Nov 062016

In my last post, Why I won’t use Direct Instruction, I was provocative and challenged some of the typical thinking about math instruction. The post generated some terrific conversation, both here and on Twitter, and although I have not changed my mind for my own classroom use, I do admit there may be times when DI has a function and purpose.

The grad class I am in has moved on, which is how classes work, and we are discussion Cooperative teaching this week. The textbook is very focused on English and Social Studies, which leaves the math and science people out a bit, but it does discuss the Jigsaw lesson plan at some length. The Jigsaw is a good strategy, and it is useful in math class for sure, but there are so many others!

To create a better list, I asked the #MTBoS for their favorites. I won’t embed all the tweets, but will give attribution to every person who submitted and idea or link in the idea. I want to feature the lesson plan ideas and the links to them. I have not used all of these. Heck, I don’t think I have used half of these! But the collection is amazing, and although some of the ideas don’t have details, you can figure out the idea from the names of some.

The really nice thing is that these are all cooperative lesson strategies from math teachers for math teachers. If you want some ideas on how to incorporate these well tested strategies, here you go:

  1. Speed dating: Me! @gwaddellnvhs, Mary-Ellen @MathSparkles; This was one of the two I suggested. I really like this method of getting learners collaborating with a purpose.
  2. Add it up or Placemats or 4Sum or Add ’em up: Me! @gwaddellnvhs; Heather Kohn @heather_kohn; S @reilly1041; Kate Nowak@k8nowak; This is another strategy I offered in my original question. I think I got it from Kate originally, forgot the name, and then called it Placemats because of a way to set it up using butcher paper. Same idea, different names.
  3. Participation Quiz or Partner Quizzes: Martin Joyce @martinsean; Rachel @Seestur ; Used these often. Very engaging way to get everyone focused. The tricky part is creating the teams for the quiz, but that is achievable.
  4. Clipboard of quotes & actions that support each other. Update whiteboard, then go over: Martin Joyce @martinsean
  5. Whiteboard Game: Lisa Bejarano @lisabej_manitou
  6. Problems around the room: Lisa Bejarano @lisabej_manitou
  7. Also a big fan of whiteboards where students keep answers secret and then they All “flash” at the same time: Mary-Ellen @MathSparkles
  8. Pass the Pen: Madelyne Bettis @Mrs_Bettis
  9. Work on the Wall: Madelyne Bettis @Mrs_Bettis
  10. Ss work prob on board while 2nd Ss “calls” it like a baseball announcer: Mary Williams @merryfwilliams, The boys get into it with the Bob Costas enthusiastic voice, “and he is STRIKING OUT LADIES AND GENTLEMAN!!” Most of the time they are really positive though – all the sports enthusiasts enjoy announcing 🙂
  11. Ghosts in the Graveyard: Mary Williams @merryfwilliams
  12. Sage and Scribe: Briana Guzman @brianalguzman
  13. Quiz Quiz Trade: Briana Guzman @brianalguzman
  14. There can be only one (marker): Nathaniel Highstein @nhighstein
  15. Having round tables in the classroom: Rachel @Seestur Rachel really enjoys having the round tables so learners have to look at each other while working. It makes total sense to me!
  16. Tarsia Puzzles: Sheri Walker @SheriWalker72; Paula Torres @Lohstorres1; In case you don’t know what Tarsia puzzles are, Tarsia is a FREE software package to make puzzles out of sets of problems. They are really cool, and when you require them to be worked in partners, can be a great way to incorporate cooperative learning in a different way.
  17. Card Sorts: Beth Ferguson @algebrasfriend; Card sorts have been around a while, and they are highly effective. I used them in AP Stats as well as algebra. Desmos recently incorporated card sorts into the Activity builder, so you can get awesome electronic card sorts now too!
  18. Row Games: Kate Nowak  @k8nowak; Beth Ferguson @algebrasfriend; I have used Row Games too. The best part is the link takes you to a folder owned by Kate that has 3 pages of mostly word docs of teacher created games. This means you can edit and change them to make them better for your class! Also, it would be awesome if you shared back your creations to help others.

Additionally, David Wees tweeted out the following people, but didn’t give more info. I suggest contacting them directly for more information.

David later did followup with this link to TEDD (Teacher Education by Design). I poked around their site. Looks promising!

Amy Lucenta also was kind enough to let us know her ideas are found in her book from Heinemann Publishers.

I hope this helps, and if you have any other cooperative learning ideas, drop them in the comments please!

Aug 222016

A late in the day #BlAugust post.


Yesterday Jennifer tweeted this at me, and I teared up a little.

And the tweet it refers to is this one:

You see, the High Fives post is one of the most popular posts I have ever written. It was a spur of the moment, almost didn’t do it speech (kind of like the TMC16 speech on overcoming your fears) that has resonated through so many people.

For a long time, I kept track of the people tweeting and blogging about High Fives. I know I missed some. I counted over 20 different individual who tried the High Fiving, and said it changed their classroom culture for the better.

Jennifer tweeted and wrote about it a full year! after I wrote about it. How often does that happen? To me at least, not very often.

To say I am embarrassed and honored by the mentions is an understatement.

To say I am overjoyed by the fact that learners in over 20 classrooms are experiencing something different because I spoke up is exciting and amazing. We need to spread the high five energy.

So, to help more teachers and to spread the power of the high five, I wanted to revisit the video:

My original post: The video is short, only 4 minutes. In fact the last 20 seconds can be ignored as it was an announcement for the conference.

You are doing something awesome. You are walking in my classroom. Be awesome. Connect with your learners. Give them energy, and receive the energy in return.

High five to you all!

Edits added:

After I posted this article Lisa Henry posts about All The Stuff I’ve Stolen From The MTBoS. High Fives are the first thing on her list, and she explains why in a different post.


Nov 122015

I have been in Elementary school classrooms this semester observing my learners teach lessons. They are amazing, and the UTeach model of teacher education is one with which I am completely on board. My learners will have spent so much time in the classroom being observed and getting feedback that they will have no choice but to be amazing teachers. Add in the fact that my math teachers will only be taught to use interactive and engaging methods like the 5E model, and you have a home run.

BUT, as I have been in 3rd through 5th grade classrooms, I have noticed a very disturbing trend. Like this board I saw in a 5th grade classroom.

2015-11-02 12.20.48 (2)

Notice that the objective here was to “Reacquaint yourself” with the math terms by designing a city. OMG. Seriously. This was in the 5th freaking grade. No wonder geometry is such a difficult class to teach in HS, the learners are bored stiff and resentful the teacher is lecturing them on something they have spent time on already.

Next up, a 4th grade classroom. The terms I heard LEARNERS using today were; expression, equation, identity, and inverse.

No joke. 4th grade. The learners were using the terms correctly, and identifying the difference between an expression and equation and using inverses to construct identities while solving equations.

This was not a Gifted and Talented classroom, this was an at risk, high needs, pretty normal, typical classroom.

If I were to summarize what I have learned this semester as a teacher of teachers, it is this. High School teachers, we need to seriously up our game. We need to realize that the reason our learners look bored and apathetic is because we are rehashing what they already know.

We are NOT connecting to what they already know (even if we think we are.)

We are NOT challenging them to reach for deeper understanding (even if we think we are.)

And, we are NOT realizing the learners are entering our classrooms with a great deal of prior math experience and love. Connect with it. Pull it out. Create engagement.

My eyes are open, and it scares me to death what I have done in the past to my learners. The CCSS standards are working. The shifts in mathematics education are working. We must be leaders and take advantage of it.

Go spend time in elementary school classrooms. It will shock you what the learners are doing today. What are we doing?

May 292015

Wow, it has been a while since I posted anything, and I need to share a ton of things I have done. I predict that I will post a lot in the next several weeks. The school year is winding down, but my learners are ramping up. Grad school is down for the summer (with the exception of an independent study on activity theory) so I have much more time to write.

My learners are working on their final exam / projects, and they are hating me right now. They realize that the stats has a purpose, and that it is far harder than they thought. The handout for my assignment is here if you want to use it, or see what I required.

The only reason I veto projects are because it is too easy, too hard (and it is my opinion for that, although we discuss the reason why so they have an opportunity to revise and make it appropriate) or if the subject matter is just too sensitive / personal and it is in the realm of professionals, not high school learners.

Below is the list of surveys / observational studies / experiments that my learners have decided to undertake this year, broken up by period. It is a rather impressive list!

———Period 2———–

  • Social media use / grades
  • How do adults / teenagers differ in choosing restaurants
  • Does quizlet or flashcards help more in learning vocab (using ancient Sumerian words?!)
  • Does education really affect income (using census data from several zipcodes in the city)
  • Is there an association between a school’s weightlifting records and win/loss at sports?
  • Is sex ed successful?
  • Does involvement in club cheer affect grades (4 different age groups)
  • Do taller people run faster, looking at high school, college and Olympic atheletes?
  • Does appearance have an impact on grades?
  • General questions about tobacco use and quitting
  • Which costs more, male or female beauty products?
  • Quality of life of the parents / learners in school
  • Which area of the city has more trash on the sides of the roads?
  • Does music affect memory (experiment)?
  • How do you use social media?
  • What is your perception of LBGT issues?

———Period 3———–

  • How does sports affect grades?
  • Are oreos really double stuffed? (I never showed my class the story on this, this team came up with it on their own! Love it)
  • Is bullying an issue, how large?
  • Are drivers more likely to stop at a stop sign when they are being watched?
  • An experiment on what type of information changes learners opinions on drinking age.
  • Does work hours affect GPA?
  • Does being exempt from an enrichment class at school affect GPA?
  • Are cheetos packaging regarding number of pieces correct?
  • Does social media use hurt GPA?
  • Is the dress code at school appropriate?

———Period 5———–

  • Does the sugar content of cereals affect the placement of the cereals in the grocery store?
  • Does music affect memory?
  • An experiment on whether or not gender effects whether or not people help with dropped books in the hallways.
  • How does our school compare to other schools in the community service of the learners?
  • Does sexism exist in the high school population?
  • Does the perception of animal rights change from learners to adults in the building?
  • What kinds of social media is most prevalent & how should the school use social media?
  • Who is bullied most over social media, males or females?
  • How does M-M vs. F-F & hair length affect the attitudes towards GLBT youth in stores (a very daring observational study)
  • What drugs are prevalently used in the high school per grade level?
  • Is marijuana use a problem in the high school?

As you can see, there is a huge variety (and some major overlap) between the different classes and projects. Each group is working their way to answering their questions, with the final exam being a presentation of their results.

Always exciting.

Oct 222014

I just sent this email to my department today. The subject was “If you still assign drill and kill problems”.

I am posting the text of the email without comment. It was spurred by a conversation on Twitter with @DDmeyer and @JStevens009.

Text is below:

Good morning all,

Hate to be the bearer of unwelcome news this morning, but if you are not keeping up with the world of math technology, it is reaching a tipping point of changing what we do. Check out the site: and think about what it means to our profession and our classrooms.

Only around 30% of all kids have iOS devices, but in 2015 when it hits Android and the entire market is open, nearly 100% of our learners will have access to this. For free.

Kuta worksheets? Textbook problems? This type of software will render this type of homework obsolete. Desmos and TI-calculators have nearly done so already.

We have talked about the purpose and need to rethink what homework is for, and the tipping point is rapidly approaching where we really need to make some changes to what and how we handle it.

We need to think deeply about how we can create an environment of learning both in and outside the classroom, because the technology is making outside the classroom a moot point unless we make some changes long term.

Sep 172014


One thing I am really working on in AP Stats is the amount of notes, the lack of notes, and the engagement of my learners. AP Stats is one of those courses where the amount of vocab to assimilate is so huge, that it cannot all be done by activities. I have found that a mixture of activities and notes, and assignments and cycling back again helps tremendously.

I have the one slide from my notes today above. The literal, not figurative, brick wall between the two ideas of mean & standard deviation and median & IQR was very well communicated this year. The learners told me they understood. The formative checks I did supported that.

I still am not confident. Too many learners mess up this idea every year for me to take the face value word on it. I will be giving some questions over the next couple of days to make sure.

The re-writing of my slides to be word minimal, picture heavy, and discussion focused has changed how the class goes when I am doing notes, at least. I am happy with that aspect, and the learners I have asked directly about the notes have told me they are very useful and not boring.

That is something at least!


PhD spillover

As an aside, the class on non-parametric statistics has taught me one thing that has impacted my AP Class. The structure I used last year as far as how I teach the content is right on the money.

2014-09-16 16.08.00

In the PhD level class, we look at every problem first from the perspective of “is it categorical or quantitative” and then “how many variables”. So far, we have limited the decision to just categorical, non-normal problems (hence the non-parametric! label of the course.)

For Inference section, the course will be divided up into a. quantitative 1 sample, a1. confidence interval, a2 hypothesis testing; b. quantitative 2 sample b1. confidence interval, b2. hypothesis testing, etc. I think this structure leads better to the advanced level stats if they take a next class.

It is also the exact opposite of what our textbook does. Oh well. I didn’t use the textbook structure for 2nd semester anyway for the last 3 years. This just reinforces that decision as a good one.


Finally, some lesson ideas I am working on.

2014-09-16 16.09.51 2014-09-16 16.09.01

That’s right. Funky dice!

On the left we have odd shaped, non-standard dice. Awesome. Are they fair? Not sure. On the right we have, yes, for reals, 5 sided, 7 sided and up dice. No joke. I once argued that a 5 sided fair die could not exist. Is it fair? Not sure. I am writing some lessons for expected value to take advantage of both of these.

I also received word from Robert at that my order of weighted dice is coming soon.

Heh heh heh. That’s right. Real, honest to goodness (well, dishonest to goodness) weighted dice.

Expected value here we come! More later on this idea.

Sep 022014



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.


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!

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.

2014-08-12 15.33.57 2014-08-12 15.34.25 2014-08-12 15.34.57 2014-08-12 15.35.17 2014-08-12 15.35.53 2014-08-12 15.33.27 2014-08-12 15.36.28


May 222014

My Algebra 2 Honors learners were struggling with radians and the unit circle so I broke out the creative guns and went all manipulatives on them. It worked.

The file I used is a PDF I created in Publisher that you can download here from this link.

It is very simple, but very effective. It has a Unit Circle with only the axis marked and 3 triangles with a “finger spot” for holding it in place.


Before I had them cut them out, they wrote the hypotenuse length inside each (which is 1) and the other two side lengths inside as well.

Now the magic occurred. I had them use these triangles with the side lengths written in to tell me the radians and coordinates of the endpoint for each.

All they had to do is move the triangles around, “rotate them” through the angles and use the triangles to document the endpoints.


The connections to “Hey, all we are doing is cutting up a pizza” and “there are clearly 6 pieces of the 30 degree, 4 pieces of the 45 degree and 3 pieces of the 60 degree triangles in the top part of the circle” were immediate.

The harder discussion of the endpoint coordinates were only hampered by the learners that did not follow direction and write the side lengths. Once they had the side lengths in, they saw the connection immediately.

It was nice to be able to have the connections made with the unit circle so easily and now they are all making the unit circle from memory with no problem.



Apr 162014

This post is a quick one, to simply thank Kate Nowak for saying something publicly that I have said privately for a couple of years now. In her post on the NCTM Technology strand, (which everyone should read first. It is okay, I will wait. …. Still here, still waiting, it is okay, really, go read it if you haven’t)  she said this:

Dear Teacher: if the professional development offered by your school or district is not helping you improve your practice in clear, consistent, measurable ways, then it’s up to you to take responsibility for your professional growth.

Kate also has the following graphic as well:


The citation for the article leads me to the following link:


I have said something similar to teachers in my district for the last couple of years. I have said it to admins, and told teachers that if the PD being offered is not the quality they expect or not meeting their needs then they should leave. I have received blowback on it. I have been told that is rude, arrogant, and that we should just sit through it because someone decided it was important. I call <cough>b.s.

I have said that to the rooms that I have been leading. If this is not meeting your needs, please find a room that is. I do not want to waste your time. I mean it. Leave. Now. Get up, walk out.

If the professional development is ineffective, then we have to start acting on our professional beliefs. The old saw about teachers make the worst learners is absolutely false. We are permanent, professional learners. We make bad learners in bad learning situations!

Kate’s comment struck a chord with me, obviously. I have spent a couple of hours today writing lessons for Desmos for preservice teachers at my local university. It is professional development. It is something I will use to teach other teachers. If it does not engage them; if it does not create questions that are interesting, then I expect to be told.

Thank you Kate. I truly appreciate your words and suggestions.