they work through the ideas of “The Rules” and the differences in how addition and multiplication act with respect to distribution.

It was difficult, fun, and frustrating but they are getting the concept of solving equations, all equations, no matter what they look like.  I will spend one more day, so that means 2 and a partial period on this. I think it is time well spent.

AP Statistics

The 6 W’s a H:

Who, What, When, Where, Why, by Whom and How. This is the introduction to thinking and reading scientifically. ScienceDaily.com is my friend during these couple of days, and the biggest stumbling blocks were finding the variables (the What) and the population of interest (the Who). I have added a 6th W, “by Whom”. I have found that helps with the learners wanting to put the author’s name in the “Who” spot. If they have a place for them up front, they can’t be part of the “who”.

Yesterday’s assignment was to grab one article from ScienceDaily and detail the W’s and H.I don’t think one learner did it fully correctly, though. I know that every single learner I helped one on one did not (and that was most!).

To help, in class we did a couple of problems from the textbook, which are … okay. Nothing earth shattering; they are short, and the learners can use keywords to figure out the answers quickly. Then we did 1 article from ScienceDaily on the board. I projected it from the web and we went through it, finding all the information. That helped too.

Finally, I handed each group of 2 an article and had them discuss the W’s and H together. I circulated and answered questions. They then swapped articles and did it again.

At this point, they have read 4 to 5 different articles from ScienceDaily. That is 4 to 5 more than they have read in the past. Reading these articles is a different skill than reading the fiction that English teachers have them read, and I think this is useful to getting the learners to be in a Stats frame of mind. I hope so at least.

The assignment for next class is to redo last night’s homework. Cross it out, start over, and do it right.