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!!

Multiple Representations on the Casio Graphing Calculators

One of the key things we try to help students with when studying functions is the idea of multiple representations – i.e. graphical, symbolic (equation) and table.  Ideally, we want students to be able to discern what the function represents or looks at no matter what representation they are given, and to be able to find patterns and important components about that functions from all representations.  Students should never learn about functions just through graphing, or just through symbolic manipulations or just through looking at data points in a table – they should be able to go back and forth and determine which representation is the most useful for the situation.

Unfortunately, too often, the emphasis is on one representation at a time, or at most 2. Let’s look at the graph and find the minimum, maximum, or intersection. Or, let’s find the roots of a quadratic by factoring, or symbolic manipulation. Or, here’s a table of points, where are the x-intercepts or the y-intercepts? Ideally, we want students to be able to look at all of these representations simultaneously so that they see the relationships between the representations and come to understand what the points represent in the table, in the equation, or in the graph.

Technology is one way to show all these representations at the same time, and then quickly manipulate and explore. There are obviously many technology tools out there, but as I have stated in previous posts, the most accessible technology tool for most students and teachers is the graphing calculator, not only because of it’s affordability, but because it is a tool most students have readily available.  It would be nice if all students had computers or tablets for daily classroom use, but that is still NOT the reality.

I have put together a quick video showing Casio’s three graphing calculators – the fx-9750GII, the fx-9860GII, and the CG10/20 or Casio Prizm, and how they can display the equation, graph and table representations of a function on one screen. No matter which model you have, you can achieve the same functionality, allowing students to work with multiple representations and explore relationships quickly and efficiently.

Check it out:

Teachers & #Edtech – Ready-to-Use Lessons Can Be A Support

I am a little obsessed with edtech and integrating technology into math classrooms. It’s what I have been doing forstock-illustration-70753375-mathematical-vector-seamless-pattern-with-geometrical-plots the last 16 years of my educational career, first within my own school and district, and then, throughout the country through my work with Key Curriculum, McGraw-Hill, Kendall Hunt and Casio. I read a lot about the infusion of technology in schools these days, but my reality, when I go to schools and districts throughout the country, is that the use of technology in mathematics education is actually very, very limited. There are of course countless reasons for this – a big one being funding. Most schools I work with have 1-2 computer labs that math teachers rarely get to use, or they have a laptop cart shared between 15 math teachers. They have calculators – sometime – most of which are broken, have no batteries, or they honestly don’t know how to use. There are also the instances where there is a lot of technology available, but the teachers don’t know how to use it, don’t have resources to support it or they haven’t had a chance to find a place where it would support their curriculum.

The reasons for not using technology are many. But – in my own personal research, one of the biggest deterrents to integrating technology is lack of training and support. A recent survey of teachers by Samsung shows teachers do not feel prepared to use technology in classrooms.  Not a surprise. Unfortunately, the majority of professional development is still the one-stop workshop, where new technology/apps/ are bought and teachers are trained for a few hours on the tool, with little or no emphasis on teaching with the tool, which is the most important aspect of technology integration. Technology is only a tool – and when used appropriately, can enhance and expand learning. This involves more than learning how the tool works. It involves looking at the curriculum and instructional goals, determining what tools (of which technology is only one) are going to provide the best fit, and then creating instruction that incorporates the tool as part of the learning, not as an add on, not as something extra we do after we learn.  This is what is missing most of the time – helping teachers make technology fit into their instruction as part of the learning, not as something extra.

One of the things I found in my research is that if teachers are provided with pre-made, ready-to-use lessons that can replace current lessons and use the new technology, they are more likely to start using it, especially in the beginning stages of learning. Lack of confidence is a huge reason teachers don’t use, or continue using, new technology – this is helped if they are given a push, especially in the first stages of learning, that allows them to use technology without too much stress – i.e. the lesson is ready to go, there are teacher notes/guidelines, and it FITS INTO THEIR CURRICULUM. In the Samsung survey, 80 percent of teachers said it would be helpful to have pre-existing lesson plans that help them easily integrate technology. I found this was one of the strongest indicators of continued integration of technology in my research.  It’s one of the things Key Curriculum provided for Sketchpad, it’s one of the things Casio provides for their calculators.  If teachers are given new technology and ready-to-use lessons that show them and students how to work with the technology while learning required content, they are much more likely to use the technology.  And – the more they use, they more confident they become with it, the more likely there will be continued implementation.

To go along with ready-to-use technology lessons, ones that scaffold learning for both teachers and students, is stock-photo-41836894-colleague-students-using-laptop-in-librarycollaborative lesson planning. Teachers should have the chance to work together to plan lessons to incorporate technology. Again, in my own research, teachers expressed how the monthly collaborations with other teachers from around the district, as well as the online sharing community, really helped support their own efforts to integrate technology and gave them new ideas. Sharing ideas, planning for where technology is appropriate, learning from each other – all of this is powerful in helping teachers be more confident in using technology in instruction. There is no reason for teachers to reinvent the wheel for every lesson – if there is a premade lesson out there, or a lesson another teacher has tried, that will support others integrating technology, there should be sharing and collaboration.  Teaching is a profession, not an isolated, individual endeavor – we should be working together to improve and help students learn and help each other learn.