Summary and Synthesis

I really enjoyed the information on motivating students. I have heard about how to motivate students in other classes, but I think the more it is reinforced the better prepared I will be when I get to have my own classroom and students to motivate. I really liked the different motivational strategies that was presented in class. I think that I will be able to apply them when I am teaching. I also liked the instructional strategies that were covered because it gives me as a teacher several different ideas and things to try. I realize that if one way is not working then I can switch and try something different.

Personal concerns and next steps

The main concern that I have and have had from the start is that at the end of the semester, I still will not be prepared to take control of a mathematics classroom. I am a physical education major with a math minor so my content knowledge, I feel is not the same as that of mathematics major. This also means that I will not be able to have my student teaching in the mathematics classroom so I will have to make all of my lesson plans on my own with my content knowledge. I hope that one of the next steps that we can take is to find resources and helpful parts to add to lessons for geometry and algebra and other courses that one finds in a secondary mathematics classroom.

Summary and Synthesis

I believe it is getting harder and harder for students to become motivated in the math classroom. I know from my experiences in the classroom, most students (not all) portray a strong negative attitude to having to learn math. Mostly because they are not sure why they have to know many of the certain concepts portrayed in mathematics. I've heard this plenty of times even when I was in high school, "I'm never going to use this, so why do I need to learn it?" or even just the negative attitude to math in general. That is why I found the ten techniques to motivate students, we went over in class, very interesting and useful. It may be hard to find motivators for every math lesson, but for the lessons you do it can make the lesson that much more memorable. I think the summary of all the ten techniques is to relate mathematics with real life situations that pertain to the majority of the students in your classroom. Once a student has something they can relate to, it can potentially open their mind to what the lesson may have to offer them.

New Insight and their Implications

Working with geometry sketchpad, our group found that it is a little hard to work with. We wanted to do certain things and found out that we were unable to do them the way we wanted to. So we needed to find new ways to get the same result. It made us think about how we should teach using geometry sketchpad. We had to cut different material out of our lesson to make our lesson more understandable and workable. Some of the aspects of geometry sketchpad is really very beneficial but other aspects are flawed. Like many programs with computers their are many other ways to get the result you want out of it. Which sometimes makes it a little more difficult to work with. When you come upon difficulties with the program you are working with you need to try to simplify your strategy with that program. So one of the easiest methods is to cut your loses, meaning cut steps out. Geometry sketchpad, as a group, is a great program to use but it could be more user friendly. Many tools could be added in sketchpad that could make the program a lot more workable/usable.

Questions and Answers

Something that I am continually wondering while taking education classes that inform us about technology methods for teaching students is whether or not that technology is really getting the point across to students. I come from the small town school where the technology that we had in the classroom consisted of an overhead projector and a graphing calculator. And believe it or not, that was almost too much for me to handle. I still to this day am illiterate when it comes to computing problems on a graphing calculator and using the graphing options that we learned about in school. It makes me wonder if with all of the new technology that we are introducing to these students, are they really understanding what the concept is and why we are teaching it? Or are they just going through the motions and learning how to use cool, new technology?
After investigating that question with the technology presentation that we gave on Geometer's Sketchpad, I think it can be a little of both. I also believe that there is a balance between the two, learning the concept or learning to use the technology, that can go one way or the other depending upon how the instructor uses those tools. I believe technology is a great thing, and there are more and more students who are learning concept because of it, but what happens when we replace the paper and pencil with a computer screen and mouse? Are we creating a great way to learn or depriving our students of basic knowledge?
Again I think those questions rely heavily on how that technology is used, and I hope to be the teacher who conveys the message that learning the concept is the main objective and technology components supplement my lessons.
Just some things I have been thinking about.......

Summary and Synthesis

It was never difficult for me to be motivated about mathematics because I have always enjoyed it. However, currently I am doing my internship in an alternative learning center and have realized how difficult it can be to motivate students that either do not like math or struggle with it. It is a reoccurring battle day to day for these students to complete their assignments. I frequently hear from them, “I hate math” or “I’m never going to use this, it’s a waste of my time.” When we started discussing motivation in class I found the information very interesting and useful. I believe that as a future teacher I need to find situations that use the math being taught in my courses and relate it to the student’s life. There are many applications out there but if they are not relevant to a student’s perspective at their time and place in life it will not intrigue them enough to learn the material. When I become a teacher it will be one of my main goals to show students where they will use these processes in the “real world” which will hopefully intern motivate them to master the material.

Personal Concerns and Next Steps

After teaching the lesson with Geometry Sketchpad, two concerns came up for me regarding my teaching abilities. First, I am having a hard time trying to find the correct pace when giving the lesson. I feel as if sometimes I am talking to fast and other times I feel like I am going to slow. When you are only given a few times to present lessons, you really don't have that feeling of being comfortable. I think the more opportunities you have to present lessons, the better idea you will have for how to pace yourself and you will be more comfortable. Second, I feel like I didn't a full grasp of how to use Geometry Sketchpad. I felt out of place talking about the software because it didn't seem like it was doing what I wanted it. It showed up in the lesson when the angles were off by hundredths. I just feel that I need to have a deep understanding of how to use the software or the material at hand. In most cases I have the knowledge of the material, but I just didn't grasp the software as much I thought needed. I think that having more time with Geometry Sketchpad would have allowed me to feel better about what I was teaching and more comfortable in general.

New Insights and their Implications

To be completely honest, I am finding this course difficult. This being said, I am very happy to be enrolled in it. I know that I have forgotten a lot of what I learned back in High School (I graduated in 2001, so I am working with a little more time removed than many of my peers). Some of the terminology that we are revisiting has been beneficial. I am happy to rediscover some of the interesting pieces of knowledge that I have put in the back of my mind and, at the same time, learn to use technology with math. I came to this class prepared for a math teacher to write on a white board in front of the class. I like the new applications that are available and how harmless just "playing" with them can be. I have a feeling that I will be doing a lot of that before presenting my first lesson to my future class.

Questions and Answers

In the recent reading of Chapter 3, the final section addresses literacy in mathematics. After reading this section a couple of questions came to mind. (1) How do you make time for reading and writing in a mathematics classroom? It seems there is already so much to do and so little time. (2) How do you motivate students to read and write in math classrooms? I can see students complaining a lot about having to read and write in a math class.
In response to the first question I have regarding the time issue, my solution would be to integrate reading to the homework assignment, as suggested by the textbook, yet this would make the homework assignments even longer for the students who may not have enough time to complete all the assignment if reading was a part of it. So, in this case I would make sure I allowed ample time in class for students to get a start on the homework, including the reading, and maybe even finish it. As far as writing goes, having daily student logs or journals I think would take a lot of time for students to write every day and for me as the teacher to grade them. However, I think it would be beneficial to know what students are thinking about the material. To cut down on the time problem, I think I would have the students write in their journals only once a week, which would still allow me to gain insight from the students’ writings. Also, I could incorporate one problem including writing on tests which allow students to express mathematical concepts in their own words.
The answer to my second question seems a little harder. I think having students read books or short stories about mathematicians or mathematical concepts could interest them if the stories pertain to their lives. Reading a story that uses mathematics could engage students and motivate them to become interested in the topic being presented by the story. Finding these stories may be difficult, however. Motivating students to write may also prove difficult. Writing as part of an exam would provide external motivation since it is part of a grade, but promoting internal motivation for writing may be more difficult. The weekly student journals may be internally motivating for some students because the journals allow them to express their thoughts about mathematics without having to say them out loud. Also, the book’s suggestion for connecting the mathematical significance with a particular newspaper article may be motivating for students.
Both questions I have posed after reading this chapter have allowed me to think about how I might use reading and writing my mathematics classroom. The answers I have come up with so far may work, but they might not. I think every teacher needs to try different ways to include literacy in the mathematics classroom and see what works best for them. It may be one of those things you fail at first, but over time discover something that works in your classroom.

New Insights and Their Implications

One of the biggest things I have learned from the instructor is that it is easy to forget content from high school. It has been so long since any of us have had that level of mathematics, that it is easy to forget certain terms and definitions. I also learned that questions will arise as you are teaching that will be hard to answer. I really like the questions that are on Dr. Reins's website. They are questions that students often ask that I think would be difficult to answer on the spot. It will be a great resource for me and all of us when we get our MQFC questions and responses turned in. I believe it will make me better prepared for my first years of teaching. Some simple things that I have learned from my peers are ideas for different lessons. I enjoy hearing responses from my classmates on different ways you could teach a unit or lesson. Often times I find it hard to think of different ways to teach a lesson, so hearing input from my peers opens my mind up.

New Insights and their Implications

One of the most influential insights I've gotten from my peers and the instructor of this course is the importance of setting specific overarching goals and long-term development goals in the classroom. I believe that if a person asked teachers whether they have long-term development goals for their students, a majority of math teachers would agree. However, I'm guessing a good portion of these teachers may have an idea of the long-term development they are trying to instill in their students, but many have not actually set specific goals in this area. I've learned through discussion with my peers and the instructor that actually putting overarching goals and long-term development goals on paper makes the accomplishment of such goals more realistic. For instance, a teacher may have set a long-term development goal for students to develop self-motivation for learning mathematics. This is a very difficult goal to accomplish. However, I've learned that by setting this goal in a classroom and continually acknowledging this goal, the teacher will make the most progress in developing self-motivation amongst students in the classroom. Though the goal may seem unattainable, acknowledging it and specifically reflecting on the goal are the first steps to it's achievement.