## Thursday, April 23, 2015

### Rocketbook

Oh, I like this a lot. Interestingly, I've been using the Pilot friXion Erasable pens all year. They write smoothly and erase easily without smudging. I didn't realize they erased by the friction producing heat that turns the ink clear. Now, that's cool. But the upcoming Rocketbook is even cooler. Unlike Livescribe, you just need one notebook and will have lifetime access to the Rocketbook App. So after the initial expense, substantially less than Livescribe or similar recordable pen devices, you're all set. Check it out and be sure to watch the video. All available in July. I can't wait. As I wrote in an earlier blog, I have begun using a ScanSnap scanner to eliminate the need to save paper copies of documents, bills, statements, etc. Now, with Rocketbook, I will be able to take notes and solve problems using an inexpensive erasable pen, then upload them to DropBox, and reuse the notebook over and over. I am slowly reducing my personal carbon footprint. I love innovations like this.

## Tuesday, April 21, 2015

### Conferences and School Visits

While I wasn't able to attend MacWorld this year, I have gone to some terrific mathematics conferences and made some visits to some outstanding schools. Over the years, I've decided that the Northwest Mathematics Conference, hosted on a rotating basis by the Washington State Mathematics Council, the Oregon Council of Teachers of Mathematics, and the British Columbia Association of Math Teachers, and the California Math Council-Southern Annual Meeting are two of the best in the country. Both are fairly picky about who they let present (although they have both let me speak, so just how picky remains to be seen) and they are not so overly large that you get shut out of sessions. Probably the hottest speaker on the circuit right now is Dan Meyer who spoke to packed rooms at both conferences. They put him in huge ballrooms so there is never a problem getting a seat. The annual NCTM meeting can be overwhelming so, if you're on the west coast in the fall, give these great conferences a try.

My school visits consisted of visiting Nido de Aguilas in Santiago, Chile once again, Redwood High School in Larkspur, CA, and, the Cate School in Carpinteria, CA, again. All were interesting and very worthwhile.

Nido has progressed with student-centered-learning to the point where they have actually purchased tables for some classrooms. Moreover, the mathematics department has begun to work with students around tables. They chose to have tables that could be separated into smaller units so students could work in groups of three or four, as well as one group at the large table.

Redwood High School is one of the finest public high schools in Northern California, and has been since it's beginning in 1958. It has been recognized three times as a California Distinguished High School (1990, 1996, and, 2003) and, in 2008, was recognized by the federal government as a National Blue Ribbons Program.

The Cate School is recognized as the best independent secondary boarding school on the west coast. The mathematics department, chaired by Frank Griffin, is innovative and makes excellent use of technology in the classroom. They are using iPads extensively, as well as laptops. While at Cate I was introduced to a great graphing calculator program for both Windows and Macintosh. I though it was powerful, capable of nice 3D plots, and affordable. And, they're working on a iPad version.

My school visits consisted of visiting Nido de Aguilas in Santiago, Chile once again, Redwood High School in Larkspur, CA, and, the Cate School in Carpinteria, CA, again. All were interesting and very worthwhile.

Nido has progressed with student-centered-learning to the point where they have actually purchased tables for some classrooms. Moreover, the mathematics department has begun to work with students around tables. They chose to have tables that could be separated into smaller units so students could work in groups of three or four, as well as one group at the large table.

Redwood High School is one of the finest public high schools in Northern California, and has been since it's beginning in 1958. It has been recognized three times as a California Distinguished High School (1990, 1996, and, 2003) and, in 2008, was recognized by the federal government as a National Blue Ribbons Program.

The Cate School is recognized as the best independent secondary boarding school on the west coast. The mathematics department, chaired by Frank Griffin, is innovative and makes excellent use of technology in the classroom. They are using iPads extensively, as well as laptops. While at Cate I was introduced to a great graphing calculator program for both Windows and Macintosh. I though it was powerful, capable of nice 3D plots, and affordable. And, they're working on a iPad version.

### Update on Tablet Initiative at Exeter

As I mentioned in an earlier post, we sort of adopted a 1:1 policy with iPads at Exeter last spring, beginning this past fall. I say "sort of adopted" because rather than designate iPad as the technology of choice, the principal indicated that students should bring a tablet device in September. If they didn't currently own a tablet, an iPad would be preferred since that's what the faculty had been working with for the past four years. This has now been modified for the fall of 2015 so that students simply need to bring a tablet, no preference at all given to iPad.

So, beginning last September, every student in my classes had a tablet. The ratio of iPads to other tablets was about 12:1. Due to the nature of the courses I taught in the fall, we seemed to gravitate to Desmos as our App of choice. While I prepared some demonstrations using Desmos, what the students produced on their own was far more impressive. Using an Apple TV and projector, students were eager to display what they had produced.

Here's an example: in Mathematics 431, the third term of an accelerated/honor calculus class, we consider circles of curvature for various curves. We begin with finding the center and radius of the circle of curvature for y = cos (x) at x = 0. Eventually, students are asked to find the center and radius of the circle of curvature for y = kx^2. Here is what one student produced (to see the list of commands, click the link):

So, beginning last September, every student in my classes had a tablet. The ratio of iPads to other tablets was about 12:1. Due to the nature of the courses I taught in the fall, we seemed to gravitate to Desmos as our App of choice. While I prepared some demonstrations using Desmos, what the students produced on their own was far more impressive. Using an Apple TV and projector, students were eager to display what they had produced.

Here's an example: in Mathematics 431, the third term of an accelerated/honor calculus class, we consider circles of curvature for various curves. We begin with finding the center and radius of the circle of curvature for y = cos (x) at x = 0. Eventually, students are asked to find the center and radius of the circle of curvature for y = kx^2. Here is what one student produced (to see the list of commands, click the link):

There was no question that being able to visualize these problems helped students to understand the concepts better than simply doing them paper and pencil. Using sliders and being able to dynamically change the position of the point where the tangent, and therefore the normal, intersects the graph is a powerful way for students to understand the process.

In the winter term, I taught Mathematics 220 which is essentially a geometry course which meant the emphasis was on GeoGebra. I was fortunate to have a student with lots of experience in using GeoGebra and she became the tutor for others in the course. Once again, students were happy to share what they had done on their homework via the Apple TV. We used version 5 of GeoGebra and so had the ability to work in three dimensions.

The experience of this academic year has made me no less a fan of using technology in my teaching. In fact, I'm more enthusiastic than ever. However, because we don't have a strong, school-wide policy regarding the use of tablets - teachers were told they didn't have to use them in their classes - there are some difficulties to overcome. This spring, on the first day of class in Mathematics 330, a course I taught in the fall and one in which we made great use of Desmos, I told the students that we would be using this App as well as GeoGebra, possibly. When I asked if they had experience using these Apps, all but one student raised a hand. I was mystified that a student could have actually gone through two terms of mathematics this year and not used Desmos. Sigh. But, fortunately because Desmos is so easy to master, it has not been a problem.

While I have been referring to Desmos and GeoGebra as Apps, in fact I use the web versions of both. This means I, and my students, can create a free account and save graphs and constructions. In Desmos, I have the ability to print, share, and embed graphs (that's how I created the link above). Recently, Desmos has produced a Test Mode version.

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