Finding Function Intersections – Casio fx-9860GII vs. TI-84 Plus: Casio IS Easier!

I admit to being a TI-83/84 user for all of my teaching.  Not because I had a personal preference for a TI, but because it was what all the schools where I taught in Virginia provided and recommended. It was in our books, it was what our state tests recommended, it’s what we were told to tell students to buy. Why? Was TI better than a Casio or an HP or any other brand for that matter? No. It wasn’t…and isn’t to this day. But – TI knew how to play the market and basically embedded themselves with publishers, testing companies, schools, to the point where today, schools & teachers & publishers are convinced TI is the better calculator option. Or maybe I should say they think it is the only option.

It’s not. It’s an option. But it’s not the better option in terms of cost and in terms of ease-of-use. In my 25 years of using TI, I can honestly say I still forget how to do most operations because there are so many steps involved or I can’t remember where the menu item lives. Obviously, as the Casio Brand Ambassador, I have a definite bias in my current opinion about hand-held calculators. However, it wasn’t my opinion until about 7 years ago, when Casio approached me, in my role as Director of PD/Education Outreach at Key Curriculum, to get some advice and suggestions for quality trainers who could help support Casio PD efforts. That’s when, for the first time, I actually used a Casio calculator and realized it was really easy and quick to learn – and I could remember things!!  All the Casio PD teachers,  many who were also Key trainers and who teach in classrooms all over the country to this day, were former TI users as well. But, once they tried Casio, never looked back and encourage others to make the switch as well. In my new role, I’ve been asking these teachers why, and the first answer I always get is “it’s so much easier for the kids to use and they remember how to use it”. The second answer I always get is “they are much better calculators in what they can do”.

In European countries, Casio has a much bigger share of the market than TI – they know about quality and ease of use. Here in the U.S. we are fighting the TI machine…it’s so embedded in our math culture and it’s hard to change, as are most things in education (think Common Core!) As Terry Walsh said in his NCTM session in Atlantic City, something a college professor told him, Casio calculators are much more user friendly, but TI calculators are more user familiar”. Sticking with the familiar and avoiding change is a disservice to our students, who deserve technology tools that are affordable and intuitive to use.

I thought it would be a fun idea, since Casio is always saying how much easier it is to use a Casio vs. a TI calculator, to actually show how. I picked two comparable graphing calculators: The Casio fx-9860GII SD ($79.99) and the TI-84 Plus ($139.00) to do a side-by-side comparison of a relatively common algebraic skill – finding the intersection of two functions. (Note: This is NOT a lesson on teaching this algebraic concept, so please, please, do not think this is how I would help students understand how to find the intersections or what those intersections represent in real-world context. There is a whole lot of discovery, hands-on learning, conversations, etc. that would occur if this were an actual lesson). What this video demonstrates is a step-by-step “how do you find the intersection of two functions using each graphing calculator” – nothing more, nothing less. The point being to actually demonstrate, talk-the-talk, walk-the-walk, and show ONE example of how a Casio graphing calculator is easier to use than a TI graphing calculator.

Watch the video: Step-by-Step Casio vs. TI Graphing Calculator


Music, M&M’s & Math – Calculating the Difference at NCTM Regionals


Mike Reiners NCTM AC 2015

It was so nice to be back at NCTM Regionals and connect with old friends and make some new ones. I had a really great time in Atlantic City (no gambling was involved!) Really happy to see The Math Forum folks up front and center as part of NCTM now, out there doing what they do best – making math engaging, thought provoking and relevant. I also ran into a lot of my former colleagues from Key Curriculum, which was a pleasant surprise and made me miss all the rest of them! I got to meet some of the Casio team, both sales folks and teacher trainers, and see and hear some of the things they are doing to help teachers use Casio technology in the classroom. I learned quite a lot from the few sessions I was able to attend as well as learning from the folks in the booth, so feeling even more excited about supporting teachers calculator usage in math instruction.


Terry Walsh NCTM AC 2015

I met Terry Walsh, a teacher from Colorado, who had a very thought-provoking session showing how released AP Calculus questions could be used with students in grades 6-12. It’s all about the questions you ask, but sixth graders can be doing integral calculus. He really emphasized how the Prizm calculator, with it’s advanced features to modify and show different parts of the graphs or slopes, could help even young mathematicians make conjectures and connections about mathematical situations. Unfortunately, Terry won’t be at the next two NCTM regionals, but if you get a chance to attend one of his sessions, definitely do so.  You’ll do some thought provoking math, experience the Prizm, and see how easy it is to visualize and help students make connections.


Mike Reiners & Casio Keyboard

Mike Reiners, a teacher from St. Paul, Minneapolis, really made the music & math connection, showing how to create functions from songs and then transforming those functions – again, all through the understanding of music.  It was fascinating and amazing to hear the music on the Casio keyboard, see the song represented as a function on the Prizm, and then, as see the transformation, understand how that impacts the function equation, and then hear how the transformation changes how the song sounds. I also loved how involved the teachers in the session were – most of whom did not have any musical training, yet were able to create the Parsons Code for a song they chose, convert this to a list of values, and then use the Prizm graphing calculator to generate the corresponding list and graph of the function. And, after some cool melodic playing from Mike, understand how to transform the functions. Students, who we all know love music, would really be able to relate to this approach to understanding transformation of functions, because they can hear and visualize at the same time. If any of you are planning to go to the NCTM Regionals in Minneapolis or Nashville, Mike will be doing his “Think Like a Synthesizer: Applying Algebraic Transformations to Music Melodies” session at both, so be sure to go.


Math Teachers calculating!

One of my favorite sessions was with Tom Beatini. First, I was impressed at the crowd that showed up at 8 am on a Friday morning – 44 people. Go math teachers! But, what made this session so great was all the math going on – three different data-collection activities, hands-on inquiry with ropes, M&M’s, and cheerios, and appropriate technology integration using the Prizm. Everyone was involved, talking, and learning from each other. What I think I loved the best was the TI-graphing-calculator users who made the effort to use the Prizm graphing-calculators and experienced for themselves how easy they were to use.  I appreciate their willingness to step out of their comfort zone. Tom really made the effort to connect the Common Core Math Practices and help his participants focus on the importance of mathematical conversations, questioning and presentations that support justification and solidify understanding. Again, if you are heading to NCTM in Minneapolis or Nashville, be sure to catch Tom’s session “Hand-held Technology + Hands-on Activities = CCSS Success”.

All in all, it was quite fun being back learning and connecting with math educators again. I am looking forward to NCTM Regional in Minneapolis, coming up November 12 & 13. I hope to see a bigger crowd, experience some more great sessions, and connect again with old friends and new. Hopefully I will see some of you there!


Tom Beatini NCTM AC 2015


Ropes Data Collection Activity


M&M’s Data Collection Activity

Wanta Bet? – NCTM 2015 Regional Atlantic City

With so many different options for educators to connect – through EdcampsTwitter Chats, Online Education Meetups, Virtual Conferences, to name a few –KeyCurriculum_NCTM2012-0486 you might think regional and national face-to-face conferences are not relevant. Wanta bet?

I am heading to the Regional NCTM Conference in Atlantic City this week. It will be my first time as part of Casio. It’s been at least a year si
nce I’ve been to an NCTM, as I took some time off while finishing up my doctorate studies. If I were to gauge my feelings regarding the upcoming conference, I would have to say I am a little nervous, a little excited and mostly thrilled to get to see some old friends, meet some new friends, and connect with math educators again. This is what is relevant about these face-to-face conferences – the connections made between like-minded educators.

Don’t get me wrong – I am a HUGE proponent of virtual and online professional learning opportunities.  I learn so much from Twitter chats I participate in, such as #edchat, and I think online discussion forums and virtual conferences are valuable because of their ability to provide anywhere learning and affordability for those who cannot travel to these face-to-face options. Edcamps are powerful in their focused, participant-led learning. But – face-to-face conferences, like the NCTM Regionals and National or any of the content-focused conferences that are out there, like ISTE, or NSTA, provide a cornucopia of possibilities and connections.

I remember my very first NCTM conference as a teacher. It was in Minneapolis, 1999. I’d been to many local and state conferences up until that time,as both a presenter and participant, but 1999 was the first time I went to a National user groupConference. I remember being overwhelmed at the sheer number of presentations to choose from, and then completely blown away by the Exhibit Hall. (Who knew, many years later, I would actually be a vendor in the Exhibit Hall)? Someone gave me some great advice – pick a focus, and choose your sessions based on your focus. I was teaching several sections of pre-Algebra, so I decided that was my goal – gain some new ideas to bring back to my classroom.

Honestly, I don’t remember what specific sessions I went to, but I do remember getting so many ideas and being so pumped about trying some new things in my classroom.  I went back to my school with all these ideas and activities to try, and was already planning for the NEXT school year. It was a long time ago, but that feeling of “WOW, I am going to be the best teacher ever now!” was very memorable, and its a feeling I still get when I attend conferences and see or hear something that gives me new ideas on how to improve my own teaching.

Here’s why I think face-to-face conferences are still relevant:

  • You have many choices of sessions, so you are more likely to find some that are relevant to your own teaching, your own interests
  • You almost always connect with someone new from a different part of the country, and you realize you are not alone in your struggles and successes, and sometimes, you realize, you might be better off or luckier than some and you get a new respect for your own situation
  • There are so many ideas, strategies, resources and opportunities that you are exposed to in one place, that you almost always leave with at least one new thing to try in your classroom or with your students/teachers.  If you can leave with ONE new thing, then it’s been a success
  • Being surrounded by other educators, doing the same thing as you, helps rejuvenate you. We are stronger together.

Here’s some suggestions for making a face-to-face conference beneficial:

  • Pick a focus, and choose sessions to go to based on that focus. Otherwise, the sheer number of choices can be overwhelming.
  • KeyCurriculum_NCTM2012-0528Spend some time in the Exhibit Hall, but keep your focus in mind. The Exhibit Hall can be overwhelming – so let your focus guide which places your stop at, what resources you look for, and what questions you ask the vendors.
  • In sessions, make an effort to introduce yourself to those at your table/around you. You will gain insight, new ideas, and connections if you do so. It is always interesting to find out what others are doing in other areas of the country.
  • If you end up in a session where a) the presenter is not so stellar; b) the information is not new or relevant to you; c) or you realize it’s Not what you thought, then leave. Do NOT be embarrassed, afraid, or worry about hurting the presenters feelings and end up wasting an hour or more of your time. Get up, walk out. As a presenter myself for over 20 years, I realize that sometimes what I am saying is not of interest to those in the room for whatever reason – I am never offended when someone leaves. Life’s too short to waste your time.  Sometimes those titles are not descriptive enough and its easy to end up in a session that was not at all what you thought it was. Leave, as unobtrusively as you possibly can, and go somewhere where the learning is relevant to your needs.
  • Spend some time seeing the city in which the conference is being held, but don’t forego the conference in order to only sight-see. You are missing incredible opportunities to learn from other educators.

Any of you out there going to Atlantic City this week, I hope to run into you. Please stop by the Casio booth and say hi – if I am there, I would love to connect! Booth #415.

Check out some Casio-related sessions:

  1. Session #111 – Thursday, 1:30-2:45 pm, Mike Reiners “Thinking Like a Synthesizer: Applying Algebraic Transformations to Musical Melodies”
  2. Session #128 – Thursday, 3:15-4:30 pm, Terry Walsh, “Exploring Released AP Calculus Questions in Grades 6-12”
  3. Session #156 – Friday, 8 – 9:15 am, Tom Beatini, “Handheld Technology + Hands-On Activities=CCSS Sucess!”

QR Codes, ClassWiz & Expanding Limited Technology

While in Japan (see my first post) the R&D folks at Casio were showing the new EDU+ app for smartphones that reads the QR codes from the ClassWiz calculator. My first reaction was “cool!”, my second reaction was “why?” since, as I thought at the time was why would you need a QR code to get to an online graphical representation of the data from the calculator when you could just use a graphing calculator?

But – a light bulb did go off as I played with both the calculator and the app and thought about schools I’d been to. I realized the whole purpose of the QR code is for those students and teachers who do not have graphing calculators, for whatever reason – i.e. grade level (they are in elementary and early middle school for example), cost prohibitive, or just not an option. The ClassWiz calculator, a scientific calculator, is new to the U.S. market this August, and is very cheap (about $27), easy to use, and can create & display graphical representations via QR codes, so an added feature that teachers and students can utilize. It’s a nice option for showing graphical representations quickly when other tools are not available.

Let me demonstrate how it works using the ClassWiz Emulator and some real-world data I got from the eeps Data Zoo (a fun place to get some interesting data to use with students). I thought the Roller Coaster Data below was interesting. I am going to do a very simple example, so I created a table to compare the largest drop to the length of the coaster.  I then chose the QR code button, which generated a QR code. Since I was in the emulator, I could just click the QR code and go directly to the visual representation on the internet. But, if I’d had my smartphone and the hand-held calculator, I could have used the app to scan the QR code and create the URL for the visual representation.

Look at the short video clip below to see how the process works:

You might be asking yourself why go to all this work if you are going to have to go on the internet anyway? Why not just use an internet graphing calculator? True enough – you could do this.  However, the reality is, most students in classrooms do not have access to computers and internet (only about 1/3 of schools have regular access to mobile devices such as laptops & tablets, for students)(see previous post). Students at the younger grades usually don’t have access to graphing calculators. The majority of the time, classrooms have the teachers computer with a projector set up, relying on whole-class demonstration. We want students hands-on, collecting their data and entering their data, which means students with the calculators.  And then, yes – have them plot their points and sketch their graphs. But – how great, if the teacher and students can quickly generate a QR code right on their calculator and the teacher can pop up a visual of the data right away and have a meaningful class discussion about the relationships students see, what might be the best type of fit for the data, should the graph go through zero and what’s the meaning of that (just to name a few questions)? Students can change the data, or compare different data, generate new QR codes and compare all these different graphs. The QR code functionality of the ClassWiz is just an example of how to expand the capabilities of the technology you have in your classroom. Another resource that allows students to explore and understand mathematics.

Calculators – A Thing of the Past?

Are calculators a technology tool that has outlived its usefulness?  Obviously, this is a loaded question.  In theory, you would think the answer is yes – what with all the one-to-one initiatives, use of mobile devices in schools (particularly smartphones), free online graphing tools, and the push for web-based apps and resources. But, the reality, from both my research and my personal experience working in schools all over the country, is the answer is no. Calculators are still a much needed technology tool and will be for some time to come.

How can that be you ask, what with so many schools all going digital? According to the 2013 SpeakUp National Research Project, only about 1/3 of students have regular access to mobile devices to use in classrooms (of which some are BYOD). Most of the time, there is no regular access to mobile devices (i.e. laptops, tablets, smartphones, etc.). Which means, from a math perspective, most of the time there is no access to math apps, or online graphing tools, or calculation/graphing tools on mobile devices.

from Speak Up 2013 National Research Project

from Speak Up 2013 National Research Project

from Speak Up 2013 National Research Project

from Speak Up 2013 National Research Project

From my personal experiences, working in large, small, rural and urban school districts, technology in classrooms runs the complete gamut – some schools have great technology – white boards, laptops, and/or tablets, internet. But – that is the rarity. What I see most often is a laptop or tablet cart that must be shared between six or more teachers, or possibly one computer lab, which is often impossible to get into, especially with all the standardized testing that happens. Students are more often than not unable to use their own mobile devises(i.e. smart phones).  Even teachers are often not allowed to, and if they are the internet access is horrible. Just last week I was in a school where the teacher was trying to access something on her phone and had to hold her phone out the window. What technology is available can also differ drastically from school to school within a single district, not just between districts. I have gone from one school in a district, where the only technology available was calculators and the teacher computer & projector, to the school down the street where every student had a laptop. Same district, same grade level (high school), vastly different resources.

According to research, 97% of teachers have a computer in their classroom.  The most used technology resources in classrooms are an interactive whiteboard and a class computer with a projector. My personal experiences confirm this – and in fact, it is what I see used more than anything – teacher computer, with a projector./screen. And sadly – the interactive whiteboards I see are used more often as just projector screens rather than truly utilizing their interactive capabilities and built-in programs.

Funding is one of the biggest reasons for the lack of technology in schools, with a huge disparity in access between lower and upper income schools (This Pew Research Study has some interesting numbers/facts). Sometimes is poor planning for implementation and/or the infrastructure needed to sustain technology initiatives (L.A. a great example of this). It is also lack of training and support for teacher’s integration of technology, as well as other factors such as large class sizes (I’ve done research in class sizes of 43 high schools students), comfort level with other resources and of course,  just the availability of resources in general. So, while I am a supporter and believer in using mobile devices such as tablets, laptops, smartphones, in the the classroom, I am also a realist, and know that we are a long, long way from this being common place. Especially as funding for schools keeps getting cut, which means purchasing costly tablets and/or computers and maintaining these is often a challenge.

So – unless somehow, educational funding makes a huge turn-around, which in this political climate is very unlikely, I don’t see all students having regular 2015-10-11_20-40-27access to mobile devices in classrooms for a long time. Which takes me back to the calculator. A cheap and easily-accessible technology resource that most schools have and, due to their relatively low cost (especially compared to a tablet and/or computer) that most parents can purchase for their children if need be. A $50 graphing calculator can allow students to explore and visualize different types of relationships, discover numerical patterns, and expand their conceptual understanding of mathematics. A $20 calculator (ClassWiz) has QR code generation capability that allows for graphical representation (teachers could project them from their class computer). Calculators can be in every students’ hand, quickly, vs. the sharing of mobile devices that often occurs when mobile devices are used in classes (due to availability) (average computer/tablet to student ratio is 1 to 5.3).

I am going to continually learn and push for technology integration in mathematics and hope that students will have access to all the great technology and mobile devices and resources out there. It’s just a slow process with lots of hurdles such as funding, access, permissions, etc. So, I am going to push the use of calculators as well because, from my perspective, calculators are NOT going away for a very long time. If it’s a choice between no technology or an affordable calculator that will help push students further and support the exploration and deeper understanding of mathematical concepts, it seems a no-brainer – get a calculator and help students explore! It’s a big reason behind my decision to partner with Casio. I do not see calculators disappearing from math education any time soon, and I really like Casio for several reasons, some of which are they are cheaper and better calculators that are a heck of a lot easier to use. I also get to be a part of helping Casio develop and evolve both their calculators and their web-based solutions, and interact with math educators around the world, so I see all this as a win-win!

A Global Perspective

I have just come on as Casio America’s Brand Ambassador, a part-time position that will be evolving in the next several IMG_1437months.  As I explore my partnership with Casio, my main goal is to help share with math educators how Casio Education and its technology products can support mathematics teaching and learning in a variety of ways.

As my first endeavor in this position, I was lucky to be included in Casio Internationals’ 11th Global Teacher meeting at the Casio Research and Development offices in Hamura, Japan (outside of Tokyo).  This was a two-day meeting that included the R&D engineers, teachers and Casio managers from all over the world, coming together to share new ideas in how to improve and create new Casio products that support mathematics. The goal of this collaboration, using ideas and real-world anecdotes from actual teachers using the tools as well as creative ideas from the R&D engineers, was to focus on what is best for students and teachers, and how Casio can enhance technology integration in mathematics education.

There were many truly memorable things from this whole experience, including meeting teachers from all over the world (Australia, France, Germany, Finland, Middle East, Singapore, India, Japan, U.S.), exploring Japan for the first time, and eating some food I never thought would pass my lips (i.e. squid, octopus, urchin, jellyfish, and sharkfin, & bird-nest soup). My experiences in Japan were diverse and informative, with a little crazy IMG_1540fun sprinkled in, such as experiencing Karaoke the Japanese way, in a room with a stage and microphones (be thankful that I am NOT sharing the video of that experienced!) The most apparent aspect of Japan, if you have never been, is how amazingly kind and considerate everyone is.  I never felt as well-taken care of – from the hotel staff, to the Casio employees, to the strangers on the street who, though they did not speak English, were willing to change their direction and walk the lost American to the train station. The Japanese people are generous to a fault and my time there was just lovely.

On the work side of things, my biggest take-a-way from the Casio Global Teacher Meeting was how diverse mathematics instruction and technology use is throughout the world. It makes me really question, even more than I already did, the comparisons of student math achievement between countries since how, what, and when mathematics is taught is so incredibly different.  (THAT is a post for another time!)  For this post, I thought it would be interesting to share some of the things about Casio Education/calculators that I learned as a result of this trip.

First – did you know that the first Casio calculator (14-A) was made in 1957 and is still working? (Being the confirmed math IMG_1505geek that I am, yes, I did get incredibly excited when I got to see the calculator in the lobby of the Casio R&D research facility). It can do the four basic operations with numbers up to 14 digits. In 1965 Casio made the world’s first electronic calculator with a memory function, which they started exporting to the US and Europe in 1966.

Second, Casio calculators have a larger share of the market in European countries. European countries have a Ministry of Education that makes technology decisions for the entire country, as opposed to the United States, where each school district, and sometimes each school, makes their own technology decisions.

Third, Casio’s ClassPad calculator (CP400 & CP330) seemed to be, based on the teacher’s present in this meeting, the most-used graphing calculator in these countries, and used in remarkable ways. It is a pen-touch-screen calculator, with drag-and-drop menus and so many other advanced functionalities. In the U.S. this calculator is not yet approved by the College Board for use on SAT & ACT, so it’s not as prevalent here – but boy, it should be!

IMG_1514Fourth, the real-world applications of mathematics in these other countries seems to be much more of a push than here in the U.S. The Japanese teacher shared a typical problem with us that students are expected to solve in mathematics on a regular basis (with no calculators, which is astounding!). All I could think, while reading through the problem was, wow – this is what the Common Core problem-solving is all about, but unfortunately, NOT what we are actually seeing in the classroom.

Fifth, teachers from all over the world have the same vision – to help students love math, to help students use technology to engage and expand mathematical understanding, and to help students become mathematical problem-solvers. While everyone was doing these things in slightly different ways, and some to more extremes than others, everyone was clearly motivated to help make mathematics engaging, understandable, and applicable.

And finally, from the R&D end of things, hearing what the Casio R&D folks were thinking of in terms of ways to improve calculators and create more engaging products for students and teachers, I was impressed with how Casio really wanted to learn about how their products were being used in the classrooms, both the
good and the bad. They listened, they asked questions, and they really wanted to know what they could do to support mathematics education. It was an incredibly informative two days of collaboration between those in the field teaching and those creating the tools being used by teachers and students.IMG_1511

So – the beginning of my Casio adventure was exciting and interesting and gave me a global perspective I did not have before. With that, I now hope to continue to learn and share my thoughts and opinions about math education and how Casio, as a global manufacturer of mathematical tools, can support teachers, students and mathematics education. Would love any ideas, questions, suggestions about things you would like to hear about related to math education, so please feel free to share some with me so I can do some research and hopefully provide some answers/solutions.