Using Pictures on the Casio Prizm CG-50 Graphing Calculator

I previously wrote a post a while back about the power of using pictures to connect mathematics to the real world. In that prior post I talk about the built-in pictures that already come with the Casio Prizm Calculator (CG-50 and CG-10), and wrote down the steps. With our new model out, the CG-50, I thought I should probably revisit this but make a quick how-to video instead just to demonstrate how easy it is and show off how many pictures are there.

Currently in my online course I am teaching, we are exploring transformations, and creating some real-world dynamic math examples, so Ferris Wheels have come up. Which got me remembering the Ferris Wheel picture that is one of the many available. Keep snowballing my thoughts, and you end up with me thinking of all the possible applications you could do with the calculator just using that one picture – i.e. what is the angle of rotation for one of the cars to ‘move’ onto another? Why are there concentric ‘circles’ as part of the structure of the ferris wheel – is this a strength issue? What is the length of one radius of the Ferris wheel (in real life – how could you calculate this from the picture? Is similarity involved?) Whats the distance between each car (measuring from the point they are attached on the Ferris wheel – so, arc length?)  And this is just one picture!

There are also ‘movies’ within the Picture Plot menu that allow you to see moving objects and plot their path as well, so again, some real-life connections to mathematical concepts right at your fingertips. As the school year is drawing to an end, this is definitely a time when you want to assess if students can make those connections of mathematics to the world around them, so exploring these types of pictures is a great way to engage students and provide them a reason for why they were learning all those math concepts. (Hopefully you were doing that all along as part of the learning process, but never too late….)

Here’s a quick video on how to access the pictures and ‘videos’ on the CG-50 Prizm, though the process is the same for the CG10 Prizm as well. Have fun exploring!

Thinking Ahead – Planning for Next Year’s Classroom Culture

I was in Austin all last week training for UT Dana Center (@UTdanacenter) International Fellows
(#UTDCIFF) and Department of Education Activities (@DoDEA) College and Career Ready Initiative teacher workshops happening this summer. A major focus for the week was on classroom culture and how important this is to mathematical learning and student discourse. Everyone at this training was either a current math teacher, a supervisor, mentor, coach, professional development provider, etc., so naturally, as part of the conversation, the following questions/concerns arose:

1. What is classroom culture and why does it matter?
2. How do you get students to talk to each other and engage in productive learning?
3. How do you respond to teachers who say things like, “well, this would never work with my students” or “I can’t get my students to talk about math when we are in groups”…

You get the picture, and I am sure you have either thought these things or heard these from teachers you work with.

The short answer – it takes planning, training, and consistency. If a teacher thinks that they can just put students into groups, give them a problem, and they are going to immediately start talking and working together, they are very quickly in for a big surprise. Especially that first time, and especially if you have never done these types of collaborative learning with your students. Which brings us back to classroom culture.  What is it and why does it matter?

There are many definitions out there of classroom culture. I will give you my perspective. Classroom culture is a classroom environment where students feel safe making mistakes, they are comfortable sharing their thinking process with other students and with the teacher, and all ideas are entertained and acknowledged. Everyone’s voice is heard, everyone gets a chance to participate, and there is respectful conversations and debate about the work being done.  This matters because then students are given permission to persevere in problem solving situations where they may not know the answer, or may have a different approach then someone else or may have a question about something another student or the teacher has shared. It ties into those mathematical practices (#1 & #3, just to name a couple):

• Make sense of problems and persevere in solving them
• Construct viable arguments and critique the reasoning of others

But, this type of engagement, discourse and collaboration with and among students doesn’t just happen. Here are what I consider the three basic elements:

1. Planning

Planning entails thinking about the structures you want to use with students (so pairs, small groups, whole class) and the types of discussions and work you want to students to engage in. There is more to it than this, but some things to think about are

• What task are students working on and what is the goal (a worksheet of 40 problems is NOT going to promote student discussion). Provide a rich task that fosters critical thinking, questioning, problem-solving.
• How do you want students to engage? Are they talking in pairs first and then sharing with the small group? Does each pair/group need to show some product (i.e. their work, their thinking, the end result).
• How will you bring the whole class together at the end? Will each group share out? Will you hang work and have a ‘gallery walk’ and come together to share?
• How will you know that students have learned or reached the goal? What should students be able to do?

You need to think of these things ahead of time, most importantly because without an engaging, rich, though provoking problem, the conversations students have won’t be productive (and can lead to all the issues mentioned previously).

2. Training

How do you get students to talk about math (or any subject?) How do you get students to work in pairs or small groups and stay focused on a task? How do you get students to listen to each other and to provide critiques without insult (i.e. no ‘that’s stupid’ or “you’re an idiot”). It takes training.  I mean that literally. You have to show and model what it is you expect of them and practice, practice, practice.  Again, there is more to this than what I am listing, but here are some ideas:

• Start those first few days/weeks of school with non-content related activities that are non-threatening, fun, and where everyone feels comfortable sharing (so talk about ‘the best horror movie’ or argue for/against a ‘beach is the best place to vacation’)
• Set up group norms – i.e. if someone is talking, everyone else is listening; everyone makes mistakes, and that’s okay, you can support them and provide alternatives, but never insult them; everyone must contribute one idea; everyone’s idea should be heard; you can disagree but must provide a reason why; etc.
• Show them how to get into small groups (so physically moving desks back and forth – it’s fun to do this a timed game); show them and practice how to talk with elbow partners, or face-partners, or the people next to them.  Practice sharing talk-time (a time works here).
• Show them and practice group ‘roles’ – i.e. timer, recorder, controller, group spokesperson, etc. Switch roles up.
• Practice different ways of calling on students (so they know they are all responsible at any time) – so person in the group/pair with the shortest hair, or the darkest colored shirt, or blue eyes….really anything works.

There are obviously lots more ways to set up these collaborative processes, but the idea behind training is that there are some expectations for talking, sharing, and working together, and if we practice these and adhere to these, then our time learning is going to be more positive and productive. Practice, practice, practice.  Which leads to consistency.

3. Consistency

I know teachers here this all the time – if you set boundaries for your classroom, you need to be consistent or students will not follow them (heck, this is true for parents as well!). Again – those first few days and weeks of school are where you set these boundaries up and start practicing with students and modeling both behaviors and actions. More importantly, follow through on any consequences. For classroom culture, this means if you have an expectation that students listen when others are talking, whether that be student or teacher, then be consistent.  If you are talking and they are not listening, stop – call it out – and then talk again. Same thing for students talking. Acknowledge when something is not adhering to expectations and call it out and then refer back to your expectations. Students very quickly learn what is expected, and if they realize that you are going to consistently hold them to these expectations, such as listening, allowing for mistakes, everyone’s ideas matter, etc., then they are going to feel comfortable speaking up and sharing their questions and their solutions/ideas. It becomes a classroom where learning is up front and center and ‘we are in this together’ becomes the norm.

CHALLENGE

I plan to do some more specific posts about classroom culture and provide some resources connected to planning and training. For now, I brought this idea of classroom culture up at the end of a school year because as teachers, you are about to embark on a summer of rest and relaxation. For most teachers I know, it is also a time where we do some personal learning and planning for next year. I would like to challenge all of you to really think about how you want your classroom culture to be next year. You need to start on day one of school creating this classroom culture, so spend some time this summer planning for that. What structures do you feel you could incorporate (i.e. pair work, small groups, etc.) and learn about those structures. What are rich tasks and go find some that would work for the content you teach. What do you want students doing when they are learning together? Go find some tips and ideas for how to create those collaborative discussions and problem-solving environments.

Only YOU can change the classroom culture in your own classroom – so think about what you want that to look like and sound like, and spend some of your summer learning and finding ways to foster this culture in your classroom when school starts in September (or August).

Exam Mode on the Prizm CG50 Graphing Calculator

As my last post stated, it’s that time of year for standardized testing. As part of this, certain states require that students use calculators that have been set to exam mode. This means that certain features of the calculator have been ‘turned off’ or are inaccessible to students while the exam is going on.  I remember spending hours setting all my calculators to exam mode for students and then having to spend hours undoing that once exams were over – quite a pain.

The beautiful thing about the CG50 Prizm graphing calculator is that you never have to undo the exam mode – it will automatically turn off exam mode after 12 hours. Which means, you can set it, students can take their test, and then next day, the calculator is ready to go again with full functionality restored.  Another nice feature is that when the calculator is in exam mode, you can actually see it on the screen – there is a green highlighted border when in exam mode. This makes it easy to walk around and visually check that the calculators are indeed still in exam mode (or were set to exam mode to begin with, if you have your students do the process for you).

I made a quick video on how to put a CG50 Prizm into exam mode. I apologize for the lighting – very hard to film the actual calculator (vs. emulator) while holding my computer video camera…and those shadows?!!  But – hopefully you can get the gist of things!!

Math Test Prep – It’s That Time of Year Where We Bore Our Students Into Failure

I know when I was teaching in the k-12 classroom, this time of year was always so frustrating as a teacher and even more frustrating and anxiety-ridden for my students. This is the time of year when standardized testing is occurring or about to occur, in the majority of states. This can mean state-tests or national tests such as the AP exams, SAT and ACT. For me, the biggest ‘anxiety inducer’ was the mandatory End-of-Course tests that all my math students were required to take and pass with a 70% or better in order to earn the credits needed to graduate. No pressure there…..

Things have changed a bit as we move into the new era of ESSA, with many states changing the standardized testing requirements, but there is definitely a lot of pressure on students to perform, and on teachers to get their students to achieve at specific levels. This impacts teacher evaluations, school evaluations, etc. I’ve always hated that these ‘one-point-in-time’ tests have such dire impacts on teachers and schools, considering they do not reflect student growth over time or other impacting factors such as absenteeism.

But – regardless, tests are out there, happening now, and causing teachers and students undo stress. I know, for me, part of the frustration was the inordinate amount of time we were ‘required’ to prep students for the test. This included days specifically set aside to practice for the tests instead of teaching, and a ridiculous number of ‘practice tests’ and test taking prep.  Boring, stress-inducing, and really kind of pointless in my opinion. I felt we spent entirely too much time preparing for tests instead of actually teaching our content and letting students continue to learn. It was as if ‘learning’ stopped and the whole school went into ‘test-prep’ mode, and we forgot what school should be about – engaging students in learning and understanding, not preparing them to take a standardized test. My thoughts were these prep times only increased students anxiety about the tests and often, the long, drawn-out, constant test prep led to student burn-out, apathy, and failure. For many students, they got so tired and bored of ‘practicing’ that when the real test(s) came along, they made beautiful designs on their bubble sheets instead of actually focusing on answering the questions. (Yep – that really happens).

What are my suggestions? Keep teaching. And not teaching to the test or for the test, but teaching. Teach new things. Teach applications of things that might be on the test but  NOT through standardized-test questions, but with real questions, real problems, and real applications of the things students should know for the test. Worksheets with multiple choice answers are NOT teaching, or learning, or engaging. Technology with “practice” problems and right/wrong answers is NOT teaching or learning. Do something with the knowledge students should be able to use and do on these tests. Create interesting learning experiences, where students have to problem-solve and apply the knowledge and talk to each other. Example: instead of 20 solve these ‘systems of equations’ problems on a worksheet, provide real-world problems where a systems of equations is needed to find the solution. Where students have to work together to create the equations and come up with the solutions. Where they get to decide the most appropriate method to solve the system. Way more interesting and much more insightful into what students know and can do.

It’s not that you shouldn’t prepare students for tests. It’s that you should do it in a way where students are applying their knowledge and engaged in applications of that knowledge. It’s not about worksheets and test-taking strategies. It’s about understanding and applying the concepts. Tests suck. Don’t feed the anxiety and the boredom and the apathy towards tests by creating rote, mundane, drill-and-kill test prep. Make it about engaging students in applying their knowledge in interesting, relevant ways. There are many resources out there that can provide excellent ‘test prep’ ideas and problems in a much more exciting way than a worksheet with 40 multiple choice problems. (Bleh).

Some fun #math sites with challenging application problems to use for ‘test-prep’:

• Yummy Math
• Mathalicious
• Illuminations
• TuvaLabs
• RealWorldMath

 

3D Graphing on the Casio CG-50 Prizm

Casio just unveiled our two new graphing calculators, the CG-50 Prizm and the CG-500 Prizm CAS. Both of these can do amazing things, and both are approved by College Board for use on the SAT, Pre-SAT and AP exams. in particular, These are so new that we are still working on the tutorials and guides (coming soon), and the emulator software is still in Beta, but  also coming soon.

3D graphing is a component of both calculators and emulator software. I plan to do several more posts demonstrating new features and the amazing possibilities, particularly with the CAS CG-500, but today, I wanted to wow you with some simple 3D 3D graphing capabilities. As a geometry teacher, having the ability to show some 3D shapes and their equations as well as cross sections makes me pretty excited.

I am using the Beta version of our software for the CG-50 and just learning this new functionality myself, so bear with me!  But – it’s hard not to see how cool and exciting this 3D functionality is, and on a graphing calculator, which is still the most commonly used hand-held technology device by math students (because of its accessibility and affordability and the inequity in schools technology resources/internet/mobile devices).

Enjoy and stay tuned for more of these in future posts.

Annual ASSM, NCSM, and NCTM – A Week of Math Ed Leadership & Collaboration

Just returning from a week of fun in San Antonio where the annual math leadership and teacher conferences were held. Casio was a proud sponsor of a few events and at NCTM we had such a blast showing off our new graphing calculators (both approved by College Board for use on the PSAT, SAT, & AP exams), the CG-50 Prizm and the CG-500 Prizm CAS (3D graphing anyone?!) Not to mention the added bonus of blowing TI out of the water! (Side note: I will be doing specific posts for each of these in the next couple of weeks showing off some of the new and exciting features).

Thought it would be fun to highlight some of the moments we had sharing math education and technology with the dedicated math leaders and teachers we met throughout the week.

ASSM & NCSM

For the second year, we were honored to sponsor the opening session of ASSM (Association of State Supervisors of Mathematics). Mike Reiners, one of our amazing math teacher leaders and Casio user from Minnesota, provided some technology talking points after the main speaker and then everyone enjoyed some good food and conversation.

At NCSM (National Council of Supervisors of Mathematics) we were able to connect with many math leaders at our exhibit booth. We had a great time sharing our new calculators at our Showcase workshop and everyone walked away with a brand new CG-50 prizm to explore

 

Benjamin Banneker Association Reception at NCTM

It was a privilege to sponsor the BBA Reception at NCTM for the 2nd year in a row. What a great group of math educators who work so hard to ensure equity for all students. We were excited to continue our scholarship for a deserving student to support their future education endeavors.

NCTM & The Calculator Face-Off Challenge

NCTM was a big endeavor, with game-show stage and podiums, screens, lights, calculator displays. Thanks to the amazing team of Chris and Lionel from Events Special Effects and our own Casio Exhibit gurus John and Jason, the vision was made into a reality and it was a pretty beautiful booth if I do say so myself. Kudos to the team – it’s hard work designing, building and creating everything, but they did an amazing job. Some behind-the-scenes photos:

We had some crazy fun at the booth with hourly game-shows, and T-shirt spotter program where we gave away Kindle-Fire to those spotted in our t-shirts. We had G-shock watch giveaways, calculator prizes for our volunteer contestants and a magician, Mark Paskell, doing some magical give-aways and tricks. (My mind is still blown away by the reproducing bunnies….) 

We loved all the connections and interactions we had with math teachers, showing offthe amazing capabilities of all our calculators, but definitely our newest CG-50 and CG-500 graphing calculators. The look on our game-show participants faces when our CG-50 just blew the TI competitor out of the water was priceless. I know I am excited by the number of converts!

Here is a slide show highlighting some great moments from the games, demonstrations, sharing and talking with math educators, winners of our T-shirt spotter program, and some magic as well. Thanks to all the great math educators who came by and participated! Big shout out to our Casio teacher contestants, Jennifer North Morris, Tom Beatini and Mike Reiners.

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Math Fun in San Antonio – NCTM 2017 Annual

Next week is the NCTM Annual Math Conference in San Antonio, TX.  It’s a great time to go to Texas, as the weather hasn’t gotten too hot. I remember the last time NCTM was in San Antonio, when I was still teaching high school, and met up with all my teacher friends. We had such a great time, not only going to different workshops at the conference, but exploring the area (a trip to the Alamo was a must) and eating and shopping along the River Walk. I am going this year as part of the education team for Casio, where there will be a lot of fun to be had at our exhibit booth and sponsored events.  I have been going to NCTM Annuals for over 23 years (what?????), and as usual, I am looking forward to reconnecting with math educators and friends from all over the country, many of whom I only get to see this one time a year. So, it’s more than just a place to learn new ideas and collaborate with like-minded educators, it’s a time to renew friendships and share memories. I certainly am hoping to catch up with as many folks as I can, even if just to share a cup of coffee or a hug as we pass in the conference hall.

Naturally, the goal of attending a conference is to learn new things to bring back to your classroom or to the educators you work with. It’s one of the aspects of these conferences I love the most – the ‘renewed’ energy and excitement that occurs when you see a strategy that you want to take back to your class or you learn a new approach to a familiar concept that you know will resonate with your students, or you find that perfect resource for an upcoming unit. I always consider these conferences as a way to reaffirm why we teach math – seeing what others are doing, sharing stories and ideas, and leaving with at least one or two ideas that are going to spark your students creativity and understanding. For me personally, I always had a key focus (say Algebra, or Geometry or technology or manipulatives) to narrow down the workshops I went to, with the goal to find a few new resources, ideas and strategies to incorporate into my teaching over the summer so that next years classes would be even better. This type of focus helped to make ‘teaching’  a new adventure every year, even if I was teaching the same subjects, and it also made sure that as a teacher, I was always challenging myself to be better and find relevant strategies and multiple ways to help my students learn.

One aspect that I always look for is technology applications and resources. I am a firm believer in the idea that technology, whether it be a calculator, a tablet, a computer, a video, can be a valuable resource to help students both learn and develop mathematical understanding, but more importantly to visualize abstract concepts and explore ‘what if’s’.  I am sure there are many of you out there as well looking for some technology workshops as you attend NCTM this year, so I wanted to share some workshops from some of the amazing teachers that work with Casio, as these are always such great hands-on experiences.

Workshops:

• Thursday, April 6 – 9:30 – 10:30, Room 213AB Conv Center: Exhibitor’s Workshop What’s New At Casio: Viewing Mathematics through a New Prizm (or Two) 

• Thursday, April 6, 3:15 – 4:30, Room 217C Conv. Center: Polar, Parametric, Rectangular Graphs – Really See the Connections! with DeeDee Henderson

• Friday, April 7, 11 – 12:00, Room Presido ABC (Grand Hyatt): Conceptualizing Polynomials with Jennifer N. Morris

• Friday, April 7, 1:30 – 2:45, Room 224 Conv. Center: Conics – The Ugly Duckling of Algebra 2 with Denise Young & Tracey Zak Johnson.

• Friday, April 7, 2:o0 – 3:00, Room 008AB Conv. Center: The Probabilities and Mathematics of “Wheel of Fortune” with Mike Reiners

• Saturday, April 8, 8:00 – 9:15, Room 006D Conv. Center: Hands-on Activities + Technology = Mathematical Understanding through Authentic Modeling with Tom Beatini

We will also be having a fun time at the booth, Thursday – Saturday, playing games, having give-aways, talking and doing mathematics with our hand-held technology, so be sure to stop by and say hi (Booth #631) and come play with math. I will be there most of the time and hope to meet some new math educators and give a hug to old friends!!