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!

Oct 122016

I had the opportunity to read a preprint edition of Malke Rosenfeld’s new book, Math on the Move, and here are my thoughts.

First off, let me start off with what this book is not. As educators we have probably sat through a professional development where someone told us that in math class, we can appeal to the “kinesthetic learning style” by having the learners up and moving around the classroom. We can appeal to “kinesthetic learners” by having them move their arms, or by doing gallery walks. I have sat through several of these. [yes, I put that phrase in quotes on purpose. I do not believe in ‘learning styles’. Multiple Intelligences, yes, learning styles, no.]

Rosenfeld’s book is not this. No where near this. This book is not about “kinesthetic learning” this is about making connections in mathematics through motion, body, and dance for elementary school learners. It is an amazing concept to think about. I really appreciate that on page 2, she says, “not all of dance is mathematical and not all math is danceable.” That sets the tone for the entire book. Rosenfeld looks for the strengths in using movement, and using the body as a thinking tool. This is a powerful idea, and the first chapter of the book is about what doesn’t and does count as using the body as a thinking tool. I loved the deep thinking this chapter provoked, because it made really think about dance and movement with respect to math.

And, let me be honest. My knowledge of math through motion is very limited. My idea of dancing is more aligned with this guy than anything that someone else would consider “dancing.” Honestly, I wondered for a moment if someone had recorded me actually dancing when I saw this gif.

dancing-gif via

But, despite the fact I am both musically and rhythmically challenged, I have always thought there was opportunity to connect math and movement. I have never figured out how, but I have been intrigued by the idea. After reading the table on page 17 I realized why.

table of nouns and verbs about math movement

The verbs of math are aligned with the verbs of dancing. The nouns of math are also aligned in large part. Looking at the list, and knowing, intellectually, about the ideas of dance, it is easy to understand how strong the connection is. Through examples of learner work, QR codes showing video of learners moving, multiple lesson examples, pictures, role playing examples, and well developed explanations, Rosenfeld shows me how to implement dance in a very constructive way in the elementary classroom. By the end of chapter 3, I was willing to try it with elementary kids tomorrow. That takes a lot for me to say, because I am secondary through and through. Little kids scare me. But I am so excited by the opportunity I see after the first three chapters of lessons that I am willing to try them. They are so interesting!

I think the real power comes later in the book when the 6 stages are developed further.

  1. Understand
  2. Experiment
  3. Create
  4. Combine
  5. Transform
  6. Communicate

These stages allow learners to move from the understanding of a concept and goal to the creation of a multi-step dance pattern and ending with the discussion and communication of the idea through a presentation of the dance. The last half of the book has QR Codes on almost every single page with video link examples. The depth of knowledge these can provide is stunning.

All in all, the more I read and find the joy in mathematical dancing, the more opportunity I see to push this into the upper levels. There is so much more that can be done with this idea beyond the boring and basic. It might even make me a better dancer! Well, no. It isn’t a miracle book, just a really good math book. It is authentic movement, not the usual fake stuff we see.

I think it is time to bring real motion in to math class, get learners moving in purposeful, meaningful ways, and leverage that motion into strong mathematical knowledge.

If you want to read a chapter for yourself, check it out on Heinemann’s website.


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.

Feb 092015

Besides the usual quote on the board today, I also have this math pickup line: How can I know hundreds of digits of pi and not know your phone number?  I am featuring a new math love / pickup line each day this week (some days will have more than one). If you want the list, Math & Multimedia is the source.

But anyway, I hate to even call this a #180 blog posting, because I gave up on that at the semester. I just was not focused enough to maintain. I don’t know how people do it. But I do want to share some of the Central Limit Theorem Love I just did.

The exercise is not my own. I stole it from Josh Tabor and I credit him fully with the idea. What you need for this exercise are pennies, chart paper, and some fun dots. That’s it. You need a lot of pennies though. By a lot I would estimate I have approximately 2500 pennies in a bucket. I don’t know exactly how many, but it is a huge number. I emailed the staff at the school and asked for pennies and they delivered. Each year I ask for more, and they deliver more. It is terrific.

Okay, on to the set up. When the learners walked in the room, they saw this:

2015-02-06 10.00.15

The instructions, the left chart paper for x’s, the middle for xbar’s and the right for p-hats. Yes, the scale is completely wrong on the p-hat chart. It should be from zero to 1. I fixed that.

Then, the learners pulled their coins, found the means, the proportion greater than 1985, and we graphed using stickers for the x’s, writing xbar and phat for the other two. At this point, we ended up with some good looking graphs. We discussed if we could tell the mean of the dates from the x graph, we decided we could not, so we OBVIOUSLY needed more data.

Do it again.

After two rounds, we ended up with these graphs:

2015-02-09 12.23.42 2015-02-09 12.23.54 2015-02-09 12.24.02


I did change the 1985 to 1995 by the time I took these pictures from my 3rd period of Stats. The newer pennies the staff gave me pulled the mean up.

I actually tore the “Actual Values” graph down and threw it on the ground because it was so useless. That was the point of that graph. I loved how the other two graphs were so clearly unimodal and symmetric. They fit the idea of the CLT perfectly. The fact they matched was just icing on the cake!

– Using this simulation for the CLT, we then looked at what happens when sample sizes are changed, whether the shape of the population matters, etc. It was very eye-opening.

Then we discussed the reason why, how, and what conditions must occur for one sample to then represent the population. The notes I used are here in pdf format. I am trying something for the end of the year where I post the notes before hand and they are required to read them as homework. I HATE going over the notes in class. So far it is a good experiment.

Next up are some in class problems.

This is the third time I have done this exercise, but only the second time I have used xbars and phats. It is very useful to have those there so the formulas make more sense.

The fact that the formula reads “the population mean is identical to the calculated mean of the sample” is very useful when the learners keep the population mean and the sample mean separate.

Sep 292014

I tortured my learners with a game, a game that was awesome and they all agreed was worth while. We played a Stats Pictionary!

I used this document.  Ch 5 – various distributions- Pictionary   I created these distributions using the Illuminations Applet called plopit.

Here are my rules:

1. Each pair gets one distribution.

2. You have to write your SOCS (Shape, Outlier, Center and Spread) so clearly, using values and descriptive words so that the other learner can duplicate the distribution without asking any questions.

3. Once the SOCS are written, trade papers, and then try to re-create the distributions from the descriptions only. DO NOT SHOW the original.

4. Once the distributions have been done, show the distributions and compare.

5. Repeat.


That’s it. Very simple. I did model one for one class. They were struggling with the idea. Once I modeled one, they were fine.

Big takeaways: They realized their SOCS sucked. The figured out what they needed to do to make them not suck, however. Also, the first round went poorly, but they quickly modified their SOCS statements to be clearer.  Finally, Spread was the one thing they still struggle with. They are getting better, but trying to estimate from a graph is hard.

We ended up doing around 4 to 5 graphs in the 35 minutes I allowed for it. It was a great experience I think.


I was asked to show my notes. This is the ppt I am using for all of 1 variable quantitative stats. I don’t think it is anything special, but I AM trying to be more creative and thoughtful with it.

I can’t get away from all the notes. I don’t know if it is me, or the material. I do know this is about 14 days worth of notes. I have not done a whole day. A few slides. Stop. Do activities. More notes tomorrow. More activities.  Check out slide 64. 🙂

Categorical & 1 variable Quantitative



Sorry to be silent last week. It was crazy and I was in a spiral of grading hell. I am not out of the grading hell, but I am out of the depression that results from the spiral. Now I am focused and getting caught up.

Sep 232014


That’s right, they got greedy, and lost. Well, everyone gained, knowledge and skills that is.  Today (and tomorrow in one period) in AP Stats we are playing The game of Greed. This is a great game, that challenges the learners in the end to make box plots and comparison statements about the created data.

You end up with some great data to use in class.

2014-09-23 10.46.52     2014-09-23 14.10.14


What is especially great is the right picture, period 5. Notice the big, fat zero? Yes, a female in the class purposefully took zero points. This was a VERY high scoring game as well, the die was very generous to them, and that zero affected everything. I just laughed when she said she was going to purposefully take a zero. It is well within the rules.

This achieved one goal of getting learners talking about the math, at least. 1 thing accomplished today for sure. They also learned more about comparing distributions and using boxplots. 2 and more things accomplished.


Algebra 2

This class was awesome today. I gave them a quiz. They had 1 quadratic function in vertex form, 1 in intercept form, and 1 in standard form. They had to turn the one they chose into the other two forms, and then answer all the questions about the function.

Oh, did I mention that if you choose the vertex form, the max points you can earn is 80% of the points? Intercept was worth 90% and standard form worth 100% of the points. They could choose 2 to do, but I would only grade the ONE they told me to.

As I walked around, I saw lots and lots of little mistakes. Silly mistakes. They would be losing, as a class, a ton of points because of not checking signs, and other silly things. I didn’t want that to happen, they knew better, but they were being inattentive to details. So, with 15 minutes of class I told them they could ask anyone in the room any question they wanted to, but they could not ask me.

They figured out pretty quickly they were being silly. Tomorrow’s quiz for real will go differently. Same set-up. Different equations.

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 162014

2014-09-16 16.08.00

You are here! That is my AP Stats objectives board for the next few weeks. Today and yesterday we finished up Categorical data analysis with Relay Cards. It was very successful. I had many learners telling me they understood what they were doing, and they were saying this even though they were making mistakes in the reading of the problems.

I like the fact they were happy with the content and realize that making mistakes in reading did not mean they were not understanding. I need to figure out a way to make sure they realize that.  This is an issue I need to think on tonight and figure out a way to pull it together for them to think on as well.

I wish I had a magic phrase that everyone would hear and just go, “Aha.  I understand that making mistakes does not mean I don’t understand, it just means I made a mistake.”

I have RADICALLY revamped the notes I am doing as well.

This is the old PPT from the book. I am ashamed to say I used this for several years.


Here is my notes for this year, same topic. Yes, the quote is from Dr. Who. I will see how many learners pick that up.



Yes, there is still text on the slide, but less. And more of a story instead of regurgitating stupid words.

histogram  I am trying to do more of this type of thing with my notes instead of the “The definition of a relative frequency histogram is” blah blah blah. So far, the learners are telling me my notes are not horrible. They read less, they write less, and they are learning more and being much more quick in doing problems and asking better questions.

So far, success on that front.

Ch 3 – Relay Cards (made by Shelli Temple)


Algebra 2

Whew, but Alg 2 is brutal.

We are working our way through a series of Quadratics. Today I introduced completing the square and justified it by needing the vertex form. All of the quadratics we have done are found here:


I started them off in vertex form, they had to provide intercept and  standard form. Now I am giving them standard form, and they provide vertex and intercept form (among all the other information found on the exploration sheet.)

They are hating me right now, but it is getting easier. The idea that ALL quadratics are factorable, is stressing them out. Some are easily factorable, some require the quadratic formula, but ALL are factorable.


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 252014

Vocab is killer in stats class. If there was one single thing that determines success or failure in stats class it is mastery of the vocabulary. I am really trying to make that a smoother transition, and I think so far it has been successful.

One new thing I tried is Shelli Temple’s (@druinok) Quiz-Quiz Trade exercise.

They are 32 flash cards with a sampling situation on the front and the answer on the back. Nothing truly spectacular in difficulty setting up, but really, how much of what we do is super complicated.

I gave one class about 30 minutes to do in class, and the others 15, but all of them had great questions about why this was cluster, but that was stratified, etc.

On the quiz they are getting, the question I am most looking forward to the answers is: “Explain the difference between cluster and stratified sampling.” I hope this helps them see the differences in a sharper, more focused way.

And then there is tonight. This is a short post because of tonight.

I leave school in 15 minutes for UNR, where at 4:00 pm I have my first grad school class to begin my Ph.D. process. I am a little nervous, but a LOT excited.

I am not clear in my mind if I am going to use this blog as a platform for reflecting on my studies, or if I should keep them separate and start a new one.

Any guidance from the readers? All 2 of you? 🙂

Anyway, off to a class in Qualitative Research in Education.