CAMT 2016 – Worth the Texas Heat

canal-san-antonio-tx-view-one-canals-downtown-texas-31902254CAMT (Conference for the Advancement of Mathematics Teaching) starts tomorrow in San Antonio, TX. Texas math teachers know all about CAMT – it is a tradition, so you can be sure that Texas math teachers will be well represented. It’s a huge conference with a large attendee turnout not only from Texas but from all over.  When I was living in Houston, I attended and spoke at CAMT every year – it’s a great conference with a really fun vibe – perhaps because it always happens in the summer and everyone is on summer break and feeling relaxed and pumped to get some new ideas for the upcoming year.  Whatever the reason, it’s always a great conference and is in beautiful San Antonio, TX this year, with it’s lovely River Walk and great restaurants and shops.  If you are attending, I wish you a successful conference where you learn new things to bring back to your classroom or schools.

Casio will be there naturally,  with our fabulous Texas folks, Amy Chow and Marty Frank there ready to do some math with Casio technology and work with leaders and teachers on supporting their tech needs. Be sure to stop by booth #133 and check out all the calculators and resource books for all grade levels and subjects, and do some comparisons and hands-on learning.  We also have several presenters who are doing some great technology workshops, which I have listed below:

  1. Wednesday, June 29 from 11:30 – 12:30 pm in Room 302 (Ballroom)
    • Grades 3rd – 5th
    • Presenter: Sandra Browning
    • It’s Elementary! Gain a deeper understanding of how technology helps students in grades 3-5 gain deeper understanding of patterns that build to proportional reasoning, an important concept in grades 5-8.
  2. Thursday, June 30 from 10:00 – 11:00 am in Room 005 (River level)
    • Grades 9 – 12
    • Presenter: Tracey Zak Johnson
    • Pushing the Limits of Your Graphing Calculator for the EOC Algebra Test. Make the difference between passing and failing the STAAR exam with the natural-display graphing calculator. Learn testing strategies and bring life to linear and quadratic equations using real-life situations. This is a hands-on session so come learn and use technology to enhance math instruction.
  3. Thursday, June 30 from 1:00 – 2:00 pm in Room 217D (Concourse Level)
    • Grades 6 – 8
    • Presenter: Kathy Mittag from
    • Have Fun Teaching Middle School TEKS Statistics Concepts. A hands-on workshop where participants will collect real-world data and then explore the concepts of mean, median and use various plots, such as stem-and-leaf, box, and histograms to explore and analyze data. TEKS statistics concepts will be highlighted in this session.
  4. Thursday, June 20 from 2:30 – 3:30 pm in Room 005 (River Level)
    • Grades 9 – 12
    • Presenter: Tracey Zak Johnson
    • “Real Life” Math. This will be an exciting session, using real situations/pictures and designing a curve of best fit to model the data. Data interpretation from 8th grade math through calculus will be explored and all participants leave with free trial software to take the lesson back to their classrooms to help their students understand quadratics.
  5. Friday, July 1 from 11:30 am – 12:30 pm in Room 005 (River Level)
    • Grades 9 – 12
    • Presenter: Catherine Tabor
    • Polarizing Art. Delve into the exciting world of polar coordinates and equations through the use of polar art. Examine how changes in variables can cause radical changes in the graphs.  Participants will create beautiful pieces of polar art using calculator technology and see what students have created. Participants will leave with ready to use lesson for their classroom.
  6. Friday, July 1 from 1:00 – 2:00 pm in Room 301 (Ballroom Level)
    • Grade 9 -12
    • Presenter: Kathy Mittag
    • A Hands-on Mathematics Function Activity Integrating Science Gas Laws & beautiful-river-walk-san-antonio-26039500Technology. New ides to integrate math, science, and technology to support student learning. This is a hands-on workshop using inexpensive manipulatives to model functions for scientific gas laws. We will cover topics such as measurement, mean, graphing, tables, independent/dependent variables, direct/indirect/inverse functions, dimensional analysis, domain, range, problem solving, interpretation of function graphs, percent error, and TEKS.

Those of you going – enjoy your conference, learn a lot, stop by say hi to Amy and Marty at booth #133, check out the sessions above – you will have a great time and walk away with some ready-to-use ideas for integrating technology. And don’t forget to enjoy San Antonio!

Visuals to Start Interesting Conversations & Problem-Solving

I realize most teachers and students in the U.S. are just beginning their summer vacations, so thinking about math and problem-solving is most likely the last thing on their minds. But – if any of you are like me, the summer was always a time to regroup, rejuvenate, and come up with new and brilliant ideas to utilize in math class starting in the fall.  I often spent my summers taking a class or finding projects to use/create, so always looking for ways to enliven my math instruction.

This morning, with all the news about UK voting to leave the EU, shocking news to be sure, I couldn’t help notice the many different visuals being bandied about to visually show how the votes were laid out.  It’s fascinating to look at these different representations, and then to just consider all the possible questions that arise.  Here are some examples of the visuals I have seen:

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The interesting thing with these visuals is they are all showing the same “results”, but from different perspectives or different ‘groupings’.  I love the map one – it clearly shows how the countries played out in the vote.  Now – this is NOT a post about the referendum – you will have to go to your news sources for information there.  But – from the math teacher side, all these visuals about the same results just got me thinking about how really great questions and problem solving could arise from the simple act of putting up a graph of some results and asking students “what do you think or wonder?” and letting them then investigate. For example, if we look at just the map, and don’t give them any numbers, they might wonder is it half blue/half yellow? How could they then determine the actual area of each colored portion of the graph?

Here’s a couple more pulled from the Prizm Resource Page:

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If you were to just throw these up on the screen at the beginning of class and ask the students to come up with some things they wanted to know about these visuals, it would lead to some student-generated questions that then would require the use of mathematics and possibly some background/related research, to find the answers.  If we are thinking about the mathematical practices, or habits of mind we are trying to instill in our students – such as analyzing, communicating, persevering, applying, arguing, critically-thinking, problem-solving, rather than giving them all the information and then asking them to ‘calculate’ the solution, why not let them find answers to questions that interest them? They would be applying mathematics in several ways, perhaps incorporating skills they have not yet learned but need – and in the process realizing that mathematics is useful and interesting.

Try it – find an interesting visual – graph, picture, etc. that spark in you some interesting questions that need math to solve. Put them in your “things to add to my class for the fall” and then get back to summer!


What’s a Km? A Travelers Lament

I am traveling in England and Paris this week, partly for pleasure, partly for work.  I will be training math teachers in the north west part of England, and was able to add on some sightseeing days and a quick hop over to Paris while here as well. It’s been a wonderful experience so far. The tube (i.e. subway) is so easy to get around on, everyone is so friendly (and those accents!!), and let’s just say you will never get better fish-n-chips anywhere else. The history is amazing, not to mention all the beautiful sites and countryside. I was unable to get tea with the Queen – perhaps next time!

What I am finding, as an American, is that I am at a distinct disadvantage when trying to determine how far away something is or how much something weighs or the amount of something (i.e. size of a coffee for example). The reason being Americans use the standard measurement system (i.e. miles, inches, gallons, ounces, etc.) and England (and every other industrialized country in the world EXCEPT America, and possibly Lyberia and Myanmar) use the metric system.  Here’s what I found:

“The metric system has been officially sanctioned for use in the United States since 1866, but the US remains the only industrialized country that has not adopted the metric system as its official system of measurement. Many sources also cite Liberia andMyanmar as the only other countries not to have done so.”

downloadWhy? It makes no sense.  Yes, yes – change is hard (think of all those road signs that would have to be changed!) But seriously, the metric system is so much easier!!!  Think about decimals – one of the foundations for students in mathematics – it’s based on powers of 10, as is the metric system.  Why then do we confuse our students by using standard measurements and making them do the horrible conversions between standard and metric?  Wouldn’t it make more sense to reinforce the idea of powers of 10 by using the metric system?  And wouldn’t it make more sense for America to measure like the rest of the world?

I am a math teacher, and even I am struggling with conceptualizing what a KM is compared to a imagesmile (i.e. 1 km is approximately .6 of a mile, FYI).  Being so entrenched in my standardized measurements, I have to admit I feel quite the idiot when I look at my Google maps and it tells me something is 22 km away – how far is that?!! Obviously I can do the calculation/estimate in my head, or if desperate, whip out the old calculator, but the fact that I can’t visualize/conceptualize it in my head is frustrating to me. And when asked if I want 240 mL or 350 mL of coffee – um…what? (i.e. 8 oz vs 12 oz apparently). I look at the posted speed of 80 km/h, in my head I think – wow…that’s FAST, because I am thinking in miles/h.  But – it’s really only about 50 mph (see conversion above). I guess this is my biggest frustration – I think in standard measures because that’s what I am programmed to do, but everything here is metric, so sometimes my brain hurts trying to ‘rethink’.

All this converting has me questioning why America doesn’t embrace the metric system…. are we just so entrenched in the standard measurements that we can’t do it at this point? Do we just like being “different”? What are your thoughts?

Functionality & Affordability Matter

Another post in my series comparing Casio calculators to TI:

I just came from a meeting at Casio America’s headquarters where we discussed ways to help parents, teachers and students get their hands on Casio calculators. In thinking about the message that Casio is trying to instill in it’s customers – that of “Functionality and Affordability”, I thought perhaps I would clarify what that message means.

Affordability – well, obviously that has to do with cost. Basically, if you go into a store such as Walmart, to buy your child calculator, you see a wide assortment of calculators with varying prices. The prices are remarkably different as you progress to graphing calculators, and TI calculators clearly top the list in expense. It can be confusing if you don’t really know anything about the calculators and are just comparing prices – the obvious choice for our cost-conscious consumers is to go with the less expensive choice, but what often happens is schools/teachers name a specific calculator type or brand, which more often than not is the most expensive one.  The question then becomes what’s the difference? Parents probably ask themselves “Will my student be at a disadvantage if we choose to save money and go with the more affordable option?”  Here’s where “Functionality” comes into play.

Functionality has to do with ease-of-use, processing speed, menu options, memory, etc.  When a student has to use a calculator to do mathematics, how hard is it to figure out the steps, to find the menus, etc. Here is where Casio definitely has the advantage over TI, because Casio calculators don’t require students to remember complicated processes or where menus and operations/calculations are – rather the options appear right on the screen as students are working, not hidden in an app or a button. The processing speed is also significantly faster. So, the more affordable calculators function more quickly and are more intuitive and easy to use and remember compared to the more expensive options. And are allowed on all standardized tests, just like the more expensive options.

As an example, here’s a quick comparison of Casio’s 9750GII graphing calculator, at $47, compared to the top-selling TI graphing calculator, the TI-84, at $102, or the TI-84 +, at $122 (these are all Walmart Prices). You will see that the Casio is menu driven, performs quicker and graphs prettier, than the more expensive TI-84+ option. This is a fairly simple problem – graph a quadratic function and find its root (s). The TI has much more complicated functionality, requiring students to find the right menu, create ‘boundaries’ around the root, and make a guess before getting the coordinates of the root. Then repeat the process if there is more than one root.  Also, notice that on the Casio, you can toggle back and forth between the roots (if there is more than one), it shows the function on the screen, along with the root (s) and word “root” so you know what you are looking at.

So – to answer the question: NO your student will NOT be at a disadvantage if you choose the more affordable option because you are getting better functionality. Seems like an advantage to me.


Math – Always Something New or Different

If you hadn’t heard, a group of Georgia Tech Mathematicians have proved the Kelmans-Seymour Conjecture, a 40-year old problem. Here is a an article that describes the conjecture and its proof in more detail for those of you interested: Georgia Tech Mathematicians Solve 40-year old Math Mystery” Now, I personally had no idea what this conjecture was till after reading the article – Graph Theory was not something I spent a lot of time on in college or in my teaching career.  What struck me was that this conjecture has been out there for 40 years with people trying to prove it, and it took a collaboration of over 39 years between six mathematicians to prove it:

“One made the conjecture. One tried for years to prove it and failed but passed on his insights. One advanced the mathematical basis for 10 more years. One helped that person solve part of the proof. And two more finally helped him complete the rest of the proof.”

Elapsed time: 39 years.” (Ben Brumfield | May 25, 2016)

Here’s what I love about this – it shows that math is a collaborative endeavor, that takes time and different approaches and insights and that something new can always be discovered or proved. Which is what we should be focusing on in K-12 math education, instead of the idea that there is one answer to a problem.  The standards for mathematical practice (part of the Common Core and based on NCTM Principles to Actions) are all about this collaboration, problem-solving, communication. It’s slow to take hold, and politics is working against it, but look at what can be accomplished when mathematicians, i.e. students, work together to problem-solve?

Math is not a single-solution, one-way only, or  learn-in-isolation. Let’s support the practices, let’s support teachers, let’s support students and create mathematical learning experiences that promote collaboration, real, relevant problem-solving.  It requires teachers being willing to accept multiple approaches and multiple methods of explanation (verbal, written, visual). It requires noise – collaboration is not sitting quietly at your desk.  It requires “mess” – using whatever tools or resources help students think about problems. It requires time.  But think about the new and different math that students will create and explore – and think about how much better prepared they will be for the mess that is the world.  That’s ‘college and career ready’ in my opinion.