Week 5

Designing my Online Individual Project

Online MAT 1A (1st semester Calculus) course
I would like to design an online MAT 1A Calculus course at Riverside Community College.  We do not have any transferable math courses offered and taught online at RCC currently, so this design will be an original.  This course will be a 4 unit course that is transferable to the CSU and UC systems in place of the 1st part of the Calculus series.  The prerequisite for this course will be MAT 10 (Pre-Calculus) or placement into this course through the assessment exam.

The class will cover functions, limits, continuity, differentiation, inverse functions, applications of the derivative including maximum and minimum problems along with very basic integration.  Applications with the graphing calculator will also be explored in this course as well.  If the students are unable to purchase a graphing calculator, there are websites that allow the students to use a free version of an online graphing calculator.
http://www.coolmath.com/graphit/index.html

Calculus is typically taught through class lectures, discussions, and demonstrations of problems on the whiteboard.  Students in the class are given drill and practice problems in class in which everybody  should be arriving at the same answers.  Therefore, the material and content of the course will have more convergent answers, so the instructor and the students should be arriving at the same conclusions.

The main concern or problem in the first semester of calculus is defining the formal definition of a limit of a function and how to prove that the limit does actually exist.  This is done using the epsilon-delta definition and the students will go crazy over how to do this.  Another difficult section would be the application of the derivative functions in everyday life like with related rates and optimization problems.  One way to help clarify these topics might be to have some links to videos or animations that might help explain the problems rather than see the step by step process on the computer.
Here is an example of related rates:  
related rate
Another example using a U-tube video
related rate 2
Here is an example of optimization problems:
optimization 1

This online course should serve students who are working during the day when most of our calculus classes are offered and also allow students the freedom to take this class in a distant education format.  Another situation that might also be solved is the problem of conflicting Calculus with other science classes that require Calculus as a prerequisite or co-requisite to the course such as Chemistry and Physics.  Every semester we have problems deciding when we are going to offer our Calculus classes because we know that a majority of the students taking this course will also be enrolled in a science class as well.  The science courses have labs that do not make it feasible to offer those classes online, so the best solution would be to offer the Calculus class online.

Instructor Characteristics
The two instructors that I would choose for this online MAT 1A class would be either Sheila Pisa or Kathleen Saxon.  Both of these instructors have taught the MAT 1A class numerous times in the traditional format.  Saxon has the most experience with online education, teaching at least 2-3 online/hybrid courses every semester.  Pisa is one semester shy of completing her ED in Instructional Technology from Pepperdine University and has the most experience of anybody at RCC in the creation of new online classes from scratch.

Both of these instructors would provide excellent instructor and feedback to their students.  They both have similar teaching styles with demonstration, practice, drill and evaluation.  The main reason I would choose either of these instructors is because of their love for the use of technology in the classroom and their experience with online learning and education.  Both of these instructors have used CMS other than MyMathLab and are familiar with Camtasia so they can create their own videos to post online if needed.

Student Characteristics
The students in this class should be self-motivated.  My first thoughts would be that if the students are willing to take an online Calculus course, then they should be ready to work and learn.  They understand the importance of learning the material presented and how this knowledge will not only be useful this semester but in classes they plan to take in the future.  I would assume that most of the students would have experience with technology beyond just simple web browsing and email.  Perhaps some of the students might even be some of our online tutors in our online mathlab on campus.  Therefore, they would be experienced in using programs such as WebCT and MyMathLab.

For the student to student interaction, I would think that blogs or a discussion board might be the best solution.  That way all of the students can read other students postings and make comments to questions or solutions that are presented.

Course Goals
The course goals for this online Calculus class would be the same as the traditional course.
Students should be able to:

1. Calculate the limit of a function.
2. Determine the continuity of a function.
3. Find the derivatives of algebraic and transcendental functions.
4. Solve related rate problems.
5. Apply the absolute and relative extrema to curve sketching and optimization problems.
6. Use Newton's method to approximate the roots of a function.
7. Evaluate a definite integral using Riemann sums.

Course Objectives
These are the course objectives for the goals stated above.


      1.  Calculate the limit of a function.
           1.1  Given a transcendental function, correctly identify the limit of the function.
           1.1.1  The student will be able to calculate the limit of transcendental functions using the limit rules.
           1.2  Find the limit of linear and non-linear functions as the value approaches infinity.
           1.2.1  The student will be able to calculate the limit of linear and non-linear functions as the value approaches infinity using the limit rules.
           1.3  Find the limit of functions using the formal definition of the limit of a function.
           1.3.1  The student will be able to write out the formal definition using the epsilon-delta definition, thus proving that the limit exists and is equal to the calculated value.
           1.4  Find the limit of functions from the graph of the function.
           1.4.1  The student will be able to examine a graph and determine the value of the limit at any point on the graph.

      2.  Determine the continuity of a function.
           2.1  Determine and declare the 3 requirements for the formal definition of continuity of a function.
           2.1.1  The student will identify that the value of the function must exist at the point.
           2.1.2  The student will calculate the value of the limit using the limit rules at the point.
           2.1.3  The student will compare the results from the value of the function and the value of the limit of the function at the point in question and show that the two results are equal to each other, thus proving that the function is continuous at that point.

       3.  Find the derivatives of algebraic and transcendental functions.
            3.1  Define the derivative rules for algebraic functions
            3.1.1  The student will identify the power rule, sum, difference product and quotient rules for differentiation.
            3.1.2  The student will calculate the derivative of algebraic functions using the product and quotient rules of differentiation.
            3.2  The student will identify the derivative rules for transcendental functions.
            3.2.1  The student will calculate the derivative of transcendental functions using the product and quotient rules of differentiation.

         4.  Solve related rate problems.
             4.1  Identify the characteristic of the basic related rate problem.
             4.1.1  The student will identify the two rates and describe how they are related to each other.
             4.1.2  The student will calculate the missing component in the related rate problem by solving the formula for the missing term.

          5.  Apply the absolute and relative extrema to curve sketching and optimization problems.
              5.1  Describe the characteristics and differences between absolute and relative extrema.
              5.1.1  The student will calculate the absolute extrema of a continuous function on a closed interval.
              5.1.2  The student will calculate the relative extrema of a continuous function on a closed interval.
              5.2  Determine the characteristics of a typical optimization problem.
              5.2.1  Identify the closed intervals for the optimization probelm.
              5.2.2  Find the derivative of the function that describes the optimization problem.
              5.2.3  Correctly identify extraneous solutions and disregard those as possible solutions.

          6.  Use Newton's method to approximate the roots of a function.
              6.1  Understand the process of how Newton's method approximates the zero value of a function.
              6.1.1  The student will graph the function and graph the tangent lines approximating the zero values and their value approaches the target value.
              6.1.2  The student will calculate the approximate value of the target value by using Newton's formula and see how close this approximation is to the true value.

          7.  Evaluate a definite intergral using Riemann sums.
              7.1  Define the fundamental theorem of calculus.
              7.1.1  Use the fundamental theorem of calculus to find the area under a curve.
              7.2  Present application problems of using the definite interval of Riemann sums.
              7.2.1  The students will find the area under a curve.
              7.2.2  The students will apply the Mean Value Theorem to find the value of the definite integral.

Interactions
For the interactions in this course, I will focus on the first 4 course objectives.  They are as follows:

1. Calculate the limit of a function.
2. Determine the continuity of a function.
3. Find the derivatives of algebraic and transcendental functions.
4. Solve related rate problems.

 Calculate the limit of a function.
Student-Content Interaction:

• Student will read the mathematical definition of the limit of a function.
• Student will watch instructional videos of how the limit of a function is found using calculus.

Student-Instructor Interaction:

• Instructor will provide sample problems in which the students will download from the website.
• Student will work and solve limit problems.  Email the solutions only back to the instructor before deadline.
• If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes.

Student-Student Interaction:

• Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.
• Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.

Determine the continuity of a function.
Student-Content Interaction:

• Students will read the requirements for a continuous function. 
  

 Student-Instructor Interaction:

• The instructor will post various functions and the student will determine whether the functions are continuous or not continuous.  If the function is not continuous, the student must state why this is so.
• The instructor will post graphs of functions and the students will determine whether the functions are continuous or not continuous.  If the graph is not continuous, the student must state why this is so.

Student-Student Interaction:

• Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.
•  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.

Find the derivatives of algebraic and transcendental functions.
Student-Content Interaction:

• Students will read and learn the definition of the derivative of an algebraic and transcendental function.  
• Students will be able to prove the formal definition of the derivative of a function. 
  

Student-Instructor Interaction:

• The instructor will post sample functions in which the students will download from the website and work to find the derivative function.  If the derivative cannot be found, the student must state why.
• The students will email the solutions to the derivatives back to the instructor.
• If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes.

Student-Student Interaction:

• Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.
•  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.

Solve related rate problems.
Student-Content Interaction:

• Students will read and watch videos describing the characteristics of related rate problems.

Student-Instructor Interaction:

• The instructor will post sample related rate problems for the students to download from the website.  The students will identify the two rates and present how the rates are related to each other.
• The students will proceed to solve the problems and email the solutions back to the instructor. 
• If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes.

Student-Student Interaction:

• Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.
•  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.

Course Level Design

Session  1 Introduction to the class. Review of the syllabus. Discuss the proctored exams.	Student-Content:  Podcast presentation of the instructor’s background and what is expected from the class.  The presentation and the syllabus will describe in detail what exactly is expected from the first week. Student-Instructor:  Students will email the instructor their preferred email address that they check most frequently.  The students will create a blog site and email the instructor the address for their site.  Student will also need to let the instructor know if they cannot make it to the mathlab for their proctored exams.  If not, the students must let the instructor know who their proctor will be and provide an email address for the proctor. Student-Student:  Students will create a blog site The students will describe a little bit of themselves and tell why they are taking this class and what they hope to learn from this class.
Session  2 Review of Pre-Calculus material. Introduction to limits. 1.       Calculate the limit of a function. 1.1  Given a transcendental function, correctly identify the limit of the function.	Student-Content:  Podcast presentation of how the limit is found.  Also, the textbook’s description of the definition of the limit of function. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Student will work and solve limit problems.  Email the solutions  back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  3 1.       Calculate the limit of a function.          1.1  Given a transcendental function,      correctly identify the limit of the function.            1.1.1  The student will be able to calculate the limit of transcendental functions using the limit rules.            1.2  Find the limit of linear and non-linear functions as the value approaches infinity.            1.2.1  The student will be able to calculate the limit of linear and non-linear functions as the value approaches infinity using the limit rules.	Student-Content:  Podcast presentation of how the limit is found.  Also the textbook’s description of the definition of the limit, how the rules apply and how to find the limit as the function values approach infinity or negative infinity. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Student will work and solve limit problems.  Email the solutions  back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  4 1.       Calculate the limit of a function.           1.3  Find the limit of functions using the formal definition of the limit of a function.            1.3.1  The student will be able to write out the formal definition using the epsilon-delta definition, thus proving that the limit exists and is equal to the calculated value.            1.4  Find the limit of functions from the graph of the function.            1.4.1  The student will be able to examine a graph and determine the value of the limit at any point on the graph.	Student-Content:  Podcast presentation of how the limit is found using the formal definition of epsilon delta.  Also the textbook’s description of the definition of the limit, how to determine the limit from the graph of a function and how to draw the graph of a function given the equation. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Student will work and solve limit problems and write out the formal definition of proofs to limit functions.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  5 2.       Determine the continuity of a function.            2.1  Determine and declare the 3 requirements for the formal definition of continuity of a function.            2.1.1  The student will identify that the value of the function must exist at the point.            2.1.2  The student will calculate the value of the limit using the limit rules at the point.            2.1.3  The student will compare the results from the value of the function and the value of the limit of the function at the point in question and show that the two results are equal to each other, thus proving that the function is continuous at that point.	Student-Content:  Podcast presentation of how continuity is determined.  Also the textbook’s description of the 3 requirements before a function is determined to be continuous. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Student will work on continuity of function problems and determine whether given functions are continuous or not.  If not, the students must provide reason and which requirement is not satisfied for the conditions.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  6   3.  Find the derivatives of algebraic and transcendental functions.             3.1  Define the derivative rules for algebraic functions             3.1.1  The student will identify the power rule, sum, difference product and quotient rules for differentiation.	Student-Content:  Podcast presentation of how derivatives of functions are determined.  Also the textbook’s description of the rules for differentiation of functions. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Students will work on differentiation of functions using the rules presented in the podcast.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  7 3.  Find the derivatives of algebraic and transcendental functions.            3.1.2  The student will calculate the derivative of algebraic functions using the product and quotient rules of differentiation.             3.2  The student will identify the derivative rules for transcendental functions.             3.2.1  The student will calculate the derivative of transcendental functions using the product and quotient rules of differentiation.	Student-Content:  Podcast presentation of how derivatives of functions are determined.  Also the textbook’s description of the rules for differentiation of functions. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Students will work on differentiation of functions using the rules presented in the podcast.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  8 4.  Solve related rate problems.              4.1  Identify the characteristic of the basic related rate problem. Midterm Exam week covering the first 7 sessions. Students will either take the midterm in the mathlab or find an approved proctor for their exam.	Student-Content:  Podcast presentation of the basic characteristics of related rate problems.  Review some examples of the typical basic types of related rate problems often found in Calculus.   Also review the textbook’s examples of related rate problems and the characteristics that all related rate problems have in common. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Students will identify the basic rates, how they are related and which formula they should differentiate.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  9 4.  Solve related rate problems.              4.1.1  The student will identify the two rates and describe how they are related to each other.                4.1.2  The student will calculate the missing component in the related rate problem by solving the formula for the missing term.	Student-Content:  Podcast presentation of the basic characteristics of related rate problems.  Review some examples of the typical basic types of related rate problems often found in Calculus.   Also review the textbook’s examples of related rate problems and the characteristics that all related rate problems have in common. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Students will identify the basic rates, how they are related and which formula they should differentiate.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  10 5.  Apply the absolute and relative extrema to curve sketching and optimization problems.               5.1  Describe the characteristics and differences between absolute and relative extrema.               5.1.1  The student will calculate the absolute extrema of a continuous function on a closed interval.               5.1.2  The student will calculate the relative extrema of a continuous function on a closed interval.	Student-Content:  Podcast presentation of the basic characteristics of absolute and relative extrema problems.  Discuss the differences between absolute and relative extrema.  Define a closed interval.  Also review the textbook’s examples of absolute and relative extrema problems. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Students will identify absolute and relative extrema characteristics.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  11 5.  Apply the absolute and relative extrema to curve sketching and optimization problems.               5.2  Determine the characteristics of a typical optimization problem.               5.2.1  Identify the closed intervals for the optimization probelm.               5.2.2  Find the derivative of the function that describes the optimization problem.               5.2.3  Correctly identify extraneous solutions and disregard those as possible solutions.	Student-Content:  Podcast presentation of the basic characteristics of optimization problems.  Discuss the typical types of optimization problems and the importance of optimization in everyday life.  Also review the textbook’s examples of optimization problems. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Students will solve optimization problems.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  12 6.  Use Newton's method to approximate the roots of a function.                 6.1  Understand the process of how Newton's method approximates the zero value of a function.	Student-Content:  Podcast presentation of the basic characteristics of Newton’s Method.  Discuss the purpose and show some examples of how this method can be used to solve calculus related problems.  Also review the textbook’s examples of Newton’s Method problems. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Students will solve Newton’s Method problems.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  13 6.  Use Newton's method to approximate the roots of a function.              6.1.1  The student will graph the function and graph the tangent lines approximating the zero values and their value approaches the target value.               6.1.2  The student will calculate the approximate value of the target value by using Newton's formula and see how close this approximation is to the true value.	Student-Content:  Podcast presentation of the basic characteristics of Newton’s Method.  Show the graphing method of how Newton’s Method would provide an approximation for the true value.  Show some examples of how this method can be used to solve calculus related problems.  Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Students will solve Newton’s Method problems by graphing.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  14 7.  Evaluate a definite intergral using Riemann sums.               7.1  Define the fundamental theorem of calculus.               7.1.1  Use the fundamental theorem of calculus to find the area under a curve.	Student-Content:  Podcast presentation of the basic characteristics of the definite integral.  Define the fundamental theorem of calculus and show how this theorem can be used to find the area under a curve.  Also review the textbook’s examples of Riemann sums. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Students will use the fundamental theorem of calculus to solve problems.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  15 7.  Evaluate a definite intergral using Riemann sums.               7.2  Present application problems of using the definite interval of Riemann sums.               7.2.1  The students will find the area under a curve.               7.2.2  The students will apply the Mean Value Theorem to find the value of the definite integral.	Student-Content:  Podcast presentation of the basic characteristics of the definite integral.  Define the fundamental theorem of calculus and show how this theorem can be used to find the area under a curve.  Also review the textbook’s examples of Riemann sums. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Students will use the fundamental theorem of calculus to solve problems.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  16 Final exam covering all 15 sessions. Students will either take the final exam in the mathlab or find an approved proctor for their exam.	Student-Content:  Final exam will either be provided in the mathlab computer by protected passwords on MyMathLab or the approved proctor will type in the password for the student. Student-Instructor:  Once the student has completed the exam, a score will be assigned and that score will be sent electronically to the instructor for grades. Student-Student:  none.

Week 4

1.  Explain what is meant by the dichotomy between the Internet as Content Transmitter and Internet as Communication Tool.  Explain your perspective on this dichotomy.

 The dichotomy of using the Internet as Content Transmitter can be viewed as how the Internet delivers the content of the material in an online class from the instructor to the students of the class.  Most of the time this is done through online readings or podcast presentations that the instructor creates or assigns for the students to view.  The learning process is how much of the information the students can retain and recall from the presentations or readings from the instructor.

Using the Internet as a Communication Tool can be viewed as how the instructor and students in an online class use the Internet as a means of discussing material or content about the class.  This can be done through email, discussion forums or discussion boards or with blogs.  I personally enjoy using the Internet as a communication tool because the discussion is asynchronous and the students in online learning environments probably chose this method of instruction because of their busy schedules and lives.  This gives everyone in the class an opportunity to participate in class discussions when they find a convenient time.

In the online math courses that I have taught, I have used the internet for presentations as well as a means for communication.  I have prepared and created my own video podcasts explaining how a math problem is solved.  The most recent video explained the process of how to approach, translate and solve an application (word problem) related to work.  Then I would assign several similar problems for the students to work on and ask them to email me back their solutions.  I would give them a week in which they can respond and I would work with them until they were able to arrive at the correct solution.  If there were many students who did not get the correct answer on a particular problem, I would create a camtasia video showing how the solution to that problem can be solved.

2.  How can good instructional design ensure that the course meets student needs?

Most of the students in online courses chose this format of instruction because of the asynchronous learning environment.  Many students may have work hours or family obligations that prevent them from being able to attend a traditional class on particular days and times.  For this reason, the design of a good online class should allow asynchronous learning.  I believe that the students should not be always required to be online at the same day on certain days of the week.  Sometimes this format is good, especially when real time responses are important or synchronous discussion is useful.  But a majority of the design of an online class should allow for students to work 24 hours a day, 7 days a week.

Students also want to feel a sense of contact or connection with their instructor.  A good instructional design would allow of dialogue between the instructor and the students and between students or peers in the class.  Students want to feel a sense being able to contact the instructor if he/she has any questions related to the content or material presented in the class and can expect a response fairly quickly.  This is what is described as instructional presence.

3.  How can good instructional design ensure course quality?

I believe that good instructional design is related to the quality of the course when both the instructor and the students feel satisfaction from participating in an online course.  The students need to feel as if they are learning something that is beneficial  and worth their time.  They need to feel instructional presence in the class.  They should feel respected by the instructor.  The assignments in the class should be presented in a clear, concise manner which is easily understood and the students should not feel that all they are doing for an online class is busy work which is going to have little or no benefit in future classes or career.

The instructor needs to feel satisfaction from teaching the class.  The instructor does not have the benefit of seeing the students' reaction to material that is presented in an online class to see if they are understanding the content or the assignments.  The instructor also may also not be able to get a sense if their students respect them as the instructor of the course.  I often find that my online students are more distant from me and only contact me when they have questions related to math problems.  This is very seldom since our software packages include videos and solutions to most of the problems.  This almost makes me feel as if I am not actually teaching the class but allowing the program to teach my students math.

4.  What is the difference between course level and individual activity level design?

The course level design of an online class is designing a class that is either synchronous or asynchronous, totally online or hybrid, deciding what types of technologies would be used in the class.  This should be based on what technologies the instructor is familiar or comfortable with as well as what most of the students in the class have access or available to them.  A course design that I have used in the past were camtasia videos to show math concepts.  It was very difficult trying to explain to my online students how the solution to a quadratic equation was found through email.  But once I used a tablet pc and camtasia, all of my writings and voice were recorded and I could send a short video to the student showing them the steps necessary in arriving at the solution.  This is very similar to what the students would experience in a face to face class.

The individual activity level design would describe how the students are engaged in the learning of the material for the class.  I feel in mathematics that students should practice as many problems on their own, then be able to explain to a peer in the class how the solution is found.  Most of the time, if the student can explain a solution to another student, then they have mastered the concept.  In an online class, the students can explain their solution using a discussion board or discussion forum.  This is sometimes difficult for the students because of the lack of mathematical characters available on the keyboards, but the students can write out their solutions on paper and scan their solutions in PDF format online for other students to view, along with their explanations.

5.  Using the first three stages of the ADDIE instructional design model, explain how you would go about developing an online course.

I would like to eventually develop an online course for our MAT 1A Calculus class.  This is a university level transferable course that would serve maybe 30-50 students per semester.  The main reason I would like to develop this course online is because these students are the most dedicated and mature students at the community college level.  The students in this class would hopefully understand the importance of thoroughly understanding the material and the importance of calculus in other courses in their future such as physics.

In my analysis stage of this course, I would survey the students in the prerequisite course which is Pre-Calculus.  I would find out past experiences with online courses, experiences with technologies such as course management programs or online software packages and their ability to clear explain a math problem through written dialogue.  I would give them a simple problem on the survey in which they could solve and then need to write out the solution so I could get a sense of how clearly they can explain themselves through written dialogue.

For the instructor, I would need to find out who would be willing to try teaching this course since very few community colleges in California teach calculus online.  I believe the reason for this is because the content of the material in this class is very hard to explain without having the students in front of you.  Also, as an instructor, it would be difficult to determine whether the students are understanding all of the concepts presented and explained in an online class.  I would also like to find out what technologies the instructor is comfortable using. 

The content for the calculus course would be standard.  We have a course outline of record requiring certain topics to be taught in the calculus course.  I would just need to make sure that all of the required topics were covered during the course of the semester in a logical manner.

The exams for an online calculus course would definitely need to be proctored, either on campus in a math lab setting, testing center or learning center on campus or with an off campus approved proctor, such as a librarian or professor willing to proctor the exam.  The exams would be a combination of multiple choice and free response.  The free response questions would be on paper and need to be scanned if done from an off campus location.  These could be emailed directly to the instructor.

The design of the course would be a combination of using WebCT and MyMathLab.  The WebCT would be used for the delivery of the instructor created videos and explanation of various problems asked during discussions.  Also, the discussion board in WebCT would be used by students and the instructor for creating dialogue throughout the course.

MyMathLab would be the primary source of content material for the course.  The students would have access to an online textbook, sample and practice problems, instructional videos and 24/7 online assistance with MyMathLab's tutorial service.  The instructor's role would be to assign the homework problems and design exams based on the homework problems from MyMathLab.  A majority of the learning would occur using this program.

The development of this class would be to offer it one semester along with a traditional calculus course to see which course was more popular with the students.  I believe the students would be able to judge for themselves whether they feel online or face to face instructional would be best for their needs. 

The testing of the course materials could easily be done using a common final exam for both courses.  Since the same material would be on the course outline of record, a common final exam could be developed based on topics that are required for the course.  The results and averages for the common final could be compared after the semester to determine whether the students did better in traditional face to face classes or an online learning environment.

James

Week 3

Interactions in Online Classes


Here is my file of the interactions matrix:

	Learner-Content	Learner-Instructor	Learner-Learner
Video Presentation	X
Lecture	X
Chat		X	X
Discussion		X	X
Skype	X	X	X
Websites	X
Email	X	X	X
Blogs	X	X	X

For online classes, I believe that interaction between the instructor and the students is the most important interaction.  Learner-Content interaction is important to teach the material and explain concepts that are needed for the instruction of the course.  Learner-Learner interaction is also important to motivate students in the class and to encourage other students who might be shy or quiet in a face to face class.  Also this type of interaction is commonly used in traditional face to face classes.  However, the Learner-Instructor interaction is what I find the most beneficial in both the online classes that I have taken and the online classes that I have taught.

The Learner-Instructor interaction is important because most online students are independent learners.  Most of the students can figure things out on their own or else they would not have registered for an online class.  Therefore, the instructor's feedback and guidance can help make sure that all of the students in an online class are on the right track and thinking in a focused manner.  The instructor can help students if they are having trouble or difficulties with an area and can help motivate students who are behind or confused with the material.  I have also found that when the instructor responds back to just me as a student, I feel a more 'personal belonging' to the class rather than when the instructor responds back to the entire class.  This personal bond with the class makes me feel more important as a student and motivates me to perform better in the class that I might otherwise do.

As an online instructor, I would focus on the Learner-Content and Learner-Instructor interactions.  I teach elementary and intermediate algebra online.  For the learner-content interaction, I usually let MyMathLab teach most of the content material for the class since the e-pak and the textbook go hand in hand.  80% of the students can learn the material just fine with this program.  For the other 20%, this would require the learner-instructor interactions.  I answer questions on particular problems through email discussions or skype calls.  I have also started using my tablet pc and camtasia to create a video screen capture of the problems that students have and record my voice working though the problems.  This way the students can not only see the process on how the problem is solved, but can also hear what I am explaining at the same time.

For example, in my intermediate algebra class, one of the most difficult topics for students to grasp online is the use of matrices to solve system of equation problems.  We use only 3 steps to manipulate a matrix, but unless students can see the process, it is often very difficult for them to grasp through readings and examples on a website.  Therefore, I would usually create 2 or 3 videos for them explaining how I go through the process of solving a system of equations by using matrices and then send the link to the video to the students.  I have found this to be more successful that trying to explaining to each student one by one on how to solve the problems.  I used to refer the students to youtube videos of professors going through the process to simulate myself explaining the process, but I prefer the camtasia videos now.

A majority of the students in elementary and intermediate algebra are not as motivated as students in a calculus course.  Therefore, it is essential that as an online instructor, I keep the students motivated and interested in the course and still teach the required material and content for the course.  I always check email and responds to students' questions within a 24 hour time frame.  I never let email go for more than 1 day.  I think the students appreciate this quick response and feel more comfortable emailing me as an instructor questions and concerns they may have with the class.

James