Nov 062014
 

I haven’t posted in a while, mainly because I am just so happy with how my classes are going. I will focus on Alg 2 here, because these awesome learners are just knocking my socks off.

I am in the polynomial unit, knee deep in graphing, and increasing, decreasing, relative mins, relative max’s, absolute mins, etc. This is the problem set we were working on today in class:

problemset

Here are the questions I ask (docx format) for every single graph, from lines all the way through sin & cos at the end of the year.

Yes, some of these are going to be Does Not Exist. That is okay. Just because we don’t need to think about asymptotes with cubics does not mean we shouldn’t ask about them.

A little back story before I say something about my learners. I used to teach the textbook. I admit it. I sucked, horribly. My learners did not connect anything with anything and they did not see how to connect topic from one unit to the next. I was frustrated. So I first came up with my list of functions in (h,k) form, wrote it on my board and changed how I approached algebra.

2014-08-10 15.43.46

That was a win. But, then I was frustrated because every time I changed the graph, added an exponent, I had to teach a new set of vocab, but everything was the same; so why was I teaching new stuff? Why couldn’t I teach all the vocab up front, and then just explore the heck out of each function family?

Short answer was, I could. So, I did. That is where the form above came from. I introduced it last last year, and used it and modified it and tweaked it and the learners responded.

Enter this year, this class. I have everything set on day 1. We entered the year thinking about connections and planning our math and discussing end behaviors of lines (wow, that was easy, hey, they are always the same!, etc). Then quadratics, and we completed the square to get vertex forms, and we factored, and saw how intercept, standard and vertex forms were all the same function, and and and.

Enter polynomials.

We have done them from standard form, and done the division to get intercept form, we have broken these guys down every which way. I have tossed them fifth degree and fourth degree polynomials, they didn’t even blink. “Oh, so this just adds a hump to it.” I have explored more in polynomials this year than ever before.

And, since it is a constant review of prior material (“If this works with quartics, will it work with quadratics too? Yes”) I am constantly cycling and eliminating the mistakes my learners made in previous sections and on previous exams.

Which brings us to the problem set above. That is a killer set. The 4th and 5th are tricky, and they struggled. Until one of the class members said, “Don’t all we have to do is distribute them and so it is just a bigger distribution problem?”

Done. And. Done.

Now, of course there is a nicer way to do it. Substitute “u” or some other variable in for (x-3) in the fourth problem so you are multiplying binomials first. It saves time. BUT, it was not necessary to show it. They know distributing, so distributing is what works and they rocked the socks of of it.

So, why have I not been posting much? Because I have been enjoying the heck out of teaching. These learners are taking these ideas and running with them.  And I love it and them.

Sep 112014
 

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

2014-09-11 12.28.03  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:

TI-84NEWvs.  TI-84OLD

 

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: calc directory

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.

—————-

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.

functionfun  File can be downloaded too.

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.

Sep 102014
 

 

highfiveToday it happened! WooHoo! I was completely excited today. I earned the high five from one of my learners. On the 20th of August, I noted that one single learner had not given me a high five, and in fact that she refused to give me a high five. Well today, after working really hard all period on rational exponent problems, and rocking the heck out of the problems, she gave me a five at the end of class.

She had a giant grin on her face, she was excited because she was making connections and understanding, and she was into it. I finally earned the five because she realized I was not leading them along, I was not tormenting them by asking questions all the time, they were learning BECAUSE I was asking questions all the time.

Yay.

I also had a different learner walk in and tell me she was reading my blog and realized the high fives were a placebo to make them feel good about math. I smiled, told her yes, and high fived her. She laughed.

Did we do content today? Absolutely. Algebra 2 was rocking the rational exponents. AP Stats was starting conditional and marginal distributions. But today was awesome because of the relationships I am building with my learners.

It was a GREAT day.

Sep 042014
 

questionmark via

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.

——————-

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.

Sep 022014
 

success

 

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!

Jan 172014
 

[I really need to return to blogging. My lack of focus on reflection has hampered me this semester, and I need to fix that. To that end, I am making a commitment to blog and to jog. Those are the foci this year of the ellipse that is my world.]

Yea, how often does that happen that a class gets excited about logs? It has not happened to me in several years, but this year I found a way. We started the second semester with graphing again. We have a standard list of things we look for, identify, and document on every single graph. The list is:

Domain:

Range:

Asymptototes (vertical and / or slant):

Minimums:

Maximums:

Vertex:

Y-intercept:

X-intercept:

End state behavior:

Every graph we do, we have to document all of these items. If we graph a line, most of the list is “none” but it creates the connection between all the graphs. Every graph has the same questions, it is just that some of the graphs / functions do not have those features.

So, I am doing this file on Desmos, and we are documenting. They have done all these as homework, so really we are checking answers and ensuring learning. Then weird things happen. They notice the symmetry of the inverses.

Nice.

Then they ask to see the graph of the line of symmetry. Even nicer. THEN! OMG. We put the translation into the h-k form of the line, and we see the translation of the line of symmetry.  [Okay, seriously. If you are not using the h-k forms to make connections, why not. See This post, or This post or any other of the several posts I have on this topic.]

And then I graph the exponential. …. …. They know there must be an inverse, but nothing we have done in class looks like that. …. And then, because I have the list of all the h-k forms on the board, someone asks, “Is that what the log thingy is for?”

And now they have a reason to learn logs. They are intrigued by logs. They are asking questions about logs. Because EVERYTHING in math has a forwards and a backwards, addition has subtraction, squares have square roots, and exponentials have logarithms.

They are interested and inquisitive about a topic that normally is not approached this way. I have done something good I think. Only time will tell if I can continue that on this topic.

Feb 012013
 

MyFavFri-t.gif

 

Yea, that’s right. I just had 2 classes in a row teach themselves and others how to complete the square with circles and ellipses. How did I accomplish this miracle, because I really do consider it to be a miracle.

In my Advanced Algebra Class we have the following problem called, creatively enough, The Lost Hiker.

Suppose you need to find yet another lost hiker.  Fortunately you have information from 3 different radio transmitters.  From this information you know that he is:

25 miles from Transmitter A

5 miles from Transmitter B and

13 miles from Transmitter C

These radio transmitters are at the following coordinates:

Transmitter A – (25.5, 7.5)

Transmitter B – (-2.5, 3.5)

Transmitter C – (6.5, -11.5)

Use this information to find the coordinates of the lost hiker using the intersections of the theoretical circles.  Show your work below.

There are 4 major steps here; 1. Write the equation of 3 circles, 2. Expand the circle equations, 3. “Collapse” the circles through polynomial subtraction to 2 lines, and 4. Solve the system of lines.

We worked on these for 3 days. These problems are huge and complex, and one single minus sign incorrect means the whole thing works out wrong. But they persevered for three periods in class, until every single learner could do 3 unique problems on their own, and get the correct answer.

I have an excel spreadsheet programmed to calculate an infinite number of nice problems with solutions. The solutions are posted on the board w/ a magnet, and I walk around with a bunch of problems in my hand. Get one right, here is another.

Well, at the end of 3 days, I wrote the following equation on the board and asked them to turn it back into a circle.

x2+ y2 – 6x + 8y = 12

It took them all of 1 minute to have the entire class finished. One learner who failed Alg2 taught the rest how to do it because it was, “Easy, just take the -6, divide by two, because when you square it you have two of them.”

Then I wrote 5 problems on the board.

x2+ y2 – 4x + 12y = 10

x2+ y2 + 2x – 10y = -8

x2+ y2 – 4x + 7y = -20

2x2+ 3y2 + 6x + 15y = 0

4x2+ 5y2 + 16x – 100y = 27

The first two were just some more practice. The question was asked, “Can we have a decimal?” When the answer was yes, they didn’t bat an eye.

The last two did make them think, but they had the factoring done correctly on the left side, they just needed a little hinting for the right side of the equals.

Why did it work so nicely? I think because they really were engaged with the lost hiker problem and honestly worked them. And they worked. They agonized over why they didn’t get the correct answer. They gave me dirty looks, and when we found the minus sign they missed or the extra number they wrote in, they were angry at themselves.

But they persisted! It was a thing of beauty and I loved it.

When they did the completing the square on their own, with only some gentle nudging from me, I told them how proud of them I am. They needed to hear it.

Heck, they EARNED it.

Dec 182012
 

My AP Stat class has been frustrating me the last couple of weeks. They have been very blah. Not interested in being aggressive in their learning, not thinking about the formulas for stats, and in general willing to just sit there and expect the knowledge to jump into their heads with no effort.

It came to a head last week where we did a problem as a warm-up, then did two problems from homework, and when I handed out an AP FRQ, they all looked at me as if it was the first time they had ever seen the problem when in reality we had just did three of the identical problems prior.

Yea, I was frustrated.

But, instead of freaking out, I started asking them questions, mainly, “Why?” It turns out they were feeling overwhelmed and frustrated too. The formula sheet was a complete mystery to them, the concepts where going over their heads, and they wanted to freak out as well.

So I burned a day going over the formula sheet.

Guess what, no one has ever taught them how to understand what is on the formula sheet. That should not be a surprise to me, but it is. So here is a sample of what I did:

image

7 elements in the definition of mean are; xbar, equals, sigma, x, i, n, and divide by. I made them explain what each was, and the fact that the equals sign can mean different things was the toughest. So was the fact that the ‘1’s’ in standard deviation are different. We really discussed what these things meant.

Each formula / equation / definition has the number of elements indicated, and a “Hand or Calc?” statement next to it. I didn’t want them to understand the formula and then forget they are supposed to do standard deviation in their calc not by hand. But they need to understand the formula too.

No one has ever done this with them in any class before, this was the first time they have had to really understand a formula sheet. They hated it. They struggled, they discussed, they asked questions, they growled and shot me dirty looks, and EVERY SINGLE person said it helped them understand the formulas better. This, in turn, means they understand the class better.

Success is a beautiful thing when it works. This worked.

Here is the docx if you want it. It is formatted for use in Interactive Notebooks.

Nov 042012
 

A little background before I explain what was said to me.

I was part of an IREX grant program that brings teachers from other countries to the US to learn about education, etc. My part of this was to host a teacher from Jordan for 6 weeks in my classroom 2 times per week, and mentor him on mathematics education, technology, etc.

It was a great program, and I learned a lot from interacting with Mr. S. and I think we will built a relationship that will continue in the future for the benefit of us both.

With that said, on his last day in my classroom he told me something that really changed how I viewed myself and my classroom behavior.

He said (and I am paraphrasing here) that in 2008 he wrote an essay for a teaching award in Jordan and in the essay he said he wanted to be the kind of teacher that leads learners to the result, but doesn’t tell them how to get there. He wanted to be the kind of teacher that creates problems for the learners to solve, and lets them work through the problems together, and the learn along the way how to solve other problems because of that. And then he said he wanted to be the kind of teacher that has a mutual respect in the classroom that allows for a good exchange of ideas between learners and teacher.

I said, of course, I think we all want to be that teacher. To which he dropped the largest complement I think I could ever get.

Mr. S. then said, “I wrote that 4 years ago, and I have never seen that kind of classroom until I had the opportunity to sit in yours. You are that teacher I said I wanted to be several years ago.”

You know, it took me several hours of thinking of that to really realize just what he said and what it means to me. I don’t think I have ever had someone say anything so nice, so supportive and so mentally Earth shattering to me.

I have never considered myself to be the teacher he described, but clearly this veteran teacher from Jordan, with many years of experience, and national awards in his own country thinks I am. And he thinks it because he spent 2 days a week, for 6 weeks in my classroom.

How do I live up to that? It still shocks me, and it was 4 days ago he said it. I guess I have never thought of myself that way, but maybe I should start. So I can grow, develop and continue to improve.

Or does that improvement come because I DON’T think it is true? I am not sure, but I am still blown away.

Thank you Mr. S. for making me think of myself in a very new way. I hope I can return the favor someday, because you have impacted me tremendously.

Aug 022012
 

I am rather late to the gate with these thoughts, in large part because I drove (well, rode my motorcycle) to St. Louis from Reno, which took 4 days to get home. More on that in a different post when I do the math from the trip video.

If you ask one of the teachers from my department about me, one thing almost all of them will say or agree with is that I hate paper. I hate paper note, paper suggestions, paper anything. I ask my department to submit everything to me through email, because I lose paper notes, throw away binders, and just downright hate keeping track of paper.

With that said, I admit I took 11 pages of notes, kept track of them through 4 days of a conference, and 2000 miles of motorcycle riding. This event meant that much to me, and that is saying a lot.

I am going to start on day 1 and work through all my notes. I am composing this more for myself than anyone else. Like all of my reflective posts, it really doesn’t matter if anyone else ever reads them. This is the place where I reflect and compose my thoughts for my future self (because if I do it on paper, it gets thrown away!)

Wednesday – A personal exploration:

To say I was nervous on Wednesday would be an understatement. I had just ridden 1900 miles over three days to meet with a group of people I had never met and only talked to through twitter, emails and blogs. Yea, I was nervous. You see, I am an incredible introvert. I attended a NCTM conference my first year as a teacher with 2 other teachers from my school. At the end of the conference, I had spoken with exactly 3 people in a meaningful way, 2 of which came with me. I attended sessions and sat in the back. I wandered the floor and just kind of nodded and said the minimum I had to.

At that point I realized that if I was going to become a half way decent teacher, I had to overcome this fear of putting myself out there. Even riding my motorcycle to the event is a sign of my hesitance to talk to people. I was riding alone, where the only conversation going on was inside my helmet. If I flew I might have to actually talk to someone (although I usually don’t when I fly, either.) This has been my most difficult challenge as a teacher, because it is so incredibly easy to just stay in my room and never reach out. I used to actually have it on my to do list every week, “Make contact with other teachers.” I don’t any more, but the tendencies remain.

So I walked into the hotel dirty and sweaty from riding in the heat and the first thing that happens is Lisa H. tries to give me a hug! Okay, ice broken, I can deal and grow.

After a shower so I was feeling like a human being again, a group of us walked up to the nearby mall and had a nice dinner at a southwestern restaurant and chatted. It was nice, and it gave me a chance to get to know people in a very casual way. It definitely was the right thing to do. I did think about staying in the hotel and sleeping, but decided otherwise. I am glad I did.

The actual events of the week after the break (warning it is long & detailed):

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