Journal for Christopher Whitworth

 

Monday (June 2, 2003)

1) What are your thoughts and feelings about the mathematics content, open-ended nature of the investigations, and the use of technology for learning?

My opinion about the mathematics content is it’s very broad.  For example, a basic geometry course could easily be broken up into three or four separate courses that would go into much more detail.  There is so much to learn and understand about the contents in mathematics, and the information must be obtained from building and linking prior knowledge to current skills being learned.  The investigations that we have touched upon have shown me that my mathematical background may not be strong enough to teach math effectively for a full year.  But, as a science teacher, I feel that I may have enough knowledge to successfully incorporate math into my science lessons.  The general use of technology in not just math, but all subjects is very important.  With the importance and imminence of technology in today’s world, we must learn how to keep up with the rise of modern technology use.  Tools such as Geometers Sketchpad 4.0 and Graphing Calculator 3.0 are excellent means of implementing technology in mathematics[MP1] .

2)*

Describe any mathematical concepts that were unfamiliar to you today.

The only concepts that were unfamiliar today were topics that needed to be refreshed in my mind.  It has either been late in high school or early in my college years since I have seen some of this material.

3)* Do you feel that the technology enhanced your learning and future teaching of geometry? Explain.

Definitely.  Some of the material that was discussed today would have been excruciating for middle school and high school students to learn without using Geometers Sketchpad 4.0, etc.  The use of technology has greatly improved the techniques and strategies of teaching and learning this material.

4) Other insights and critical learning incidents.

One thing that I learned today that I did not previously know was what a ‘lune’ was.  Another thing that I learned today was not only do young students have problems learning geometric concepts, but some adults are clueless about the material as well[MP2] .

 

 

 

Tuesday (June 3, 2003)

1) What are your thoughts and feelings about the mathematics content, open-ended nature of the investigations, and the use of technology for learning?

I feel much better about the content that was covered today.  I really enjoy being able to ‘play’ with the programs.  I feel like I learn best by being able to make my own mistakes and learning from them[MP3] .  Today, some of the material began to register in my mind.  In geometry, there is so much material that can be made easier by using the programs that we have used in this course.  The technology we are using is superb for learning mathematical concepts.

2)* Compare the use of compass and straight edge with the use of GSP.

Using the compass and straight edge allows room for error in mathematics, but using GSP is incredibly accurate.  It is virtually impossible for one to be one-tenth of a hundredth from an actual value when measuring an angle, etc., but GSP allows one to be as close as possible to a correct value if not 100% correct. [MP4]  Students can understand things better by the ‘hands-on’ method, but when students are more concerned with being precise, GSP will allow less room for error. 

3)* Did these investigations help you learn any connections between triangles and circles?  Explain.

Yes.  I did make the connection that you can discover the measure of angles and arcs by using triangles and circles together in the same problem.

4) Other insights and critical learning incidents.

I feel great about the work I completed today!  The ‘write-up’ that I made really made me think about how to direct people (students) on completing a math problem step-by-step.  I learned the importance of explaining a problem step-by-step[MP5] .

 

 

 

 

 

 

 

 

 

 

Wednesday (June 4, 2003)

1) What are your thoughts and feelings about the mathematics content, open-ended nature of the investigations, and the use of technology for learning?

The mathematics content covered today just about blew my mind.  I must have been asleep when the teacher covered most of this material in high school!  Just as always, I started to learn most of the material today, not by listening to the lectures, but by the ‘hands-on’ approach[MP6] .  I learned it best by making my own mistakes and exploring.  Technology as a tool for learning is excellent!  I love using these programs.  If I was made to sit from 9:00 – 4:00 using protractors, etc., you might find me easily falling asleep and not learning a single thing.  Technology makes it more interesting!

2)* What did you learn from the GSP approach to parabolas, ellipses and hyperbolas?

I did not know that you could measure and/or find parabolas, ellipses, and hyperbolas by using GSP.  I was really amazed.  I also did not know that moving the orthocenter of a triangle would create a parabolic path[MP7] .  But, this information is very interesting.

3)* Have you ever used small group presentations in your class in order to do several similar investigations?  If so, what would you do differently?  If not, do you think it would be helpful to try this approach in the future?

I mostly teach science and social studies and have not even imagined of using GSP in my science lessons.  I believe that I will actually use GSP, etc. in my lessons next year.  Some of the topics that I feel GSP can benefit the students (and myself) could possibly be lessons on volume, area, perimeter, and orbits.

4) Other insights and critical learning incidents.

I became insightful today about using this in my classroom.  I began to think about lessons in which I wish I had had the program to enhance learning and teaching.

 

 

 

 

 

Thursday (June 5, 2003)

1) What are your thoughts and feelings about the mathematics content, open-ended nature of the investigations, and the use of technology for learning?

I felt very confident about my mathematical ability today.  I believe that the presentation of the convex quadrilateral with four triangles of equal area inside of it was the point where I began to feel like I have actually learned some of the material presented in this course.  I would not have figured out that the triangles had the same area if it weren’t for the time given to ‘play’ on Geometers Sketchpad 4.0.  The time to make your own mistakes and learn from them is terrific for learning.  Graphing Calculator 3.1 was introduced today.  I really enjoyed using this program.  It created a lot of three-dimensional and 4-dimensional designs and patterns.

2)* How has your view of this class changed over the week?

On Monday, I was actually thinking that there was no way that I could use any of these programs in my classroom.  The main two reasons is that I didn’t feel confident enough to use them and I didn’t know if Barrow County had access to the programs.  Now, since I have been given a copy of Geometers Sketchpad 4.0 and have had experience using both programs, I believe that I will most definitely use them in my classroom.

3)* What have you learned about how students learn this week?

Students learn best by the hands-on method and by making mistakes.  I was very overwhelmed about the material covered this week, but after given time to ‘play’ with the programs and learn from my mistakes, I have become more confident in using these programs.

4) Other insights and critical learning incidents.

Everything is starting to make sense now!  I have chosen lesson plans that were used in my class last year and have modified them so that I could use Geometers Sketchpad 4.0 with them.  I didn’t include actual math lessons, but physical science lessons that deal with geometric concepts.

 

 

 

 

 

 

 

Friday (June 6, 2003)

1) What are your thoughts and feelings about the mathematics content, open-ended nature of the investigations, and the use of technology for learning?

 

 

 

 

 

 

 

2)* insert today's general prompt here

 

 

 

 

 

 

 

3)* insert personal question for your team here

 

 

 

 

 

 

 

4) Other insights and critical learning incidents.

 

 

 

 

 

 

 

 

 

 

 

Sometime during the Summer…

1) What are your thoughts and feelings about the mathematics content, open-ended nature of the investigations, and the use of technology for learning?

 

 

 

 

 

 

 

2) Other insights and critical learning incidents.

 

 

 

 

 

 

 

 

 

 

 

 

After the site visit

1) What are your thoughts and feelings about the mathematics content, open-ended nature of the investigations, and the use of technology for learning?

 

 

 

 

 

 

 

 

2) Other insights and critical learning incidents.

 

 

 

 

 

 

 

 

 



* The teacher educators will be updating those prompts daily themselves

 

* The teacher educators will be updating those prompts daily themselves

 

* The teacher educators will be updating those prompts daily themselves

 

* The teacher educators will be updating those prompts daily themselves

 

* The teacher educators will be updating those prompts daily themselves

 


 [MP1]You have a great attitude!  I’m sure your students will benefit from your enthusiasm.

 

 [MP2]Ha!  You are absolutely right.  You also saw this morning that even teacher-educators have to struggle sometimes.  I think it’s good for our students to see us persist in trying to solve a problem.

 

 [MP3] And I’m sure you see that your students will probably learn best in the same manner.

 

 [MP4] But do you think the students understand any concepts better by doing at least some constructions “by hand?”

 

 [MP5]  I’m so glad!  I hope this process will help you in planning lessons for your classroom.

 

 [MP6] I’m so glad you feel that way – I know your students will benefit from using a hands-on approach as well and I hope you’ll be able to incorporate this into your classes.  Even if you’re not using GSP, you can use the “discovery” method for your students to learn.

 

 [MP7]  Don’t feel bad . . . I didn’t remember most of that either!!  But isn’t it neat?