Oct 142015

Okay, it was yesterday, but I was crazy busy and didn’t post it.

Yesterday, out of the blue, one of the learners I had three years ago tweeted this:


This is one of the times that makes me proud to be a teacher. It also makes me proud to know that I have had a positive impact on other learners who didn’t tell me this, but who are experiencing it daily.

Rock on, Cassidy. You make me smile. Thank you!

Aug 152015

At #TMC15 I shared my favorite of the “High 5”. Richard Villanueva is awesome enough to record them all and post, so I will just share the video of what I said. It is short and sweet:

There is the video. I want to stress a few points.

  1. Giving high fives to my learners absolutely changed me. I got 150 high fives every day. How can you NOT be in a great mood getting 35 high fives several times a day, every day.
  2. I am serious. I didn’t teach math. I taught people the subject of math. The high fives was just one step that demonstrated this philosophy.
  3. This was an evolution of my approach that on the first day of class scared me to death. I was freaked out and thinking that it was going to be a massive failure.
  4. I was wrong.
  5. It was the single thing I did all year long that had the greatest impact on my classroom environment, my relationship with my learners, and my own personal attitude.

I wrote about it last year as it occurred:

Before school started: August 10th: School started on the 11th.

After 1 week of school: August 20th

After 1 month of school: August 27th

I finally EARNED a high five from my one holdout: September 10th  : This is the one high five I am most proud of.

That was last year. Then #TMC happened. After #TMC15, several teachers told me they were going to try it. We had several Twitter conversations about it at different times with different teachers. A sample is below. And this is ONLY a small sample of the more relevant tweets.






And here are some captured images from @misscalcul8. Elissastartpic2Elissa2 elissa3  Elissa1 And finally: pic1Elissa    

Let’s pause and reflect a moment.    What effort did it take me to give a high five? Very little. I had to get over my introvertedness. I had to fight my impulse to just stand there and say hi, and I had to make the effort to actually acknowledge each learner one at a time with the motion. I had to grab some hand sanitizer afterwards as I was walking into class. …. 

Yea, that is really what it cost me. That’s it.

Not to diminish the fright / frustration / and uncomfortableness that the introversion creates, but getting over it did not damage me in any way.  

What did I gain? My learners received the one on one acknowledgement from me every day. They walked into my classroom looking forward to the personal contact that went beyond the subject and touched them personally. Learners who were just standing in the hallway saw it and started asking for a high five every day. They recognized that it was something to get and feel good about themselves.

It changed my outlook on the class period. Every period be came a 1st period of the day. Every period was a “good morning” because every period started with 30 to 35 high fives. How could every period NOT be a fresh start, a clean slate, and a new beginning. It changed the class outlook towards me. I wasn’t just that weird math teacher (and I was) who wore strange socks everyday (because I did). I was also the math teacher who treated them like human beings. I also was the math teacher who acknowledged they were weird learners (because they were) who struggled with the ideas (because they did) and who needed the reassurance that if they kept trying they would get it (because they absolutely DID.)  

The cost / benefit analysis there is pretty clear. What it cost me was very little. What I gained was huge. What my learners gained was even greater.  


I am not teaching high school anymore. I am teaching college and the standards are different, the expectations are different, and the stakes are different. Guess what I am NOT going to give up. I think these outcomes are too valuable. It will definitely be a radical departure for the college setting. It is worth it.  


Edit: Some research to back up why it works: http://www.teachers.net/wong/OCT13   More teachers on board! Yay!    








These next three go together. Wow, the power in these three tweets.




Amy posted on her blog the following paragraph.

High fives at the door. Glenn’s “my favorite” has been popular for good reason. It is simple, but we have already discovered it is powerful. My colleagues and I decided to make it a department thing, and also roped in the two non-math teachers in our hallway. So the 200 hallway is officially the “high-five hallway” at our school. I am surprised by how something so small has already helped me feel more connected to my students, and how the classroom atmosphere gets an immediate boost. You just can’t be too grumpy after a high-five.

Chris Shore said:

High 5’sGlenn Waddell (@gwaddellnvhs): Glenn was right. Offering the High 5’s at the door does more for my mood and mental preparation for the class than it did for the kids.

Bob, on his blog, said:

GREETING STUDENTS WITH HIGH FIVES – Intertwined with all of the mathy goodness of Twitter Math Camp this past July was a simple and powerful device for student engagement from my friend Glenn Waddell – the High Five.

Each day last year, Glenn met his students at the door to give them a high five – a simple, caring gesture to establish a positive tone for class. I often meet students at the door before class or linger in the hallway for informal chat, but I love the tradition and rapport Glenn establishes here and hope to emulate it.

Lisa, on her blog, was even more positive about the effects:

After five days of being at the door and high fiving students, students are positioning their books to be ready to give me a high five as they approach my class. I have had students high five me in the hall when I am not at my door and walking in the hallway (when I don’t have a class). It makes me smile.

This is only one paragraph of a much longer post by Lisa, but you get the sense right there something amazing is happening.

Stephanie Bower tried it too. Her post says so much about it.

Most of the time, the high-fives give me a chance to gauge the moods of each student in a split-second. (Glenn pointed this out too.) I can tell by the tone of their high-five, the way they return my verbal greeting, and their body language if something is “off” that day.


[And yes, that graphic is golden, and will be stolen and reused. Forever.]

highfiveclub Thank you @conniehamilton.

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.

Polynomials in Alg 2

 Alg 2, Personal  Comments Off on Polynomials in Alg 2
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.

Quiet but busy day

 Alg 2, Personal, Technology  Comments Off on Quiet but busy day
Sep 112014

Today was my quiet day, only two classes. But, I was busy all lunch upgrading my learners calculators!

2014-09-11 12.28.03  Yes, that is the pile I have done today at lunch. About 5 learners have already come in and picked their calculator up, thank goodness. I am a bit nervous having $1200 of calculators sitting on my shelf, especially when they are not mine!

This is one of the things that we don’t often realize takes up a ton of time. The learners don’t realize that these things have operating systems, and that the operating systems change from time to time. When learners are buying calcs on eBay (which I always encourage because TI=ripoff) the calcs often come with out of date OS’s and are lacking functions that truly make the calc useful.

For example, look at the following two prompts, both come directly off of the TI-84:

TI-84NEWvs.  TI-84OLD


Which one of these screens would you rather see when typing in information?  Me too. The left one is much more friendly.  I say at the beginning of my class, every day for the next two weeks, “You want me to make sure your calculator is updated. Please come see me.” We had a 2 minute discussion of what the current versions were the other day when we were talking calculators too.

I think this is the biggest change so far this year on the calculator front. Last year, I had 5% of my learners ask me to update their calcs. This year, I am up to around 40% already. That is worth it. I am really annoyed in May when someone says, “Yea, I knew there was something about updating, but I never bothered.” That person probably is not trying for a 5.

How to make this process easy? For the NSpires, have 2 4 port hubs with cables plugged in. This allows you to shove out updates to 8 similar calcs all at once using the Teacher Software.

For the TI-83 and 84’s you have to update one at a time, but it is fairly quick using TI-Connect.

Oh, and it helps if you have a directory that looks like this: calc directory

All the current OS update files, old update files (bcs the NSpire must be updated to 1.7 before you can take it to 3.9), 83, 84, 84C images, etc. I download all the new files when they update (2 times a year for the NSpires, really TI?)

What a pain in the butt. But it helps my learners.


AP Stats:

Not much happened today. It was a continuation of yesterday (same content, different period). Tomorrow is my 3 in a row stats day.  I am going to challenge them with some bad graphs and another short relay card race on contingency tables. Then, moving on to 1 variable quantitative stats. Yay!

Alg 2 Honors:

It was an AMAZEBALLS Day.  We did this exercise with one quadratic function. Just one. But the conversation we had was so amazing. I gave then one, factorable function in Vertex form. Then we started going to town. The “wow, look at the connection here” and “oh, I get it why it was this!” and “wow, this is all the same stuff!” was terrific.

The homework was to do one more.  The future of this looks like doing another one. Then, I will give one in standard form, and we will have to teach completing the square. And they will get one that has imaginary roots, and I will discuss imaginary numbers. This one page will get used 200 times throughout the year to deeply understand the functions and the connections between functions.

functionfun  File can be downloaded too.

And the day was awesome because I said about 20 words, and my learners said about 200. I am shooting for a 5% ratio tomorrow.

I earned my High 5 today

 Personal  Comments Off on I earned my High 5 today
Sep 102014


highfiveToday it happened! WooHoo! I was completely excited today. I earned the high five from one of my learners. On the 20th of August, I noted that one single learner had not given me a high five, and in fact that she refused to give me a high five. Well today, after working really hard all period on rational exponent problems, and rocking the heck out of the problems, she gave me a five at the end of class.

She had a giant grin on her face, she was excited because she was making connections and understanding, and she was into it. I finally earned the five because she realized I was not leading them along, I was not tormenting them by asking questions all the time, they were learning BECAUSE I was asking questions all the time.


I also had a different learner walk in and tell me she was reading my blog and realized the high fives were a placebo to make them feel good about math. I smiled, told her yes, and high fived her. She laughed.

Did we do content today? Absolutely. Algebra 2 was rocking the rational exponents. AP Stats was starting conditional and marginal distributions. But today was awesome because of the relationships I am building with my learners.

It was a GREAT day.

Sep 042014

questionmark via

Before I get into yesterday’s classes, because I don’t have a ton to say about them (they were a repeat of Tuesday’s classes, essentially) I learned something last night about AP Statistics in my “Applied Research Design and Analysis in Education I” also called “Non-Parametric Statistics 1” class.

What I learned is that AP Stats is absolutely a college level, advanced as heck, class. This class has two pre-reqs, neither of which I have taken. On the first day of class we did binomial stats, and last night we did Chi-Square Goodness of Fit. Next week we are doing Chi-Square test of homogeneity and independence.

That’s right. In the first three weeks of a 700 level class (that is the highest level that UNR has, I know that numbering schema’s differ from Uni to Uni) we are only covering topics that are taught in AP Stats. After 2 pre-req classes. That I didn’t take (thank you Dr. Quinn for that most excellent advice). I think the 4th week is where half of the content is new-ish.  The vocab and structure used in “Qualitative Research in Education” has also been a nice review of AP Stats vocab so far.

If you ever doubt that AP Stats is not a college level class, throw those doubts away. Bury them. Ignore them. AP Stats is absolutely a fantastic class for preparing learners for college.


On to my classes. Just a quick update to the AP Stats exercise of “I have, Who Has” from my last post.

Three tweets radically changed how I will be teaching this and using this technique in the future:

Much better instructions, and I will be doing that in the future.

As for my Algebra Learners, who were frustrated with the whole speed dating exercise last class class? They rocked it out of the park and were excited at the end of class.

They are coming along I think.

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!

A class excited about logs

 Alg 2, Lesson idea, Success YES!, Technology  Comments Off on A class excited about logs
Jan 172014

[I really need to return to blogging. My lack of focus on reflection has hampered me this semester, and I need to fix that. To that end, I am making a commitment to blog and to jog. Those are the foci this year of the ellipse that is my world.]

Yea, how often does that happen that a class gets excited about logs? It has not happened to me in several years, but this year I found a way. We started the second semester with graphing again. We have a standard list of things we look for, identify, and document on every single graph. The list is:



Asymptototes (vertical and / or slant):






End state behavior:

Every graph we do, we have to document all of these items. If we graph a line, most of the list is “none” but it creates the connection between all the graphs. Every graph has the same questions, it is just that some of the graphs / functions do not have those features.

So, I am doing this file on Desmos, and we are documenting. They have done all these as homework, so really we are checking answers and ensuring learning. Then weird things happen. They notice the symmetry of the inverses.


Then they ask to see the graph of the line of symmetry. Even nicer. THEN! OMG. We put the translation into the h-k form of the line, and we see the translation of the line of symmetry.  [Okay, seriously. If you are not using the h-k forms to make connections, why not. See This post, or This post or any other of the several posts I have on this topic.]

And then I graph the exponential. …. …. They know there must be an inverse, but nothing we have done in class looks like that. …. And then, because I have the list of all the h-k forms on the board, someone asks, “Is that what the log thingy is for?”

And now they have a reason to learn logs. They are intrigued by logs. They are asking questions about logs. Because EVERYTHING in math has a forwards and a backwards, addition has subtraction, squares have square roots, and exponentials have logarithms.

They are interested and inquisitive about a topic that normally is not approached this way. I have done something good I think. Only time will tell if I can continue that on this topic.

Feb 012013



Yea, that’s right. I just had 2 classes in a row teach themselves and others how to complete the square with circles and ellipses. How did I accomplish this miracle, because I really do consider it to be a miracle.

In my Advanced Algebra Class we have the following problem called, creatively enough, The Lost Hiker.

Suppose you need to find yet another lost hiker.  Fortunately you have information from 3 different radio transmitters.  From this information you know that he is:

25 miles from Transmitter A

5 miles from Transmitter B and

13 miles from Transmitter C

These radio transmitters are at the following coordinates:

Transmitter A – (25.5, 7.5)

Transmitter B – (-2.5, 3.5)

Transmitter C – (6.5, -11.5)

Use this information to find the coordinates of the lost hiker using the intersections of the theoretical circles.  Show your work below.

There are 4 major steps here; 1. Write the equation of 3 circles, 2. Expand the circle equations, 3. “Collapse” the circles through polynomial subtraction to 2 lines, and 4. Solve the system of lines.

We worked on these for 3 days. These problems are huge and complex, and one single minus sign incorrect means the whole thing works out wrong. But they persevered for three periods in class, until every single learner could do 3 unique problems on their own, and get the correct answer.

I have an excel spreadsheet programmed to calculate an infinite number of nice problems with solutions. The solutions are posted on the board w/ a magnet, and I walk around with a bunch of problems in my hand. Get one right, here is another.

Well, at the end of 3 days, I wrote the following equation on the board and asked them to turn it back into a circle.

x2+ y2 – 6x + 8y = 12

It took them all of 1 minute to have the entire class finished. One learner who failed Alg2 taught the rest how to do it because it was, “Easy, just take the -6, divide by two, because when you square it you have two of them.”

Then I wrote 5 problems on the board.

x2+ y2 – 4x + 12y = 10

x2+ y2 + 2x – 10y = -8

x2+ y2 – 4x + 7y = -20

2x2+ 3y2 + 6x + 15y = 0

4x2+ 5y2 + 16x – 100y = 27

The first two were just some more practice. The question was asked, “Can we have a decimal?” When the answer was yes, they didn’t bat an eye.

The last two did make them think, but they had the factoring done correctly on the left side, they just needed a little hinting for the right side of the equals.

Why did it work so nicely? I think because they really were engaged with the lost hiker problem and honestly worked them. And they worked. They agonized over why they didn’t get the correct answer. They gave me dirty looks, and when we found the minus sign they missed or the extra number they wrote in, they were angry at themselves.

But they persisted! It was a thing of beauty and I loved it.

When they did the completing the square on their own, with only some gentle nudging from me, I told them how proud of them I am. They needed to hear it.

Heck, they EARNED it.