Remembering the Reason for Memorial Day

With Memorial Day Weeekend upon us, I thought it appropriate to do a little research and posting about what Memorial Day actually represents, something I believe many of us forget amidst the weekend barbecues, beach outings, and other ‘holiday’ celebrations. Being the math person that I am, I wanted to focus a bit on “numbers” surrounding Memorial Day. Which, in retrospect, is very sad and alarming. But – it makes you appreciate our military even more and the sacrifice they and their families make to protect our U.S. Freedoms and allow us to celebrate this weekend.

I found this infographic by John S. Kerman at WalletHub that pretty much did all the work for me, so I am including the link and infographic here. Some of the numbers are fun facts and some are startling numbers that hopefully will make you stop, think, and remember those who have given their lives. When you eat that hot dog, or enjoy a sleep in on Monday because you have the day off, remember the 1.3 million service men/women who have given their lives for that right. And don’t forget at 3 pm to honor them as part of the National Moment of Remembrance.


Memorial Day 2016 By The Numbers

Source: WalletHub

Multiple Entry Points and Rich Math Tasks

I was reading this article the other day about how a strength-based approach to learning math (and learning in general) redefines who is “smart” and allows all students to succeed. In her article, Katrina Schwartz has some quotes and reflections from former students who learned math using the complex instruction method, and who were all successful.  They talked about how “math class made them feel safe, heard and able to express their ideas without fear”.  Wow – how often do you hear something like that?!!

Complex instruction is based on the idea that learning is collaborative, where students are learning using rich tasks with multiple entry points and pathways, and each student has a role and accountability. This isimage15 not a post about complex instruction however. What I was thinking about while reading the article was in fact about the Common Core Standards for Mathematical Practice and how they support what the students were expressing in the article – that math class “was a process and it required other people. It wasn’t just you and your work and not talking.”

If you actually read the 8 mathematical practices, you will notice over and over again words like communicate, justify, analyze, plan, make sense, look for entry points, reason, ask questions, make viable arguments, apply.  The practices are all about communicating and talking and finding multiple entry ways to solve problems. And working and talking with others to get there. Like complex instruction, these problems should be rich, where in fact, there are multiple entry points and possible solution pathways. Where each students strengths can support the process and help build the understanding of others. Learning is collaborative, NOT an isolating experience that a worksheet or a lecture so often create.

The Common Core gets a bad rap because so many publishers and testing companies have standardized it – by providing ‘common core problems/strategies’ that are in fact limiting and narrowly focused so they can be graded easily. When I see parents and students and teachers complaining about “common core problems”, I get so angry because what I am actually seeing are ‘forced entry points’ – meaning, rather than allowing all students to approach a problem from their mathematical strength and understanding, they are forced to choose between 1, 2 maybe 3, ways to solve a problem, which may NOT be understandable methods for them.  Therefore, NOT Common Core (or Complex Instruction). As it says in the practices: “Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution”. It does not say mathematically proficient students are given specific entry points to solve a problem.

image16My hope is that with the changes in standardized testing on the horizon under the Every Student Succeeds Act, that math teachers and classrooms can truly begin to focus on students strengths and learning, not preparing for a test. To actually provide learning experiences focused on allowing students to work from their strengths. But it requires a willingness to have a noisy classroom with students talking and collaborating.  It requires  rich mathematical tasks, not standardized worksheets and drill and practice,  that truly provide multiple entry points. This in turn requires teachers who are willing to accept multiple solutions from students rather than the traditional one-way, algorithmic approach we tend to focus on. And it requires support for teachers – in resources, training, time, and expectations.

Read the article by Katrina Schwartz – it also has links to information about Complex Instruction and great feedback from San Francisco Unified School District who has made a concerted effort to teach mathematics this way. Read the Common Core Standards for Mathematical Practice. If you are not already doing so, try to incorporate some of these practices into your math instruction. It’s not what you teach, but HOW you teach, that has an impact on students.  Every student can learn math – it’s up to you to create a culture that helps them believe that.

Casio vs. TI – Finding Max/Min Points of Functions

DispCap1In this weeks’ comparison of the Casio vs. TI calculators, I demonstrate how to find a max/min of a given function, using the Casio Prizm and the TI-84+ CE. In my example I use a cubic function because it allowed me to show both a maximum point and a minimum point on the curve. Why might students be asked to find a max/min point of a function you ask?  Well, besides the obvious ‘on a standardized test’ question, what we really want students to be able to do and understand is what the max/min points mean in the context of the problem/situation. In a real-world application, how does that max/min point help us understand what is going on in the problem? The short answer is it provides specific points where ‘something’ has happened, and finding these points provides insight, allowing students to ask different questions or analyze the situation.

Here is a common example: A quadratic function might be used to model the path of a ball as it is thrown or hit, with x representing time and y representing its’ height.  So the max point in this case would be the maximum height of the ball at a given point in time before it begins its descent back to earth. We want students to be able to find that max/min point, in context, so they can answer questions or make conjectures about the ball. For instance, in this ball example, is it possible to change the angle the ball is thrown/hit to increase the max height, but keep the time the same? Being able to quickly find these max/min points so that interesting questions and conjectures can be made and students can apply mathematics in challenging and deeper ways is one benefit of using technology, such as graphing calculators. The max/min points can be a starting point for deeper exploration.

Below is a quick video on how to find a max/min point of a function (using a cubic as the example, since it has an example of both a maximum and minimum point).

More than Calculators – Teacher Support & Resources

I received a message the other day from a reader who commented on how much he liked the Prizm, but because 2016-05-13_12-52-22Casio didn’t have any resources to support the learning of the Prizm, he was a little reluctant to try it.  My first reaction was “What?!! We have a TON of resources!!”  My second reaction was to ask myself why might he think this? I was able to answer my own question when I searched for our resources – the issue being they are a bit hidden among all of Casio’s other products, (which, just so you know, is of course in the process of changing as we create a more user-friendly web-page).

In the meantime, I want you to see the great teacher/student resources we have! Let me share with you the resources we have that supports teachers (and students), from complete subject-specific or grade-specific resource books (i.e. complete lessons), so sample lessons and activities (free), to online course for Prizm (free) to webinars (free).  There are teacher-created resources and quick-start guides.  Casio WANTS teachers and students to use their calculators and get the help and support they need to use them appropriately.

  1. Free online activities and sample questions:
    • These include grade-level activities and specific Casio Prizm-vs-TI 84 activities
    • Scrolling down the page you will find sports activities for use with five different calculators
    • Keep scrolling to our Quick Start Guides for 6 of our calculators (including Prizm)
    • Keep scrolling to Subject-specific Teacher Resource Guides and Calculator Tips
    • Scroll further to see all our grade-level and subject-level resource books that contain complete lessons
  2. If you look at our products page, under Software & Additional Products, you will be able to scroll through all our grade-specific/subject-specific resource books:
  3. Here’s a short-link to our Casio Lesson Library (with teacher created activities):
  4. Short-link to Guided tours for the Prizm:
  5. 2016-05-13_12-56-04If you are interested in the Prizm, we have a whole webpage dedicated to Prizm activities and support, which includes lessons, videos, and also has the OS updates. 
  6. We have a free online course for the Prizm (self-paced).  If you complete the course, you get the Prizm (fx-CG) emulator software for free.
  7. Free webinars on many math topics (statistics, geometry, algebra, calculus, etc.)(you do have to register your email to view these, but they are free):
  8. Links to manuals for specific calculators:
  9. And let’s not forget the videos showing you how-to’s and comparisons!  and

As you can see, we have a ton of support for teachers and students wanting to use and learn-to-use Casio calculators to support their instruction and/or math learning. We hope those of you out there excited to start working with Casio calculators start using these supports. We are educators here at Casio and want you to love the calculators as much as we do!!

Plotting Vertical Lines – Casio Prizm vs TI-84

To play off of the #NCTMannual Calculator Face-off challenge, I am going to try to post a weekly comparison of Casio calculators compared to TI calculators. My thoughts on this, as expressed in my recent post, Casio vs. TI – Calculator Face-off NCTM and Beyond, are that too many teachers and schools are stuck in the mind-set that TI is the ONLY option for calculators out there.  This is clearly not the case, and also, clearly NOT the best choice in calculators when you take into consideration functionality and affordability, especially to address technology equity issues that are such a hugeconcern in schools.  Casio is simply more affordable, easier to use, and has better functionality.

With that in mind, I want to keep it up-front and center so that those of you out there in the market for calculators can actually see side-by-side comparisons and make educated decisions vs. the “it’s what we always do” type of decisions.

Side Note: We are getting some “feedback” from our TI-users, who are not happy about these comparisons – probably because they are new to being challenged. Granted, when comparing calculators from any vendor, there are going to be certain concepts or procedures that might be faster and and maybe more efficient when on one compared to the other – no calculator will always be the winner -it’s bound to happen. But – overall, and consistently, based on teacher and student feedback and our own personal experiences with both,  Casio is superior in it’s functionality, is definitely more affordable, and is easier for students to use because it is much more intuitive and there is less hunt-and-find-the-right-menu going on. It’s right there on the screen with a Casio, not hidden in apps or ‘math’ or ‘test’ buttons.  If we consider why we use technology in the mathematics classroom – it’s NOT to ‘get the answer’ (or shouldn’t be!), it’s about using technology appropriately to allow students to be more efficient in their process so they can explore, discover , make conjectures, test hypothesis, and make comparisons. Getting bogged down in “where do I find this?” is not conducive to productive student learning and exploration.

There are several Casio vs. TI comparisons videos already – all of them currently Prizm vs. TI-84.  I am adding today’s video, where I compare how to plot a vertical line on the Prizm vs. the TI-84. You will note the process is similar, with a significant difference being Casio creates a true plot of a vertical line, where you can find actual points on the plot, and TI is only a drawing. It is not possible to use the “drawing” to find specific coordinate points on the plot accurately or efficiently.

Here’s this weeks video comparison.  Stay tuned for future comparisons with the Prizm and other Casio Calculators.