I have to say first, the I really enjoyed this class because of its applications and use outside of the college classroom. Many of the classes I have taken up until now have been almost "idealistic" with no real application to teaching.
I loved learning about the different technologies that are out there and how they can be used in the classroom. I learned the most about Geometer's Sketch Pad and the graphing calculator.
I think that I will use Excel, Geometer's Sketch Pad, and the graphing calculator the most.
I wouldn't say that my view of technology necessarily changed, but was modified. I would say that I am more informed of what technology actually is. I had previously thought of the graphing calculator, smartboards, and computers as the only technology that can be used in the classroom. I know have many other options (some that are even more accessible to students).
I feel that I now understand the technologies that we learned about and I can use them easily (which I feel is half the battle). I like that we had to find ways to use them in the classroom.
I think it would have also been beneficial to do more presentations to the class (quick and informal) of how we used a particular technology. I think this would have given me more ways to use a piece of technology in the classroom. The presentations that we gave the last two classes were so helpful because I was able to get more ideas on how to incorporate a technology into a particular topic. I found the last two classes extremely helpful and insightful. So, maybe if there was a way to brainstorm or even present various ways a particular technology could be used for a topic, or a grade level would be a helpful addition to the class.
Overall, I really enjoyed this class and am so thankful for its applications to the mathematics classroom. I will definitely feel confident using any of the technologies (except perhaps SPSS) in my classroom.
Thanks for an informative but fun semester!
Monday, May 5, 2008
Monday, April 28, 2008
Graphing Calculator Article
I wrote a literature review last semester about the effect of calculators in the math classroom. One of the articles that I used was: http://proquest.umi.com/pqdweb?did=144961131&Fmt=3&clientId=12354&RQT=309&VName=PQD
This article focuses on graphing calculators. (I don't think the link is working. I got the article through Sage's Library and I can't figure out how to get the link to go through. Sorry.)
Summary: The researchers, Thompson and Senk worked with students using two different curricula to teach the same mathematics course. One of the curricula was a traditional algebra curriculum and the other was a new reformed algebra curriculum. The new reformed curriculum involved the use of graphing calculators and the traditional curriculum did not use graphing calculators. The study used four math classes and matched them so that two of the classes received the new curriculum and two did not. All four classes were taught for one school year and given a test at the end of the year. The results of the exam were compared with the type of curriculum that was used. The outcome of the tests showed that the students in the new curriculum that used calculators performed better than those who were exposed to the traditional curriculum that did not use calculators. The differences between the scores of the students in the two curricula were found to be statistically significant
Review: Although the article suggests that using graphing calculators allowed students to perform better on their final exam, there are many problems with the study that should be used to lightly interpret the results. The biggest problem that I found was that there were different teachers for the classes. This means that there was no control over how the teachers taught the students, and that graphing calculators might not be the only reason the students perfomed better. What I conclude then, is that a curriculum that involves graphing calculators (among other things) helps students perform better.
This article focuses on graphing calculators. (I don't think the link is working. I got the article through Sage's Library and I can't figure out how to get the link to go through. Sorry.)
Summary: The researchers, Thompson and Senk worked with students using two different curricula to teach the same mathematics course. One of the curricula was a traditional algebra curriculum and the other was a new reformed algebra curriculum. The new reformed curriculum involved the use of graphing calculators and the traditional curriculum did not use graphing calculators. The study used four math classes and matched them so that two of the classes received the new curriculum and two did not. All four classes were taught for one school year and given a test at the end of the year. The results of the exam were compared with the type of curriculum that was used. The outcome of the tests showed that the students in the new curriculum that used calculators performed better than those who were exposed to the traditional curriculum that did not use calculators. The differences between the scores of the students in the two curricula were found to be statistically significant
Review: Although the article suggests that using graphing calculators allowed students to perform better on their final exam, there are many problems with the study that should be used to lightly interpret the results. The biggest problem that I found was that there were different teachers for the classes. This means that there was no control over how the teachers taught the students, and that graphing calculators might not be the only reason the students perfomed better. What I conclude then, is that a curriculum that involves graphing calculators (among other things) helps students perform better.
Monday, April 14, 2008
Statistics
For a student that is having trouble seeing the use in statistics I would first ask them what they are interested in. (Usual response will probably be movies, sports, etc.). I would then find statistics that can be found in their interest. Statistics are everywhere so it would be easy to find a connection between the student's interest and statistics. Our powerpoint assignment would be another way to show a student how applicable statistics is. I think the main goal should be to show a student that statistics is really used many places and does have meaning. Once that is accomplished, the student should be able to understand the lessons in class and begin to do well. Obviously, a teacher may be caught off guard when they get the "how am I ever going to use this?" question. At that point I may not have an exact answer at the moment, but will definitely come to the next class with a response. Students need to see that the mathematics topics they are learning do have an impact and relavance in their lives.
Monday, March 3, 2008
"Pitfalls" to Teaching Geometry Dynamically
I thought that the article presented many valid points and it was nice to actually read an article that discusses the pitfalls of technology. I am usually instructed to read articles that only present the positives which can be misleading.
The pitfalls that impacted me were:
1-Although students are using the software they may not actually be learning anything.
2-Students may be misled by the "picture" or construction
For the first pitfall, I think it is important to remember that just because students are on a computer and using it for mathematics does not mean that they are learning. I think that this occurs in the classroom frequently and students are hurt in the long run. Just because students are using a piece of technology does not mean that instruction does not need to occur as well. When I teach I plan on using both as a means of reaching as many students as I can.
The second pitfall is something I had not thought of, but makes complete sense. I think that students should have to do many trials of a construction in order to help them make a decision about the validity of their proof. Once students have a specific idea as to whether a statement may be true or false, they should then move to a formal proof (without using the technology) to help them decide for sure. It is very true that a picture on GSP can be very misleading and just happen to work out, when in reality it was a stroke of luck and not a definite case. Therefore, paper and pen and formal proofs need to be done as well.
-Another pitfall that was not mentioned was that teachers themselves need to be proficient at using the technology. I feel that sometimes a technology is introduced to a school and the teachers are just expected to know how to use it. Staff development days need to be used for teachers to learn how to use the software and know it well enough to be able to use it in their classrooms. Also, I know of schools that have the resources but the teachers are not instructed on how to use them. They are basically just applications on their computers that end up not being used because the teachers are not aware of how to do so. The article mentioned that students need to master the software, but before that can even occur, teachers need to be the ones to have it mastered!
The pitfalls that impacted me were:
1-Although students are using the software they may not actually be learning anything.
2-Students may be misled by the "picture" or construction
For the first pitfall, I think it is important to remember that just because students are on a computer and using it for mathematics does not mean that they are learning. I think that this occurs in the classroom frequently and students are hurt in the long run. Just because students are using a piece of technology does not mean that instruction does not need to occur as well. When I teach I plan on using both as a means of reaching as many students as I can.
The second pitfall is something I had not thought of, but makes complete sense. I think that students should have to do many trials of a construction in order to help them make a decision about the validity of their proof. Once students have a specific idea as to whether a statement may be true or false, they should then move to a formal proof (without using the technology) to help them decide for sure. It is very true that a picture on GSP can be very misleading and just happen to work out, when in reality it was a stroke of luck and not a definite case. Therefore, paper and pen and formal proofs need to be done as well.
-Another pitfall that was not mentioned was that teachers themselves need to be proficient at using the technology. I feel that sometimes a technology is introduced to a school and the teachers are just expected to know how to use it. Staff development days need to be used for teachers to learn how to use the software and know it well enough to be able to use it in their classrooms. Also, I know of schools that have the resources but the teachers are not instructed on how to use them. They are basically just applications on their computers that end up not being used because the teachers are not aware of how to do so. The article mentioned that students need to master the software, but before that can even occur, teachers need to be the ones to have it mastered!
Saturday, February 9, 2008
Technology
I remember how helpful the graphing calculator was when I was in high school, particularly 11th and 12th grades. In 11th grade we learned how to graph sin, cos, and tan functions. I remember having a difficult time remembering how high to put the graph and how to know when one full cycle had occured. My teacher showed us how to do the graphs in the calculator and that was extremely helpful for me. That way I could double check my graphs and be sure that my graph was hitting the correct spots. Also, in 12th grade we graphed polar functions (which to tell you the truth I don't remember much of), but what I do remember is that they were strange and again I had a difficult time graphing them on my own. The graphing calculator was very helpful as I needed to know exactly where the graph would hit and what type of shape it formed.
Before I begin teaching I definitely need to become more proficient on the graphing calculator again. I would love to be able to show my students how to do something on the graphing calculator so that they could visually see how something happens. Many students learn visually, so this would aide to their understanding. Especially during graphing units where the particulars of the graph have to be known, I would show my students how to graph using the calculator as an additional tool to help them master graphing. I still would have them learn to graph on paper, but with the graphing calculator as a guide to getting the graph correct.
Before I begin teaching I definitely need to become more proficient on the graphing calculator again. I would love to be able to show my students how to do something on the graphing calculator so that they could visually see how something happens. Many students learn visually, so this would aide to their understanding. Especially during graphing units where the particulars of the graph have to be known, I would show my students how to graph using the calculator as an additional tool to help them master graphing. I still would have them learn to graph on paper, but with the graphing calculator as a guide to getting the graph correct.
Monday, February 4, 2008
Why do I need to blog?
This is a difficult question for me to answer because I am not a fan of blogging. However, as I am thinking about how I could use it in the classroom it does have its benefits.
1. Personally, blogging can be use as a way to reflect. Reflection is very beneficial as it can help a teacher grow and make lessons and activities better for their students. For student teaching we were required to keep a journal to reflect upon the day's activities and I found it easier to set up a blog rather than type in word and print out each journal. Since it is so simple and can easily be set up, blogger is a great way to reflect, especially for those who are reluctant reflectors (Me!!!) anyway.
2. I think that blogger could be used for classroom group work. A teacher could assign a math problem and instead of using class time for the students to work together they could do it as a group on blogger. My idea is that one person would begin and share some ideas about how to begin the problem and then another group member would respond to the presented ideas and agree, disagree, and add to the discussion. This process would continue until the group "solved" the problem to the best of their ability. I think the group would have to be limited to 2 or 3 in order to have good discussion and problem solving occur. Also, the problem used for the group to solve should not contain too many equations because that would be difficult for students to type into the blog. Using a blog to do group work is a nice way to be sure that all members are participating. In a classroom setting it may be difficult to determine if every member participated, but on blogger you could easily see who tried and who took the time to think about the problem and then begin to solve it. I think this would need a few trial runs before the students were able to successfully work with blogger to solve a problem in a group, but I think it has many benefits!
3. The last way I think blogging could be used in the classroom is for teachers to communicate with their students. As students are doing their homework they may have questions that arise that will prevent them from moving on or completing the work. If they "blogged" a question to the teacher they might get an answer to their question and then be able to do the homework. The only problem with this is that the teacher would need to check frequently through the night to see if anyone has posted. I think that Christa mentioned that if you connect to your email address you could get an email stating that a student posted, so maybe that would be the direction to go. From my experience of being in the high school, many students said to me "I didn't understand anything" as I checked off their homework. Obviously I know that isn't true, but if this blogging set up was in play, then the students would have no excuse for not getting help and would be more responsible for their grade that they would be given on their homework. This might be more of a pain than something helpful, I'm not sure, but I think it would be worth a try and if it fails then the teacher can scrap it or modify it enough so that it works for both the students and the teacher.
1. Personally, blogging can be use as a way to reflect. Reflection is very beneficial as it can help a teacher grow and make lessons and activities better for their students. For student teaching we were required to keep a journal to reflect upon the day's activities and I found it easier to set up a blog rather than type in word and print out each journal. Since it is so simple and can easily be set up, blogger is a great way to reflect, especially for those who are reluctant reflectors (Me!!!) anyway.
2. I think that blogger could be used for classroom group work. A teacher could assign a math problem and instead of using class time for the students to work together they could do it as a group on blogger. My idea is that one person would begin and share some ideas about how to begin the problem and then another group member would respond to the presented ideas and agree, disagree, and add to the discussion. This process would continue until the group "solved" the problem to the best of their ability. I think the group would have to be limited to 2 or 3 in order to have good discussion and problem solving occur. Also, the problem used for the group to solve should not contain too many equations because that would be difficult for students to type into the blog. Using a blog to do group work is a nice way to be sure that all members are participating. In a classroom setting it may be difficult to determine if every member participated, but on blogger you could easily see who tried and who took the time to think about the problem and then begin to solve it. I think this would need a few trial runs before the students were able to successfully work with blogger to solve a problem in a group, but I think it has many benefits!
3. The last way I think blogging could be used in the classroom is for teachers to communicate with their students. As students are doing their homework they may have questions that arise that will prevent them from moving on or completing the work. If they "blogged" a question to the teacher they might get an answer to their question and then be able to do the homework. The only problem with this is that the teacher would need to check frequently through the night to see if anyone has posted. I think that Christa mentioned that if you connect to your email address you could get an email stating that a student posted, so maybe that would be the direction to go. From my experience of being in the high school, many students said to me "I didn't understand anything" as I checked off their homework. Obviously I know that isn't true, but if this blogging set up was in play, then the students would have no excuse for not getting help and would be more responsible for their grade that they would be given on their homework. This might be more of a pain than something helpful, I'm not sure, but I think it would be worth a try and if it fails then the teacher can scrap it or modify it enough so that it works for both the students and the teacher.
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