danaleeling

Friday the sessions moved into the PICS dining hall. There I hooked up a television to a ChromeCast unit using ED District One's free WiFi. A shout out of thanks to Senator Ferny Perman for his role in supporting the deployment of Internet to schools in his district. The ChromeCast and Internet allowed me to demonstrate Schoology , open educational resources , and Desmos to the mathematics instructors. The session led off with a demonstration of capabilities of Schoology. In the brief time I could only scratch the surface of the vast depth and breadth of capabilities in Schoology. I showed the teachers the assignment submission system, online testing, attendance, gradebook, grade setup, the use of custom marking rubrics. I mentioned messaging and the phone app for Schoology. I then showed the teachers the open educational resource from OpenStax that I used in my  algebra and trigonometry  course this past summer, OpenStax Algebra and Trigonometry . While OpenStax...

As discussed at the end of the third day, the fourth day opened with a look at exponential and logarithmic functions. The opening example looked at the exponential increase in the number of biological ancestors for a person. The second example was whether the number of characters used or the length matters more towards password security. Notes on whether varying characters or length matters more to password security are available online as part of a longer set of notes on topics in algebra and trigonometry . This example builds off of an XKCD piece and an article on brute force password cracking . Mid-morning break was precipitated by precipitation. Heavy rain on the roof made further explanation impossible. Above water from a gutter forms a parabola, while spherical rain drops fall behind the parabola. On the right side of the board is baby growth data from the chart below. On the left is a logarithmic problem that initially appears to result in a solution but the appar...

The third day of the workshop opened with a brief description of " the shape of numbers " with the target audience being some of the elementary education mathematics teachers who had joined the workshop. The separation between geometry and algebra has always seemed to make the two subjects appear rather disconnected. Perhaps the most fundamental object in Cartesian coordinate geometry is the point. All of the points a constant distance from a point might arguably be the simplest planar shape. The construction requires only a string and a piece of chalk. If the center is at (0, 0) and an arbitrary point on the circle of radius r is at (x, y), then the distance formula assures us that (x-0)²+(y-0)²=r² or x²+y²=r². If the center is at (h,k) then (x-h)²+(y-k)²=r² describes the circle. What of all the points that are equidistant from a point P and a line L? If (0,0) is arranged as midway between the point P and the line L, then (x-0)²+(y-k)²=(x-x)²+(y-(-k))² after the squar...

Tuesday began with constructions demonstrated on the board. So much of geometry was originally built on constructions and then proving relationships in those constructions. Yet modern texts tend to give short shrift to constructions. The following diagrams were done using Desmos/Geometry . A point was introduced with a brief overview of the issue of whether a point is truly zero-dimensional or has a finite but infinitesimal size that is non-zero. This was then set aside to note that the first two-dimensional shape is the circle: all of the points a constant distance from a single point. In some sense the circle precedes the line in simplicity, and the circumference of a circle is one-dimensional. Although the first polygon is arguably the equilateral triangle, which follows from the construction of the hexagon, a square was presented next as this illustrates the construction of a perpendicular bisector to a line. The square is rotated by 45° from the usual upright orientation. ...

Day one of the Pohnpei Department of Education mathematics content workshop focused on Algebra I. Morning attendance was eleven, with an additional member joining in the afternoon. After a brief opening ceremony and warm welcoming remarks by the coordinator of teacher training, the mathematics teachers adjourned to a classroom at Pohnpei Islands Central high School. I began the day with Al Jabr , a concrete system modeling mathematics that I use with early algebra students to cover a wide variety of mathematical and algebraic concepts. I began with arithmetic, using basalt rocks for positive integers and coral pebbles for negative integers. The expansion to yarn circles permits the working of single variable problems. An egg carton was used to extend to quadratic functions. I learned during the morning that all of the Algebra I classes at all of the high schools were using Glencoe's Algebra: Concepts and Applications from 2006. I also learned that, varying wit...

The call came in from Chuuk from an uncle. Her father had been rushed to the hospital, his condition unstable and deteriorating. The family had chipped in, a ticket was already waiting for her on the Sunday night flight. That the final examination for the summer course was coming up on Tuesday was far from her mind. The class had focused on using online technologies. The textbook was an  OpenStax  online text, the graphing mathematical engine used was  Desmos , and all assignments and tests were being done in  Schoology learning management system , including the final examination. The students were accustomed to remote communication technologies including the use of Schoology messaging.  Every student had one or another form of personal technology . When I learned she had flown to Chuuk, I reached out and connected with her. With less than 24 hours until the test, working with the Dean of the Chuuk campus arrangements were made Monday for her to sit the e...

On the first day of class in MS 101 Algebra and Trigonometry a survey sought to determine whether the class would be willing to experimentally pilot test the use of an online open educational resource textbook. Twenty-one students completed the survey. The results  of the day one survey indicated that 19 of the 21 were willing to attempt using an online open educational resource, the Algebra and Trigonometry text available from OpenStax produced by a team of instructors led by senior contributing author Jay Abramson of Arizona State University and hosted by  Rice University . At the end of the term a second survey was administered to twenty-six students that explored whether as a result of the summer experience the students preferred a hard copy or an online textbook. The survey also asked whether they would recommend that students in future classes use an online textbook. A strong majority of the students still preferred the online text at the end of the term, and t...