Final Project: Flipping a Trigonometry Unit


Well, it’s done.

It was a good experience to make my own math videos.  I still have a long way to go to making them better.  The journey has begun.

The editing took longer than I had hoped and I still see lots of flaws, but one has to be content at some point.

Here is my final project and reflection on the course:

Compiling and Organizing


A lesser known Trigonometric Identity

I’m on the other side.  My flipped unit is drawing to a close with a summative assessment coming up next week.

The concepts and information has been presented in my little videos and practice and reinforcement has happened during class time.

Will students be able to demonstrate evidence of their learning on their summative assessments?

Ask me next week.

Has this unit and its methodologies been more successful for more students than a more traditional teaching style?

Well, I’ve got my student survey ready and will get it out to my students in the coming days.  Hopefully this, and the student interviews will give me some indication.

This is in no way a rigorous experiment.  I did not have a control group of students set up, I did not try this “flipped” methodology across a variety of syllabus topics (yet), but rather focused on circular functions and trigonometry.  As I do tabulate and compile my results and data in its various forms I will have to make sure to view it in this light.

I have been noting the highs and lows of the process.  I am currently begin to story-board how the presentation of my final project will take shape.   I’m keeping my focus on how or if this project reaches the redefinition of the use of technology in the classroom.

Stay tune to this blog and hopefully within a week or two I will have all of this packaged up and ready to share.


Getting the Ducks in a Row…


Back to work in the second semester took off like the olympic 100m final.  Sprinting around trying to keep up with the ever increasing “to do” list.  I have been thinking and strategizing about my final project but have not had the time to share my thinking.    Next week I disconnect for the week while I lead a handful of high school students out into the back hills of northern Thailand; therefore, I wanted to make sure that I communicated how my ducks are lining up.

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A few years ago I started dabbling with a tablet PC and looking at ways it might help me be a little more mobile during my daily math lessons, allow students to interact more with the math and thirdly, help me create my own help videos for my students.  As most mathematics teachers out there will agree, for a math classroom to truly make the digital leap, students and teachers need to be able to write on the screen, typing math just doesn’t work.

I then moved to a Mac school, the tablet PC wasn’t really an option for me or my students (at least on a wide scale).  Recently drawing on the lead of a new colleague we have been exploring the possibilities of how an iPad might just be the tool which will bridge the void between the math classroom and daily computer use in a 1:1 environment.  My colleague introduced me to a sweet iPad app called Doceri.  I’ve just bought myself an iPad pen and have been practicing with it.  My colleague and I are also collaborating with our high school technology coordinator and are exploring the idea of piloting class sets of iPads, iPens and Doceri to create truly interactive math classroom.

YouTube Preview Image

With the possibility of iPad and looking at new e-math text books, I’m excited about how our math classrooms might evolve.  However, back to the task at hand- my final project.  The iPad and Doceri are the tools I have decided to utilize to help me create my videos.  I will then flip several weeks of my class by posting my videos on my Haiku site for my students to view outside of class.  It is my hope to get off the “stage” for a while and help students with engaging in-class activities to help them solidify their learning.

I’m looking at a series of trigonometry lesson to unleash this on my 11th grader IB SL students.  These lessons should be coming up at the end of this month or early next month.   So, my tools are ready, I’m practicing up and after a much needed “unplugged week”, I will be ready to pull the trigger.



Looking Ahead


As course 4 comes to a close we are beginning to look ahead to next semester and course 5 where we will re-designing a unit from the ground up to embed technology meaningfully and authentically as a means to enhancing learning.  Throughout the first 4 courses I have taken some risks, gained some new skills, and re-thought a lot about what I do, day in and day out.

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I have begun to kick around a few ideas about where I am going to head with this final project next semester.

The first is to create more digital stories to introduce new math concepts.  I would create a bit of a library of these so as the years go on I could pull them out and use them as hooks.  As I got thinking about this I wondered if I could incorporate these hooks into little mini lessons, this then sort of mutated into my second idea.

This idea, and the one which I feel is more the direction which I might head is to flip an entire unit of my IB Standard Level math class.  Although I have dabbled in flipping a few lesson over the last year or so, this time I really want to pull it all apart and put a stamp on it.  I would like to create all my own videos instead of using Khan’s Academy or Brightstorm as I have done in the past.  I plan to set up some online diagnostic and formative assessments for the students.  I need to put a little more time and thought into what exactly will happen during the in-class portion of all this learning.

I feel this would be a good option for a course 5 project since I see a lot of potential in a HS flipped math class, as I blogged about in my post, The Game Changer.  The feedback I have received from my students so far leads me to believe they will engage in this style of lesson, they will move at their level of readiness and I personally am excited about taking a break from being the “sage on the stage” for a while.

A colleague and I team teach the SL class. I have three sections of it and he has two.  We use common assessments and do our best to move at a similar pace using similar learning activities.  I will therefore need to get buy in from my colleague.  Fortunately he is quite tech savvy so I don’t think I will have to work to hard to sell the idea.  In fact, I imagine he will jump right on board and most likely help out with some of the “grunt” work ( A few more pints might end up on my bill on Friday evening happy hours:).

One concern is the education of parents.  I did have one parent question me after flipping a few lessons early in the semester.   They seemed to think that I was sub-contracting my job to the internet, looking for an easy way out.   I was quick to point out the benefits I believed of this model such as more 1 on 1 or small group work during class sessions, being able to give more individual feedback to learners on a daily bases.  They still seemed skeptical and it was the type of parent who if their student does not perform as well on this particular unit will be the first one to walk in the door to discuss this with myself or even the administration.  Hence, I will need to be very proactive with my communication of this redesigned unit to bring in all stake-holders.

One of the great things about the flipped classroom is the new skills and attitudes students are required to develop.  These are the skills which they seem to have been birthed into them by growing up as digital natives.  It is far from an uncommon sight to see a group of my students huddled around their computers watching videos.  Teachers in their other classes are sending them to view videos more and more.  Socially, they watch You-Tube with their friends and for many of my students this is more comfortable than watching their dear old math teacher in a live performance for 80mins every other day.

A Word from the Management


This year my teaching schedule only includes 11th and 12th graders, so that gives me another year to process what everyday 1:1 laptops will look like in my classroom. The 9th and 10th graders were all given a computer on day one this year.  This is not to say that many of my students don’t bring their laptops to class.  Our current math text book has an online version. I post all class notes, practice handouts and solutions on my Haiku page and we use programs in class such as Autograph and GeoGebra.  Students are sometimes given exploratory tasks or an IB Internal Assessment to work on. They either bring in their own computers or I grab one of the lap top carts in our department in situations like these.  Suffice to say, there are often computers open on students’ desks in my classroom.  As we wrap up Course # 4 we are asked to discuss management of laptops and electronic devices with students in our learning environments and to reflect upon our own use of devices in the classroom.

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Maybe this post has got me at a bad time; earlier this evening I received an email from anonymous student, with Facebook screen shots of another student posting photos of one of my assessments to his friends who had not yet taken the assessment.  There will always be cheaters in school, but by allowing/encouraging digital tools in class we certainly have made it easier and more tempting for them.

Smartphones have some amazing calculator applications, however, I do not permit students to have them on desks during a lessons or assessments for several reasons. For one, as in the situation mentioned above, students can photograph assessments which gives them or their classmates an unfair advantage to higher test scores at the expense of actually learning the material.

Secondly, students can text each other.  I experienced this a few years ago while allowing students to use calculator functions but found they were texting each other the answers. Thirdly, as in Clint Hamada’s post, How Will We Manage on the Coetail online cohort blog, allowing smart phones in class is like permitting note passing but to the nth degree. This leads to his point that electronic devices act as a magnifier for posible management problems.  It is hard for students to stay engaged when they are constantly texting others.  However, not allowing smart phones to be visible in class results in more students asking to go to the bathroom so they can answer the vibration in their pocket.  A colleague of mine had a policy that phones had to be left on the teacher’s desk during bathroom breaks.  You can imagine what happend to the number of bathroom visits that semester.

The number of lap tops in my daily classes has been on the rise and many students have them out during class.  I do my best to keeping moving around during a lesson, proximity does a whole lot of the police work for you.  As many teachers will mention, if a student looks a little bit too excited about what is going on on his lap top screen there is a good chance it is not coming from my engaging lesson.  Then of course there are many times when students just need to have them closed so they can focus on a point being made by myself or a classmate, in the same way I would say, “Pencils down”  I now say, “Lids closed.”

With teaching soon-to-be college kids, we have a lot of discussions on how they will be personally responsible for their time management in college.  No more parents bugging then, chasing down teachers, keeping tabs on their assignments and how they spend their time (at least I hope not).  Letting students know that I trust them to make smart choices with their laptops in class, and expressing my disappointment when I see they are not making the right choices has seemed to have had a pretty go effect so far.

I’m sure in the coming years when every student has a computer open on their desk, my methods of instruction and management will further evolve to help student engagement and learning.


Chalk to Google Talk


I began teaching math in 1998.  I had a chalk board in my classroom. It was soon replaced by a white board, but the thought of a digital white board or “smart board”  was inconceivable for me at that time.  I taught geometry constructions with a compass and ruler, no GeoGebra, and if I wanted to use a spread sheet program I had to book out one of the school’s two computer labs for the period.

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Every May I get 275 IB math exams from all over the world sent to me-ON MY COMPUTER- which I grade and then click a button and the assessed papers are whisked away through cyber-space to IB headquarters in the UK.  This is still a little mind boggling for me today. If I tried to explain this to the young chalk-wielding math teacher back in 1998, I’m sure he would have muttered something about a sci-fi novel.

In this short time, technology has come so far.  It seems to me, though I really have no hard evidence to prove this, that the rate of change (in the math world we call this a derivative) of this technology is getting steeper each year.  The changes are happening faster and faster.  The me in 2027 will most likely have some pretty incredible things to explain to the me of today.

I enjoy imagining what this will look like, although I don’t think I am going to like or agree with all the advancements in both education and socialization.

Education has been on the move for some time now irrelevant of location.  From correspondence courses to online degrees.  But now even more exciting innovations in education such as MOOC (Massive Open Online Courses) are popping up where learning is evolving from one central figure (the professor/teacher) holding all the knowledge to a collaborative learning community learning together in online communities.

I’m involved in the International Baccalaureate (IB) math program as a teacher and a grader.  IB has now opened up an online campus through Pamoja Education.  Students who attend a school which does not offer a particular IB course can now take these courses online.  I’m keen to get involved in programs such as this.  If I think about where and how I will be teaching in 5-10-15 years time, I imagine I will begin to be involved in programs such as Pamoja where I can continue to do what I am passionate about, teaching mathematics, but without being confined in classroom walls.

The Game Changer


Some would call me a skeptic, I think of myself as a realist.  Over the years I’ve been to a lot of conferences, listened to many keynotes, watched countless TED-talks.  I’ve been inspired by the big ideas and the call for changes to the way we educate today.  I get fired up, but then reality sets in and I realize that many of these big ideas are just that, big ideas.  Monday morning comes and they just don’t seems as doable, practical, feasible any more.  The flipped classroom is not one of these.

From moment I heard of it a few year ago I was immediately excited about it and the feeling did not go away on Monday morning.  I was working at a place where a colleague was experimenting with making instructional math videos, about this same time I was introduced to Khan’s Academy.  With these two sources of videos I began experimenting with a few lessons, sending my students to view video’s in the evenings and spending class time in small groups practicing and extending the concepts.  Some loved it, some liked it, a few missed my teaching (the videos were not mine). I didn’t set up a control group and collect data on common assessments so I cannot say what affects it had on student learning. At worst it was a break from our normal class routine.  At best it was an extremely effective and efficient way to help my students learn difficult concepts at a pace they were comfortable with.

In the picture below, my 4 year old daughter watches her teenage cousin “flip”.  Other than the obvious inverted position of my niece to the theme of this post, there is a second reason I included this photo.  My daughter was amazed by the technology she watched her big cousin use while they spent time together this summer.  Smart phones, ipad, computers, these things were just seamless to her life.   In the same way my daughter anticipates the day she can stick the back-flip off the dock, she was also dreaming of following in the shoes of a digital native.  Watching math lessons on YouTube will be par for the course for her.

Check Out Big Cousin Flipping!

In my opinion high school mathematics classes are fertile soil for flipped instruction.  It is easy to fall into the trap of long, boring lectures shooting for the middle. Some kids are bored because they understood it after the first example, and some kids are lost since the material is moving way too fast.  What I have experienced so far with flipped lessons is an environment where I could engage more learners in a 1 to 1 or small group setting, thereby differentiating instruction and coaching learners as they explore and master new concepts.

I’m inspired to begin to create my own videos and personalize the process a little more.  I think this is a very realistic thing for me to incorporate into my final project of this Coetails course.


Tool Train To Transformation


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Sometimes I beat myself up a little about my level of integration or embedment in my high school mathematics classroom.  What else can I do without taking big chunks of time out of covering the IB (or other) curriculum?

This week I was considering the various models/frameworks for enhancing technology integration.  I looked at the SAMR Model which “aims to enable teachers to design, develop, and integrate digital learning experiences that utilize technology to transform learning experiences to lead to high levels of achievement for students.”  The model moves through 4 stages: Substitution, Augmentation, Modification and all the way to Redefinition of the learning experience where the technology allows for the creation of new tasks that would otherwise be inconceivable without the technology.  At a first read, this later stage seems beyond what I can imagine; however, when I think about how the technology tools I already have embedded in my math classes have added to student learning, I realize that this may have been inconceivable to me a few years ago.  GDC, Graphic Display Calculators do so much more than multiply large numbers.  In class we can run regression analysis and perform statistical hypothesis testing in seconds.  We can graph complex functions of real-life (ugly) numbers and effortlessly find maximums, minimums or points of intersection.  These kind of calculations would have previously taken hours or been avoided all together in math classrooms.

The Florida Center for Instructional Technology has a pretty slick Technology Integration Matrix (TIM) equipped with links to lesson outlines and videos of classes in action as they move through similar levels as the SAMR model- entry, adoption, adaptation, infusion, and transformation.  I watched some of the “top end” or “transformational” videos that dealt with the mathematics strands and saw some neat projects teachers did with some gifted students, or end-of-unit explorations with real life data, collaborative review projects and even elective classes in video game design.  I guess I was expecting to find examples of how teachers used new technologies to transform their everyday classroom, making it this utopian 21st Century Classroom, or even helping struggling or disengaged students (why do we never see videos of these students?) to help them learn the basics.

Watching the above videos linked from the TIM rubric did cause me to reflect on my technology embedment in my classes.  I am using it every day as I mentioned above with GDC’s.  We also frequently use program such as Autograph and GeoGebra (see video) to  make the math come alive.

I use Google’s Haiku as the back bone or e-presence of my class.  Everything we do in class is reflected on it, discussions are had, information disseminated, student generated review projects or topic experts are posted.   I often use applets I find on the web to enhance points or speed up calculations or simulations.  Yesterday in class we were exploring the Central Limit Theorem and and needed to collect many samples of size n=25, we could have spent the whole class doing this or we could just click a few buttons on this statistical applet and collect 10,000 samples of 25, and nicely plot them to show it’s tendency towards a normal distribution regards of distribution of the parent population.

If you took GDC and computers out of my math classroom, it would be a very different environment, topics would only be explored on a primitive level and I don’t believe students would be as engaged in their mathematical learning.  This thinking leads me to stop beating myself up and reassure myself that I am well on the road to Transformation as I evaluate my own practices of technology integration.


Someone Has To Be Responsible, Or Do They?



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A common questions educators are asking themselves today is, “How do we prepare our students for future employment when we are not even sure what types of jobs will exist when they are in the work force?”

One thing that can be agreed upon is that computers and technology will play a major roll in the lives and future jobs of all of our students.  If this is true, then shouldn’t one of the core jobs of our educational institutions today be to train our students in computer technology?   But then a similar question arises; “How do we prepare our students for use of this technology when we are not even sure how the technology will have evolved by the day they have earned their first pay check?”

Some schools have required computer technology classes to meet their technology standards while others have chosen to do their best to integrate computer skills into the curriculum as a way of matching the National Educational Technology Standards for Students or their own independent standards.  By having specific classes, schools can ensure students are exposed to the skills they need to meet.  The down side is, if these skills are done in isolation and without context they we be soon forgotten or meaningless.  Wrapping the standards into the curriculum will bring authenticity to the standard, but you might be entrusting the technology education to teachers who are not specialized or current with technology and technology standards may not be met.

A third opinion says that today’s students’ very existence is wrapped up in the use of technology; their socialization, communication, and entertainment would be greatly impacted if technology was taken out of the equation.  Even if they are not exposed to databases or other programs included in computer courses they would have the know-how to teach themselves this when the need arises.

David Warlick in his blog post What Difference Might One “S” Make?  struggles with the above issue of how/should schools tackle meeting Technology Standards.  His idea is as follows:  Instead of teaching computer application‘s’, schools should focus their efforts on teaching computer application.  Instead of a focus on different softwares in isolation, students would “simply learn to apply computers to solve problems or accomplish goals”. Warlick does not see the need to be concerned that students would master all the standards, but rather they would conceive how computers would assist them to accomplish tasks which are interesting to them, and therefore gain the skills and confidence to do this.

This project based learning is not limited to the learning of technology.  Other disciplines such as mathematics are excited by the prospect of students collaborating around a real life task. Students will sink their teeth into and become excited about mathematics in the process of accomplishing something “bigger” and more interesting.

Here is a clip of some forward thinking and project based learning in a geometry class.

Sound exciting, authentic and is leading the way in student learning.  A few years ago I was a part of this large departure from the traditional math curriculum to focus on large projects.  In my experience, it was pretty difficult to pull off. Unfortunately, unlike Warlick, I could not shrug off the fact that we would not have time to meet all the curriculum standards in return for more authentic experiences. It was also hard to find a catch-all experience that would engage all the different learner’s interests.

Educators will continue to debate how we should be meeting standards in all disciplines.  Technology standards are unique in that they cross discipline lines.  This fact draws us all into the discussion and gives us the responsibility to make ensure they are met.

Richter Scale- Making Sense of Logarithms


As Coetail Course #3 comes to a close we were challenged to put together our new found knowledge of presentation zen, mixed with our budding technical skills and visual presentation techniques to create a presentation to add to our blog.

Last week in one of my math classes we were discussing Logarithms.  The concept of the Richter Scale to measure earthquakes came up and a quick discussion was had.  Some students seemed a little miffed by it so I thought I would use this opportunity to create a short presentation to help them make the connection.

I used several tools.  I started with Smartboard’s Notebook program to create some slides in which I brought the students step-by-step through the idea of common logs.  From there I used QuickTime Player to make some screen capture movies with my voice over.  I uploaded these along with relevantly searched images, fitting music and then some clips I found on Youtube into i-Movie.  I then dove into i-Movie for the first time.  I experimented with my imports, matching the audio and the visual, fading volume, trimming clips, adding text and creating voice overs.  A lot of trial and error.  I’m sure to the trained eye it is still a bit rough, but in the end I was pleased with my first digital story.


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