Theory Of Knowledge and Radiolab

As well as teaching the International Baccalaureate Standard Level Math class I have two Junior classes of TOK (Theory Of Knowledge). The syllabus categorizes ‘ways of knowing‘ and ‘areas of knowledge‘ with in which structure we work. The overall objective of the class appears very much to support students in becoming more conscious thinkers who can clearly articulate claims, ideas and beliefs and be ready to support their thinking with evidence or statements of faith and students who can hear and respect (and more importantly understand) the validity of a different perspective.

The National Public Radio show I am taken with is “Radiolab  a show about curiosity. Where sound illuminates ideas, and the boundaries blur between science, philosophy, and human experience.” Clips from this show are made for the Theory Of Knowledge Class. Whether it is in the area of Science and the nature of time:

YouTube Preview Image

Or whether it’s transient global amnesia and the nature of memory:

YouTube Preview Image

On October 31st Radiolab aired an episode called “Haunted” that gave a spooky jump for listeners and had them follow the story of a young man whose parents die and leave him with unresolved emotional issues. (I am inferring the issues but go ahead and listen and you’ll see what I mean). The account of this guys experience lead up to a ‘paranormal team’ visiting his home and contacting the spirits with various consequences and more questions raised.


(Jon Feinstein ‘Ghost’ from Flickr)

I set my students up (they were already prepared to a certain extent) to simply note what became known and in what ways was that knowledge acquired. Afterward I had them take two minutes to write down one particular example from their notes so as to be able to share with their table group; after a further three minutes we switched to class discussion with the main objective (from my point of view) being to have them clearly articulate what was known and the way in which it was known. For example… a student soon made the statement that they knew there was a ghost because they ‘felt it’s presence’. Ding ding ding…. In  Theory of Knowledge ‘perception’ is strictly ‘sense perception’ and when you use the word felt it implies the sense of touch. Either way unpacking the phrase ‘felt it’s presence’ was both fun and enlightening. It becomes clear quite quickly that your choice of words are important when clearly communicating an idea! (Especially when you have external assessments that expect you to use language in a very specific manner).

As to the existence of Ghosts the jury is still out but the discussion became a lot stronger and the understanding of what was known (and to what extent) and in which ways that was known grew tremendously.




Posted in Uncategorized | Leave a comment

Course Five Final Project Reflection

My Final Project entailed networking a set of TInspire Calculators with in the class and using that network to share graphing documents with all the students.

The graphing documents were generated using TInspire software on a central computer; students would photograph images and either email them to me or post them on the class facebook page where we could select interesting items and insert them onto a graphing document.

Once the document was ready to go it could be transferred to the student handheld calculators where they could apply various functions to model curves with in the image.

Students could then communicate (among peers) how they transformed functions to best fit the curve.

The project covered elements of the IB syllabus and had students actively involved in looking at the world around them with ‘Math eyes’; as such the project also supported the development of students who would be ready to tackle an Internal Assessment in their Senior year. In addition to all this it was fun to get out of the classroom and do something different.

Here is the project video:

As I have mentioned in a previous blog the inserting of an image into a graphing document using the software was not obvious. Not only this but finding clear directions for the process was laborious  and in the end unsatisfying; even the youtube videos that I discovered seemed to obscure rather than enlighten and it was a struggle to piece together the process I needed to use. I have a home in Seattle and there is a group of teachers that meet fairly regularly at Mercer Island High School to discuss and share ideas for teaching with the TInspire calculators. This last summer I was back for a short two week period in July/August and had no opportunity to visit with this group; I think it would have been worth rescheduling my Summer to have had that opportunity! (That was never going to happen but hey…I’ll have plenty of questions the next time I do get an opportunity).

During the project many conversations came up that were not conversations one would normally encounter. For example the question of scale. Students noticed that if they changed the scale on their graphing axis then they would generate a ‘different’ function that modeled the curve as well as another students. “How can you tell if a function is the same curve as another function even when it has different parameters?” “Why is this function the ‘same’ but with different numbers?’ “How do you choose what scale to use?” These are the rich conversations that really link text book Math with what is actually out there!

The most demanding aspect to all this was the production of a ‘video’ using imovie on the School iPad. It turns out that when the iPads were bought the Admin at the time felt the need to ‘lock down’ the iPads to the point where it was very difficult to use them. When I checked out an iPad the Librarian was unable to give me a cable and plug to charge the iPad with; my instructions were to return it at the end of every day to be charged. Needless to say that wasn’t overly convenient so I managed to ‘borrow’ a chord and charger from another source. The next issue to arise was transferring images and video that I had on my desktop to the iPad. A day later and my friends in the Tech department had undone security settings and installed Google Drive and I was up and running. On finishing the video I spent two days (not continuously!) with Tech endeavoring to upload the imovie to youtube (and when that didn’t work and they couldn’t figure out why that didn’t work) to email (and when that didn’t work and they couldn’t figure out why that didn’t work) to Vimeo (which after much frustration and two error messages…) “Bingo”. I could download it from Vimeo and upload it to Youtube.

I am highly unlikely to use an iPad again and I am definitely not going to use a School iPad ever again. This is a nuisance as it might well be that using the TInspire software on the iPad is a better way to go. At this point I am going to look at other options before considering that avenue of approach though. (I really really do not want to have to fight and struggle with these School iPads.)

I am going to use the Calculators and develop this project as the rewards were high and the discussion and degree of student interaction was also high. I intend to work out the best way for students to share their calculator work (and graphs) using word documents or Facebook posts or…  Once students can share their process with ease communication will strengthen the depth of their understanding and more ideas and options will open up.



Posted in Uncategorized | Leave a comment

Navigating TInspire Navigator

The most time consuming aspect to this TInspire project has been acquiring the skills to navigate the navigator software. A key aspect to the work I am doing with my students is uploading images to a graphing document that can be sent to all of the students handheld devices. If any of you are “Wittertainees” you’ll know from a recent podcast episode that when they asked their producer how to start a ‘snapchat’ he responded with the advice “well you just start up a snapchat”. This is how the Texas Instruments website approaches their directions for uploading images. It was not helpful (much). After googling for advice and watching youtubes that did to a greater or lesser extent support my initiative I wrestled the problem to the ground by prolonged tinkering with the software.

YouTube Preview Image

The main issue with networking TInspires using a local wifi network and the ‘yellow caps’ is that it appears to very buggy. My first advice is to only set up the Navigator Access Point (which you plug into your computers USB port) after you have the software running and ready to go. If you plug in the Navigator system before hand the software will not recognize it but in a wonderfully annoying turn of events won’t inform you of that fact either.

Once these issues are sorted out you’ll need to recognize that your image will probably require some altering in ‘Paint’ before you use it as key features need to fill the handheld screen rather than obscurely shelter in the midst of detail. Students quickly learn to focus in on the key pattern or shape and enlarge that element.

In order to look at patterns in everyday objects students could take photos or search the internet but once the image was found the most effective way to transfer the image to a handheld was to email me the image or a link to the image and then for myself or the student to use the software on the main computer to send the image to the students handheld or to every ones handhelds. The nice thing about this was that sharing an experience and comparing mathematical models became far easier.

In retrospect I very much wish I had taken the time in the summer to attend one of the many TInspire workshops that Texas Instruments put on. It would have been well worth it in terms of frustration and hours spent unlocking the machinations of the system.





Posted in online1 | Tagged , , , , | 1 Comment

IB course fived

My initial panic is latching on to the apparent disparity between my fairly demanding IB Math curriculum and the less traditional richness of the course five project examples I am viewing.

In my room I have TInspire Calculators and the networking caps that enable us to collaborate in new ways. I think for the sake of sanity I need to continue with my focus on using technology in conjunction with this new system to endeavor to develop a course 5 project.

On board

I feel like this ant. On board but rather overwhelmed.

My goal for this coming week is to tinker and play with the TInspire system and try it out with some of my students to get a feel for what we might actually be able to do with it. Next weekend I am in Bangkok for an IB workshop and I will network to see if fellow IB Math teachers have brain storming sparks to fire up the experience.

Posted in Uncategorized | 1 Comment

Course Four Final Project

Well I feel fine about where I am heading for a Course five final project; it’s a green light full wave on.

I will have the networking capability for the TInspire Calculators in August and I will have a class set of Nspires.

I will be able to transfer documents that provide students with interactive assignments that I can monitor in real time and collect assessment data that can guide the direction the class goes in. Students have the individual freedom to interact with a math model and play with relationships in their own time.

Pedagogically the big step is to move from a mind set that lends itself to lecture and being apparently in control to openness and conversation which best supports the growth of the individual. It means stepping away from direct control and into a much more dynamic environment.

My main concern is the technical demands of setting up the system and then the anxiety of introducing the system to students when I am not entirely sure what I am doing. The other side of this coin is that I have students who are more than capable of figuring this system out and showing me how to use it! I also have colleagues with some experience with Nspire networking who are able to support me in using it.

My students will need to move away from the text book orientation that they have been cultured in. They often want very much to know what to do and which questions to answer and whether they have completed problems like the ones that they will encounter in the test. This Math is much more about acquiring that deeper understanding and doing so through inquiry and exploration. That exploration works best with a playful mind and an initiative that encourages one to ask the ‘What if..?’ questions. In establishing this approach to Math I must integrate the more traditional element in order to anchor the learning in a way that reassures the students.


Posted in Uncategorized | 1 Comment

What’s new where’s newer?

This year I have used Facebook groups (based out of my School email address) in my Theory Of Knowledge Class and Senior Math Class. Although there has been a greater degree of interactivity and communication is far far stronger I still have students who in final assignments had clearly not fully understood the deeper intention of the activity. This ‘missing of the point’ might be quite subtle but was apparent to everyone when the poorer quality assignments were presented to peers. This has led me to consider the need for ‘Google documents’ to be integrated into the technology; peer editing before a completion data would be both very useful and with Google documents transparent enough to be assessed as part of the process.

In math classes I am determined to develop the use of the TI nspire calculators with the networking ‘hats’ that can be fitted to them and explore the potential for ‘mini projects’ that I suspect will come to the fore when students acquire the skill sets that the Nspire offers. At the moment the TInspire is a great tool for doing the number crunching required to analyze statistical scenarios and real life calculus problems that would otherwise be out of reach. The next step is to marry those tools with applications that students have not normally considered.

My stance in relation to laptops in class (and students in ISY do not always bring a laptop to School in which case they may find a notebook is available for borrowing at the Library) is that frequently they can be distracting. I know that students cannot multi-task in the moment; they think they can but demonstrably this is not the case, so I usually simply set the expectation that for certain periods of time laptops are expected to be closed. It often seems to be a relief when a boundary is set and the laptops are offline for a time. At our School students have many opportunities to interact online and at Lunchtime I am most likely to see them hanging out together or playing Basketball which strikes me as the healthier option.

Personally I spend way to much time on the Guardian Newspaper when I get in an hour and a half before class starts and that’s before I check my Mail. An old fashioned egg timer wouldn’t be a bad idea, at least I’d know when I was hard boiled.


Posted in Uncategorized | 1 Comment

Math to become more TInspiring

Once upon a time in a Summer School far far away literacy skills were introduced in mini lessons and applied with short literary texts that strongly mirrored the chunkier novels and technical writings that students and life long learners were going to meet in the years to come.

This story must have continued to develop but since I have moved on to international Schools and Mathematics I have lost the thread of literacy in Education. Yet perhaps that thread is winding through the maze of coetail course four, perhaps in order to find the light all I need do is pick up the thread and follow it.

There is no doubt that projects in Math can be overly time consuming given the requirements of a demanding syllabus. One a year might be integrated successfully into the time table and that includes the actual Internal Assessment that forms part of the IB. There is also no doubt that projects deepen the understanding a student has of the Math that they are using and until they have had that experience they tend to be simply in training to be good problem solvers in a test environment.

In literacy the key was to develop mini lessons and utilize shorter texts. In math the key must be to engage the student with shorter Math experiences that mirror the world about them and in a playful way allow an interactive component. This combination appears to be offered with the TI Nspire Calculator.

TI-Nspire is a flexible ICT platform that enables students to explore different mathematical structures, concepts and expressions. It does this by dynamically linking software applications, which include Calculator, Graphs, Geometry, Lists & Spreadsheet, Data & Statistics and Notes.

As the advertising blurb continues to say (and reasonable so in my some what limited experience) “TI-Nspire helps maths and science teachers to stimulate student investigation, enjoyment and learning, and to develop their own professional skills.

I have been using the new TI Nspire calculator this year and many of my students now own their own machine; along with this we have invested in classroom ‘sets’ and in talking with my colleagues we are going to network the classroom set using ‘hats’ that fit on to the ends of the calculators and wirelessly connect them to a central computer.

The great thing about this is that the community that is now blossoming around this device has encouraged the development of a great deal of excellent resources that are ready to be incorporated into your class. For instance here is a lesson that utilizes data from 50 cities from around the world. The teacher guide, student notes and inspire calculator package is available ready for download and what is more the material is all interactive and begs for students to engage more deeply with ‘mini projects’ in that they could then gather information about the city that they live in and analyze that information using the skills they have just developed. From here it is not difficult to envision students connecting with students in different cities and exchanging communications about the places that they live; this communication would naturally bring up questions about the information that is important to share and the most effective ways of presenting that information. The educational experience would become more open ended and potentially acquire an organic characteristic as it grew in new directions. The key would be to look at the elements of project work with in the frame of a mini project mind set.

When I begin the new year in August with my fresh set of Juniors I will be starting with trigonometry and the use of Radian measure rather than degrees. Looking at the resources available I immediately see that there is an activity that is ready to go and fairly straightforward so that I can guide students in the use of the Inspire as well as involve them with the material to hand.

The trick then will be to move smoothly in to more creative uses of the material as students will have acquired some mastery of the basic skill set; the calculator and the ability to connect lends itself directly to student autonomy and with an added twist of purpose the three factors for motivation that Dan Pink identifies could find students much more deeply involved with the Math.

(Dan Pinks talk on motivation is best appreciated in the animated version):

I think it’s time to jump in.

Posted in Uncategorized | 1 Comment

When you engage…

The flipped classroom Infographic by Knewton and ‘Column Five Media’ boldly states that since switching to flipping the failure rate among Freshman for Math has dropped from 44% to 19%. I assume they are talking about a Freshman class greater than 5 students and that indeed if you hand the reins to the students they’ll be far more inclined to ride into the sunset and be much more prepared to actively engage in activities during class. The passive approach just went out the window.

Out the Window

I’m still stuck (to some extent) in the passive culture. My students still expect to be lectured and still feel comfortable being told exactly what to do. I do use the MyiMaths system and set assignments online regularly although these assignments consolidate work we have already done. I found that students balked at the lessons provided with assignments and did not push through the resistance they mustered when expected to complete a lesson online without class time instruction.

I have students who have identified useful online Math ‘lessons’ and I have contributed to that pool of resources with PatrickJMT who produces excellent mini lessons in Math. However I am still in a position where I do not have the where with all to create and post lessons of my own and I have yet to organize an overall program that facilitates a flipped approach. At this time it would be more than feasible to do so.

I read through the Q and A with the Authors of “A New Culture Of Learning” and enthusiastic and glowing as it is I still find myself thinking that I’d be more on board once I’d jumped in (which is kind of ironic) and found that ‘Yes’ the students could still engage with an IB Math syllabus in a timely fashion even if the approach was some what organic. In the interview which sold the book admirably I found tantalizing tit bits such as “Once we rethink what it means to learn in a way that is based on passion, imagination, inquiry and questing, it becomes easy to reshape classrooms to those goals.” But what that actually looks like I don’t know… which means I need to buy the book.

I do know what hanging out looks like and it was one of the most constructive educational experiences I remember having outside of High School growing up. We would gather down the Pub on a Friday evening and discussion would take off in all sorts of directions but often it came from classroom arguments and the discussion itself required that you were very clear on what you were arguing and you found your self challenged strongly if you could not support your points. Now we may have had promising debates in High School classes but it was these Friday evenings that were the most formative. Of course we never talked Math down the Pub but that may have been because there were so few Math geeks ‘online’. That’s the beauty of the internet you can choose your niche with a higher degree of selectivity.

Reading about the Flipped Classroom Model Sal Khan (of Khan Academy) hit the nail on the head with “If I was a teacher, this is exactly the type of class I’d want to teach (flipped-), I don’t have to prepare in a traditional sense. But I do have to prepare for projects and all that, so I have to prepare for creative things” That’s the nub here… you must then be ready with creative things that mirror the content students have been acquiring outside of traditional class time. If the educational experience becomes about creative involvement the content engagement is unforced; it a simple precursor with meaning.

My students definitely develop a far deeper level of understanding when they apply Math to an investigation or modeling of the world around them and this timely endeavor must be offered up as an experience along with the more mundane readying for IB exam style problem solving.




Posted in Uncategorized | 1 Comment

Give Up The Idea Of Curriculum

Seymour Papert is ready to deconstruct schooling. In an ideal educational community the student centered pathway would weave and weave richly in the gardens of thought and experience.

I, like Seymor, have a Math orientation as I teach IB Mathematics. The syllabus is well rounded and rather demanding, and I usually find myself lecturing traditionally far more than is effective for communicating essential ideas. It is also very clear to me that the most effective educational experience the students have during this course is the development and completion of a project that uses Math to take a look at a real world scenario.

This year I had a student who when given the paper and pencil problems that required him to use geometric sequences and series he knew how to identify the variables and organize his mathematics and generate an answer. On the face of it he was demonstrating evidence of achieving at a high level.

Then he became interested in Kochs snowflake and it’s fractal nature, a property that is also seen as one zooms closer and closer in toward the coastline of a country.

Fractal Snowflake Cupcakes - 24

The general pattern repeats at higher and higher scales and there seems no end to the twists and turns of the ‘perimeter’.

The project demanded that he understand Geometric progression in a way that was new and authentically demonstrated a deep understanding. He had no clear signposts to follow and he had to discover the underlying patterns for himself before he could model them with math. Then in a quite brilliant twist he realized that there was limit to this fractal patterning. If you zoom in closely enough the Universe is in fact ‘grainy’ (like the TV has pixels) and you reach a point where there is no more finer detail to zoom in on. This twist was not laid out as a problem for him, he had to generate the question as well as investigate what it actually might mean when you applied Math that included this limit. His experience was rich and deep.

Now if this student had not had some lectured material and had not developed his Math in an organized and constructive fashion (the curriculum?) would he have been in a position to have taken on the project to begin with? Would he have said “OK, I seem to need to learn about this…what is this? How do I do this?”

Where is the balance in project and artificial flat pack Ikeducation?

I don’t think the balance is easy to find, especially if you have many students in a class. Seymour says “Again, one of my favorite little analogies: If I wanted to become a better carpenter, I’d go find a good carpenter, and I’ll work with this carpenter on doing carpentry or making things. And that’s how I’ll get to be a better carpenter. ”  Well that’s all very well and good but as my Father knew very well, if you are excepted as an apprentice carpenter you are in all likelihood one of two apprentices and you will spend much of your initial time repetitively doing the same basic process.

Seymour is an idealist and his romance drives us forward but the practicalities of project based education must also be firmly assessed.

Challenge based Learning has many similarities with Project based learning and in reading about it has an intangible quality in speaking about compelling issues. Again the spirit of the work is vital and the authenticity of the work must be undeniable as students identify real world situations to work with. The experience must reflect the skills of the adult work/living environment closely but I find myself asking questions once again about balance and content. If we are as a school being expected to offer an educational experience that means that students can reasonable apply to MIT (or other academically demanding institute) then there are academic expectations that must be met and meeting those expectations requires time and commitment to be prepared for those academic environments.

In rethinking how one does business it would be important to not throw the Baby out with the Bath water.




Posted in Uncategorized | 4 Comments

We’re already capable of going to the Moon

This year we’ve been transitioning to working with the TI-nspire which for those of you unfamiliar with High School Math is a calculator that has a touch pad control and a high resolution color screen to work with. What is more is that it far exceeds the computing power available to the Apollo mission that guided Neil Armstrong’s foot toward that first giant leap.

Now that’s technology. Or rather it’s classroom technology.

Not having come fully to grips with all of the possibilities as yet I have noticed that students in my classroom now have the option of using this technology to investigate the world around them to a far more sophisticated degree then just a few years ago. One of my students utilized the computing power available to not only model the curves of the Shwedagon Pagoda as fourth degree polynomials but then looked at Logarithmic models before using the calculator to infer the volume generated when rotating the curve around an axis.

Using this technology (and local rumors) she eventually estimated the value of the gold needed to ‘plate’ the Shwedagon Pagoda. Oddly enough it wasn’t far from the value estimated to have been stolen from Thailand during the series of wars that led up to the 19th century. 🙂

One of my other students did some work that involved Normal Distributions and that was only possible because of the computing power he held in his right hand.

On the other hand a deep meaningful understanding of Mathematics requires no technology (beyond a blackboard) what so ever. This is made clear when you have the pleasure of attending one of James Tanton’s workshops. James Tanton uses a whiteboard and some markers and changes the way you look at Math forever. Try his ‘Exploding Dots‘ course and thank me for the recommendation later; I guarantee you’ll be astonished.

And there’s the trick. I knew who to send you to and I made that communication using a link which did indeed connect you to where I thought you would best be served educationally. The pedagogy and the content and the technology in one paragraph. What is more I guarantee you the experience is accessible to everyone and worthwhile for everybody, go on try it.

In terms of the daily grind I make use of the MyiMaths website which I can use to tailor homework assignments that supplement or consolidate classroom experiences. The site does cost but a School license is very affordable and I can see very quickly who is struggling with a concept.

I have set up Facebook groups (using my School gmail account) this year one of which is for my Seniors. As a communication system it really is hard to beat. We took a calculus test before the Water Festival (I am off right now) and on Saturday as I was grading I realized we had some general issues regarding using the GDC (Graphing Display Calculator) and using it on IB Paper Two style questions that involved using the ‘intersection’ facility. I got right online and posted a heads up with online links that would facilitate appropriate revision. Now it’s a ‘no brainer’ but the thing is with out technology or rather classroom appropriate technology I could not have done that and students would return from break having lost momentum. As it is the flow continues.

The interactive simulations that are available online are staggering. As a High School student in the seventies I struggled with one text book and a simple (non graphing) calculator to come to grips with trigonometric transformations. To say this was a challenging task is to underplay the demands on the imagination. Today I have links that give the student a real time playground for exploring theses concepts and even looking at them in a Physical environment.

We haven’t just gone to the Moon we’ve left the known Solar System in the course of the last two decades. “Life but not as we know it Jim.” was never such a prescient catch phrase for the later part of the twentieth century and behind all that wasn’t so much the technology as the inspired teamwork and collaboration that puts everything together and makes things happen.

“Apollo was the combination of technologies, none of which was particularly dramatic. Combining it was the achievement. This was a bunch of people who didn’t know how to fail. Apollo was a triumph of management, not engineering.”

Tim Stevenson,

(Chief engineer at Leicester University’s Space Research Centre)

So as I step forward in Education I need remember that it isn’t so much the technology as the effective networking  of the technologically capable that drives us forward.

Posted in Uncategorized | 1 Comment