#Edtech Professional Development – Comfort, Confidence & Relevance

I did an article several months ago about technology professional development and ready-to-use lessons being one way to support teachers implementation entitled Teachers and #Edtech – REady-to-use Lessons Can be A Support. Obviously, this is only one of many things schools and education leaders can do to help support technology implementation and ensure that the technology use is sustained over time as well as actually improves and supports student learning. I wanted to just share a couple more things that I found in my own doctoral work that education leaders need to consider PRIOR to purchase technology, as well as AFTER purchasing technology.

keycurriculum_nctm2012-0414I have spent years researching, creating, and doing professional development, much of it specific to technology integration in mathematics, whether that be online learning, dynamic software or calculators. I have been all over the country (and now the world as well!) providing teachers and administrators with face-to-face workshops, online learning, and blended professional development to support technology integration. My doctoral work was specifically focused on technology professional development with math teachers and was a long term, embedded study over 3 years. From my own research, which supports other educational research findings on PD and technology integration, here’s is a condensed list of things education leaders can do (before, during and after professional development) that make a difference in the success and/or failure of technology integration into classroom practice:

  1. Curriculum & district expectations
    • Ensure technology used actually supports standards and content taught
    • Make sure there is relevance of professional development content/resources to what teachers actually teach and do in the classroom
    • Provide content-focused, ready-to-use activities/lessons that utilize the technology
    • Set clear expectations from administration that using the technology was expected & supported
  2. Teaching practices
    • Professional development should emphasize using technology to teach specific content keycurriculum_nctm2012-0486
    • Professional development should provide classroom management and teaching strategies for using the technology
    • Multiple teaching strategies need to be modeled in professional development (questioning, collaboration)
    • Teachers are given time to collaboratively plan lessons and practice using technology with their content/classroom
  3. Sustained Professional Development
    • Long-term support must be provided
    • There should be continued training on technology as well as content-focused implementation of technology
    • Coaching, modeling, active learning should be key components of sustained professional development
    • Teachers need sufficient opportunities to collaborate & time for practice and feedback
  4. Internal & External Factors are accounted for and controlled
    • Access to technology should actually be available(seems a no brainer?!). Technology integration won’t work if students access to the technology is limited.
    • Teachers must believe students will benefit from use of technology (so PD emphasizes relevance) and be confident in their ability to use it (so sustained PD is provided and teachers are supported in many ways)
    • Time is provided.  Time for teachers to learn and practice implementation, time for students to learn, and time for changes to take place BEFORE judgements/assessments are made
    • Classroom structures need to support the use of the technology. So – class size, other competing technologies and/or resources are de-emphasized, support for changing classroom teaching strategies, etc. are all considered and addressed prior to and during implementation

image16The importance of providing teachers with resources they can use right away with students that are relevant to what they are actually teaching is so crucial, especially when a new technology is introduced. If the beginning of trying to use a new technology is filled with frustration and angst, the chance of that technology being a lasting education tool is unlikely. Comfort, confidence, and relevance make a big difference in the success of technology as a learning tool – if you provide those resources up front, and then as teachers see the benefit and get more comfortable with using the technology with students over time, you will see continued use. Follow that up with sustained support through collaborative lesson planning, coaching, online on-demand support and resources – so many possibilities, and you will see a big difference in the successful implementation of technology. ROI as they say – return on investment if you invest the resources, time, and support from the very start.

These are just a few things to keep in mind as you consider new technology for classrooms or as you re-consider how to support current technology implementation.

NOTE: A great example of this relevant, hands-on PD approach, with sustained support afterwards, is offered by Casio’s technology workshops.  At these mini-workshops you get to ‘do technology’ using content-focused, hands-on math activities that can be used immediately with students, you get the technology itself (Casio fx-9750GII) and you get on-demand, sustained support via our tutorials and ready-to-use lessons, content webinars, and guided tours. The idea here is teachers get their hands on technology and do content-specific activities that help them see the relevance of the technology to their teaching and student learning. They then have ready-to-resources to implement immediately, getting them more comfortable with the technology. And they have a place to find additional resources as they become more adept with using the technology with their students. The resources and support help the use of technology become an integral part of teaching practice.

 

NCTM Regionals -What’s the Point?

NCTM Regionals in Phoenix, AZ and Philadelphia, PA are going on this week and next (Phoenix, AZ is October 26-28, Philadelphia, PA is October 31 – November 2). The regional conferences are significantly smaller than the National conferences, and draw much more of a local group of math teachers versus the more wide-spread attendance, both national and international, at the NCTM Annual Conference (this year in San Antonio, TX, April 5-8, 2017). There use to be 3 regional conferences, and this year we are down to two, so the question arises, what’s the point? Are these Regional Conferences worth the time and effort? Well – as a math teacher who faithfully attended regional conferences for years and years, my answer is yes.

Here’s my short list of why there is in fact, a very definite “point’ to the NCTM Regionals:

  1. They are in the fall, after teachers have had a chance to get their classes going, image20understand their students, and get in the swing of things. It’s about the time when the dust has settled and teachers are looking for some new ideas, engaging activities, technology apps and devices – anything to help support student learning. The Regionals’ provide a chance to spark some creativity for teachers who are finally having some breathing room after the chaos of the start of a new school year.
  2. These are much more local conferences, so there’s a lot of teachers from the same area as both presenters and attendees – it builds some camaraderie, with many local schools and districts providing a day or two of professional learning time for their teachers to attend. It supports local math initiatives and provides teachers with new ideas and strategies that they then take back and share with other teachers and their students.
  3. The Regional conferences are less expensive, allowing for more teachers who want to attend to actually do so. Often times schools/districts will pay for teachers to go to the Regionals since they are a more affordable and they can send more teachers as well (more bang for their buck).
  4. keycurriculum_nctm2012-0442They occur early in a school year, so that math leaders and those who make ‘funding’ decisions can check out new curriculum, textbooks, technology, professional development, and math resources at the Exhibit Hall and at sessions. This allows for them to arrange for samples or pilots or meetings to plan for things like textbook adoptions or technology purchases or professional development support. Teachers often go to these Regional events and bring ideas back to their school leaders of what might be good for their schools/students. There is time to research, try-out, and get a feel for what resources might be best before any funding/purchases need to be made (usually the Spring).
  5. It provides a place to learn more about mathematics standards, Education Policy (like ESSA), standardized testing, and other math-related issues that impact teaching and student achievement
  6. It’s an opportunity for math educators to get together to collaborate, learn, share and get informed and rejuvenated about mathematics education. That’s the most important thing – educators learning together to find new and different ways to engage their students in mathematics learning. Nothing more powerful than that.

So – yes. There is a point. Hopefully there are many of you out there who are able toimage12 take
advantage of the NCTM Regionals this year. If not, the same can be said of your local and state math conferences, so don’t pass up the chance to attend those if you can.

Casio is in attendance at both Phoenix and Philadelphia NCTM Regionals, so be sure to stop by the booth and gets some hands-on play time with our technology and math resources. Not to mention entering the raffle for a free graphing calculator. We also have workshops happening at both conferences, so be sure to check those out as well.

Phoenix:

  1. Thursday, October 27
    • Exploring the Connection Between Recursive Sequences and Composition of Functions  Room 102 C, Grades 10-12, 9:30 – 10:30 am
    • You’ve Got To Move it! Transforming Mathematics – Room 227 AB, Grade Levels 8-10, 1:30 Pm – 2:45 pmimg_4198
  2. Friday October 28
    • Linear or Not Linear: That is the Question  Room 101AB, 8 – 9 am
    • The Probabilities of “Wheel of Fortune” – Room West 301A, 8 – 9 am

Philadelpha

  1. Tuesday, November 1
    • Problem Solving for Middle Grades Pre-Service Teachers   Room 105AB, Coaches/Leaders/Teacher Educators, 11:30 am – 12:30 pm
    • Polar, Parametric, Rectangular – Can You See the Connection?  Room Franklin 3/4, Grade Levels 10-12, 3:15-4:15 pm
  2. Wednesday, November 2
    • Hands-on Activities & Technology=Mathematical Understanding Through Authentic Modeling    Room Franklin 3/4, Grade 8-10, 9:45 – 11:00am
    • Exploring the Connection Between Recursive Sequences and Composition of Functions   Room 201B, Grades 8-10, 12:30 – 1:30 pm

 

Math and The Electoral College

With the election looming, and yet another Presidential Debate this evening (anyone else dreading it?) and more polls than you can shake a stick at, it seems appropriate to think about the math behind the Electoral College. I admit to really not understanding this whole system – and I know I am not alone. With the rampant conspiracy theories about the November 8 election, and a ‘rigged election’ and cries to eliminate the Electoral College and go to a popular vote only, it had me diving into “what does the Electoral College mean, why do we vote this way, and is it fair?” I think this is a GREAT conversation and critical thinking activity to have with students, especially in classes like statistics where you can actually study and do ‘mock votes’ and see what the outcomes are with or without the Electoral College.

A quick summary of what the Electoral College is – and please note, I still am a little iffy about whether I truly get it. In 1787 the delegates of the Constitutional Congress made the decision to do this indirect way of voting for the President of the USA. It was a compromise between those who wanted a) individual citizens to vote for President (1 person, 1 vote, majority wins); b) letting State legislators choose the President; or c) letting congress choose the next President. The idea was to create a method where the best candidate was chosen. Individuals in a state vote for President – the winner in that state gets all the states electoral votes (though some split the electoral votes now), and the electors (who are elected by voters),  put in the final vote for President. The person who gets the majority of Electoral Votes (270 or more) wins. Still confused? How is this fair?  Bear with me….I am hoping I can figure that out myself!

If you look at the image above, which outlines the number of Electoral votes per state, you can see a huge difference – some states have an enormous number of Electoral Votes, and some very few. As you can see – size might matter (CA, TX, FL), but not always – VA is relatively small and yet has 13 Electoral Votes compared to say Montana, a larger state with only 3 Electoral Votes. So – how is the number of Electoral Votes determined? Hawaii gets 4 vs the very large state of Alaska only 3. So – it must have something to do with population numbers, which in fact is the case. The number of Electoral Votes is the number of state representatives in Congress (both Senate and House of Representatives), which are based on the population of the state. Every state will have at least 3 Electoral Votes (2 Senators, 1 Congressman). Obviously you now see why winning states like CA, TX, FL, PA, and NY are so crucial because of their large populations and large number of Electoral Votes.

I have been reading a lot and searching for good websites that might be helpful for teachers wanting to figure this out with their students. There are several sites that talk about the Electoral College and what it is – I didn’t find these too helpful from a teaching perspective, but they may be of interest to some of you from a historical, “why do we do this” perspective.

  1. Nice interactive map – http://www.270towin.com/
  2. Article about the ‘fair or unfair’ aspect of Electoral College and the funding – not sure it answers the questions but makes you think: https://blogs.scientificamerican.com/guest-blog/the-funky-math-of-the-electoral-college/
  3. This is a nice site with lots of historical perspective and answers to questions, like does my vote count? http://www.learnnc.org/lp/media/lessons/davidwalbert7232004-02/electoralcollege.html
  4. This article makes a case for the Electoral College system being fair: http://www.politico.com/story/2012/12/keep-electoral-college-for-fair-presidential-votes-084651

Here are some sites I found that would be helpful for doing some simulations and having interesting conversations with students. Many of these are interactive, with the ability to create election results (or simulated) to get a better understanding of how the Electoral College system works, and hopefully make a determination about whether it is fair or not.

  1. This was my favorite – be sure to check out the “Play Presidential Politics” link, as it has a simulation vote where you can create your own populations for states.  Would be great for students. http://www.sciencebuzz.org/topics/electoral-college-math
  2. Lots of information (some of which I used) in kid-friendly language: http://www.congressforkids.net/Elections_electoralcollege.htm
  3. Nice lesson here – some interaction/lesson plan info as well: http://www.scholastic.com/teachers/article/math-majority-rules
  4. Yummy Math – nice lesson here (using the picture above!) http://www.yummymath.com/2016/electoral-college-vs-the-popular-vote/
  5. From NCTM – a lesson on the “fairness” of the elections – Love Illuminations! https://illuminations.nctm.org/lesson.aspx?id=2825

So – is it fair or not fair? Does your vote count? I am not sure I can give you a definitive answer. It probably depends who you are, who you want to win, and where you live. But, in my readings looking at several charts that compared the ‘weights’ of individual votes toward the outcome (i.e. Does your vote count?), I think my personal opinion is yes, your vote does count, and yes, it is fair.

Notice Alaska, with a smaller population, has a much more weighted vote compared to CA. This may not seem fair – but, Alaska, a huge state with many diverse needs and interests but with a small population, deserves an equal representation in the government, which may not happen in a one-vote majority rule election, if we look at populations sizes of CA or NY, with their enormous populations. This is why the Electoral College was created in the first place – so every state gets a fair share of representation for their interests in the outcome, no matter their populations size, and those ‘states’ with larger populations don’t end up  deciding everything. NY’s interests are vastly different than Alaska’s, after all. A popular vote would be unfair because those larger states, who lean more one way or another, would control the outcome, leaving those states with fewer people, left out of the equation, and their interests not accounted for or lost in the process. My personal conclusion – I am actually for the Electoral College, after all my reading and my still foggy, but much better, understanding of the system.

One final note – look at the overall United States (in chart above) – the total population, the total Electoral votes, and the weight of each individual vote.  It’s 1.

So YES – your vote counts – get out and VOTE!  (And make it an educated vote, based on candidates proposed policies and plans – not based on emotion).

 

Conics – Casio Prizm vs. TI-84+CE

I am currently teaching a course at Drexel University and we are starting a unit on circles. I loved using Sketchpad when teaching because it allowed for dynamic manipulation of objects (shapes, functions) so that students could visually see the impact of variables to the shape, size, position of the object. Unfortunately, my students (math teachers in a Masters Math Teaching Program) do not have access to Sketchpad, though one does use Geogebra, and as this is a course focused on teaching, they need to use what they have access to in their own classrooms with their students. For many of them this does not involve any technology at all, which is sad, but for some, they do have access to graphing calculators.

Naturally, this got me exploring what the graphing calculators could do, and surprise, surprise, I noticed quite a difference between the Casio Prizm and the TI-84+CE graphing calculators, which are the ones my class seems to have. I was investigating conics, and in particular circles, and what options the graphing calculators gave me, especially when thinking about dynamically modifying the variables to see how each impacts the graph of the circle. Here’s is a quick summary of what I found:

  1. Both TI-84 & Casio Prizm can graph conics (circles, ellipses, hyperbola, and parabola, though how to access these conic graphs is different on both.
    • It is more apparent/easy to find on the Casio (there is a Conic Graph menu).
    • TI requires knowing that there is a Conic app in the app menu, which is a button on the calculator. It is not seen from the main screen, and if you don’t know it exists, you won’t know it’s available.
  2. Both provide more than one equation form for each conic.
  3. Both show the graph of the conic, but how is very different.
    • Casio shows the graph on the coordinate grid, where you can see the whole grid, see values on each axis, and identify quadrant and key points on the graph
    • TI shows the graph in the entire window with a weird yellow frame around it. It is difficult to determine where on the coordinate grid the graph appears – there are axis marks, but no values, not origin, making it difficult for students to understand where on the coordinate grid the graph is. Very difficult to identify quadrant and key points on the graph.
  4. Both allow you to enter different values for each coefficient variable,
    • Casio has a modify feature that allows you to see the equation, graph, and coefficient variables on one screen. You can then modify one coefficient at a time and see it dynamically change on the graph, allowing students to visually see how each impacts the graph and see the conic change shape, location, and/or size.
    • TI84+CE only shows the graph or the equation/coefficients – never together.  You have to go back and forth between them when changing values. The TI does not clearly show where on the grid the graph is, does not show a size change (all conics look the same size, but the grid scale is changing). It’s actually very confusing and would be difficult to help student visually see the impact of changing coefficient variables on the size, location and shape.

Below is a video I made showing how to graph a circle and modify the coefficients on both calculators so you can see the differences I am talking about.

Hopefully you will come to the same conclusion I did – Casio Prizm is far superior when graphing conics than the TI84+CE.

Mastery NOT Test Scores

I like to browse the TED Talks site because there are so many interesting topics and speakers. Sometimes inspiring, sometimes funny, sometimes educational – always with something to learn or provide a new perspective. I tend to look for things on technology, math, education – topics that are of interest to me because of what I do in my daily life. I found this recently uploaded talk from Sal Kahn, the founder of Khan Academy. He’s done a couple Ted Talks I think, but I hadn’t seen this one before, and found the topic to be one that I have pondered myself. Shouldn’t our education system be built on helping students master concepts rather than focused on learning specific content in a specific order to pass tests? Our current system is designed to push a group of students  through a set curriculum at the same pace, where those who don’t quite make it accumulate gaps in learning, and therefore start the next set of curriculum behind.  And the gaps keep building, creating a group of students who are left behind, or don’t think they are capable of learning some things (like math, or science), when in fact, had they been allowed the time to master, they could have learned and gone beyond.

It’s an interesting idea – one that would be very difficult to incorporate into our current education system – a system that is very resistant to change. I do know there are schools and classrooms, often charter schools, that are focused on this idea of mastery over testing. I think the Common Core at its core is based on the idea of mastery – building and mastering basic content knowledge prior to moving on to the next steps/content. However, when placed in an educational system that compartmentalizes students by grade and by subject and assesses by testing, the focus will always end up being on passing the ‘test’, so we will always leave some students with gaps.

I am not sure what the answer is – personalized learning is a big ‘buzz’ word these days. With technology and the ability to differentiate classrooms for students, maybe ‘mastery’ is becoming a focus. So perhaps there are changes afoot. Maybe ESSA will de-emphasize the standardized testing frenzy our education system is currently suffering from and we can focus on helping students become masters of their own education. We want students to learn from their mistakes rather than hit a wall and stop learning or trying new challenges because they “can’t”. Let’s hope that change is afoot in education – as Sal Kahn says, it’s an imperative – I really think that this is all based on the idea that if we let people tap into their potential by mastering concepts, by being able to exercise agency over their learning, that they can get there.”

Watch the Ted Talk – it’ll make you think, and as an educator, maybe think about making a change.