danaleeling

MS 101 Algebra and Trigonometry summer 2017 administered a course wide student learning outcome common mathematics assessment (CMA). A student using Desmos earlier in the term, the textbook available on her smartphone Summer 2017 twenty-six students from two sections each with 13 students sat the CMA. As with any course, the focus and parameters vary by instructor. My own approach includes open book evaluations, the elimination of rote memorization, a de-emphasis on trigonometric manipulations, the use of trigonometry in contexts such as Scalable Vector Graphics, and the use of the Desmos graphing calculator. I was not involved in writing the CMA, which was administered as multiple choice and true/false questions using from within Schoology learning management system. Performance on the CMA from two summers ago , the last time the course ran in the summer, averaged 51%. This summer the overall average was 50% with the 8:00 section averaging 47% and the 3:30 section avera...

Underneath the focus on physical systems, SC 130 Physical Science is built on a foundation of connecting physical systems to their mathematical models and communicating the results in writing. Laboratory exercises lead to the writing of a full laboratory report. The majority of the laboratories investigate systems that involve a linear mathematical relationship. Reports include xy scatter graphs, best fit linear trend lines, slope, and y-intercept analysis. The course outline includes the learning outcome, "Students will generate mathematical models for physical science systems." This serves a general education program learning outcome, "Students will be able to present and interpret numeric information in graphic forms," which in turn serves an institutional learning outcome for quantitative reasoning: "Students will be able to reason and solve quantitative problems from a wide array of authentic contexts and everyday life situations; comprehend and can c...

With the first use of Desmos in my summer algebra and trigonometry course, I opted to end the term with having the students put together their own creation in Desmos. I provided minimal guidance to the students. I wanted this to be as wide open as possible. I too am still learning all that Desmos can do. I did set up a preliminary marking rubric for the exercise and made this visible in Schoology . --> Criteria 4 3 2 1 Presentation mechanics:Presentor delivered clearly, concisely, demonstrated familiarity with the Desmos creation. Exceeds expectations: Well delivered exhibiting preparation and knowledge of their Desmos creation. Spoke clearly and always towards the audience. Meets expectations: Presentor showed evidence of preparation and some familiarity with the Desmos creation. Usually faced the audience. Does not meet expectations: Presentor was only able to vaguely explain their work, sometimes with their back to the audience. Severe does not meet expectations: Little...

In the algebra and trigonometry class I transition into vectors using a projectile motion demonstration on the lawn.  A ball is thrown into a parabolic trajectory. The launch angle is tracked with a protractor, a radar gun for sports is used to obtain the speed of the ball. Back in the classroom the horizontal and vertical components of the velocity are used to work out the distance the ball travels and the height to which the ball rises. As an exercise in Desmos , I put together a demonstrator that takes any angle and speed as inputs, calculates the distance and height, and plots the arc on the graph. I then added a ball that "flies" along the arc. The Desmos projectile motion demonstrator is available online .

Laboratory 14 remains a laboratory in search of a more mathematically interesting model. Past attempts have looked at speed versus distance for a flying disk. The intent is to study a system with an unknown mathematical model.  The massive complication is launch angle. Launch angle changes everything. Herlinda volunteered into radar gun duty This term I decided to see if measuring time might iron out another known kink beyond the launch angle kink - the curved flight path. Some throws curve, but the measured distance is straight line. Perhaps time aloft would better reflect the launch velocity. The flying disk throwing crew Herlinda accomplished the radar work both fearlessly and with style I usually handle the radar gun because the throwers are told to fire the flying disk directly at the radar gun, and thus at me. I never ask a student to take on this task.  The results were even more chaotic than distance data usually generates. The failure to...

In an earlier post I noted that Desmos did not directly plot polar coordinates. Not only was I incorrect, but Desmos responded to my blog to correct me! Although I had at some point seen that one could define a function f(x)=3x+5 and then have Desmos calculate f(6), I had not absorbed how this might be used to plot polar coordinates. The above works beautifully . Realizing that I could effectively program Desmos, I applied this thinking to demonstrating how to add two vectors when given the magnitudes m and the direction angles theta. The graph calculates the i and j components for the two vectors and then adds the vectors, graphically displaying the result while also providing information on the magnitude and direction of the vector sum. m1 and theta1 are the magnitude and direction angle for one of the two vectors, m2 and theta2 are the magnitude and direction for the other vector. All four are dynamically interactive and can be changed. The diagram purports to illustra...

Vectors and chapter 10.8 of the OpenStax Algebra and Trigonometry text would land on the same day as the planetary distances exercise in physical science. This meant juggling gear for the back-to-back one and half classes. A surveyor's wheel, the "sun" ball, BBs, a variety of marbles, along with 13 Planets and planetary distances were all for physical science. The RipStik, tape measure, radar gun, four square ball, chalk, and stopwatch (not shown) were for the vector exercise in algebra and trigonometry. In algebra and trigonometry I opted to use a 500 cm run for the RipStik. Due to rain, I fired the four square ball perpendicular to my rolling path towards the building. The covered walkway provided shelter from the rain. More equipment deployed in the vector exercise, the broom was used to sweep rocks from my rolling path. A look at the layout of the experiment. The 500 cm start point. The ball would be released at the second line. The...