[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.

Oh what a difference a class period makes.

So earlier today on my prep I posted about the steps I was making in changing / modifying the culture of my classroom. And let’s be honest, I was proud of the conscious efforts I was making in changing the hearts and minds of the learners.

And then the last period of the day hit and I was crushed. The class is working on spreadsheets and financial mathematics and is being introduced to compounding interest through the calculations the “hard way” before we do the formula.

These can be tricky, and if one cell is off by a little bit, the spreadsheet numbers go all wonky and you KNOW something is wrong.

So after working in pairs (it was a group assignment) all period, and I was circulating over and over again giving prompts and suggestions (but never fixing) about the thinking behind the sheets, one female learner asks to stay after class and work.

No problem. I would love to help her I say.. This Senior Female (let’s call her S.F.) says to me after everyone leaves, “I try to remain quiet in class because I feel like I don’t know this stuff as well as others and I just like to think. I don’t want to bother you that much in class.”

That shattering sound you hear is my heart breaking.

So S.F. doesn’t like to speak up in class because she feels like she doesn’t have as good of knowledge as others, and S.F. doesn’t like to “bother me”. Did I tell you that S.F. is female? Did I tell you she is African American?

Heart breaking.

Oh, and what was she doing wrong? Nothing. She had one small error in a spreadsheet covering 40 rows of compounding annually.

That “Status” thing that Ilana Horn was talking about at TMC13? There it is.

I can do all I want to change the culture of my classroom, but S.F. is bringing in a status of “not good enough” and “bothers teacher” and she has learned this over 12 years of classroom time.

What chance do I have to undo 12 years of learned status?

That shattering sound you hear is my heart breaking, again.

I think Ilana’s book is rising to the top of my must read pile. As well as her articles (if I can get my hands on them). This is too important to leave it alone.

—————–

picture via flickr

At TMC13  I attended Ilana Horn‘s (@tchmathculture on Twitter) presentation on Culture in the Classroom. I didn’t write much down during the talk because I ended up thinking so much about the things she was saying and it is hard to describe the video we watched in words.

But, there are some pretty serious take-aways from the presentation that I have acted on and implemented. First, the serious topic of how much culture is created by you (the teacher), how much culture is brought to you by the learners (from prior teachers) and how much culture is created by the learners independently is very eye opening.

Think about that for a second. There really are three independent sources of the current classroom culture in our classrooms. I have certain expectations; the learners have learned how to “play school” in other classrooms; and finally the way they interact with each other independently of what my expectations and other teacher’s expectations are all mash together into creating the current “Classroom Culture” of what happens in my room.

I had never really looked at it in this three part way, and definitely not considered that my expectations are only 1/3 (maybe!) of what is going to occur in my room.

Eyes opened. Jaw dropped. Now what do I do?

….

Enter some serious thinking and changes to how I opened the year. I wanted to open the year in a totally different way, so that that culture could be more of my own expectations and less of what other teachers wanted them to do in prior years.

Some other things I am aware of and have done.

Seating charts – I used a totally random way to construct them. I handed out cards at the beginning of the year with A – 8 on them. Each number was a table number, and that is where they sat. Seating was completely random, they recognized it, and they commented on it.

Next, no syllabus until middle of week 2. I didn’t talk at them. They worked. They worked bell to bell on interesting and engaging lessons. They noticed and commented on that too!

So far, in all of my classes the homework turn in rate is around 95%. That is exceedingly high for my school (very high FRL rate). I think it is because the homework makes sense to them. I have been asking them to create their OWN problems and solve, not do mine out of a book.

Finally, and most importantly, I have been overly encouraging of questions, noticing, wondering, and thinking. Everyone has gotten involved. Each table must come up with a solution or a question or a noticing, so they need to discuss at the table level and class level.

I am hoping this encourages all learners to take more possession of their own learning. Only time will tell at this point. I will say thinking about this has made me add a tag to my writing. Culture. I think it does need to stand on its own.

I am trying a new approach to my first week of classes. Instead of the usual first day where we hand out syllabi, and go over policies and procedures, and bore everyone, including me, to death I am trying something completely different.

First off, I am keeping my room set up in groups. I have 6 groups of 4 each and 2 groups of 5 each for a total of 34 desks. That is my largest class so far, so I will keep that arrangement. I did this last year for the first time, and it was successful. I am working on making it more so this year.

On each table (I think of each groups of desks as a table) is a paper that says:

Please fill out and share with the individuals at your table. Once everyone at the table has shared, raise your hands so Mr. Waddell can pick up this paper.

Table # ________________________

My name is: _______ I prefer to be called: ________

3 things that make me interesting are:

1. ___________________________________
2. ___________________________________
3. ___________________________________

Last year I realized that even after a couple of weeks, some of the tables had not even really shared their names. I am forcing the issue with this file (in word docx format). There is space for 5 learners to write their names since I have 2 tables of 5.

Next, in my Algebra 2 class, they are getting a problem. Here it is, in its entirety.

I need new phones for my house, and we are currently not on contract so we can switch to any company.

I need 2 smartphones and a plan to go with them.

Your task:  In your groups, create a poster that lays out the 2 year cost of my 2 new phones and plan. Each person’s handwriting must be represented equally on the poster for everyone to receive full credit. Decide which plan I should get, and explain why clearly enough that my non-mathy significant other will understand. Graphical depictions of the costs would be helpful.

On the desks will be a poster paper, some markers, and that is all. Of course, I have more information for them, and when they write down a question that needs that information to be answered, I will give it to them. Not until they ask AND have a question written down and ready to be answered will I give it to them, however. If you want that file, it is also in docx format.

Finally, and this is the one I think I am most proud of as a first day lesson, is the literal equation solving review for my Algebra 3 course. I am also going to be using this in my Alg 2 class as a day 2 review.

Start off by using the first 6 minutes of this video:

Right, the “game” they propose is AWESOME. The fact they then also show how they are creating equations to solve is amazing, and if we push the game into the CCSS model and require the writing out of steps to accomplish, then we will end up with something REALLY cool.

So, I created this document (yup, in docx so you can edit it as well).

The first page is explanatory and the link. The second page is the “game” as it is presented by Numberphile, and the third page is 7 literal equations from the AP Physics formulas sheet.

My goal is to have the learners in 1 70 minute class period work together, write out the steps to the game in each case, and then apply those steps to something that learners normally have a HUGE difficulty with.

Why am I doing this? I want to set the tone for the year that the learners need to write, they need to discuss, and they need to ask questions. These are challenging tasks that require the learner to process and develop ideas, not simply puke up something that I have told them previously.

That is my goal.

Will it work? I don’t know. I will find out on Monday.

I am going to summarize the conclusions and hiccups my learners had in their AP Statistics projects. One thing that I took away from this process this year was next year I the learners want to be more involved in the project requirements earlier in the year. I need to leverage the technology they will use in real life all year long, not just at the end.

The downside to this is that it will take the place of some of the technology they will use on the AP exam. I am not too upset by this, however, because the exam is focused on what statistics they know, not whether or not they can use a calculator. I think it will be a good fit, and allow them to be even more successful in DOING statistics, not just talking about statistics.

With that said for next year, the results this year were very interesting and in some cases very frustrating.

I will put all the results below the break because it will be long.

Tonight we had a discussion of “5 Practices for Orchestrating Productive Mathematics Discussions” (B&N, Amazon) on Twitter, and I wanted to post the Storify here. One caveat, one of the members, MrHodotNet is protected so he didn’t show up in the timeline. I copied and pasted his contributions at the end, but they are not in order.

The link to the Storify.com transcript is here.

The transcript can be read after the break.

The AP exam is over, finals are in two weeks, and my learners have been busy bees constructing knowledge for the community.

That is their goal in this post-AP Exam stage of the class. Their charge and challenge is to do something that constructs, creates, or consolidates knowledge for the school or the community. Below are the projects that have come out of this as examples, in no particular order.

Group 1:  This group took last year’s project of finding out which is the cheaper grocery store (Smith’s, Walmart, Raleys and Scolari’s – they found out Smith’s & Walmart were the same) and are extending it. This year they are seeing if last years results are still true, AND then extending the matched pair to a two sample to compare last year’s prices to this year’s prices.  The manager of Smith’s is very interested in the outcome of this.

Group 2: Does Walmart change their prices based on the income level of the zip code the store is located in? So far the results show no, but that hasn’t been finalized yet.

Group 3: Are high school students prepared for disasters. This group wanted to do something related to the zombie apocalypse. I used my veto power. Now they are back down to earth doing a multistage cluster & stratified sample of the school.

Group 4: What percent of our seniors go out of state for college and how does this compare to previous years? The trouble is, our counselors have never kept track of this! There is no data base or spreadsheet for previous years. So, this group had to collect the information (census) from all the seniors, build a spreadsheet to house the information and then compare vs. the numbers we were able to get from our local university.  When they are done they are giving the results and database to the counselors to maintain.

Group 5: This group of 1 person originally proposed a nationwide survey. I talked them out of it. Then they proposed a city wide survey. Again, talked them out of it. There wasn’t enough time to accomplish such aggressive projects. In the end, the person narrowed the idea down to “what impacts graduation rates the most, income or poverty in Washoe County School District?” This is achievable. The group is collecting information from census bureau data and grad rate data and then doing a regression test on the data. There are some interesting results so far.

Group 6:  Are freshmen aware of or comfortable with basic science based on their middle school and freshmen biology class? They took questions from the science standards and talked to science teachers to create a short quiz based on the standards. They did a random sample of freshmen classes and then sampled randomly 5 from those classes using a deck of cards. The sample is VERY small, but the process is good.

Group 7: Do gasoline prices fluctuate together in an area at the gas pump AND do the prices move with the price of light sweet crude on the international market? Whew, big project dealing with daily checking at 7 gas stations and market prices. They have a very interesting topic, and the mechanics of it will require a regression test.

Group 8: Another one person group, but this time the learner is interested if course “difficulty” can be quantified. The learner was upset at being told that certain classes are harder than others and therefore should not be taken because it would hurt the GPA. When the learner asked “how do you know?” to the counselor the learner was not given a straight answer. To help, I received a complete grade distribution of every class in the school, removed the teacher names and replaced with a random word that starts with either “d” or “g” (for no reason, just to make it difficult) and this is what the learner is using. So far, so good. Although I am not sure the question can be achieved, it is worth doing.

Group 9: This group is interested in whether the plans of the senior class changed from when they were freshmen. A cluster sample is being done on the government classes to get senior viewpoints.

and finally,

Group 10: A multistage sample to see if being involved in sports helps or hurts GPA. They are all athletes and they all have different opinions on what the outcome will be.

I am excited to see the results of many of these, and I will be sharing the results with store managers in the area, the local newspaper in several cases, as well as next year’s group of AP learners.

Any suggestions or questions for them (or me)?

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.

One thing that I have struggled with is to make review meaningful for AP Stats. I absolutely hate the “here is the review, the test will be similar” wink wink, where all you do is change some numbers and voila, there is the actual exam.

That doesn’t seem honest to me, when I am supposed to be preparing them to think critically and learn material. It doesn’t seem honest for regular classes and it is doubly dishonest in AP classes. This year I have really been thinking and working on this issue more in my classes. To that end, this is my review project this year. 1 day in, and I think it is mostly successful.

I started off with a data set. I took it from my proficiency materials, stripped out anything that could be used to identify a particular learner, and then deleted 20 digits and put in blanks. The blanks were filled in using digits from the learners own student id number. Now, the learners can discuss HOW to do the problems, but they cannot get answers from anyone else. I can easily check their answers using JMP or another statistics program if I question their work. The nice thing, is almost everyone’s graphs will look similar, but not identical. Similar enough I can help w/o needing to do the entire process because I know what it is supposed to look like.

Now comes the questions. heh heh heh. 10, simple, innocuous questions.

For instance, here are the first 3 questions:

1. Describe the 3 variables completely, including types of variable, appropriate graphs of the values and complete description of the distributions, including all appropriate statistics. J K L

2. A passing score on the math test is a 242, while for the reading test a 300 is required. Is passing the proficiency exam in either math or reading independent of gender? Construct appropriate graphs to help explain why or why not. J K L

Create a bar chart of reading and math scores broken down by gender. Explain what the graph says about the pass rates of males and females.

The “JKL” at the end is the Wingding’s font for “smiley face” “straight face” and “frowny face”. They can rate themselves on each question.

The files are embedded here in both docx and pdf format if you would like copies.

How did it go, you ask?

I am giving them 3 class periods to work on it. I am glad, because after day 1, they accomplished most of question number 1!

I was stunned by them asking “How do I make a histogram?”. Like we didn’t do it 100 times at the beginning of the year.

Ooops, that is the problem. They learned it for the test, and promptly forgot it. Now I am forcing them to actually go back and relearn everything we have covered the entire year. They are cursing me, but it is working. I have had a lot of “aha’s” because they didn’t learn it well the first time, and now they are being forced to figure it out. It is working.

I wonder if I can’t teach the material this way to begin with? Can’t I give them a data set and say “Go”. We can figure out how to handle it together?

Makes a person go hmmm.

After spending a hectic week planning and organizing for the department, I finally got to work on my classroom in a serious way on Friday and Saturday. It all came together and my classroom is ready.

So in the spirit of sharing, here is what my classroom looks like to the learners entering my room this morning. All photos can be clicked on to embiggen.

Notice the little numbers held up by the Target \$1.00 photo holders? How about the groups? This is the first time I have tried groups, and the encouragement of my twitter PLN has made me go for it.

Let’s take a little tour. Entering the room closer:

My podium has on the side places / states I have visited on my motorcycle tours. There are quite a lot of different places, and this summer took me further East than I ever have been before. Some observant visitors here who attended #TMC12 and went to the Cardinals game will recognize a couple of the stickers.

In the podium I have a computer, a Smart Panel, an Elmo, and a KVM switch to further manage the managerie. In addition, the mess of cables snaking up the wall are 2 video cables, a sound cable, an S-Video cable and a 5 jack RCA cable which allows me to hook up an iPad or iPod to the projector. I have future proofed myself moderately well. Dang it is a mess though. That will be a future project somehow. Any ideas?

The right side of the room (with the door just peeking) is where I will post the date, the agendas of the day, and a quote of the day. I have 2 documents that total almost 200 pages of quotes in word format. I have always wanted something to do with them, and now I have a place for my quotes.

Looking straight ahead in the room. My projector projects onto the whiteboard. I don’t have a screen, and although I could get one, I have found the whiteboard gives me much more flexibility. The only downside is the board is 3 square boards, not one long one, with silver aluminum edging around them. Last year I used white electrical tape; I was not happy with the results. The tape absorbed colors easily, and wouldn’t stay white. Problem solved with sandpaper and multiple coats of whiteboard paint to the edges. Now the edging is white, not silver so they blend in and won’t hold color. It WILL stay white.

Continuing the leftward look:

I have a cart on the left in the corner. It was open last year, so looked trashy. I used the Command Adhesive picture hangers to put fabric over 1 side. Now it looks all Star Wars, and matches the board on the right side. Yay.

And finally all the way over to the left, with my curtains and my trophy case for Speech & Debate. First tournament is in 3 weeks, so I have a lot of work to do in the next few weeks! eek.