Sarah+Rochester

= Welcome to my page! =

My name is Sarah Rochester and I am a senior Mathematics Teaching major at Clemson University. After graduation I hope to become a teacher in the International Schools Services program, where I would be teaching mathematics to students around the world. In my spare time I enjoy solving puzzles and spending time with friends and family.



What are your current beliefs concerning the use of technological aids in the teaching of mathematics?
I believe that using technology in a math classroom is essential to students' learning. Utilizing SMART boards in a classroom can help students in many ways. If students are learning how to graph, rather than drawing a coordinate plane on the board, the SMART board has a blank graph so students can see more clearly how to plot points/lines. It has animated spinners, dice, and coins so when teaching probability, you can spin a spinner on the SMART board to demonstrate examples. It also has a feature that allows teachers to input students' names so that while you are teaching at the board, you can randomly call on a student to answer a question to ensure that all the students are paying attention and are engaged in the lesson at all times. Another important technology in mathematics is a graphing calculator. This is helpful when students are learning about functions because students can plug an equation into the calculator and see what the graph should look like. Also, most graphing calculators have a number generator so teachers can use this feature to teach probability. Another unique tool that can be used on a calculator is called a Calculator-Based Ranger (CBR). This records the distance a student is away from the CBR and plots it on a distance vs time graph. You can also try to match a plot that the calculator generates by moving farther from and closer to the CBR. These are just a few examples of how technology can be utilized in a classroom. I think that if students are using these tools they will get more out of each lesson because they would be more involved in the classroom if they are having fun with these interactive technologies.

When I was in high school the only technology we used were graphing calculators, but that was before SMART boards were installed in the math classes in our school. On a rare occasion our teacher would show us a new math website on the projector and encouraged us to use these websites outside the classroom. We used the CBR's with our calculators, which was a fun way to learn about what happens to the graph of distance vs time, and how we can tell what the speed is on the graph of dist/time. When I got to college I learned many different tools to use in a classroom through my EdF 315 class (computer programs that are useful in the classroom), along with other classes that worked more with calculators.

===Please give me a brief summary of your experiences using technology--i.e. in what aspects have you used the computer and/or other technology devises? Be sure to include any technology you used in teaching experiences as well as personal experiences.===

In EdF 315 we learned how to use Google Sites, Google Documents (including documents, presentations, spreadsheets, and forms), Prezi, Discovery Education, and SMART board technologies, along with other learning tools. I also have experience with TI-84, TI-89, and Casio fx-CG10 (prizm) calculators.

= Online Assessment Tools =

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[|Click to Answer Poll]

A) What are the benefits and challenges for this technology?
One benefit is that Poll Everywhere is a great way to get students engaged in class. Using cell phones and computers to answer questions is fun compared to a regular warm-up or worksheet. It is also a good way to assess whether or not your students understand the content; you get immediate feedback and can adjust your lessons according to students' understanding. A challenge would be using computers and cell phones during the class period. Students do not have access to computers in every class, and taking cell phones out to answer the poll would be distracting. It would also exclude any students who didn't have cell phones. Finally, cell phone reception is not dependable. Some schools even have cell phone signal-blocking technology so students cannot use their phones in class.

B) Would you use this technology in your future class? Why?
I could see this being beneficial as a warm-up with questions assessing information that was taught the class before to see whether you need to review the material or move on with new information. However, I think using cell phones would be too distracting in the classroom, especially the first year teaching. We could try to use the poll in class and if the phones become too distracting we will stop using polls. It could also be utilized as a form of extra credit; students could use computers at home or in the library to vote on a poll before the next class. This would also be a good way to assess students' understanding of content.

My video can be found at http://www.mathtv.com/videos_by_topic. Follow this link, then my video is the first one under the section "solve x^2-5x-6=0."
 * Video Recording **

This video is useful for showing students how to find the roots of an equation using the quadratic formula. The instructor shows how to find the constants a, b, and c, and apply them to the quadratic equation. Then he shows that students would get the same answer by factoring the equation.

= Microsoft Mathematics 4.0 =



Would you use Microsoft Mathematics 4.0 in your future classroom? If yes, how would you use it? If not, why not?
This calculator is a really great tool to utilize in the classroom. It has some features that I have not seen on some other calculators. For example, on Math 4.0 you can divide two complex numbers and the calculator will compute your answer. Then you can choose to view step-by-step instructions showing how the calculator got the answer. This is great because students do not always understand how to divide by complex numbers, but the calculator shows each step and explains what to do to get to the next step. It is also good for showing how to find answers to systems of equations both graphically and algebraically. It is also easier to pull a computer program up to use the calculator than plugging up your calculator to the overhead, so it is a good way to save time.

Would you recommend your students to use this software at home as a homework supporter? Why or why not?
I am unsure because there are benefits and disadvantages to using this software outside the classroom. This would be a good way for students to access a high-quality calculator at home if they cannot afford to buy an expensive graphing calculator. However, I think students might abuse the calculator by using it to do all of their homework. If a student has an assignment and they can see every step of how the calculator got an answer, students could just copy the steps the calculator used to get the right answer without actually doing the work themselves. Normally if a student uses a calculator to get an answer, he/she will just write an answer down on their paper without showing steps. I think that because of this problem and because I would have no way of telling whether students were cheating by letting the calculator do the whole problem, I would not use this software as a homework supporter in my classroom.

===What kind of mathematical view(s) emerge(s) from the Microsoft Mathematics 4.0? Assume that you are a high school student and you use this software at home or during some of your mathematics classes with the guidance of your teacher. How would you view or perceive mathematics in the light of this software? Explain it.=== I think this calculator makes the mathematics look more simple and more interesting. If you are struggling with a problem you can type in a similar one and see how the calculator solves it, then apply the same algorithm to your problem. It is also easier to see the meaning of a problem with the graphing feature because we can graph systems of equations and solve them and if we have two equations that show gym prices for gym 1 vs gym 2, and want to see when the price of gym 1 is equal to gym 2, we can look at the graph, rather than trying to think about when the price would be the same.

= Smart Board Math Tools  =

**This is the link to the lesson activity I chose:**
[|Smart Board Lesson]

**The standard for the lesson activity:**
MA.9-12.DA-3.2: Organize and interpret data by using pictographs, bar graphs, pie charts, dot plots, histograms, time-series plots, stem-and-leaf plots, box-and-whiskers plots, and scatterplots.

Description:
This SMART Board tool shows a question set that could be used in the lesson as a review or even as an assessment of prior knowledge of graphs used to display data (there were no lessons listed under any high school data and analysis sections for any grade that had whole lessons, only problem sets--so I chose a problem set since I am teaching probability and statistics in school). The activity entails answering questions that are posed in the quiz. There are true/false questions along with multiple choice questions which guide students' thinking about the material that they learned (or will learn if you are using this to see students' prior knowledge).

This is different from a traditional lecture because you can give students a quiz on the SMART Board to quiz the whole class at once rather than giving them their own paper. This way you can choose to either ask the questions and let them solve one question at a time individually or you could move through the quiz together as a class, or a combination of both. If you give students problems one by one to work on you can walk around the room to see which students know how to solve the problem and which do not, then you can determine how you will change your lecture according to how well they have learned the material.

It would be difficult to give a quiz using MS Mathematics 4.0 during instruction because you cannot construct histograms, pie charts, bar graphs, etc. using the MS Mathematics 4.0 software. SMART Board software allows you to construct many different types of displays, from histograms to pie charts, dot plots, box-and-whisker-plots, and scatterplots. Because of this it would be much more beneficial to use SMART Board technology when constructing a lesson on graphical displays.

Students may be distracted by giving a quiz on the SMART Board. Most students would feel pressured to work quickly in order to keep up with the teacher flipping through the questions, which affects how well they do on the quiz. Another potential problem is that some students like to look through all the problems before starting the quiz, or want to know how many questions are on the quiz, etc. There could be many issues with students taking a quiz on the SMART Board, which is why I believe it would be beneficial only to use this as a review or as a whole-group activity that you go over with the students.

= GeoGebra  = a) Yes, I think dynamic mathematics environments contribute to students' learning because they help students visualize the important mathematical concepts that they may not see otherwise. For example, if we ask students to find the value of x which gives the maximum volume of a box with x-sized squares cut from each corner of a piece of paper, they would probably be confused and would not understand what the question was asking. However, using dynamic visuals in GeoGebra helps students see how changing the value of x can affect the height, width, and length of the box, which could help them find the connections to using derivatives to find the maximum and minimum values of the function. b) When comparing the two dynamic worksheet generators, GeoGebra and GSP, I found that there are pros and cons to each one. For me, GeoGebra seemed more user-friendly initially, and I picked up on it more quickly than GSP, but that may be because I learned to use GSP first and I had experience using dynamic worksheets. I like how in GeoGebra you can use sliders to change the appearance of the objects in the worksheet and check boxes to make them appear and disappear. You can also make objects change under certain specific conditions by using a conditional statement. However, I favor GSP more for actually constructing objects and proving theorems because I think the tools (especially finding angle measures, dynamic text, etc.) are easier to use on GSP than GeoGebra in the long-run, and I believe there are more tools and options as well. I also favor GSP because of the way objects (segments, points, circles, etc.) are labeled in GSP--they are given one name, where in GeoGebra the labeling will sometimes name these objects multiple names for one object.