Session 3 - Response to Prompts

A. Interactions Matrix

	Learner-Content	Learner-Instructor	Learner-Learner
Video Presentation	X
Lecture	X
Chat		X	X
Discussion		X	X
Slideshow	X
Online Readings	X
Story by a Teacher	X
Field Trips	X
Worksheet	X		X
Lab	X		X
Case Study	X		X
Mock Trial	X	X	X
Reading Eggspress (online gaming situations/quizzes)	X		X
Stories by learners			X
Scavenger Hunts		X	X
Real world activities: i.e. building a clinometer and using the angle of sight to determine the height of a building on campus	X	X	X

  

B. Discuss of the types of interactions that are most often used in the content area for which you expect to design instruction. Be sure to explain the content area, the types of students and types of objectives with which you will be working.

Content Area:  My expected content area would be any mathematics taught at the high school level. This material ranges from pre-algebra up through AP Statistics or AP Calculus.

Types of Students: The type of students would vary widely from course to course as the students taking a pre-algebra course to strengthen their skills would have a very different set of conditions to consider in contrast to students taking online AP Statistics. Therefore, for the purposes of these answers, I will respond from the frame of my proposed course in my last blog. Therefore, the students this course is targeted to reach would be students (most likely 9^th graders who will be 10^th graders in the following year or 10^th graders who will be 11^th graders in the following year) who for one reason or another would like to advance through Honors Algebra 2 over the summer to enable them to take Honors Pre-Calculus in the following school year. To engage in the course, they would need to be recommended by their previous math teachers as not only having excellent base math skills (Algebra 1 particularly), but they would also need to be motivated, hard workers and have access to the technology components necessary to complete the online course. (Library access would be fine, but they need to have a prepared plan of attack to participate.)

Learning Objectives: The objective of this course would be to have students master the following topics to be used and applied in subsequent courses (math and otherwise, perhaps in Bruce’s automotive systems course!):

Building on their work with linear, quadratic, and exponential functions, students extend their repertoire of functions to include polynomial, rational, and radical functions. Students work closely with the expressions that define the functions, and continue to expand and hone their abilities to model situations and to solve equations, including solving quadratic equations over the set of complex numbers and solving exponential equations using the properties of logarithms. The five main units are:

·           Polynomial, Rational and Radical Relationships

·           Trigonometric Functions

·           Modeling with Functions

·           Inferences and Conclusions from Data

·           Applications of Probability

Learner-content: Students would be expected to engage with the content in several ways throughout the course. The coursework would consist of podcasts of material, viewing of power points, and required readings in the book. These materials would then be used by the students to engage in the production of work that demonstrates their understanding of the material. Their work could be done by hand, creating online responses in an interface, creation of power points, prezis or videos demonstrating understanding and application.

Learner-instructor: Students interaction with the instructor would come through appointed guaranteed “office hours” for synchronous chat, discussion boards where requests for help, clarification, and enhancement of understandings or extensions could be discussed. Additionally, students would interact with the instructor when turning in work for assessment.

Learner-learner: While I feel like this interaction should be maximized, the format of the course (an advancement course for 9^th and 10^th graders) and the fact that it must be approved by the school district, making too much required work in the learner-learner interaction would overwhelm the students. While this work will be minimized, students will interact on the discussion boards a minimum of once per assignment cluster (this works out to an average of 10 times per unit) by sharing a particular problem or general problem that they a) continue to find difficult or b) were finding repetitively difficult but have since made a breakthrough and share that breakthrough. Students would then have a minimum required interaction of 3 responses to their peers to force them to look through the difficulties or aha’s of others as they are likely to overlap and have a good chance to gain understanding from each other. For subsequent iterations of the course, after success has been proven, I’d love to start incorporating a group project about midway through that requires them to synthesize the first half of the class into an application problem. I would expect this requirement to have little to no support from administration before the class has run through successfully to show that it can be done.

C. Chapters 2, 3 and 4 of the Horton text discuss three categories of activities: Absorb, Do, and Connect. After reading these chapters you are to locate one or more online classes and identify one Absorb, one Do and one Connect activity. Present your findings using this format:

URL:	https://www.edx.org/course/mitx/mitx-6-041x-introduction-probability-1296#prerequisites More generically: https://www.edx.org/student-faq
Course Content:	The world is full of uncertainty: accidents, storms, unruly financial markets, noisy communications. The world is also full of data. Probabilistic modeling and the related field of statistical inference are the keys to analyzing data and making scientifically sound predictions. Probabilistic models use the language of mathematics. But instead of relying on the traditional "theorem - proof" format, we develop the material in an intuitive -- but still rigorous and mathematically precise -- manner. Furthermore, while the applications are multiple and evident, we emphasize the basic concepts and methodologies that are universally applicable. The course covers all of the basic probability concepts, including: •   multiple discrete or continuous random variables, expectations, and conditional distributions •   laws of large numbers •   the main tools of Bayesian inference methods •   an introduction to random processes (Poisson processes and Markov chains) The contents of this course are essentially the same as those of the corresponding MIT class (Probabilistic Systems Analysis and Applied Probability) -- a course that has been offered and continuously refined over more than 50 years. It is a challenging class, but it will enable you to apply the tools of probability theory to real-world applications or your research.
Instructor Characteristics:	This course has 7 people “on staff” all connected with MIT.      The lead instructors are John Tsitsiklis and Patrick Jaillet; both resident instructors at MIT in the Department of Electrical Engineering and Computer Science. It would seem reasonable to assume that both possess high levels of technological skill. Their online teaching experience, however, is unclear, so their ability to apply their knowledge and experience to an online format could only be evaluated by gaining additional information or taking the class.      The other 5 people working to monitor the course are either graduate students in the same department (3) or recent graduates of the same dept. (2). The same assumptions of technological skill and online teaching experience will be made.
Intended Students/Probable Student Characteristics:	The edx website states: EdX courses are open to everyone. All you need is access to a computer with a current browser and an Internet connection and, of course, a desire to learn.      This particular course has the following prerequisites: College-level calculus (single-variable and multivariable). Although this is not a mathematics course, it does rely on the language and some tools from mathematics. It requires a level of comfort with mathematical reasoning, familiarity with sequences, limits, infinite series, the chain rule, as well as the ability to work with ordinary or multiple integrals.      Combining all of that together, I would expect that a student taking this course is self-motivated (their only reward is knowledge), has a high level of comfort with technology and mathematics.
Identify the Type of Activity: Absorb - Do - Connect	Activities Absorb-Do-Connect Video lectures Absorb Short test problems –  in lecture Do Readings Absorb Video Solutions for problems Connect Discussion board – interaction w/ other students & teachers Connect Exams Connect
Identify and Discuss the Interactions in the Activity:	It is my understanding that they have tried to make this course as similar as the face-to-face offering of the course at MIT. So: 1)   The course is organized along units that are aligned with the chapters of the textbook that is required for the course. 2)   Each unit has from 1 to 3 lecture sequences. 3)   These lectures are series of short video clips intermixed with short test problems to test the understanding of the previous material presented. 4)   Each unit also consists of multiple options of supplementary material designed to clarify, enhance or extend the learning and understanding for that unit. 5)   Discussion boards for students to interact both with other students to work through problems together and/or seek clarification from the teachers are monitored on a regular basis. 6)   There are 11 weekly homework assignments which students work through to master the material and demonstrate this mastery to the teachers. 7)   There are 2 midterm exams and 1 final exam to test what the students have learned through the course of the class.

Live long and prosper,

Michelle