Assignment Six

A) Explain when and how CAS software can be used to enhance teaching and understanding.

CAS software plays and important role in enhancing teaching and understanding. The CAS software I will be referring to is Maple. Maple really enhances teaching and understanding in upper level mathematics courses. The reason I think Maple should be used in upper level mathematics courses like advanced high school courses or college level courses is because Maple is a very powerful program with wonderful features, but in order to truly use Maple you need to know your mathematics. Maple is just a tool and it requires that you know some mathematics before you use it. Classes such as freshman mathematics or basic algebra courses are not enough math knowledge for the students to appreciate what Maple can provide. Once the students are in Algebra 2 and Calculus 1 and 2, the students can appreciate Maple. Once the students are in Calculus 3 or Differential Equations, then the students can see the impressive features of Maple with its 3-D graphing abilities.

Maple should be implemented into mathematics courses as an exploratory feature. In Maple students can see very good graphical representations of what they have been working with. Also, the students can explore by trying new problems or alter the problems they are working on. For example, the students can change the numbers in their problems and see what the results are. Then the students can try to figure out why the results came out the way they did. A warning with implementing Maple is the programming language in order to use Maple can be very complicated, so I would recommend creating step by step labs on how to write basic programs in Maple. Also, give the student a detailed overview on what Maple is and how it works.

B) Design a project that will incorporate web-friendly mathematical software that can be used on-line to explore, explain or expand a concept in a course.

You will be using the website:

http://www.illuminations.nctm.org/imath/912/LinearRelationships/student/index.html#first

This website allows the students to plot points and it will do the linear regression.

To complete the linear regression you need to estimate the equation on the line in slope-intercept form: y = mx + b.

Plot the four points on a graph. Draw a line through the 4 points as close to the center of the points while hitting 2 coordinates.

Pick the 2 points you intersected and determine the slope (m) using the formula:

You have found a slope, now pick a coordinate from above and fill in the y, m, and x and solve for b. You could also estimate your y-intercept by the line you drew on your hand written graph.

Now that you have the “m” and “b”, write the equation of the line: y = ___________

Note: It may be difficult to plot the points on the website, just get as close as possible.

Note: Your linear regression will probably not be exactly like the website. That is okay. The intention is that they are close.

You will be using the website:

http://www.illuminations.nctm.org/imath/912/LinearRelationships/student/index.html#first

This website allows the students to plot points and it will do the linear regression.

To complete the linear regression you need to estimate the equation on the line in slope-intercept form: y = mx + b.

Plot the four points on a graph. Draw a line through the 4 points as close to the center of the points while hitting 2 coordinates.

Pick the 2 points you intersected and determine the slope (m) using the formula:

You have found a slope, now pick a coordinate from above and fill in the y, m, and x and solve for b. You could also estimate your y-intercept by the line you drew on your hand written graph.

Now that you have the “m” and “b”, write the equation of the line: y = -0.59x + 1.9

Note: It may be difficult to plot the points on the website, just get as close as possible.

Note: Your linear regression will probably not be exactly like the website. That is okay. The intention is that they are close.

C) Write a one page paper position paper on using Power Point in mathematics courses.

Power Point is a very good presentation computer program. I have been using Power Point for about 5 years. I have attended workshops on best practices on how to use and implement Power Point effectively. My personal position on Power Point for teaching mathematics is it has some good points and bad points, but overall it depends on how you teach and how much work you want to put into it.

Some downfalls of using Power Point are the equation editor, trying to show math problems step by step, and the amount of work required to set up Power Point for a mathematics course. In mathematics we use many math symbols located in various places in a problem. Power Point allows you to create math symbols, but it is not very easy. In order to type an equation in Power Point you need to use the equation editor which is separate from regular typing in Power Point. Once you type the equation you need to paste it into your slide, then it does not match the text that you typed before. It is not the easiest process. Another downfall is to show a problem step by step you must be very careful with your spacing and when to use an underline. You also have the problems with the equation editor. Finally, the amount the amount of work required to type problems into Power Point is not worth it. I would rather write the problems on the board. Also, because a student may ask for a problem not on the presentation, so I would have to write on the board anyway.

Power Point also has some benefits like saving time on writing vocabulary and other word notes, once you created the presentation it can be used forever without any more work, it can be a good tool to teach over the internet, and with graphics it can make the presentation better. Power Point saves from writing long vocabulary definitions over and over again. Then you don’t have to worry about penmanship problems when it is typed. Once the presentation is created, then it can be used over and over again without any more work which is great for when you are teaching multiple classes. The presentation can also be placed into a web page where students who missed a class can still get the material or students who are learning over the Internet. Finally, using Power Point can make the presentation more interesting with the use of colors, sounds, and graphics that can not be drawn on the board.

In conclusion, Power Point is a great tool that is great for certain aspects of a class and not for other aspects. I would use Power Point for vocabulary or word notes, to teach a lesson over the internet, and to jazz up a presentation. I would not use Power Point to write all the solutions to the homework or to show how to solve complicated math problems. Overall it is a great tool that can be implemented into mathematics courses effectively.