Success

I have to say I almost left Mr. Godbold’s presentation. It started off on a odd note, where he told us what he wanted to go over, then said we couldn’t do all of it, but we would be lucky if we did half, and then repeated himself for about 10 minutes. He looked and came across as very nervous.

But then he got rolling, and he had some gems that were worth sticking around for.

One of the first things he said when he was interacting with the AP Stat teachers in the room was that he forbids the use of pronouns in his room. A teacher responded to a question he asked with something along the lines of, “It is ….” He asked what “It” was and waited for a response, and then we could move forward.

That moment was actually very powerful for me. Pronouns really are hard to use in conversation without perfect understanding of what is being talked about. In writing it can be just as dangerous. Consider the fact that in this posting, I used two pronouns as shortcuts in the first paragraph alone, when I KNEW I was going to be talking about pronoun usage and how bad it is to use them (and I just used another!)

Our learners in AP Stats use pronouns all the time, and they know exactly what they are meaning when they write / say them. Other people don’t, however. The readers certainly may not. So one little step we, as teachers / facilitators must do is sharpen their usage of language to make them better communicators. Banning pronouns may be unwieldy at first, but useful later!

Second, Mr. Godbold had a fantastic way of demonstrating a very tough idea, what happens when someone says “given that”. I know my learners really struggled with the idea that given that removes things from being considered. Here is the entire process Mr. Godbold used to demonstrate the process.

First thing, collect some data. It really can be anything, but he used “principle residence in FL” and “traveled to conference without flying”, among others. Those two are the important data points we need for this explanation. We had an n = 21 in the room (excluding Mr. Godbold) and 2 pp lived in FL, 7 pp drove.

Second, Mr. Godbold explained that he has a number line on his floor that goes from 0 to 1. Any stat teacher immediately grasps the use of that particular arrangement. Next he had all the people in the room line up on a wall, and the first person was on Zero, the last person was on One.

He asked who were the 2 people from Florida, and had them move to the Zero and just off Zero spots. Now, we can see that the P(FL) = 2/27. All he did was rearrange the people a small bit, but it did make the probability clear.

Next, he asked, “What is the probability of living in Florida GIVEN THAT you drove.” Now he asked us, the teachers, this question, and he said he would not do that with a class that was not completely familiar with the idea. Even with teachers of stats, it caused some confusion. A couple of people sat down immediately. Other people were unsure what to do, but we eventually all agreed that the flyers needed to sit down, and the remaining 7 people needed to spread out!

Now we had 7 people from 0 to 1, instead of 21 pp, and they took up the same amount of space, and now we just had to count to see how many Florida residents were among the 7! (Both were among the 7, so the P = 2/7)

Bingo! The “Given That” removes people from consideration for the second calculation. Mr. Godbold then showed a contingency table on the screen, and it is clear how this exercise applies to contingency tables early in the year, as well as probability later in the year.

For no other reason that this one exercise I am glad I stayed in Mr. Godbolds presentation. My idea is to use this with the beginning of year questionnaire I do with the class. It gives me a reason to have them pull out the questions later in the year, something I have been struggling with.

Mr. Godbold also discussed independence visually, which is important since it was question number 2 on the 2011 AP Exam.  He also had a great handout for the presentation as well that dealt with probability and independence, and getting the learners to visually understand what independence looks like. It is nice, and I will probably use it in class. I will link to an electronic copy of it, once the NCTM gets it uploaded to the website this week.

Thank you Mr. Godbold!

Resources: Anytime I go to an event like this, I always google the person’s name whose session I am in. When I did that for Mr. Godbold, some great things came up.

He presented at the AAAPSTA, and has some great resources listed there as well, found in the 25 Sep 2010 section.

Timothy Kanold was the Superintendent of Adlai Stevenson High School District in Illinois. This school is a huge success story, because it went from bottom of the bottom to top of the top. They did this through a strong commitment to PLC’s and communication. Now Mr. Kanold did not spend a second on his Keynote today telling us this. He didn’t have to. Anyone in education knows what Adelai Stevenson did, and it had nothing to do with testing kids to death or any other of the Bill Gates / Michelle Rhee type “reforms.”

Let’s walk through my notes from Mr. Kanold’s presentation today. He was a dynamic and amazing presenter, who knows how to hold the attention of the room.

He began with a story of his 15 year old daughter who has a best friend in a different math class. The friend had a teacher who had rich content and reasoning skills as an expectation, and his daughter did not. This, of course, caused a “minor” conflict and caused him to become involved.

Mr. Kanold was aghast to discover that the school his daughter attended (he didn’t tell us which school that was) did not have certain departmental norms.  Mr. Kanold asked one very simple question, “How is it possible that in 1 department two teachers could have such different expectations that one teacher uses Reasoning and Sense Making and the other teacher does not.” The answer there, as everywhere, is the same, “Because I can.”

And then Mr. Kanold asked the most important question of the morning, “How is that acceptable?”

The answer, of course, must be that it is not acceptable.

Mr. Kanold then challenged everyone in the room to write down 1 element of their TPOV, their Teachable Point of View. A TPOV is something he has taken from Noel Tichy, and is defined as, “A cohesive set of ideas and concepts that a person is able to clearly articulate to others.”  The NCTM has a TPOV, it is found on page 14 of the Reasoning and Sense Making book. But do I have a TPOV? Does my Department? All good questions. (I will write about my TPOV later.)

The next challenge asked by Mr. Kanold was, “How will you close the gap between the vision and the reality of adult action.”

Wow, that is tough. Of course, we have to have some standard to evaluate that gap, which leads us into some methods of distinguishing bad or irrelevant (my words) evidence from actual evidence. There are 5 kinds or levels of certainty in our actions.

1. Opinion: This is where a teachers says, “This is what I believe.” “I believe this sincerely.” It is an opinion the teacher holds about the ability or capabilities of their learners, either collectively or individually.
2. Experience: Here the the teacher says, “This is what I have seen based on my personal experience.” My personal favorite example of this is where a teachers says, “Well, based on what I have seen, we will have to agree to disagree.”
3. Local Evidence: Here the teacher says, “This is what I have seen based on the experiences of my friends and colleagues.”
4. Preponderance of Evidence: now we are up to evidence based on what we know as a profession.
5. Mathematical Certainty: finally, at this level, we are basing decisions on evidence that is so certain there is no need for debate.

If we ever come across evidence that is at the level 5, then we need to not even discuss it, we just need to do it immediately! It is so absolutely amazing, and so rare, that not doing it breaks all rules of rationality. Decisions based on Mathematical Certainty are absolutely non-negotiable.

So is there anything that can reach that level of certainty? Mr. Kanald’s answer is Yes.

That thing is the fact that Professional Development that is offered over the course of 6 – 12 months and spans 30 – 100 hours, that deals with non-negotiable behaviors and expectations of success, where the PD is connected to results in the classroom (strong, demonstrable results), and designed to be an ongoing contextual subject matter requirement has an effect size of .73.

Let’s compare that to the well established effect size of poverty in the classroom. The poverty effect size is .57. The effect size of a fully functioning PLC, based on results in the classroom and best practices is .73. PLC’s have a bigger impact on learner success than poverty!

If we don’t act on that, we are crazy. We must act, and act NOW. That is decision making at the level of Mathematical Certainty.

Mr. Kanold really motivated and sharpened my thinking on my own PLC time. He gave me a copy (actually he gave 75 pp) of his book, The Five Disciplines of PLC Leaders, which has free reproducibles here.

He blogs at http://tkanold.blogspot.com and his twitter is @tkanold. To say I will be following and reading his material in the future will be to say the sun will rise tomorrow.

Some other books he mentioned during his presentation that are worth following up on / reading:

Embedded Formative Assessment by Dylan Wiliam

The Fifth Discipline by Peter Senge. Mr. Kanold said this book was very instrumental in shaping some of his ideas on PLC’s.

Today had some more very good things happen at the Institute.

I think the first thing is the definition of an “Institute” versus a “Conference”. That distinction was made yesterday, and then briefly discussed again today in a session.

Now these are not formal definitions, found in a dictionary. These are rough and dirty definitions formed through discussion. I attended a NCTM “Conference” in Salt Lake City a couple of years ago. It was huge. Hundreds of vendors, probably a hundred presentations over the course of 4 days, with a schedule that was packed to the gills. Honestly, that “Conference” was a huge waste of dollars.

Oh, yes, I took home some resources. One or two presenters had resources on CD, and I think I even got one website out of the deal. I sat through 10 presentations and listened.

Yup, it was EXACTLY like the worst math class you ever took. Sit down, listen, take notes.

Compare that with the “Institute”. WE are involved, engaged, asking questions, and sharing with each other, both audience to presenter (lots of question opportunities for audience to ask questions) and among audience to audience. We are given working time to share and collaborate built into the schedule, and the presentations are stranded. The stranding means you don’t have 4 stats presentations at the same time so you have to miss out on something. The Institute is designed to have good workflow, with sessions in the middle and end to have collaborative work.

Nice.

So, let’s start with some of the great recommendations I have taken from today. First off, some books that came very strongly recommended by William McCallum.

1. Mathematical Discovery by George Poyla and is out of print and very expensive to buy on the used market. And by very expensive, if you click the link you will see Amazon has copies, for $165!!!!! Go check it out of the library and photocopy it. It will only cost you $20 and 30 minutes of time. That is highway robbery.

2. The Stanford Mathematics Problem Book, published by Dover Press. $6.95. This book was recommended repeatedly, and is available on Amazon and other fine bookstores. It is nice because it has problems, hints and solutions, and the problems are good problems for high school reasoning and sense making activities.

3. Unpublished Ph.D. dissertation by Sarah Donaldson, 2011, Teaching through problem solving: Practices of four high school mathematics teachers. Not sure where to get this as a high school teacher. College students and teachers have access to everything, but high school teachers get screwed on these types of important works. In this dissertation 5 things were identified as being best practices:

1. Teach problem solving strategies
2. Model problem solving
3. Limit teacher input (hmm, recall yesterday’s post where Dan Meyer said the teacher should stay out of the way)
4. Promoting meta-cognition by the learners
5. Highlight multiple solutions by the learners

Some websites I found out about today that will definitely benefit my teaching. There is no particular order to these sites. I just went down my notebook and put them in the order I wrote them down.

• Illustrativemathematics.org – very bare. Like mother hubbard’s cupboard bare. I am hoping for more content here soon.
• http://commoncoretools.wordpress.com/ William McCollum, who was one of the major authors of the CCSS, has a blog where he has documented and will continue to document developments and resources for implementing the CCSS.
• Park City Math Institute – Honestly not sure what is on this site yet. It was thrown out by another teacher I overheard, “Hey that can be found on PCMI!” I wrote down pcmi, and then had to do some searching. Honestly, it looks like a promising resource.
• www.insidemathematics.org – a website to help with the CCSS rollout and help for teachers to make the adjustment. Looks like a well made site. I have not examined content yet.
• www.nctm.org/hsfocus – so far it looks like a page selling the NCTM books. There is some additional content, but it is lean on the content and large on the selling. It does not really fit with the approach and styling of the “Institute”. It seems far more “Conference” focused instead. Of course, it is a work in progress. I hope.
• www.nctm.org/reasoninghandouts – This is the official place for the handouts, not the /hsforum. It was another miscommunication with the NCTM that some of the employees of the NCTM handed out the /hsforum on Friday mornings session. Unfortunately, it was not corrected until Saturday’s closing session.
• www.nctm.org/reasoningforum – not much going on yet, but the NCTM needs to do some major push to get people to know it is there, populate it with posts from the presenters, and start using it. The biggest need is the presenters without websites need to post their take on their presentation here.
• www.rossmanchance.com – a very nice collection of applets for statistics that may replace the scattered applets that I have been using and suggesting.
• nctmrsm11.mrmeyer.com – Dan Meyer’s site where he is posting all of the materials from his presentations. This is what I would expect of a professional teaching organization. And it is only a one man show!

Ideas that came up that I will want to follow-up on later during the summer and school year.

• First off, in the keynote today with Gary Martin and Eric Robinson, Eric pointed out that questions like x² – 7x + 12 have no reasoning required, just rote recall. But what if we replaced that factoring question with this one: x² – ?x + 12.  What numbers could go in the question mark? What integers? What fractions? Why? Now the problem becomes interesting and has multiple points of entry and multiple answers. Just a simple tweak, but enormous payoff. (Thank you to Eric Robinson for this idea.)
• Notice that this question is not contextual like Dan Meyer’s questions. It is not always about contextual problems, but sometimes it is just about INTERESTING problems. After all, they publish sodukus in the newspaper not because just math teachers do them, but they are interesting and challenging. (Thank you to Gary Martin for this idea.)

Okay, that is enough for now.

My only complaint, and for me, it is a big one. Thanks be unto the NCTM for choosing a hotel that charges $14.95 per day for internet access to teachers! Like many of you, I had my pay cut this year, and I paid my own way cross country to attend this conference (so far total cost is estimated to be $1300, not counting all the meals.) This lack of internet is pretty much my major annoyance with this beautiful hotel. The Comfort Inn I stayed at in Lewiston MT offers free internet for $80 per night, but the Renaissance at SeaWorld can’t for $149.00, except in the lobby. Really? I call call (cough) Bullhouy.

That really is the question posed by Dan Meyer in his opening keynote speech at the NCTM Reasoning and Sense Making Conference Institute. Honestly, I had never heard of Clever Hans, and unless you are a fan of esoteric German animal trivia, you might not have heard of him either. Clever Hans was a horse that had amazing powers of reading the people around him. The horse could do any math the audience could do.

I won’t bore anyone with the story, especially since Lisa Henry did such a great job explaining it on her blog, and Wikipedia and other sites have thoroughly explained it as well. The story is extremely relevant to math education today, and more importantly, important to the practice of math educators today.

As I was listening to Dan, I recalled a comment a learner made to me. I had just asked a learner, “Why” when she gave me an answer to something. The learner tried to explain, and couldn’t. Another learner came to her defense, and together they figured out she was correct, and they explained why. At that point, Learner 1 turned to me with a very angry look on her face (all made up, she is a great actress) and said, “Mr. Waddell. You tricked me. You are only supposed to ask why when we give wrong answers.” The class then went on to tell me that I have a great poker face, and that I am supposed to let them know when they get something right by smiling or something.

I had just accidently stumbled upon the Clever Hans Effect, and didn’t know it. I just wanted to know if the learner understood the problem.

Imagine that. The learners in the class understood the issue better than I, the teacher did. They were instructing me when it was okay to ask them if they were sure, and how to non-verbally communicate with them when they are supposed to stop clomping their hoof guessing the correct answer. Thankfully I ignored them.

I didn’t have a name to describe what occurred that day, but I do now, and Clever Hans will now and forever be in my first day of class discussion.

But of course, the keynote was far more than just a talk about a horse. It was about how to take a boring, dry, and thoroughly massacred problem, and turn it into something that might actually have some interest to learners.

Dan breaks his problem solving process into 4 steps.

1. Visualize

2. Abstract

3. Decompose

4. Verbalize

Of these, I personally find the Verbalizing of the problem the most important. Verbalizing a problem is asking the truly relevant and interesting question in just a few words. Taking a long and boring question from a text book (how about the “which cell phone service should I get that is now de rigour for textbook companies) and turning it on its head.

The new question should be something along the lines of:

1. What cell phone plan would you buy?

2. [insert some image of local cell phone advertisements here] Make the insert local, relevant, and complete.

3. And this is probably the most important part as a teacher. WALK AWAY for a bit and let the learners abstract the question. You see, the textbooks do that for the learners. They break the problem down into nice, clean, manageable chunks that are easy to digest. We need to let the learners look at the actual ads, the actual, messy, ugly details of the ad and decide for themselves what is important.

4. After that, then they will decompose the question and figure out an answer and then justify the answer.

Guess what, some may choose a plan I would not. The real question at that point is, “Why?” Did the learners overlook something, or did they just think the 2 gig plan fit their needs better than the 5 gig plan?

Why do I need to always decide for them?

And that is a great way to run a rich question with Reasoning & Sense Making. I will have more to say on this later. Right now, I am in Orlando, and some fun beckons.

After all, it is not always about the math. (yea, right!)

It is time to start thinking about such things!

First, room arrangement. This year I am expecting to have between 30 and 37 learners in each class. In the past, I have had my room arranged in a large, double sided U. This allowed for maximum conversation and collaboration, as well as random number usage for picking learners. Six ‘rows’, 5 to 6 desks per row, leads to a perfect random dice throw to pick a learner for answers, boardwork, victim, etc.  For this year, I will have to make sure I can shoe-horn 6 in each row for sure.

Class rules on wall. My rules are simple:

1. Your behavior should contribute to the learning of all people in the room.
2. Don’t stop trying and participate every day.
3. All school rules will be followed in the classroom.

That’s it. Just those three rules. They have worked for me well over the last 3 years, so I will keep them.

The rest of the room: I have very little math on my walls. It is all philosophy (go figure! I love philosophy) and these statistics posters. I love these posters because they look like history teacher posters, but are really math. Love it.

Okay, so the stage is set. Room is not arranged as a typical math teacher room. check

Room does not have math all over the walls, but quotes from philosophers and mathematicians, and colorful, focused posters. check

Now, we come to the first day when learners walk in.

1. Seating chart projected on wall. They find their seats based on seating chart.
2. I have warmup page on desk for them. (only time I do this all year!)
3. Once bell rings, hit remote and ppt moves to warmup. I am still at door greeting the slowpokes, and they have to see me to find their seat.
4. After warmup is done (I don’t give the answer, they can argue about it, but I won’t give the correct answer,) then we move on to introductions. I think this is important. They want to know they can trust me and that I know what I am talking about. If they wonder who I am, they will not buy in.
5. My introduction of myself to them the last two years has been a video I have made of my motorcycle trips. I find mathematical problems along the way and I present those to them via a personal video. (I have had learners remember these to the end of the year, and they always ask me if I am going to do it for next year. They appear to like them.)
6. Notice that to this point, I still have not spoken very much. Even telling them about me, I didn’t have to talk or lecture to them about me!
7. Okay, we are 15 – 20 minutes into a 70 minute class. Now I go over class expectations. I have
   done this in previous years. They get a page with the blanks, I have a page with the answers, they fill it in. In week 2, I give the the full syllabus with all the details. That sets me apart from the rest of the teachers who hand a multipage syllabus on the first day of class.
8. Now we are up to 30 to 40 minutes into 70 minute class. 40 minutes left. Next thing I do is required by school sometime in first two weeks and we take a walk to the outside and see where we meet for fire drills. I have a Google Earth / Google street view walk through I do with seniors and juniors, freshman and sophomores we actually walk out side. Again, this sets me apart from the other teachers.
9. Okay, 30 minutes left in class. Now we do a project / lesson. In AP Stats I hand out a questionnaire and start data collection. In Algebra 2, I will handout the beginning project for the first month of class.

And then the bell rings. We have accomplished a great deal. First assignment / project given. They know a lot about me. They know this won’t be a class with tons of personal stories and time spent off track. They know I am passionate about math. So much so, that I ride around for 2600 miles and look for math! They also know I have some very diverse and broad interests, and this class will not be the boring, rest your head on your hand and take notes class!

And that is a successful first day.

It was the best of conversations, it was the worst of conversations, but in the end, it was an educational conversation for my cousins and I.

Okay, enough with the Dickens reference. During the summer I take a little motorcycle trip. Okay, not so little. I do around 2500 miles from Nevada to Montana and back to see family and some beautiful country. During the trip this summer, I attended a family reunion north of Missoula, MT, and a family picnic in Helena, MT. During each family event, I met with a very bright and talented young girl who was going into the 5th grade. I will call the first one C1 (for Cousin 1, they are actually my cousin’s daughter, but cousin is close enough) and the second one C2. These two bright young girls have some amazing similarities.

Both C1 and C2 come from very supportive families with several siblings. They both have college graduates either as parents and / or grandparents. Both C1 and C2 are entering the 5th grade next school year, and they both are encouraged to do well and school and are given any resource or opportunity they need to succeed in school.

And then the similarities end. There are some irrelevant differences. They each live in a different state (Utah and Montana), but the school districts are similar sized (I looked them up.) Because of this, and because I don’t know any different, I will assume that both C1 and C2 are given similar opportunities in the school for success. [Okay, this might be a deal killer of an assumption, but I have to make it in order to not be angry at what is to come.]

There are also some amazingly important differences. I asked C1 what she likes best about school. Her answer was “Lunch” and then “Recess” and then “Friends”. Even after all that, I couldn’t get her to name an academic subject. When I asked her about math, her reply made my die a little inside. She said, “Math is icky. Math is where you do this.”  The ‘this’ was put her head on her left hand, a thoroughly bored expression on her face, she looked up at the imaginary board, and then with her right hand she mimicked taking notes and writing numbers.

I died. Seriously. I wanted to cry right in front of her. C1 thinks that math is the time when you are bored stiff, quietly taking notes on something on the board. Later, just to make sure I was not imagining that she was as bright as I thought, we walked down to the railroad tracks about a 1/2 mile away. I challenged her to give me an estimate on how many steps it would take. She said 200 the first time. We started walking, and she counted to 100 before she looked up and said she was too far off. I asked her to revise her estimate. She squared the number to 4000 (in her head, as a 4th grader!). Then she said that 4000 was too big, and she cut the number in half to 2000. Then she said that she guessed, based on the 100 steps she counted already, that the number of steps it would take would be between 1500 and 2000.

Yea, she is bored in math class. Go figure.

Then I visit with C2 in another city. C2 and I have met once a year for the last 2 years. Last year, we talked about mathematical patterns in oven hot pads she was making, then had a discussion of 9’s, adding, multiplying, and dividing, and the neat patterns that are present when doing math with 9’s. That was when she was just finished with the 3rd grade, and entering the 4th grade.

This year, that was old hat. She wanted to know some addition “fun math tricks”. (her words) I asked her if she remembered the things we discussed last year, figuring that she would have forgotten some things and I could re-cover them. No. She had expanded on them. She went on to explain to me the difference between prime numbers and composite numbers, and factoring and dividing.

Long story short, we ended up doing modular arithmetic, in mod 5, 7, and 9. She, on her own, continued to do tables for the multiplicative inverses in mod 11 and 12. Why 11 and 12? 11 is prime, so they all work, while 12 is composite, so there are numbers that don’t have inverses. AS A 5TH GRADER!

I found out that C2 will be taken to the middle school and doing 7th grade math while in 5th grade. C1 will be doing 5th grade math in 5th grade, but could be doing so much more. The best of conversations, the worst of conversations, all rolled up in one week.

What did I learn? I learned that some learners are being driven away from math. Whipped, beaten, and driven away, even though they are smart and very capable. I learned that WE are teaching some learners that math is a subject to be feared and avoided, not because they can’t do it, but because WE have not given them a REASON to do it.

Why are we doing this?

I admit it, I read the funny pages first thing on Sunday morning. Okay, maybe I should first admit that I have a daily subscription to the newspaper and read it cover to cover every day. But, on Sundays, I read the comics first.

Yesterday’s Doonesbury was an instant classic in my mind, worthy of my comics wall. Here is a link to it. I will wait while you read the whole thing. … … …

I know, right! They nailed the problem with memorizing random facts in only 5 panels. The other 3 are there just to be funny and set the mood, but panel 3 and 7 are the set up and punch lines.

…

The three panels in between show Zip’s friend asking some random questions on science, philosophy  and history, along with the fractional seconds it took Google to spit back the correct answer.

I took an informal poll last year in my class year, and around 50% of the class had smartphones that could access the internet. The rest of my learners could text questions to Google and get answers back (they had texting, most of them did not know they could do that) and all of them knew about Cha-Cha.

So what are the “Profound questions about what it means to be a student?” Here is my weak attempt at listing some.

1. In an era where every learner has never known a time when information was not immediately findable, why do we (teachers) spend so much time asking learners to memorize formulas and facts?
2. The comic makes an implicit assumption that faster is better. Is that correct? Is it important that a learner memorizes a fact and can recall it on demand, even if that means more time?
3. The other assumption Zip makes is that Google or Cha-Cha are more accurate than his own brain, memory, understanding. Is that correct? I know I have asked questions in my classes and some learner says, “Why should I do that, I will just Cha-Cha the answer.” My response was, “Go for it, get your phone out and do it.” [That shocked the heck out of him, but he did it, and Cha-Cha failed!]
4. Is there a middle ground? Can there be vital things they need to memorize, important things they don’t, and less important info they can look up?
5. Is the goal of the lesson understanding (in the context of UbD) or rote memorization?
6. Finally, what evidence is necessary for demonstrating the difference between the two in 5?

I think Doonesbury fit very nicely in my current PLN content discussions. Now it is time to do something about it.

Several months ago I wrote about 53 free android apps for education. Because technology advances and new apps come out and apps change, I will have to update that list. I know the Andy-83 app has been pulled and replaced because of demands of TI, so clearly some updating is necessary.

But this post is about the 5 apps I have spent the most time with over the last month. These are all free apps, although some of them have paid versions as well, and all of them have iPhone versions also.

First up is CardioTrainer by Worksmart Labs. I tried a couple of other apps for a short time, but this app does what I wanted. I am not an exercise freak, in fact I have exercised more in the last month that in the year prior. So, I am walking and biking, doing yard work and hiking a bit, and this app keeps track of it all. It uses the GPS to track where and how far I have walked or biked, has voice prompts (which I don’t really use) and music integration if you use the phone as your music player.

I really like how it uploads to twitter and facebook, so I can be public with my exercise routine, which keeps me honest and motivated. It keeps track of distance, time, elevation, sets checkpoints on the routes, and uploads all of this to the companies servers for online viewing, uploads to Google Health (oops that is being discontinued) and stores it on the phone. In addition, the online website allows for the entire data package to be downloaded as a .csv file to be imported into excel. Nice.  Basically, this one program works for 20 different exercise routines, is incredibly flexible, and accurate. I like it.

Second up is Push-ups by Rittr Labs. Yup, can you tell that health is a focus for me right now? My goal is to exercise every day for 1 year to establish a pattern and habit of health. Now walking, hiking, biking are good exercise, but they do nothing for the upper body. Push-ups helps you work up to doing 75, 100 or 125 consecutive push-ups. It sets up a routine of doing reps every other day, starting off from a beginning point you set, and at the end of the workout asking if the suggested rep count was too easy, just right or too hard. It then adjusts the next workout based on your answer. I am currently up to around 40 – 50 per day. Not bad, but my goal is 100 consecutive. I figure by the end of summer I will be close.

Third up is Common Core by MasteryConnect. It is a simple app, that has tremendous power for me. My district is going to be implementing the Common Core State Standards this upcoming school year, so having a quick and easy way to read the standards, find the standards and just have quick reference for the new standards is very important to me. This program serves that need, and I have been using it to find standards as I am building curriculum this summer.

Fourth up is Software Data Cable by Proid Mobile. Remembering to bring the cable with me when I need to hook up my phone to my computer is a pain. When I am at home and need a quick file from my phone this program is awesome. I make sure the wi-fi button on my phone is active, then I open the app. It takes a second and then shows the ftp address of my phone based on its address from my router. From there, I type in the address in my web browser and BAM, I have access to all the files on the SD card and memory. Need a photo, download it.

Yes the cable is faster and easier, if you have it handy. But walking down stairs and getting it from the charger is just so far to walk! (wait, … er, doesn’t that conflict with the first 2 apps? Yes, now stop asking questions.)

Finally, the last app I will talk about is TweetDeck. I had some trouble choosing between this or Words with Friends. I spend a lot of time with both, but more time with Tweetdeck. I use it to keep track of my Twitter and Facebook feeds simultaneously, both at home and away. It is easier to read both on my phone with this app than it is opening up the computer and reading there. If there is a long post I want to do on FB, then I use the computer. But for quick notes to friends, a short response, etc, Tweetdeck makes it much easier to manage the info stream. I have also downloaded the desktop client from TweetDeck.com and found it to be very usable and useful, especially when doing book clubs on twitter!

When I last left this topic, I had a rather different arrangement of the Essential Understandings based on a theme of graphing, algebraic arithmetic and solving. We took this to our department head, and had a discussion with her about these. Her very valid concern with that arrangement was that the learners may not see the connections between quadratics and graphing, factoring, completing the square, etc. and polynomials and graphing, etc.

So, we have re-arranged our essential understandings by “theme” of type of function.

Below you will find our new arrangement for the Alg 2 first semester. The “Keys to Success” is a series of brochures and self check mastery, and the parenthetical numbers are the book section numbers. The book is not the driving force on this though, the district’s blueprint is. We won’t get the final version of that until July sometime.

The goal is to have the learners connect the graph, the algebra, and everything else we do inside the them together. We will be doing essentially the same mathematics 4 times, and then I need to make the connections clear and consistent through the classwork and assignments.

Now that we have an list of essential understandings, we need to go through and decide what demonstration and transfer of skills will be considered as evidence for the learner understanding the understanding. That is the next step.

Keys to Success (chap 1 & 2: reviews of alg 1)

1. Integers
2. Expressions
3. Evaluate
4. Solve
5. Slope
6. Graph Lines
7. Equations – Lines
8. Exponents
9. Factoring
10. Parent Functions

theme: Linear functions

• Can you graph more than one equation on the same graph? (3.1)
• Can you explain where the multiple equations intersect or not intersect, and what that means? (3.1)
• Can you solve a system of equations with substitution? (3.2)
• Can you solve a system of equations with elimination? (3.2)
• Can you graph two or more inequalities on the same graph? (3.30
• Can you shade correctly the two or more regions indicated by the inequality? (3.3)
• Can you add and subtract matrices? (3.5)
• Can you do scalar multiplication with matrices? (3.5)
• Can you find the determinant of a 2×2 matrix or larger matrix with and without technology? (3.6, 3.7)
• Can you multiply two matrices together with and without technology? (3.6, 3.7)
• Can you use inverse matrices to solve linear systems with more than 2 equations? (3.4 & 3.8)

theme: Quadratic Functions

• Can you graph a quadratic function, labeling the values of the vertex, axis of symmetry, and the minimum or maximum & solutions or zeros? (4.1 & 4.2)
• Can you solve quadratic equations by factoring where a = 0?  (4.3 & 4.4)
• Can you solve quadratic equations by factoring where a  0? (4.3 & 4.4)
• Can you solve quadratic equations using square roots? (4.5)
• Can you compare and contrast the different methods of solving quadratics? (4.5)
• Can you complete the square for a = 1? (4.7)
• Can you complete the square for a  1? (4.7)
• Can you add and subtract complex numbers? (4.6)
• Can you multiply and divide complex numbers? (4.6)
• Can you graph complex numbers? (4.6)
• Can you use the quadratic formula to solve quadratic equations? (4.8)
• Can you use the discriminant to determine if the roots are real or complex? (4.8)
• (rethink in July)
• Can you use quadratics in real world situations? (4.10)

theme: Polynomial Functions

• Can you describe the end state, rise and fall, max and min, and zeros of a polynomial function? (5.2)
• Can you evaluate a polynomial function given a value? (5.2)
• Can you add and subtract polynomial functions? (5.3)
• Can you multiply polynomial functions? (5.3)
• Can you factor perfect cube trinomials? (5.4)
• Can you factor non perfect cubes by grouping? (5.4)
• Can you divide polynomials through standard long division? (5.5)
• Can you divide polynomials through synthetic division? (5.5)

Okay, I have to admit, I haven’t really designed my own curriculum for algebra 2 before. I just looked at the district blueprint, saw what chapters they expected me to cover, and did that. Sometimes I figured out homework assignments the morning of. Sometimes I had homework planned out weeks in advance. But I had never really thought about how to teach the curriculum from the top down before.

And then I met Holly Young and the Washoe County School Districts RPDP and began the Student Learning Facilitator program (SLF) and began to read the book Understanding by Design by Wiggins and McTighe (UbD).

Darn her! She threw my whole process upside down and made me realize how much I sucked. And then my school changed their schedule to a odd block arrangement which takes our class minutes from 90 to 71 (but increases minutes over the semester and increases class meetings! Yea!) And then the Common Core State Standards is coming out, and we will have to rewrite everything anyway.

So this summer, another teacher and I sat down immediately after school was out to start planning next year’s Algebra 2 class. It is the first time she has taught it, and it I have not taught it for 2 years, so it is new to me, given the changes to our school this year.

Read on to see some of the details of our planning.

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