Final Project
Here is my final project for this quarter. I have created the materials for one lesson for a newly developed online MAT 1A Calculus class. I am not quite sure when or if we will ever implement an online class like calculus since this is one of our transferable courses we teach at the community college level, but it was fun to experiment and use what I have learned from this course as well as other ETEC classes in the past to see if I could make something like this work.
Please click the link below to go directly to the class.
MAT 1A Online
The login is "namekata"
The password is "etec676d"
This class was created from MyMathLab. The students would go to WebCT, which is our school's CMS. From there, I would have a copy of my course syllabus for them to read, and also a link directing them to MyMathLab. I would also have a copy of how to register for MyMathLab on WebCT.
How to Register for MyMathLab
The students would then be able to register and get started using MyMathLab. For each section I would create a lecture video and the dictated notes transcribed into a Word document for those students who have disabilities.
The students would have access to additional videos that I have found and viewed to verify accuracy in what is being presented to the students. I would include those videos in the videos tab. I would also create a PowerPoint presentation for each lecture for the students so they have a set of notes from which they make want to refer back to.
The homework for each lecture would be presented in the homework tab. The students would be able to try the homework problems as many times as necessary to get the problem correct. Each time they ask the computer for help, in order to receive credit, they would need to complete a similar problem on their own. I would have due deadlines for each of the homework assignments so that the students would stay on track.
Please view my lecture videos, PowerPoint, definition of related rates, and sample problems and videos. Comments and suggestions are always welcomed.
Also, look at the course outline of record and the syllabus that I have created for this class. All of the topics from the district's course outline of record are covered by MyMathLab.
Thanks!
James
Tuesday, December 8, 2009
Sunday, December 6, 2009
Week 10
Delivering Online Learning Resources
I have been enrolled in both hybrid and online learning classes for the last 3 years at Cal State. I have used discussion boards, blogs, email, digital drop boxes, and threaded discussions to submit my assignments, depending on the class and the instructor. The easiest has been the digital drop box, email and blogs. I did not care for the threaded discussions because I would need to scroll through the list of previous discussed comments just to read the latest. The discussion boards worked out okay, but I would prefer to use the blog because for me, it is simply easier to use and navigate from one student to the next.
In the classes that I have taught online, we use MyMathLab for the eLearning of the material and the turning in of the homework. The students would complete their set of online homework assignments and then submit them to CourseCompass. I would, as their instructor, check their grade online. Therefore, I would not actually need to grade any of their homework problems or test problems because the program would do it form me. The downside to this method would be if a student make it almost to the end of a problem but then messed up near the end, I would not be able to find their mistake. All of the exams were multiple choice, which I do not like in a math class. The reason for my lack of multiple choice is because there is no partial credit and if the student has the correct answer in a different form, they might not get credit for the problem simply because they cannot recognize their answer can be converted to another format.
I have also tried sending out the final exam via email and having the students work through the problems at home and scanning their work and sending the exam back to me. This method worked for a majority of the online students during that one semester that I tried this method, but I realized that not all of the students in my class had access to a scanner. And sometimes when they tried scanning the final exam, their resolution was not high enough to give me a clear idea of what they were doing. Or they would scan the pages out of order and I would need to print out their exams and try to figure out the order in which the pages should be in.
I know that other instructors emailed out their final exams and have their students print out the final, work on the problems on the printed pages, and then mail through the postal service the final exam back to the school to the instructor. This method works also, but sometimes students have claimed to have mailed their test back to the school and the instructor never got their final. This could be an issue.
For the online calculus course, I would use MyMathLab to submit all of the homework assignments and to collect quiz information. As far as the exams, I would use the free response option on MyMathLab to create my questions, but put a password on the exams that someone would need to enter before the student can have access to the exam. This would require each student to come to our Math Lab on campus to have an approved instructor check their photo ID and then enter the password for them, or for the students who cannot come to campus for whatever reason, to find an approved proctor for the exam. The proctor would be someone that the instructor has contacted and checked references prior to giving out the password for the exam to.
The instructor would also need to consider creating some video podcast lectures perhaps on Jing or Camtasia for each section, explaining the process of how to go through several examples that the instructor find useful or important to that section. There are some videos already on MyMathLab, but I feel that if an instructor wants to teach an online class, (especially Calculus) they should do more for their students' learning that rely on a software package to teach their students. There should be some sense of teaching by the instructor for the students to grasp. Otherwise, if all the students did was learn from the program alone, it wouldn't really matter who was teaching the class; all classes would be the same.
I know that it is left to the instructor to decide how the course grade will be determined, but I would suggest to the instructor to assign a majority of the grade based on proctored exams. The quizzes and homework could be done at home with the use of a tutor or textbook, but the student's grade that determines whether they really know and understand the material to move on to the next level should be based on how well that student proves themselves on proctored exams. I have experienced too many times as chair of the mathematics department at our college students who have taken the previous online class and passed with an "A" or "B" and not be adequately prepared and ready for the next level of math.
Just my ideas of how I would teach an online calculus class.
James
I have been enrolled in both hybrid and online learning classes for the last 3 years at Cal State. I have used discussion boards, blogs, email, digital drop boxes, and threaded discussions to submit my assignments, depending on the class and the instructor. The easiest has been the digital drop box, email and blogs. I did not care for the threaded discussions because I would need to scroll through the list of previous discussed comments just to read the latest. The discussion boards worked out okay, but I would prefer to use the blog because for me, it is simply easier to use and navigate from one student to the next.
In the classes that I have taught online, we use MyMathLab for the eLearning of the material and the turning in of the homework. The students would complete their set of online homework assignments and then submit them to CourseCompass. I would, as their instructor, check their grade online. Therefore, I would not actually need to grade any of their homework problems or test problems because the program would do it form me. The downside to this method would be if a student make it almost to the end of a problem but then messed up near the end, I would not be able to find their mistake. All of the exams were multiple choice, which I do not like in a math class. The reason for my lack of multiple choice is because there is no partial credit and if the student has the correct answer in a different form, they might not get credit for the problem simply because they cannot recognize their answer can be converted to another format.
I have also tried sending out the final exam via email and having the students work through the problems at home and scanning their work and sending the exam back to me. This method worked for a majority of the online students during that one semester that I tried this method, but I realized that not all of the students in my class had access to a scanner. And sometimes when they tried scanning the final exam, their resolution was not high enough to give me a clear idea of what they were doing. Or they would scan the pages out of order and I would need to print out their exams and try to figure out the order in which the pages should be in.
I know that other instructors emailed out their final exams and have their students print out the final, work on the problems on the printed pages, and then mail through the postal service the final exam back to the school to the instructor. This method works also, but sometimes students have claimed to have mailed their test back to the school and the instructor never got their final. This could be an issue.
For the online calculus course, I would use MyMathLab to submit all of the homework assignments and to collect quiz information. As far as the exams, I would use the free response option on MyMathLab to create my questions, but put a password on the exams that someone would need to enter before the student can have access to the exam. This would require each student to come to our Math Lab on campus to have an approved instructor check their photo ID and then enter the password for them, or for the students who cannot come to campus for whatever reason, to find an approved proctor for the exam. The proctor would be someone that the instructor has contacted and checked references prior to giving out the password for the exam to.
The instructor would also need to consider creating some video podcast lectures perhaps on Jing or Camtasia for each section, explaining the process of how to go through several examples that the instructor find useful or important to that section. There are some videos already on MyMathLab, but I feel that if an instructor wants to teach an online class, (especially Calculus) they should do more for their students' learning that rely on a software package to teach their students. There should be some sense of teaching by the instructor for the students to grasp. Otherwise, if all the students did was learn from the program alone, it wouldn't really matter who was teaching the class; all classes would be the same.
I know that it is left to the instructor to decide how the course grade will be determined, but I would suggest to the instructor to assign a majority of the grade based on proctored exams. The quizzes and homework could be done at home with the use of a tutor or textbook, but the student's grade that determines whether they really know and understand the material to move on to the next level should be based on how well that student proves themselves on proctored exams. I have experienced too many times as chair of the mathematics department at our college students who have taken the previous online class and passed with an "A" or "B" and not be adequately prepared and ready for the next level of math.
Just my ideas of how I would teach an online calculus class.
James
Sunday, November 29, 2009
Week 9
Week 9 Projects
Well, this week I have created the MyMathLab version of my online MAT 1A Calculus class. I created all of the homework assignments for the students, along with quizzes on each chapter and the proctored online math midterms they will need to complete.
The orientation for my online class will be uploaded to WebCT. This would be the first site that the students in my online class would access. Since I am not teaching an online class this semester, I do not actually have access to WebCT this semester, but once I am assigned the online class, WebCT space would be reserved for me and I could actually upload my orientation outline stating that the students would register and login to MyMathLab instead of WebCT for actual mathematics instruction, lectures, PowerPoints, exams and videos. For now, most of the instructions that the students would need to get started in my online class are clearly explained in the syllabus of the class.
The syllabus was created using Dreamweaver and it hyperlinked for easy navigation. The students can also print out a hard copy of the syllabus if they would prefer. Everything is included in the syllabus such as short description of the course, information about me, email address and phone numbers, grading scale for the course and lecture schedule for the short videos I plan to create for the course. The students should be able to determine what information is going to be covered in the class from week to week.
I have also included the official course outline of record for the students viewing. This is the contract between the district, students and instructors of the materials that should be covered in each class we offer at RCC. I have made sure that all of the required topics are covered in both lectures and homework assignments and the main topics are tested on the midterms and quizzes. This will ensure that if a student passes my class, he or she cannot state that one of the required topics were not covered in this section.
The homework for the entire semester has been selected and assigned by me as of this morning. I made sure that the students would be able to complete the assignments in the given 8-10 hours that are required for outside work in a traditional MAT 1A class per week. Some students might take longer to completed, but for the average student working their way through calculus, they should be able to complete all of the assignments for that week in 8 to 10 hours.
The quizzes for each chapter were created and assigned as well. I have carefully chosen questions that will reflect the students' understanding of the material that is important to MAT 1A and might be useful in the next sequential course which is MAT 1B. The time limit for each chapters' quiz was set to 2 hours and there are 20 questions on each quiz. Since the quizzes are not proctored, the students might be able to use the textbook or other outside sources to help with their score, but realize that they will actually need to know the material for the 2 midterm exams and the final exam which are proctored and closed book.
The midterms and final exam were also created for this online class. The questions were again hand chosen to reflect the students' understanding of the material that is essential to this class. The midterms and final exam are closed book and proctored exams that the students will take with the computer. I have allowed for partial credit on the midterms and final exam. The password for the proctors to type in after they have check proper photo identification to ensure that it is the correct student taking the exam is "ETEC."
The students that I would expect to take this class would be dedication students who are self motivated and understand the importance of learning the material and how it will apply to following semesters and even in other classes such as physics, chemistry and biology. I would expect them to want to learn as much as they can squeeze out of this course to better prepare them for the future. Some of the students might actually be math majors and would want to benefit from all they can from the asynchronous lectures and multimedia textbook format this class has to offer. If another instructor wanted to copy my course and use it as their own, I would not have a problem and would offer as much assistance as needed to help my colleague with their course. I personally believe that working together as a team to create a better and more successful learning environment for all of the students is the most important aspect of an online Calculus class.
I will still need to create some videos for one lesson, and plan on getting that done by next week.
Please look at what I have created so far.
MAT 1A Online
The login is "namekata"
The password is "etec676d"
Please let me know what you think or suggestions to the course that will make it better. Feel free to explore the course and the content areas.
James
Well, this week I have created the MyMathLab version of my online MAT 1A Calculus class. I created all of the homework assignments for the students, along with quizzes on each chapter and the proctored online math midterms they will need to complete.
The orientation for my online class will be uploaded to WebCT. This would be the first site that the students in my online class would access. Since I am not teaching an online class this semester, I do not actually have access to WebCT this semester, but once I am assigned the online class, WebCT space would be reserved for me and I could actually upload my orientation outline stating that the students would register and login to MyMathLab instead of WebCT for actual mathematics instruction, lectures, PowerPoints, exams and videos. For now, most of the instructions that the students would need to get started in my online class are clearly explained in the syllabus of the class.
The syllabus was created using Dreamweaver and it hyperlinked for easy navigation. The students can also print out a hard copy of the syllabus if they would prefer. Everything is included in the syllabus such as short description of the course, information about me, email address and phone numbers, grading scale for the course and lecture schedule for the short videos I plan to create for the course. The students should be able to determine what information is going to be covered in the class from week to week.
I have also included the official course outline of record for the students viewing. This is the contract between the district, students and instructors of the materials that should be covered in each class we offer at RCC. I have made sure that all of the required topics are covered in both lectures and homework assignments and the main topics are tested on the midterms and quizzes. This will ensure that if a student passes my class, he or she cannot state that one of the required topics were not covered in this section.
The homework for the entire semester has been selected and assigned by me as of this morning. I made sure that the students would be able to complete the assignments in the given 8-10 hours that are required for outside work in a traditional MAT 1A class per week. Some students might take longer to completed, but for the average student working their way through calculus, they should be able to complete all of the assignments for that week in 8 to 10 hours.
The quizzes for each chapter were created and assigned as well. I have carefully chosen questions that will reflect the students' understanding of the material that is important to MAT 1A and might be useful in the next sequential course which is MAT 1B. The time limit for each chapters' quiz was set to 2 hours and there are 20 questions on each quiz. Since the quizzes are not proctored, the students might be able to use the textbook or other outside sources to help with their score, but realize that they will actually need to know the material for the 2 midterm exams and the final exam which are proctored and closed book.
The midterms and final exam were also created for this online class. The questions were again hand chosen to reflect the students' understanding of the material that is essential to this class. The midterms and final exam are closed book and proctored exams that the students will take with the computer. I have allowed for partial credit on the midterms and final exam. The password for the proctors to type in after they have check proper photo identification to ensure that it is the correct student taking the exam is "ETEC."
The students that I would expect to take this class would be dedication students who are self motivated and understand the importance of learning the material and how it will apply to following semesters and even in other classes such as physics, chemistry and biology. I would expect them to want to learn as much as they can squeeze out of this course to better prepare them for the future. Some of the students might actually be math majors and would want to benefit from all they can from the asynchronous lectures and multimedia textbook format this class has to offer. If another instructor wanted to copy my course and use it as their own, I would not have a problem and would offer as much assistance as needed to help my colleague with their course. I personally believe that working together as a team to create a better and more successful learning environment for all of the students is the most important aspect of an online Calculus class.
I will still need to create some videos for one lesson, and plan on getting that done by next week.
Please look at what I have created so far.
MAT 1A Online
The login is "namekata"
The password is "etec676d"
Please let me know what you think or suggestions to the course that will make it better. Feel free to explore the course and the content areas.
James
Monday, November 23, 2009
Week 8
Development-Testing
The media that I create using Camtasia would be tested to insure quality assuarance, both in the presentation of the materials and the quality of the material to make sure the desired students learning outcomes are being met. For my online class, I plan to upload a majority of my videos to WebCT, (our college's management's system) but that does not necessarily mean that every video will be compliant to ADA standards. I will need to create word documents explaining each step of the method to solve every problem that I create a video for. I want to create captions for the videos, but I am not quite sure if Camtasia would allow me to do this. I am thinking that I would need to create a PowerPoint to go along with Camtasia that has the closed captioning feature for the hearing impaired.
I would test my videos for completeness and validity by asking several colleagues to view the videos before posting to WebCT. This would check for accuracy, correctness and clearness of the explanations. I would also be checking for this three criteria as I created the videos as well.
I would then need to upload the videos to WebCT and have some sample students try the videos in settings where students would be watching the videos from. (etc. home, mathlab, work...) I would want to take note of any difficulties in download speeds, choppiness of the videos and audio with slow connection speeds and other issues that actual students might run into. I would also have this group of students test the videos on different platforms, such as Windows XP, Vista, 7 and Macintosh systems as well.
As far as quality checking and testing, I would definitely run my videos through a sample set of students. I would probably choose a controlled sample like a traditional class to view the videos and to give me any feedback and details/corrections on my videos. The reason I would choose a traditional class was so that I can ask for feedback when we meet as a class. I could also make any corrections/suggestions and then asked the traditional students to take a look at the videos again to see if improvements were made.
After the videos are posted, if there are any corrections and/or suggestions made by online students, I would need to remove the videos from WebCT, make the corrections, and then re-upload the videos for others to view. This would take time and more effort, but still would be possible. Hopefully, it I won't need to do this very often.
James
The media that I create using Camtasia would be tested to insure quality assuarance, both in the presentation of the materials and the quality of the material to make sure the desired students learning outcomes are being met. For my online class, I plan to upload a majority of my videos to WebCT, (our college's management's system) but that does not necessarily mean that every video will be compliant to ADA standards. I will need to create word documents explaining each step of the method to solve every problem that I create a video for. I want to create captions for the videos, but I am not quite sure if Camtasia would allow me to do this. I am thinking that I would need to create a PowerPoint to go along with Camtasia that has the closed captioning feature for the hearing impaired.
I would test my videos for completeness and validity by asking several colleagues to view the videos before posting to WebCT. This would check for accuracy, correctness and clearness of the explanations. I would also be checking for this three criteria as I created the videos as well.
I would then need to upload the videos to WebCT and have some sample students try the videos in settings where students would be watching the videos from. (etc. home, mathlab, work...) I would want to take note of any difficulties in download speeds, choppiness of the videos and audio with slow connection speeds and other issues that actual students might run into. I would also have this group of students test the videos on different platforms, such as Windows XP, Vista, 7 and Macintosh systems as well.
As far as quality checking and testing, I would definitely run my videos through a sample set of students. I would probably choose a controlled sample like a traditional class to view the videos and to give me any feedback and details/corrections on my videos. The reason I would choose a traditional class was so that I can ask for feedback when we meet as a class. I could also make any corrections/suggestions and then asked the traditional students to take a look at the videos again to see if improvements were made.
After the videos are posted, if there are any corrections and/or suggestions made by online students, I would need to remove the videos from WebCT, make the corrections, and then re-upload the videos for others to view. This would take time and more effort, but still would be possible. Hopefully, it I won't need to do this very often.
James
Sunday, November 15, 2009
Week 7
New Media for Online Learning
I have taught 3 online classes in my teaching career and every time I teach a class online, I am using a new media of communicating with the students in the class. I like to explore and find interesting ways in which I am able to reach out to my students and answer/assist them with any problems or difficulties they may be encountering with mathematics.
My first experience with my online math class was using the e-pak and emails between myself and the students. I would post bulletins on the bulletin board when there was a test or quiz coming up, but I would also send out a mass email so that the students in the class wouldn't be surprised or unaware. Using email seemed to work out good for the students because all of the students who were active participants in the class checked their emails almost everyday of the semester. I would also check my emails everyday and usually get back to student questions within 24 hours of them emailing me a question.
The only problem that I discovered with emailing my students is that I felt distant from them. I like face to face classes where I can "read" the expressions on students' faces to see if they are actually understanding the material I am lecturing on. By using the e-pak and emailing responses back to students when they had questions, I couldn't get that sense of satisfaction like as if I were actually teaching the class in front of them. I actually didn't really feel as if I was teaching my class but instead just answering questions like a tutor and letting the e-pak teach the students the mathematics.
So the second online class I thought I would incorporate the discussion board idea and have students post homework questions on the discussion boards and give credit to other students who can successfully explain the solutions. I would sometimes post more difficult questions for the students to answer as well. This provided more interaction with both the students and myself and students were always checking the discussion board for the latest post to see if they knew the answer to questions that were being posted.
This new form of communication between the instructor and students was a little better than just emailing alone. I still emailed reminders out to students and they would still email questions they had regarding certain problems, but at least we had more than one form of communication that we could use.
The last online class that I taught was an intermediate algebra class and I wanted to use some of the technologies that Dr. Newberry has used in this class. So in addition to the discussion board, email, and the e-pak from the publisher, I thought I would try podcasts and creating my own videos for more difficult problems in algebra. For extra credit, I would post on the discussion board a difficult problem and the students would be able to attempt to answer the questions my posting their responses on the discussion board. The student with the first correct response would be award the extra credit points for that problem. If none of the students could answer the problem, I would create a Camtasia video explaining how the solution was found. At first, these were audio only, but with the addition of a tablet pc, I was able to do screen recordings of the step by step procedures of how the solution was found. The students really appreciated the videos and most of the students found the screen captures to be more helpful.
It seems like every time I teach an online class, I learn more and more of the capabilities of the media that is available and the amount of communication that students want from the class. I have not had the experience of using a threaded discussion in my own online class. I have used Skype to communicate with students over the internet, but Skype requires that we communicate synchronously. But the advantage of using Skype was that there was no loss of understanding between me and the student. The student could ask me a direct question when something was not clear.
I have never heard about Second Life until this week in the podcast. I would like to explore they new form of media to see how I could integrate this into my online classes. It sounds like something that community college students might benefit from and enjoy using in the future. Perhaps this could help students who normally have a phobia of mathematics become more comfortable discussing math related problems if they do not have a fear of embarrassment from their peers.
James
I have taught 3 online classes in my teaching career and every time I teach a class online, I am using a new media of communicating with the students in the class. I like to explore and find interesting ways in which I am able to reach out to my students and answer/assist them with any problems or difficulties they may be encountering with mathematics.
My first experience with my online math class was using the e-pak and emails between myself and the students. I would post bulletins on the bulletin board when there was a test or quiz coming up, but I would also send out a mass email so that the students in the class wouldn't be surprised or unaware. Using email seemed to work out good for the students because all of the students who were active participants in the class checked their emails almost everyday of the semester. I would also check my emails everyday and usually get back to student questions within 24 hours of them emailing me a question.
The only problem that I discovered with emailing my students is that I felt distant from them. I like face to face classes where I can "read" the expressions on students' faces to see if they are actually understanding the material I am lecturing on. By using the e-pak and emailing responses back to students when they had questions, I couldn't get that sense of satisfaction like as if I were actually teaching the class in front of them. I actually didn't really feel as if I was teaching my class but instead just answering questions like a tutor and letting the e-pak teach the students the mathematics.
So the second online class I thought I would incorporate the discussion board idea and have students post homework questions on the discussion boards and give credit to other students who can successfully explain the solutions. I would sometimes post more difficult questions for the students to answer as well. This provided more interaction with both the students and myself and students were always checking the discussion board for the latest post to see if they knew the answer to questions that were being posted.
This new form of communication between the instructor and students was a little better than just emailing alone. I still emailed reminders out to students and they would still email questions they had regarding certain problems, but at least we had more than one form of communication that we could use.
The last online class that I taught was an intermediate algebra class and I wanted to use some of the technologies that Dr. Newberry has used in this class. So in addition to the discussion board, email, and the e-pak from the publisher, I thought I would try podcasts and creating my own videos for more difficult problems in algebra. For extra credit, I would post on the discussion board a difficult problem and the students would be able to attempt to answer the questions my posting their responses on the discussion board. The student with the first correct response would be award the extra credit points for that problem. If none of the students could answer the problem, I would create a Camtasia video explaining how the solution was found. At first, these were audio only, but with the addition of a tablet pc, I was able to do screen recordings of the step by step procedures of how the solution was found. The students really appreciated the videos and most of the students found the screen captures to be more helpful.
It seems like every time I teach an online class, I learn more and more of the capabilities of the media that is available and the amount of communication that students want from the class. I have not had the experience of using a threaded discussion in my own online class. I have used Skype to communicate with students over the internet, but Skype requires that we communicate synchronously. But the advantage of using Skype was that there was no loss of understanding between me and the student. The student could ask me a direct question when something was not clear.
I have never heard about Second Life until this week in the podcast. I would like to explore they new form of media to see how I could integrate this into my online classes. It sounds like something that community college students might benefit from and enjoy using in the future. Perhaps this could help students who normally have a phobia of mathematics become more comfortable discussing math related problems if they do not have a fear of embarrassment from their peers.
James
Sunday, November 8, 2009
Week 6
Hello everyone,
This week's assignment is a little difficult for me to complete. I think the assignment is to design and develop the media for one lesson from last week's course outline. So my lesson I will choose is one of the main objectives for Calculus students. This topic is related rates.
I would start the students off with the wikipedia definition of related rates. This would give the students a chance to interact with the content of reading the material online. I might also suggest that the students view a video explaining the walk-thru solution to a related rate problem so they can see the steps involved in solving the problems.
video 1
video 2
video 3
I would then present the students in my class with my video podcast of my explanation of related rate problems along with a sample problem for them to work through.
my video
I would assign either some problems from the textbook or from a worksheet online that the students could download and work on. These problems would be considered their homework assignment and they could work on them alone or in small groups.
homework
James
This week's assignment is a little difficult for me to complete. I think the assignment is to design and develop the media for one lesson from last week's course outline. So my lesson I will choose is one of the main objectives for Calculus students. This topic is related rates.
I would start the students off with the wikipedia definition of related rates. This would give the students a chance to interact with the content of reading the material online. I might also suggest that the students view a video explaining the walk-thru solution to a related rate problem so they can see the steps involved in solving the problems.
video 1
video 2
video 3
I would then present the students in my class with my video podcast of my explanation of related rate problems along with a sample problem for them to work through.
my video
I would assign either some problems from the textbook or from a worksheet online that the students could download and work on. These problems would be considered their homework assignment and they could work on them alone or in small groups.
homework
James
Saturday, October 31, 2009
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:
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:
Student-Content Interaction:
Determine the continuity of a function.
Student-Content Interaction:
Student-Content Interaction:
Student-Content Interaction:
Course Level Design
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:
- Calculate the limit of a function.
- Determine the continuity of a function.
- Find the derivatives of algebraic and transcendental functions.
- Solve related rate problems.
- Apply the absolute and relative extrema to curve sketching and optimization problems.
- Use Newton's method to approximate the roots of a function.
- Evaluate a definite integral using Riemann sums.
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:
- Calculate the limit of a function.
- Determine the continuity of a function.
- Find the derivatives of algebraic and transcendental functions.
- Solve related rate problems.
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.
- 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.
- 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.
- 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.
- 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.
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.
- 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.
- 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.
Student-Content Interaction:
- Students will read and watch videos describing the characteristics of related rate problems.
- 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.
- 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. |
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