Start the Year with Math Tool Explorations

chinese-28911__180In my last post, I talked about creating a classroom culture that promotes classroom discourse. The time to begin this is the start of the school year, when students are getting to know each other, getting to know you, and getting use to the ‘learning’ environment. My suggestion was to start these first couple of weeks with activities that are not necessarily content related, but more ‘interest’ related, because students are much more comfortable talking to others, i.e. strangers, about summer movies or vacations than they are about math. There’s no worry about not knowing something or saying the wrong thing – remember the focus in these first two days is to help students learn to communicate with each other, work together, and understand that your classroom is about learning together and everyone has a voice. Those first few times of group work or collaboration, keep it simple – remember the focus is on creating a ‘safe’ place for discussion – listening and sharing with others.  After they’ve had some time, then you begin to introduce content to the mix.

One of the things I liked to do during those first few days of school as part of this classroom culture, was to introduce the technology and other tools we would be using during the year. This allowed students to get familiar with the tools in a non-threatening, simple math focused way, ask questions, get help, and basically become comfortable using stock-photo-16971778-school-suppliesthe tools. It provided a lot of engagement and interaction as well.

For example, since I used Sketchpad weekly, I made sure that first week of school classes were in the computer lab a couple times and playing around with Sketchpad (I did not have laptops or iPads…just a lab that I signed up for 2 times a week).  It was very informal these first few times, focused on getting familiar with the program and the tools of the software so that when we did eventually use it as part of our content, they’d have had their playtime already and we could focus on using it to learn math. Same thing with protractors, compass, rulers, tangrams, calculators and whatever other tools I might be using for the subjects I was teaching (usually Geometry & Algebra). We would have “explore time”, where students would be given some simple math objects or activities – i.e. angles, sides, shapes, treasure hunts, and work together to use the tools to measure angles, sides, etc. They had to confer with each other if they got different answers, help each other if they weren’t sure how to read/use a tool, and I would also do some review of how the tools were used as well (particularly the protractor).


For the calculators, they would have a scavenger hunt – things like find the on button, graph a line, solve an equation, etc. and they would have a quick-start guide to help them. Even if students had their own calculators that were different, the scavenger hunt still worked and helped everyone learn to use their own calculator.  Just letting them explore on their own and teach each other helped foster collaboration, brought out some class leadership skills, and let provided some valuable time learning tools that saved time in the long run when those tools would be needed for more difficult learning of math concepts.

Today’s classrooms I realize might be a bit more diverse with technology tools – especially if students are bringing their own devices.  But – it’s still important to provide time for students to explore and play with tools. Providing some focused math explorations (i.e. measuring objects or creating a scavenger hunt), even if students have different devices, still allows for them to get comfortable with tools they will be using for learning. It alsoOLYMPUS DIGITAL CAMERA

allows you to understand the different devices and tools students have and get a handle on where you might need to make some adjustments.

It’s pretty easy to create simple math tool explorations – think of the tool, what will students need to use the tool for, and then create a couple of ‘to-do’ activities. Provide Cheat-sheets for the more advanced tools (i.e. calculators or Sketchpad software for example) that students can reference, but really rely on students figuring it out on their own or working together to figure out how to use a tool. That’s part of the challenge, and part of the classroom culture creation – depending on each other when you are stuck or protractor-769048__180want to verify your solution.



  • Create a sheet with several different angles and have students measure
  • Give them some specific angle measures that they then need to create the angles
  • Give them shapes (polygons) and ask them to measure the angles

stock-photo-100095203-geometric-shapes-on-darkSketchpad/Geogebra dynamic math software

  • Have them do basic constructions – i.e. draw a circle, make a segment, construct a line, make two lines meet at a 90 degree angle, construct a triangle
  • Measure things they constructed
  • Play with all the tools and describe what each one does

Calculators (graphing for this example) (provide a reference/cheat sheet, for example: (Some very basic sample questions below just to give an idea)

  • Where is the on button (describe location)
  • How do you turn off the calculator?
  • What happens when you push the Graph Menu?
  • How do you enter a y= equation?
  • Enter 3 and 3/4 into your calculator – change it to a decimal – how did you do it?



Creating a Classroom Culture That Encourages Student Discourse

I just spent two days earlier this week working with middle school math teachers. Our focus was on the 6 – 8 Common Core Geometry standards, and how they build on elementary geometric concepts and continue to build that understanding that students need when they get into high school geometry. As part of our work, we also focused on the Math Practices, because it’s the intentional alignment of practices and content to create engaging mathematics activities that really help students develop the deeper understandings. By that I mean you shouldn’t be teaching the content standards in isolation – they should be combined with helping students make sense of the problems, choosing appropriate tools to explore and apply the standards, and really explaining and justifying the conclusions they make.  Practices and content go hand-in-hand.

In our many collaborative discussions these past two days, as we really dived into both practices and content, what was very apparent was how important it is to create a collaborative, safe, classroom. Mathematics classrooms should constantly focus on vocabulary use (by both teacher and students), modeling, discussing your thought process (in many ways – spoken, written, pictorally), explaining and clarifying your thinking, asking questions, and really focusing on all types of communication. Mistakes or misconceptions that students have should be expressed freely, without fear of embarrassment, and students should be free to try multiple pathways to solutions and multiples ways to express their understanding. Students are not going to talk about mathematics if they feel they will be laughed at or considered ‘stupid’ – and that requires a classroom culture that fosters real communication between students that involves listening, ‘arguing’ against someones responses in a constructive, polite way, and a sense that it’s okay to make mistakes because we are all in this together, learning.

What the teachers expressed as their “ah-ha” from our days together was that in order to create these types of classrooms and math learning, you have to start the process right at the beginning of the year, during those first weeks of school, when students are new and class is unknown, and math concepts are relatively familiar since we are starting, in theory, where we left off at the summer. Those first couple weeks of school are the perfect time to create that collaborative classroom culture.

My suggestion was to start, day one, creating the idea that in this class we will be talking with each other, sharing ideas, and learning together, but we need some guidelines. So day one, don’t go over your rules – students know the rules. Instead, start having conversations – putting kids in small groups, and practice how to work and talk together using something non-math related to help foster the idea that in your class, communicating and listening are encouraged. For example, small groups of 2-3, and each group must decide what the best and worst movie they saw this summer was and give reasons for both.  Then have groups share out, using some simple group share out routines like the person in the group with the longest hair tell us about your groups best movie.  Be very explicit in how they communicate – ie., one person talks, everyone listens; write down your ideas, so one person records, etc.  Day two, do the same thing, but this time maybe use a simple math concept – i.e., in your groups, explain why a square might be a rectangle, or why is a circle different from a square?  Something appropriate for your grade level, but something that you know most of the students are familiar with.  Again – the idea is to learn how to communicate in the classroom – how to create that culture of collaboration, listening, and justification.  Day 3 – maybe introduce a math tool students will be using this year – like a calculator, protractor, compass, ruler, software, etc.  Have students explore and write down things they notice (give them simple things to do), things they have questions about.  Have other students explain what they found or answer each others questions.  Model the use of the tool (s) yourself. Lot’s of options, but the point being to get kids thinking, talking, listening, and understanding that if they have questions or concerns it’s okay to voice them.

Do a little bit each day – change the groups up, do it whole class, do it with partners. The idea is that you are helping students learn to talk to each other constructively so that when you get into the real learning of new math concepts, they are already comfortable with each other, with some of the learning tools they will be using, and understand that in this math class, we work together and listen to each other and support each other.

Learning is not an isolated activity – we, as teachers, are there to facilitate learning and help students become active, productive, problem-solvers. This happens in classrooms where it is okay to communicate, it is okay to make mistakes, it is okay to have your own approaches to problems but that requires justification of those approaches so others can learn from them.  The more you create this type of learning environment, the more your students will persevere in tackling those tough learning moments.

Test-Driving Classroom Technology

45785364I am a huge proponent of using technology in the classroom, particularly in mathematics. If technology is used appropriately, it can do several things: provide visuals for concepts that are often hard for students to grasp; allow for students to explore and test conjectures; provide opportunities to go beyond basic understandings and get into deeper meaning and more complex structures; provide multiple ways to practice and learn; and obviously, foster engagement. These are just some of the benefits.  There is of course a downside to technology – lack of training for teachers often leads to using technology just as a digital replacement of paper and pencil – an electronic worksheet for example – in which case, what’s the point?  That’s NOT a great use. Or using technology when it is NOT the best option or doesn’t really enhance/support the learning goals. Or using the wrong technology. Just because you have technology doesn’t mean it’s a good fit for your learning goals/standards.

In my own research, and in my personal travels around the country working in math classrooms and with math teachers, there is a wide variety of technology available, and more often than not, this technology is NOT being used to enhance and expand learning. Often times this is because technology has been purchased with no real effort to match it to learning goals or standards, and little or no training or support for how to use the technology in the classroom has been provided. Teachers are frustrated, students are frustrated, and the technology becomes just another ‘add on’ versus a true learning tool.


What is often missing in a technology implementation is the most crucial step – planning. With planning, technology aligned to objectives becomes a focus for purchasing technology that actual supports learning goals and needs. Seems obvious – but, having been an administrator, I know that often times ‘funds’ for technology are released and must be spent quickly (i.e. for me, I was told we must put our orders in by this week or we lose the funding), so often times technology is purchased that sounds good, or looks good, but may in fact not be a good fit.

Ideally, technology should support learning goals, which can only happen if you sit down with your subject leaders/teachers, look at your standards and learning goals, and then analyze the various technology options and determine which ones support those goals. And, if possible, test these technologies out BEFORE purchasing, to ensure they do indeed support learning.  This also allows you to plan for training needs of the teachers, infrastructure, curriculum and standards alignment, etc. These are important steps – often left out of the technology implementation process – and often the reason why much of the technology in school is misused and unused.  I bet if you looked around your school you would find a lot of ‘great technology’ gathering dust.


If technology company’s were smart, and if IT and Education leaders really focused on planning for technology, there would be a lot more pilots or test-driving of technology before big purchases are made. (LAUSD and the iPad debacle comes to mind). The ability to try out technology with both teachers and students and really see if it is going to be a good fit to meet your learning goals is something that will  help your school/district make the best technology decisions and purchases. As an example, CASIO Education has a technology loaner program where you can in fact, test-drive our technology before you purchase. It makes sense – if you are thinking of purchasing some graphing calculators, why not test-drive the 9750 GII and the Prizm and see which one fits your algebra or geometry or calculus students and standards the best? Is the FX-55plus a good fit for your elementary and middle school students? These types of questions are what should arise when you plan for technology AHEAD of time and having the ability to test-drive your options before spending the money just makes sense.

You don’t buy a new car without a test drive, so why buy technology without one? Especially when making large school/district purchases.

Here’s the link to CASIO’s loaner program – check it out and go for a drive!

Calculators – Back to School Choices

gallery-1466087182-middle-school-and-high-school-school-suppliesHard to believe that summer is already over – for some students anyway.  Depends of course where you live – here in PA students don’t go back until the end of August, in VA, it’s after Labor Day, and in CA, my sisters kids are already on their 4th day of the new school year.

As a teacher and as a parent, I know the beginning of the school year involves a lot of money and making choices – new clothes, bookbags, pens, pencils, papers, notebooks, calculators.  Those long “school supply lists” seemed to get longer every year.  In part because school funding has decreased, so teachers have less to work with and count on the parents to help support classroom needs. Though, as most of you know, teachers spend a lot of their own personal money on their classrooms and students too.  Something to remember when you question the box of tissues, the dry-erase markers, and other seemingly ‘unnecessary for my child’ supplies.

These days, some of the needed supplies come with a hefty price-tag – laptops and tablets for example. Depends again on what the school/school district supplies and if your child’s school even uses such technology.  BYOD (bring your own device) schools expect you to provide these, and those that do provide the devices often require a hefty ‘rental’ fee – for obvious reasons such as damage, repairs, upkeep, etc.  But – these more expensive items are still not the norm in most schools – again, because of funding, lack of internet, lack of training on how to use these devices appropriately, etc. In my research, only about 25% of schools are using laptops/tablets on a daily basis, with most students only getting access to these a few times a month (shared laptop/tablet carts or a computer lab).

One technology tool that is still prevalent and requested, more so in middle and high school, is the calculator. Schools use to supply these, and some still do, but the cost to maintain and replace broken or lost calculators is difficult when school funding is so drastically reduced. Calculators are often added to the school supply list, like in my sisters case, where she was asked to buy two graphing calculators for her two high school students. Sometimes they request a specific brand – for no other reason than its what the teacher/school is familiar with, not considering price at all. But price matters, especially when functionality is the same and often times better. Scientific calculators have similar price tags, no matter the brand, but graphing calculators have a huge range of pricing and options – color, non-color…what to choose? Color graphing calculators in particular can be expensive – $150 for the ‘familiar’ model. But you don’t always need to get the most expensive, ‘familiar’, requested model just because it’s on the list.  Get the one that’s going to support your child’s math learning.

IMG_3406Obviously I am going to promote Casio calculators here, since I am a IMG_3407Brand Ambassador for them.  But, as a math teacher for 25 years, I am also promoting them because they are truly a better calculator and more affordable, so why wouldn’t you make that choice? If your child needs to purchase a calculator, then just go into a store, like Walmart or Target or online – and compare. In the Scientific models, pricing is similar, so how do you choose? Well- you go with functionality and Casio is easier to use and, as in the case of the fx-300Es vs the TI-30xIIs, the Casio makes fractions look like actual fractions, lets you see tables when entering data – just a few of the things it does better. Same in elementary calculators – the fx-55plus is far superior than any TI calculator and fractions look like fractions! (i.e Natural display).

Graphing calculators are trickier – there are color options, non-color options. In all cases, Casio is much more affordable than TI. Do you need a color graphing calculator is probably the real question. For more advanced mathematics courses, the color graphing calculator is the better choice for several reasons, for example they tend to have more functionality and color displays allow for easy comparison when looking at several functions on one graph. The Casio Prizm is significantly more affordable than either of TI’s color options, and as we showed at NCTM, a previous blog, and in many comparison videos, the Prizm outperforms TI.

2015-10-29_14-24-37In most instances, particularly middle school, color is not needed, in which case you can get a Casio Graphing calculator like the 9750GII or the 9860GII for 1/3 to 1/2 the price of a T. Even without color, both of these calculators outperform and are easier to use than the TI models, including color (see videos again!) And, if you only want to purchase one graphing calculator for your child to last all through high school, both of these will get them through the highest levels of math. I guess my thoughts are why pay more for a name when you can get a better calculator at a significantly more affordable price? And if the teachers or schools say it must be a specific model, that’s only because it’s what they know – it’s NOT because it’s a better product. And in this day and age, where we are all watching our money and have to make choices, I say go with the more affordable and efficient functioning option.

As you go shopping for your back to school supplies, just remember you have choices. So choose what works best for your budget, your child, and don’t forget to pick up some extra tissues and dry-erase markers for the classroom – they are definitely needed!!

Casio Global Teacher Meeting – 2016


GTM 2015

Hard to believe that a year has already gone by since I went to my first Global Teachers’ Meeting to support Casio Education initiatives. Looking back on my post from August 2015, A Global Perspective, I still felt that same sense of awe being in a room with teachers from all over the world – Algeria, France, Belgium, Japan, Australia, Finland, Germany, China, England, Italy, Spain…..A regular United Nations of math teachers!

This year the meeting was not held in Japan, as it normally is, but in Hamburg, Germany. This was due to the fact that ICME (International Congress for Mathematics Education) was being held at the University of Hamburg during the same week, so Casio, a big sponsor of ICME, wanted the two events to coincide. ICME only happens every 4 years, and I was fortunate enough to attend a couple days of the ICME conference – a math conference very different than an NCTM conference. This conference is all about researchers sharing their work and math educators collaborating and discussing the issues surrounding math education. I have a lot of reading to do because some of the research I heard about was fascinating.


GTM 2016

My take aways’ from this years Global Teacher Meeting (GTM) was again how diverse math education is in other countries, and how culture and government of education really impacts how and what is taught. Many countries have a Ministry of Education, and therefore all schools within that country are governed by the curriculum, resources, and assessments that the Ministry of Education defines. This is different from the United States, where, even though we have the Department of Education, every state controls what happens in their states, and often control is even given to individual schools. This explains why it is so difficult to enact change in United States schools because we have so many different governing bodies defining education and there is rarely any real commonality. It also, in my opinion, explains why it really is unfair for us to compare our education to many other countries since it is such a vastly different ‘thing’.

There are many other differences – respect for the teaching profession is much higher in many countries than in the US, there is more consistent use and access to technology, and a more pervasive use of diverse, inquiry-based, problem-solving focused strategies for teaching mathematics – it’s all very different. But, what is very apparent and similar in these Global Teacher Meetings, is how dedicated all the teachers from every country are to their students, to providing quality education and math instruction, and in their belief that technology is a necessary tool in supporting mathematics learning. I think I said it last year, and it’s still true this year – Casio is number one in these countries. These teachers are using Casio calculators, particularly the Classwiz-fx-991 and the ClassPad, all the time.  Pretty telling I think.

I came home this year from both the Casio GTM and my experience at ICME with renewed excitement about the possibilities for math education and integration of technology in mathematics instruction in a more equitable, pervasive way. I know Casio is really striving to get technology into the hands of every student to help bridge those access gaps. Much of the research I heard talked about the benefit of dynamic math capabilities and using technology to increase understand and expand problem-solving and critical thinking as students learn mathematics. I see great things happening this year – school starts just around the corner, so it’s a new beginning.

I leave you with a few images from Hamburg, Germany.  I was very busy being a complete math and technology geek, so unfortunately did not see much of the beautiful city.  But we did get a wonderful experience “on board” the beautiful, historic Rickmer Sailing boat, so here are some pictures from that experience.

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