Monthly Archives: July 2014
Once similarity intuition has been built with circles, we can start getting into more specific relationships with angles and segments. This post will look at using visual information from central angles and inscribed angles.
Students sometimes lack intuition for the measure of something. Andrew Stadel has developed this idea into a thorough curriculum on estimation. In my classes we started reasoning through similar exercises. Once we had a decent understanding of circle parts and whole, we moved on to other types of angles.
At this point most students have the common sense that a circle has 360 degrees, and a triangle is half that at 180 degrees. Built with this intuition in mind, we look at a triangle created by inscribed angles.
The next day we get to see the formula that collapses 3 ideas down to 1.
Dynamic Angles in…
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All circles are similar, right?
Okay, maybe it’s not given. In fact, it needs to be proven. This proof is yet another that is so easily demonstrated with dynamic math tools (like desmos and geogebra
So long as you can move one center onto the other (translate) and dilate one radius to equal the other, similarity is achieved. This works for every circle. The perfect proportional balance achieved with circles lays the foundation for most of not all relationships found in them.
Similarity gives us a simple system for comparing measures in multiple figures.
You can even explore this with repetition of congruent triangles:
Below are a couple of applications that push further with exploring the measures of circles, proportionality, and relationships in the measures.
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I just spoke with my brother, @jakebutler, just catching up on the latest. We eventually go into a conversation about concept development, and how it accelerates as history progresses. The gist was something like Moore’s law applied to the topic of impactful ideas.
A standard long term example he posed was the idea of language and documentation, tracing from spoken, to written, automated, then digital, and now multimedia. The next big thing comes faster than the last, and sometimes it feels like we’re always playing catch up. My brother works for an awesome company based out of Boston that focuses on a lot of the social aspects of healthy living, especially in the realm of technology integration.
He told me that they have long term goals, but when it comes to comprehensive and detailed planning, each of their sub teams never looks further out than 2 weeks. We started applying this format to technology in general and I in turn added the context of education and #edtech. For the most part, I would argue (as would my brother) that successful technology enhancements have gone away from the secret projects behind closed doors that take at times years to reach a level worth any public reveal, and instead have more of a micro step process. Upgrade a few things, and often. The short term plan to update and implement smaller, more frequent changes has been a necessary adaptation to the accelerating progress of technology in general.
As teachers are upgrading their curriculum and technology for near future integrations I think we need to consider the value of this short term cycle. Instead of having an entire year planned out to the day, we can maintain long term bench marks with the intention on updating our planning through small frequent upgrades. I doubt that teachers trying to implement formative and interactive technologies in the classroom would have predicted the introduction of @peardeck (read more here).
This hard for an educator to manage. We already have plenty on our plate between and the hard requirements and soft skills necessary to achieve them. If a teacher truly wants to match the current culture of technology and conceptual progression we need to have an appropriate design for our planning. We need to anticipate the change and build in the flexibility so that we can adapt on the fly.
I don’t know if I’d take it as far as this guy…
…but refusing an adaptive attitude is assuming we can predict the future of every step in growth of our students. And that sounds silly.
I’d love to hear how others have integrated this adaptive planning, with small frequent updates, into their classroom planning (tech and non-tech contexts)
I have some ideas for the next few days of posts, mostly dealing with metaphors for teaching. So far on that list is Farming, Cooking, and I’ve heard that there’s also some thoughts on fishing. Let’s take a quick commercial break brought to you by the folks at Waco, Swordsoft, Peardeck, Google, and I’m sure some others might creep in.
I used to loved interactive whiteboards. Yes, that is a past tense reference. Most of my experience with these is with the Promethean Company.
I learned to be proficient with the standard slide software ActivInspire in which I made plenty of flipcharts. It was awesome. I could make interactive presentations, I could screencast the material or export it to multiple other standard formats. Then I realized the down sides. Cost. The handcuffs that anyone in the education industry is all to familiar with. These boards are expensive. The accessories are expensive. And one major downside to the standard entry level interactive whiteboard was it’s own built in shackles. The board required that you be within arms reach to interact with it. Of course, one could buy a mobile tablet that goes with the board/software, and that brings us back issue #1: cost. Companies justify this cost by showing the awesome capabilities of the hardware and software that comes with the package.
I tried some alternatives, like Johnny Lee’s low cost interactive whiteboard that was even featured on TED. This worked every once in a while, but it still required close proximity to some board as well as constant recharging and calibration. It started me thinking on how to find low cost alternatives, something more practical for the average teacher.
I tried some Wacom tablets, starting with my first, a bluetooth model refurbished from eBay.
This again was alright, but still inconsistent and cumbersome.
A little more than a year ago my student teacher and I tried a newer model of the Wacom Tablet with an added RF wireless adapter.
I LOVE IT. Here’s why:
- connects over RF, no wifi required (you can go wireless anywhere, up to about 30′)
- low weight, I can easily hold it in my hand without feeling a strain as a roam the classroom
- reasonable cost: $80 tablet + $40 Wireless adapter kit
- battery: single charge easily lasts more than a full day of HEAVY use, often I get at least a week off one charge
But wait, what about that fancy software? Aren’t all the built in math tools wonderful? Yes they are, but Google Drawings, Google Slides, Geogebra, Desmos, and EduCreations have pretty much matched anything I’d done before. Also, that screen annotation available in those fancy software packages have been replaced by ScreenInk by Swordsoft for a whopping $2.
For those of you that are partial to iPads and apps like AirPlay mirroring, Reflector, Splashtop or SlideShark, I respect that. A tablet stylus tends to not be as precise as the Wacom technology, and this tablet with RF adapter doesn’t have a time delay like the others.
With many classrooms incorporating technology into the classroom, teachers need to be mobile now more than ever. I would also qualify that with maintaining a balance of tech use in the classroom. Electronic does not imply engaged, and a mobile teacher is needed to manage the 21st century classroom. By the way, if you didn’t catch the primary advantage, the total cost of this Wacom package (~$120) is about %10 of most other solutions. Go bug your principals and edutech purchasers to look into this. I’d be more than happy to field any questions or comments on the issue.
If you have another alternative, I’d also love to hear about that.
Just read about a blogging challenge for the month of July. I tried this with #MTBoS30 and only got up to 12. This time around I’m going to divide and conquer across four blogs I have various levels interactions with: transformulas.org, DailyDesmos, and #ggbchat.
For post 1 of 31, the theme is a derivative from others and it focuses on the past, present and future goals with 3 items for each of the Start, Stop, and Continue theme.
- Desmos API: I am so excited about this one. I’m a huge fan of @geogebra and @desmos (and pretty much any other dynamic math visualization tool). After an open invitation from Chris Lusto, I’m excited to learn from others.
- Books: I read one book this summer so far. Looking forward to the next. There’s something about the raw nature of a book that balances out my passion for and interaction with technology (my wife would probably say it leans more toward addiction).
- Cross Curricular: Late in the year this last season of school, I spoke with a science teacher about integrating geogebra applets into a physics setting. There’s too many overlaps with math and science NOT to exploit the potential collaboration opportunities. With the CCSS Standards for Mathematical Practice we are also seeing an increased focused in constructing arguments, organizing evidence, and making sense of problems. These type of frameworks lend to collaboration with Humanities. This conversation of cross curricular collaboration is too far overdue.
- Driving (as much as possible): My car, a lovely Buick that has passed from my grandparents, to my great aunt, and now onto me, is nearing it’s end. I only live 6.5 miles from work. There is also a Super Target less than a mile away. I like to ride my bike, and I feel like I don’t show it the love that it deserves. Time to stop driving (when possible) and start riding more.
- Frustrations with Growing Pains in CCSS: There is plenty of argument and frustration with the changes in education. Progress and growth doesn’t jive well with those who have established systems in place. Education is a continual evolution that I’ve learned to embrace. Those that resist this change often take plenty of shots at new ideas. I will concede that new ideas without proven track records can be a gamble. However, I feel that the mantra, “If it ain’t broke, don’t fix it” has little place in education. I feel it’s better to apply a growth mindest and look at education as “Don’t knock it till to try it.” Learning that something doesn’t work is still learning, and that should be our focus, learning.
- Playing Candy Crush: Level 140 has been stuck on my phone for a month. Seriously, why do I continue. I’m done.
- CCSS: it’s not that I have to re-learn math, or teaching, or learning. This label is probably overused if nothing else. I look at recent transitions in education, especially in math, and am glad for the increased coherence and creativity. My most recent ambition is learning more about the progressions.
- Geogebra: Recently a group of colleagues and I started a #ggbchat on twitter. I’ve only been using this software for about a year, but the potential has only grown the more interactions I have with it. I plan to get more organized with my work, especially in ways that makes the applets more user friendly for students.
- #MTBoS: OHHHH, EMMMM, GEEEEE. If you’re reading this post, hopefully you’re already aware of the gold mine that exists out there on the net. Get plugged in, buckle up, and try not to blink. You will be overwhelmed, and it will be awesome.
So now, your turn: What do you plan to Start, Stop, and Continue?