Oct 162016

This post is born out of a PhD class I am taking called “Models of Teaching.” It is a great class, but one of the requirements early in the semester was to write how I would use direct instruction in my classroom. I refused. I wrote a lengthy screed against DI. I attacked it, aggressively. What you have here is an edited, cleaned up, and less aggressive post born out of that assignment.


As a first year teacher, I was explicitly told by a principal to use direct instruction. He very carefully outlined what he expected any class to look like, and what the learners should be doing at every stage, every minute.

When that year was over, I left that school without a second thought. To deprofessionalize teaching to such a degree that someone could outline any class, any day, any lesson to the minute is reprehensible and borders on educational malpractice.

If you get the sense from this that I do not value direct instruction very highly; good.

I mean, really. Look at the way people think about education and specifically math ed. I think using comics as indicators is a great idea, because comics take a shared experience and pokes fun at it. Comics make us laugh through the pain, and there is a lot of pain in education.

Baldo, I cant believe school starts tomorrow

At the younger grades, we definitely see excitement for learning, but at some point, we beat that excitement out of kids. Why? This is a question I have asked repeatedly here, but I think DI has a lot to do with it. I mean, DI is a common way to teach math, as well as other subjects. Can we blame learners if they are bored, frustrated, and unexcited about classrooms that are taught through DI? And they are all 3.

math class is like a 40 foot long colon

Really? The punch line in this Baby Blues makes me cry. Literally. This is what the general public finds funny about math class?! But it isn’t just these comics. It goes on. And on.


The common theme of memorizing is so frustrating.


I am not advocating for “learn what you want” or unschooling, but certainly we can figure out ways to build in learner interests, right?


And DI just take us to the point repeatedly. “Oh, you weren’t paying attention while I was sharing what you were supposed to be learning? That is your problem, not mine.”

dennis-the-menace-back-to-the-salt-mines  dennis-the-menace-principal-not-warden

Yea, nothing more needs to be said here. Sigh. These were published in October. Of 2016. These are current. It makes it just that much more sad.


This Zits comic pretty much sums up the idea of Direct Instruction for me. It is clear that Jeremy (the teenager) has teachers who use DI pretty much the entire day. He is just consuming the knowledge of the teacher, puking it back for the test, and starting over each day.


And this focus on memorizing, and storing the teacher’s knowledge leaves learners doing what Paige Fox is doing here. Focus on the test, not learning. As long as the test comes out okay at the end, then all is good. Same issue Calvin had above.

But my objection to DI goes beyond the fact that it creates a horrible perception of classrooms. The philosophical underpinnings of direct instruction follow from Behaviorism and the work of B.F. Skinner.  Skinner, in his book “The Technology of Teaching” introduced wonderful machines that replaced teachers. In the behaviorist world, teaching is only necessary to introduce proper conditioning, and you do not need professionals to create those behaviors. Machines, called appropriately enough, “Teaching Machines” can replace teachers wholesale.

teaching machines by skinnerJust read the question, mark the response, check the response to the key, move a lever left if correct and right if wrong. Finish the lesson and repeat until they are all correct. This is the legitimate end result of behaviorism and the deprofessionalization of teaching. We see it in such sites as Con, er, Khan Academy, where the boring and mistake prone  lectures are used to give a false impression of learning. This kind of approach to teaching and learning is why at least one US Senator has suggested doing away with college professors and just have students watch Ken Burns videos to learn about the Civil War. Not joking. This is real. This is the direct benefactor of behaviorism.

In short, there is not enough alcohol to burn this chapter from my memory. [I leave this sentence in here from the assignment for a reason. Yes, I really did turn this sentence in, but also because it shows just how strongly I feel about this issue.]

These are harsh words. I freely admit that. I have very few, if any, kind things to say about direct instruction. I stopped teaching this way after my second year in the mathematics classroom. I would never go back, nor would I ever try to teach this way again.

It is painfully boring for the learners, and it is equally painful for the teacher. The fact it is completely ineffective to teach or learn higher order processes and skills makes it doubly not worth using.

Direct Instruction is the worst of all teaching methods, and continuing to use it just reinforces the boring nature of what learning can be. It doesn’t have to be that way! It really doesn’t.

When I write lessons, whether it was for high school or for the college classes I am teaching now, I start each lesson with these questions (replacing math with teaching now):

Am I:

–Assisting learners in creating THEIR own math understanding?


Forcing learners to curate and consume MY math understanding?

My goal is clear. I want every learner to move beyond my understanding quickly and efficiently. That can’t happen with DI. DI is a way to force learners to store my knowledge and understanding.

And, we need to figure out ways to stop asking learners to store our knowledge and instead celebrate their own. There are many constructivist teaching models. We need to use them. Find two or three that resonate with you and practice them. And then, celebrate the accomplishments of learning for more than 2 seconds.

Calvin is sad for a reason.


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.


Aug 162016

I took yesterday off of blogging because of being overwhelmed with todo lists for work. Fixed that. Yay! So, another #BlAugust post for me.


OMG! I also earned a “Star of the Week” from Meg Craig for this post! Wow. That is an honor coming from her. She also made a shortlink for the page: bit.ly/mtbosresources. I guess I better keep it updated!


Stars of The Week

Okay, on to the post.

I attended a board meeting of the local math group last night. Some of the most amazing educators in my region (not just my county), and it is a pleasure to work with all of them again. I am on the board as the Higher Ed Representative, which is a good fit.

During the course of the meeting, a call was put out by a member for resources, activities, and other things for the newsletter. Of course, I volunteered a list of 5 or so things off the top of my head from the MTBoS. There was concern about the amount of time it would take to “find” these resources, so I volunteered fix that.

This collection of #MTBoS resources is here so I can find it easily in the future and to provide a page where other teachers can be directed.

First off, what is the #MTBoS? The hashtag stands for Math Twitter Blog o’Sphere. Dan Meyer has an interesting take on the MTBoS.

Sites that are ‘organizational’ in nature:

These sites try to organize or provide structure to the #MTBoS in some way.

Exploring the MTBoS: A site created by math teachers to help organize, explain, and yes, explore the MTBoS.

Welcome to the MTBoS: A site created to welcome teachers new to the MTBoS. It gives them support, some guidance, as well as helps them find some good tweeps (Twitter peeps) to follow and get to know.

A dedicated MTBoS search engine: Have you ever wanted a lesson on XXX, but googled it and came up with a bunch of crap? This search engine searches only math teacher blogs, K-12, and will pull up lessons that are tried and tested. If the lesson sucked, the blog post will tell you that, and how to improve it.

TwitterMathCamp: An annual conference that meets in July to connect teachers. It is PD for teachers, by teachers. It also has an archive of blog posts from every year. In addition there is a wiki of sessions, My Favorites, and Keynotes.

The MTBoS Directory: This site lists teachers who are self-identified as members of the #MTBoS. Want to join? Just submit your name. That is all it takes. It has a map of members to help you find local math teachers, as well as multiple ways to sort and select people.

The hashtag #MTBoS on Twitter: Ask a question relating to math or math teaching using the hashtag, you will get an answer.

A Facebook MTBoS group: Another way to connect with math educators

A Padlet of “High Fives” for others in the #MTBoS created by Sam Shah. He is amazing. The “High Five” is relevant because of the speech I gave at TMC15.

A Chat list of Educational Chats: They list themselves as “official” but of course there is no such thing. It is rather comprehensive, and although the chats change times each year, it is pretty complete and accurate.

A MTBoS LiveBinder: This binder collects and organizes resources for the MTBoS. There are a lot of different links in this binder.

Resources / Activities created by the MTBoS (many are crowd sourced, submit your questions too!)

  • Global Math Department: Every Tuesday evening, a presentation by a different math educator on a relevant topic.
  • Daily Desmos: Different Demos challenges every day. 6-12
  • teacher.desmos.com: Yes, Desmos is a company, not a person. However, they are an active member of the MTBoS!
  • Estimation 180: Andrew Stadel’s site with different estimation challenges for each day of the year. K-12
  • Visual Patterns: Fawn Nguyen’s site with different visual patterns, challenging learners to create the equation / expression for it. K-12
  • Math Talks: Fawn Nguyen also curates this site which prompts to get your learners talking math. K-12
  • Which One Doesn’t Belong: Mary Bourassa’s site that poses the age old question. K-12
  • Math Munch: Justin Lanier’s site that has lots of fun, engaging lessons. K-12
  • Would You Rather? John Stevens asks the simple question, would you rather have this, or that? Justify with math. 6-12
  • Fraction Talks: A great visual way to get learners talking about fractions. K-12
  • Collaborative Mathematics: Poses questions to get learners engaged with each other about math. K-12
  • Open Middle: Robert Kaplinksy created this site to collect open middle questions. K-12
  • Math Mistakes: Michael Pershan is fascinated by what teachers can learn by looking at mistakes. K-12
  • Talking Math with your Kids: Christopher Danielson’s passion for doing math with little ones is celebrated. K-6
  • Math Arguments: The Math Curmudgeon curates problems to create math arguments in your classroom. 7-12

Teacher resources (not for learners necessarily)

And this is before we get into lessons from:

Bit.ly links created to archive and store awesome lessons.

  • bit.ly/desmosbank – Managed by Jedidiah Butler, a way to store all the awesome things created by teachers around the world with Desmos. Add yours too!
  • bit.ly/cardsortbank – Created at the Descon16 by Julie Reulbach to keep track of the amazing Card Sorts her group was creating. Add yours too!
  • bit.ly/mtbosresources (this page so I don’t forget it!)

These are just a few of my favorites.  For more activities, teacher created materials, sites, and just all around engaging stuff go to the Welcome to the MTBoS site. http://mathtwitterblogosphere.weebly.com/cool-things-weve-done-together.html

I hope this helps. Now that I have it typed up, I am passing it along to teachers in my region for sharing as well.

Have a wonderful day!

Edited: 17 Aug 2016

Edited 22 Aug 2016

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!

–http://onlinestatbook.com/stat_sim/sampling_dist/ 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.

Nov 062014

I haven’t posted in a while, mainly because I am just so happy with how my classes are going. I will focus on Alg 2 here, because these awesome learners are just knocking my socks off.

I am in the polynomial unit, knee deep in graphing, and increasing, decreasing, relative mins, relative max’s, absolute mins, etc. This is the problem set we were working on today in class:


Here are the questions I ask (docx format) for every single graph, from lines all the way through sin & cos at the end of the year.

Yes, some of these are going to be Does Not Exist. That is okay. Just because we don’t need to think about asymptotes with cubics does not mean we shouldn’t ask about them.

A little back story before I say something about my learners. I used to teach the textbook. I admit it. I sucked, horribly. My learners did not connect anything with anything and they did not see how to connect topic from one unit to the next. I was frustrated. So I first came up with my list of functions in (h,k) form, wrote it on my board and changed how I approached algebra.

2014-08-10 15.43.46

That was a win. But, then I was frustrated because every time I changed the graph, added an exponent, I had to teach a new set of vocab, but everything was the same; so why was I teaching new stuff? Why couldn’t I teach all the vocab up front, and then just explore the heck out of each function family?

Short answer was, I could. So, I did. That is where the form above came from. I introduced it last last year, and used it and modified it and tweaked it and the learners responded.

Enter this year, this class. I have everything set on day 1. We entered the year thinking about connections and planning our math and discussing end behaviors of lines (wow, that was easy, hey, they are always the same!, etc). Then quadratics, and we completed the square to get vertex forms, and we factored, and saw how intercept, standard and vertex forms were all the same function, and and and.

Enter polynomials.

We have done them from standard form, and done the division to get intercept form, we have broken these guys down every which way. I have tossed them fifth degree and fourth degree polynomials, they didn’t even blink. “Oh, so this just adds a hump to it.” I have explored more in polynomials this year than ever before.

And, since it is a constant review of prior material (“If this works with quartics, will it work with quadratics too? Yes”) I am constantly cycling and eliminating the mistakes my learners made in previous sections and on previous exams.

Which brings us to the problem set above. That is a killer set. The 4th and 5th are tricky, and they struggled. Until one of the class members said, “Don’t all we have to do is distribute them and so it is just a bigger distribution problem?”

Done. And. Done.

Now, of course there is a nicer way to do it. Substitute “u” or some other variable in for (x-3) in the fourth problem so you are multiplying binomials first. It saves time. BUT, it was not necessary to show it. They know distributing, so distributing is what works and they rocked the socks of of it.

So, why have I not been posting much? Because I have been enjoying the heck out of teaching. These learners are taking these ideas and running with them.  And I love it and them.

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.   http://www.shodor.org/interactivate/activities/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 182014

All models are wrong, but some are useful. George E.P. Box

AP Statistics

I was able to use this quote today in class. I was happy.

My learners were happy too, well, mostly happy. Well, okay, not happy at all at first. At first they hated me. They were struggling with learning how to do 1-variable stats, boxplots and histograms on their calculators in AP Stats. To force the issue of “you must do this, quickly and accurately” I gave them the following handout.

Ch 4 Box Plot Histogram 5 number summary INB 2013

5 data sets, all real, all crazy, none of them particularly easy. The golf data set is just weird.  These are clearly not data sets made up to look like something legit. They are data sets chosen to make them question whether or not their window is set right, whether they entered the data correctly. It forces discussion.

Then, they had this as homework.

Ch 4 – Tomato plant experiment

Yea, I am a demanding. They have until Monday, so I am not worried about the time it takes. But if they can’t make a graph, this is an impossible handout. If they try to get summary statistics by hand, they are in trouble.

I am interested to see what happens on Monday.


Algebra 2

Whew. This class started out brutal, but by the end of class they were ripping quadratic equations in standard form into (h, k) form in seconds. y=2x^2, or 3x^2, no problem. They were able to factor out the coefficient and jam on it. I was really happy about it. They struggled at first, but they were helping each other and they all had it by the end of class.

The assignment was to take 3 functions and put them all in the other two forms. Yes, the form for the second one requires the intercepts be written with complex  numbers. Are all functions factorable? Yes. Are all functions easily factorable? No.  Graphing will get them the intercepts? No. Graphing will get them the vertices at least? Yes, but (1,18) and (-3,-22) are two of the vertices. Not easy at all.

Sneaky Waddell, sneaky.

3 functions

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 http://thedicelab.com/ 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.