Jan 152017

One question that comes ups often with math majors in the program is “Why do I have to take a computer science class?”

I am not sure where the official requirement comes from, but I can say that I am extremely thankful I had a computer programming class in college. It was over 20 years ago, and it was Pascal programming, but I am very happy that I still remember the skills I learned. I don’t remember anything about Pascal, but over the last 20 years, and especially the last three weeks, I have used the heck out of those skills.

When I was in business, the programming skills allowed me do some serious Excel sheets and data crunching that got me noticed and promoted.

As a teacher, those Excel skills allowed me to strip data from the PDF reports and turn those into useful files that we could actually mine for relevant data on our learners and their learning. Those skills also allowed me to learn basic HTML and CSS coding to build websites over a Christmas break and create multiple websites.

Now, as a master teacher I have spent several weeks building a very complex database in Access to manage our check in and check out process with the hundreds (soon to be thousands) of items in our teaching supply store room. To do this, I have had to teach myself Visual Basic, Access structure, as well as some basic SQL database language.

Now don’t get me wrong.I do not have anywhere near the skills to be paid to program in any of these languages, and it is taking me 5 times longer than a real programmer would take. But, because of that Pascal programming class 26 years ago I have the ability to learn the new skills, new languages, and troubleshoot the really bad code I am writing and make it better.

Why should today’s learners learn coding? Because if this dinosaur can reap these benefits out of the class over my career, then imagine what benefits our learners today will reap over the next 25 years! It only gets more important and more essential from here.

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.


Jun 052015


I pushed my AP Stats learners to use Plot.ly this year for their projects instead of JMP as I have in previous years. I am not sure if I like it better or worse, but I definitely have some frustrations.

Let’s go through the good points first.

1. After the learners had their data in Excel, it was very easy to import the .xlsx file into plot.ly. The learners had to make some changes to the first row, but that is to be expected.

2. As long as the learners hit “save” then they did not have to worry about losing their project. I have had previous years where learners lost flash drives or computer files the week before the project is due and had to start from scratch with their hard copy. I appreciate the fact that plot.ly saves the data IF the learners hit save.

3. Once the plots are present, downloading or screen capturing the plots are easy and quick. My learners liked the ability to  quickly make many different plots and then examine them and decide what they plots were really meaning. Changing colors, counts to percents, and other elements of the graphs was easy, fast and very user friendly.

All in all, not too many downsides from the learner’s perspective.

Here are my frustrations with the program as we have been using Plot.ly.

1. Many of my learners did surveys that had categorical Yes, No or Freshmen, Sophomore, Junior Senior responses. After compiling their survey responses, their data looked similar to this:


What kind of graph would you make with this type of data? You are correct a bar chart. Bar charts are for categorical data, histograms are for quantitative. So, I do that.

badgraph Not it.  I struggle with this for three days, tweet them for help, more than 4 times, and nada. Zilch. Don’t hear anything back, and am ready to give up on Plot.ly. However, I notice they have a “contact us” in the lower right of the screen. I email them, and a very nice person responds the next day and with instructions on how to make a Histogram.

What. The. Hell. A histogram? I follow her instructions.

data2 (you get the “choose as G” by the “Group by” button) and get this:

goodgraph The y axis is in percent (which takes an extra step to get), clearly what I wanted, but it is not a histogram. I do have a problem with a “Statistics” program that calls a bar graph a histogram. The instructions to make it a stacked bar chart are easy to follow and find, I chose not to do it for this comparison.

2. Ordering the x-axis is a pain. Many of the questions my learners had dealt with the difference between freshmen, sophomores, juniors and seniors. Plot.ly ordered the x-axis based on the order of the data in the spreadsheet. Which means to reorder the x-axis we had to sort the data in excel, (but we don’t want them in alphabetical order?) and reupload.

Really Plot.ly? You don’t have a way to specify the order of the axis? I searched. Trust me I searched long and hard. I ended up just telling my learners to not worry about it.

As a comparison, this is what it looks like in JMP (version 8 is what I have).

jmpdata graphing a “fit y by x”

jmpgraph After hitting “OK”, look at all the stats automatically generated! Also, in the contingency plot (made by default btw) the width is proportional to how many in that column, so the widths AND heights are informative unlike Plot.ly. JMP also automatically generates axis by percent, not counts.

jmpsort Ordering the data is as simple as clicking on Value Ordering under column properties.

I guess what I am saying is that clearly Plot.ly is not meant to be used as I am using it in class. There are easier, faster, and more statistically correct software to use. I will have to figure out what to use for next year because I am not completely sold on Plot.ly, but JMP has to be installed on computers. There are always gives and takes to every decision.


And right after I posted this, one of my learners walks in tearing her hair out. She has a mixture of categorical and quantitative data, and Plot.ly will not graph the categorical data at all for her. The menu options work completely different for her than for everyone else. She is installing JMP and getting it done that way. Sigh.

Jun 222012

My AP Stat learners had a project for their final exam, it was very straightforward. In our area, we have 4 grocery stores.

The North Valleys w/ grocery stores
If you click the image, you will see the larger image that shows on 2 exits of the freeway the four stores (Scolari’s is a local chain) and on the far right of the map, our school. Walmart opened up only 3 months ago, so it is the new kid on the block, and of course, their marketing screams at us every day that they have the cheapest prices on groceries.

Our question was, do they really have the cheapest prices? The rest after the break.

Continue reading »

Aug 042011

I have done a very poor job of writing about advanced algebra, the course I helped co-author 4 years ago with 5 other teachers in my district. I would like to rectify that this year, and explain more about the course and honestly, get better ideas for the course.

The course is more project based, and it has four distinct, but overlapping sections. Quarter 1 is financial math, quarter 2 is math in art, quarter 3 is math in technology and quarter 4 is math in health / human body. If you go to the site http://mrwaddell.net/AAA you will see the basic structure and some of the lessons / sites I use to teach the course.

Starting off this year, I am going to do something different with the quarter 1. It always felt a little disjointed to me. We use the materials from NEFE to get us started, and then we jump in much much deeper than NEFE goes. We spend a lot of time on spreadsheets (which are nothing more than giant algebra problems using variables) polynomial equations and rational equations (another way to think of Pert and other compounding equations, ie. purchasing a car and annuities) as well as some basic ideas of personal finance.

This year, instead of just teaching each module as a standalone, I am going to tie all of the quarter 1 together with this outline.

At the end of this project, you will need to show the Banker your portfolio that demonstrates you have the financial knowledge and ability to purchase a house in the North Valleys.

Part 1: Setting S.M.A.R.T. Goals

1. Short term, medium term, & long term goals

2. Tracking your goals

3. Adjusting and rewriting your goals

Part 2: Savings & Compound Interest

1. Calculating compounding interest for n

2. Calculating compounding interest for continuously

3. Finding rate or time in both kinds of compounding (working backwards)

4. Knowing and demonstrating differences between APR and interest rate

Part 3: Career & Income

1. Identify 3 careers for yourself

2. Calculate lifetime earnings

3. Calculate $1,000,000 earnings timeline

4. Comparing 2 and 3 for your careers

Part 4: Purchasing a Car

1. Calculating your payment

2. Deciding on years of repayment

3. Comparing years to payment and making a good choice

Part 5: Investing & Credit

1. Risk vs. Reward

2. “Safe” vs. “Intermediate” vs. “Risky” investments

3. Annuities

4. Credit Cards

5. Credit Scores

Part 6: Budgeting your spending and savings

1. Creating a budget (will be working on all quarter)

2. Projecting income

3. Projecting expenses

Part 7: Buying your home

1. Put it all together for the Banker, and using the financial information gathered to justify to the banker that you are a good loan candidate

That’s right. The end goal and purpose of the portfolio will be to purchase a house. It is the biggest investment a person generally makes, but I also know of 4 learners who graduated within the last 3 years who are now homeowners. It is a reality they can achieve now, whereas 3 years ago it was out of reach.

The purpose of this structure is to create a buy-in. Now they see the end goal. This goes hand in hand with backwards design and Understanding by Design principles. I have emailed out a draft to the other Advanced Algebra teachers, and once I have it more fleshed out I will email out another copy. I also hope to get some feedback from them to see what they would add as well.

So, what do you think? Is this a viable way to put together a quarter on personal finance? Let me know in the comments.

Aug 022011

In Montana, there is a town called Haugan on I-90 near the Idaho border with an interesting building. As you approach, you see signs like this every couple of miles. [click on the pictures for a higher res image]


Outside, the place looks like any tourist trap.


Do they really have 50,000 silver dollars inside?

DSC01898 DSC01895 DSC01893 DSC01892

And at the back of the bar they have a sign saying what the current count is. I visited twice, 1 year apart.

In July 2010, it looked like this:                    In July 2011, it looked like this:

DSC01891 DSC00182

Any Questions?

[Please leave me some challenging questions in the comments. I am looking to develop this into a classroom material lesson. I also have more pictures of the inside, I just posted a few of them here.]