Aug 032016

Day one of my Knowing and Learning class will be about the syllabus, the 4 major assignments, and starting the conversation regarding what it means to Know something or Learn something.

There are going to be 4 major assignments. Two interviews, a midterm, and a lesson plan for the final. The first interview is a “expert v novice” interview. An expert is someone who has a PhD in the topic at hand, while a novice is a freshman / sophomore in the topic. My learner will come up with a short, open ended question set of interest, and compare the difference between how experts and how novices view the material. In math, it could be about factoring quadratics, or polynomial long division.

Next up is an interview of an expert regarding questioning techniques and going deeper on the issue presented before. How does the expert question others on this topic. Then a midterm on the theories presented so far, and finally a lesson plan, written according to one of the theories in the class, taking into account the information gained in the two interviews. This will pull the entire course together.

But back to the first day. How DO we get learners to understand that not everyone Learns the same things from the same lesson, and how do we get learners to understand that Knowing is different from Learning? That is a new concept for many learners. I am going to use an instrument that I asked people on Twitter to answer.

First off, because they are in my circle of friends on Twitter, I can assume these individuals are mostly teachers of math. That is a pretty good guess. There may be some higher ed people in the sample, perhaps some science teachers, but … mostly math.


Um, no. That is a totally incorrect assumption. Or is it? Just because someone majored in something other than math, that doesn’t mean they don’t teach math (after all, I majored in Physics and Philosophy.) Still, assumptions can kill.


Okay, I have to put this here. I like Google Forms, but COME ON GOOGLE! Why don’t you have the words on the graph? This is the scale used for the following responses.

act sat



I think it is interesting to note that the teachers are falling mostly on the “nurture” side of things, but not all, and not always. And notice that on testing, regardless of the test, there is almost complete agreement, but there is a difference when it comes between math and science.

Here is the scale for the next graphs.

scale 2

Compare these next graphs. Good teachers are born, not made. Most of the responses were disagree, but 7 people said no comment or agree. But, 9 people said disagree or no comment to the Theory is important to becoming a good teacher. (BTW, I was very happy to see this group had the same outcome for being a physicist as a teacher, that made me smile.)

What does it mean that more people think teachers are made, but at the same time, not all of those view theory as important? Hmm.

born not made



math facts

Interesting. Strong agreement between Math Facts and Seasons, but almost total agreement that calculus does not need to be a graduation requirement. Interesting dichotomy between the graphs. Why? Why do we place some knowledge at a higher level than other knowledge? Why isn’t all knowledge equally important?

If all knowledge is not equal, is all learning also not equal?

Honestly, I expected this type of response from the educators who use Twitter (totally a convenience and voluntary response sample.) There is nothing unexpected here. But look at the variety still. There is not complete agreement on anything.

I am excited to see what my learners say. I believe they will have much more varied responses to everything, which makes the entire exercise more interesting. Now, however, I can also show them what a group of “Experts” in education think as compared to their responses.

Which lets me set up the “Expert v. Novice” interview event better.

Thank you Tweeps. You just made my first day even better!

(btw; any other conversation or comments you want to make? These are really interesting questions!)

Aug 172014

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

2014-08-13 07.42.29 How awesome are Calculus Toms. If you know or have any influence at Toms, tell them to make them again! I am so bummed that they are not for sale anymore. This learner found them in a used clothing store and was completely excited that she found math shoes. I must be doing something positive in the classroom if my learners from last year are this excited about shoes.

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

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

2014-15 Alg 2 syllabus    Syllabus-AP Statistics

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

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

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

No, really. Super High Tech

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

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

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


Aug 122014

My goal this year is to blog more. As in, blog almost everyday. The secret to writing better is to write more. Therefore, I am going to write more as practice for writing. It is something I need to do as a professional. Here is to the effort.


I don’t give out the syllabus on day one any more. I used to. It was the regular thing to do so. “Here are my rules. blah blah blah.”

I split it up over several days now, and I start that rigmarole on day 2 instead. Here is a recap of the first day for me this year.

Honestly, it was pretty similar to last year, but better.

AP Statistics:

I gave them this problem which is familiar if you use the Practice of Statistics. That is all they had.



I then asked 2 questions:

1. Is there evidence of hiring discrimination?  We had a discussion.

2. Is there CONVINCING evidence of hiring discrimination? We discussed.

I told them AP Stats was all about moving from question 1 (opinion) to question 2 (fact based examination) and one way to do that is to do a simulation.

Enter the beans. We used a baggie and 25 beans (10 white, 15 black) to simulate the situation. Working in pairs the learners did ten trials and put ten dots on the dot plot.

[aside: last year I hated what my learners did with dot plots. The dots were haphazardly drawn, some small, some large, some to the left, some to the right, there was just no good construction. I was in Target at the end of summer and saw packages of 702 – 1/2 inch big smiley face dots for a dollar. I bought  over 10,000 dots. First day of class we we made AWESOME dotplots!]

This is what they created (1 pic for each period of class):

2014-08-12 12.21.24 2014-08-12 12.21.36 2014-08-12 12.21.30


I made a histogram out of one because they asked what was the difference.  I then led them in a round of vocabulary that can be used on the graph. All in all, a very good day.

Tomorrow opens with this cartoon.

Dilbert - stats vs magical thinking


I hope it sets the tone that the class is about deep thought and working through details, facts and evidence, not opinion.  Now I just have to maintain the tone.


Algebra 2 Honors

Oh, now this class was … different. This class is not happy with me at all. I gave them the handout and said, “Go.”

Cell Phone Project.docx

The project asks them to decide what cell phone plan my wife and I should choose. They were handed chart paper, markers, and the project description.

I only answered a question that was about information in the paper. If they were confused about the content of the plan, I answered that. If they asked about something else, nope.

They were very hostile for a while. When they asked something I typically answered, “There are 4 people in the room who knows what the answer is, 1, 2, 3, and 4.” And I pointed at them when I said the numbers. They needed to start making decisions on their own.

It worked. They get 15 minutes at the start of today’s class to finish.


Some of the learners were not happy with the fact that I was assigning them a project without “one right answer.” It will take a while to break them of that opinion. That is okay, because I have a while with them. The work they did was good. Nothing earth shattering or super impressive, but then again, it is only the first day (and 15 minutes into the second day) of school!

I am really happy with the variety of methods chosen to display the results. That was wonderful. Almost everyone chose T-Mobile as the plan of choice, but it was pointed out that if new phones were required then AT&T or Verizon would be the better choice.

All in all, a great way to start the year. We had a discussion after the presentations of why I assigned it. Comments like “to get us to work together,” “to make us realize that there sometimes can be more than one right answer,” and my favorite was, “because you wanted to make us realize this class would be about us working, not you talking.”

Yea, I liked that one the best.

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Aug 102014


This is my first “Made 4 Math Monday” post of the year, and it is probably one that I would be most proud of and is my biggest achievement. It is my Classroom, ready to rock and roll for learner tomorrow, Monday, 11 August 2014!

Here is what greets them as they walk in the door to my classroom. I will be standing outside high fiving them and handing them playing card with the number 1 – 8 on it. They will sit at the table (you can barely see the playing cards on each desk arrangement) with their number and then they will fill out a form that asks for their name and 3 things interesting about themselves.

2014-08-10 15.44.11 You can see the awesome curtains I made several years ago to hide the ugly contact paper a teacher before me put on the windows, my teacher area in the back of the room, and the desks all ready and waiting for eager learners.

Once they are situated, from left to right across the front of the room they will see this:

2014-08-10 15.43.04 2014-08-10 15.43.10 2014-08-10 15.43.14 2014-08-10 15.43.22

I did a closeup of the “Wall of Awesome” because there are some pretty funny things on there. Well, they are funny to me. I know the story, and if any learner asks, I tell them the story behind the quote too. Yes, I kind of dig Star Wars, and if you notice, I have a large “YET” on my wall on the left of the board. My 3 rules of math are above my board, all tricked out and crafted out. Thank you Meg and Shelli for the inspiration to be all “crafty”. Thank you again Meg for taking my Rules and making posters out of them.

As we continue to the right of the entrance, the learners see:

2014-08-10 15.43.46 2014-08-10 15.43.55

I have my quote of the day and the date all ready to go. I have the YEARS agenda already written out. I have not put my calculators in the handy dandy $5.00 shoe caddy from Ross yet. And some teachers have not picked up their calculators as of yet.

And then I was looking at the board and I realized I did not want to do the “you are here” I did last year, so I channeled my inner craft geek again and made these:

2014-08-10 15.45.17 One for Stats, one for Algebra. They are shiny because the glue is not dry yet, but once they are dry they will be stuck to the board with the two blue magnets sitting there.

And finally, because of this post from Jared Derksen I made a Pronoun Swear Jar. I will ask for $.25 each time a pronoun is used in class discussion. I figure the money can go towards AP Exams or an AP party at the end of the year, but either way it will go back to the learners. Nothing major, but here are pics:

2014-08-10 16.16.27 2014-08-10 16.16.21

There is my classroom. I will post about the first day activities tomorrow. I will NOT be going over the syllabus, but I DO have activities all planned out. Learning activities. My learners will be working from day one. No downtime.

I hope your first day of class goes well too!

Jul 162014

I have been thinking a lot about growth mindset lately (really, what teacher is not.) But I have really been trying to come up with positive, constructive ways to model and use it in the classroom as a way to change the learners beliefs.

One way I came up with using it is to have some statements that I can use consistently when learners are struggling in class. My personal challenge when dealing with the fixed mindset is what to say, how to constructively come back with something that will start impacting beliefs. As a teacher, we hear it, but how do we respond? It has to be consistent or we lose their focus. These cannot just be quotes on the wall, but statements delivered with conviction face to face to have an impact.

So, here are some statements I hope to use in my classroom. I am going to print them out and post them where I can see them every day in the morning and before every class to remind myself to use them until I don’t need the list any more.

Learner Says or is Doing: Teacher (ME!) says:
Learner is struggling with material “If it was easy, I would not waste your time with it”
Learner whips through problem, too easy “I apologize for wasting your time, I will find something more appropriate for you.”
“This is too hard.” “What strategies have we discussed that could help you get started?”
“This is too hard.” “It is difficult now, but so was adding in elementary school. You overcame that with effort and you will overcome this with effort.”
“I am not good at this.” “The more you practice the math, the better at it you will become.”
“This is easy.” “I am glad you understand this, can you develop a more complex idea with it that challenges you?”
“This is as good as I can do.” “You can always improve, as long as you give it some more effort. What other strategy have you not used yet?”
“I made a mistake, I can’t do this.” “Mistakes are how we learn. If it was easy, you wouldn’t be learning anything new.”
“This is good enough.” “Is this your best work to show your learning?”
“I didn’t get it on the first try, so I won’t.” “So your plan A didn’t work out. Good thing there are 25 more letters. Start on plan B.”
“You are just too hard on us. We can’t do it.” “I’m giving you this assignment because I have very high expectations and I know that you can reach them.”


The goal here is to have a bank of statements that reinforce growth mindset that are easy to memorize, adopt, use and believe in so that every day I am consistently changing the dialogue in the classroom. I have found that it is easy to get sideswiped by a comment and not have a positive response handy. My goal is to fix that.


Any suggestions? Additions? Changes?



Some resources for Growth Mindset I will also use come from: Sue is an amazing writer and teacher. Her take on this is invaluable Just download John Golden’s Implict Theory of Mathematics Learning worksheet now and give it out the first week of school. I am, and you will be glad you did it too. These are great quotes, but quotes around the room won’t cut it. It has to come from my mouth, every day.

Aug 102013

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.

Jul 182011

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.