Saturday, June 22, 2024

Modeling with Dog Food

Tomorrow is the end of the Summer 1 Term and I took my final this morning.   My next two classes officially start on Monday, so I'm looking forward to those.

As I mentioned in my last post, I am taking a Math class each term, so the one I just finished was on Math Problem Solving and had an emphasis in Modeling.  I'm trying to blog about some of the things I learned so I don't forget them!

In the first week, while we were learning the difference between modeling mathematics and mathematical modeling, our written assignment consisted of a prompt with an image like this one:

Back of a Royal Canin dog food bag
Screenshot from

In the assignment, some information was given about some dogs and we were asked to answer several questions using a chart like the one above.  We were also asked to write a personal perspective regarding the assignment and how we might use it in our classrooms.

When I originally had worked through the assignment, I guess-timated how much a dog that wasn't on the chart might eat based on the provided information.  However, as I started to reflect on how I might use this in my classroom, I wondered if I could use regression analysis to determine a mathematical relationship between the weight of the dog and the amount being suggested and use that to predict the feeding amount for a dog not on the chart instead of using a rough estimate.  

I put in the weight of the dog in pounds for the x-variable and the cups of dry food for the y-variable and did 3 different table of values, one for each activity level.  Check out those lovely linear patterns...

One of the things I really enjoyed about this class was the idea of using mathematics to model the world around us.  I don't have any dogs, so I would have never known a chart like this existed, but it is now tucked into my regression unit for statistics.

If you have any gems like this one that you are willing to share, please let me know!

Friday, June 21, 2024

New (to me) Tools for Graphing Categorical Data


As I mentioned in my last post, I am working on my master's degree in Curriculum & Instruction with an emphasis in Math Education.  My program has 7-week courses and I will be taking a math class each term, for a total of 18 hours of math and 15 hours of education courses.  

This week marks the end of the first Summer term with my next set of classes starting on Monday.  I am taking two classes per Summer term and will try two classes in the Fall terms as well, but not sure how that will work with teaching full time!  

I took my first math class in the spring, but it wasn't until I was halfway through the first summer term that I realized I needed a way to keep track of the ideas that I wanted to implement each week, so I created a short form to put in each of my math binders to help me remember those great ideas and where to find them!  Hopefully it will also help me remember what I want to blog about from each class!

My math class this term was called Math Problem Solving, and there was a large emphasis on mathematical modeling.  To be honest, I have very minimal experience with modeling, so most of our first week really focused on the difference in mathematical modeling vs. modeling mathematics.  Throughout the course, I definitely found connections to things I had learned from years of being involved with the #MTBoS, but I also learned a lot of new things as well!

One of those new learnings came during Week 2 of the course.  The reading assignment for the week dealt with several technology tools that could be used to model mathematics, including the tool on the left, called an Eikosogram.  

Click here to access the Eikosogram tool.

An eikosogram is very similar to a segmented bar chart or mosaic chart, both of which we use in statistics courses to graph and compare distributions of categorical data.  In the graph at the left, you can see the width of the bars are proportional to the size of the subgroup, then split proportionally within each bar to show the responses to the question - in this case about preferred superpower.

One of our class assignments required us to put together a dataset with some questions for our classmates to answer.

At the right, you can see the Eikosogram generator.  To create my dataset, I used data from the Census at School site.  After downloading my spreadsheet from the CaS, I did have to do some cleanup because the Eikosogram will throw an error if there are any blanks in the spreadsheet.  It also limits you to variables with 5 or fewer factors, so I had to recode some of the data, like birth month to birth season, to fit those parameters.  After that, I uploaded my CSV file to the website and started playing with the data.  For my class assignment, I asked the following questions:

  1. What proportion of the sample had birthdays in the Fall?
  2. Of those people born in the Winter, what proportion felt a lot of pressure regarding schoolwork?
  3. For summer birthdays, what was the most common response with regard to school pressure?
  4. Does birth month appear to be independent of schoolwork pressure?  Explain how you know.

The last question is the one where I think the Eikosogram really shines as a statistical tool.  If you notice on the screenshot, there's a checkbox to "Show Independence".  When you click that button, the Eikosogram will change to show what the graph would look like *IF* the variables were independent.  

The idea of independence of categorical variables is one that my students have struggled with in the past, so I think checking this box, then doing a "Notice and Wonder" protocol would be a great way for them to visually understand what it would look like if the variables were independent.  After that class discussion, you could follow up by clicking that checkbox off to go back to the original graph shown above to ask students if they think the variables are independent and why or why not.  

Another tool that was shared in the reading was a Pachinkogram, which is a visual tree diagram / conditional probability tool.

We did not use this tool in the class, but it's definitely a tool I want to explore for my stat class.  I love that you can move the sliders on the tree diagram to change the probabilities, then when you click Sample Once, little dots start falling and filling up the bins at the bottom! 

If you have used either of these tools in your classes or if you have other great tools to share, please let me know!  

Thursday, June 20, 2024

Life Update - A New Adventure

What a year this has been!  When I last posted, I was reflecting on the NCTM Annual Conference that was held in October in Washington, D.C.  What an amazing trip that was and I still have some sessions I did not get a chance to blog about, but then the holidays came... and winter came... and ... and ... and ...

One of those "ands" came this winter when I decided to apply to grad school!  I think I'm having a mid-life crisis :)

Seriously though, I just finished Year 26 in the classroom and even though I've looked at grad school several times, it was just never the right time, the right fit, the right (fill in the blank).  But this time, I decided to go for it!  One of the universities in my state has an online Master's program with 7-week classes that fit my budget and my available time, so within a few days of applying for the program, I had been accepted and on my way to a degree in Curriculum & Instruction - Math Education.

Oh my - what did I get myself into???

So much of who I am as a teacher is thanks to the #MTBoS, so it has been very validating to tie in my coursework with all of the things I have learned from so many amazing people around the globe.  

I'm currently finishing up my 2nd term in the program.  When school starts back in August, I will have 5 classes done, with a scheduled completion date of Spring 2025.  It's truly been a great experience so far, even though writing my first research paper *in this century* was slightly terrifying!

Wish me luck!