Grade Level: 7th Grade
Subject Matter: Statistics
Topic: Variability and Measures of Center Related to Data Distributions
During this unit, students will be participating in numerous group activities surrounding specific math problems from the Connected Mathematics textbook. The goals of the lessons are for students to recognize that variability occurs whenever data are collected, to identify sources of variability, to determine whether to use the mean or median to describe a distribution, and to use a variety of representations, including tables, bar graphs, and line plots, to display data distributions using an excel program.
Technology that can be used for this unit will include: document cameras, for students to display and talk about their work; computers with Microsoft Excel, so that students can create data distributions and graphs that represent those distributions; the Interactivate website, which will help students learn through guided discovery how to create a stem-and-leaf-plot to represent data; and a projector so that all computer activities can be seen by the students.
At one point during the unit, we will be working on recognizing and using appropriate graphs to represent data. Since Microsoft Excel has graphing functions built in to the program, it would be helpful to use those functions in an interactive lesson with the students. For instance, when we are creating a data set to graph, I can lead the students through step-by-step instructions as we set up a table displaying the frequency that each M&M color appears in a bag of M&M’s. There will be two columns represented: one for color, and one for the corresponding percentage that the M&M’s occurred in a bag. Then I will choose several graphs to display the data. Graphs used will include a column, a bar, a line, a scatter plot, and a pie chart. I will then lead students in a discussion regarding the graphs presented, including what we know about the data from viewing the graph, which graphs do not seem to represent the data in a meaningful way, and which graphs seem to best represent the data.
There are numerous challenges with this lesson plan. First and foremost, it is presumptive on my part that students will be able to use excel for graphing functions if they have never had prior experience using the program. Second, the graphing functions for excel can be difficult, and it may be too advanced of a process to expect that 7th graders will be able to create appropriate tables for classifying data. The recognition of the differences between categorical and numerical data may be hard for students to understand. In light of these factors, the use of excel may need to be reserved for students that have had more mathematical experiences. At the very least, a separate lesson unit may be needed in order to teach students how to properly use Excel’s graphing features.
However, if the students are successfully understanding how to use Excel and are demonstrating success in their abilities to classify data into appropriate tables, the use of a computer program will be extremely beneficial to student learning. Excel is a program that is used constantly in the job market, and being a skilled user of Excel is extremely helpful when looking for a job. Early exposure will help students realize some potential benefits that Excel may provide for them in the future. Use of Excel does not need to be limited to life after school, because once students have a solid understanding of the appropriate ways to classify and graph data, they will be able to use the graphing function for Excel to create relevant visuals for use in projects that may appear during the remainder of their educational careers.
Use of technology in the classroom, especially in the mathematics classroom will be a difficult but important dynamic to incorporate into my teaching career. As I continue to think about and consider my lessons that I will be teaching to my students, I hope to find new and exciting ways to incorporate technology into the lessons.
Saturday, October 18, 2008
Saturday, October 11, 2008
Technology and Mathematics
Incorporating technology into the classroom, especially the mathematics classroom, can be a difficult task. Many technologies that are available tend to be much too expensive to warrant their use. The SmartBoard, for example, is far too limited in its capabilities to produce relevant in-class activities to merit its purchase. Therefore, in considering technologies relevant to the mathematics classroom, the key appears to be looking for what’s inexpensive and readily available.
The unit that we’ll be exploring as we attempt to incorporate technology will revolve around the use of a basic linear equation of the form y = mx+b. The goal in using technology with this topic will revolve around manipulating equation data to demonstrate for students in real-time how changing different variables of the basic equation translates into changes of the graphical representation of the equation. This will primarily be done using both a projector, access to the internet, and a web manipulative program. Web manipulatives are available through the internet and can commonly be found through shareware. A simplistic program will suffice for manipulation of variables and demonstrating in real-time what different variable changes will look like. For instance, if we were to manipulate the “b” variable in our equation and made it larger, we could demonstrate for our students how the line shifts vertically along the y-axis of our graph. Likewise, if we make the “m” variable in our equation negative, students will be able to see that the graphic representation of the line is reflected across the y-axis. Once students have been allowed to watch these real-time changes of variables, then we can switch our focus to a traditional whiteboard for the duration of the lesson. In my mind, this is where a SmartBoard could come into play, if one was available. However, since I cannot truly justify the cost of a SmartBoard when a traditional whiteboard will suffice, there is simply no utility in purchasing one. Students can demonstrate their knowledge of variable manipulation on a whiteboard, which will sufficiently wrap up the use of technology for this particular topic.
It should be noted that the use of a web manipulative may not be flawless in its design. Relying on technology at any point can cause major slowdowns during class lectures due to technology failures that can occur. For instance, it is entirely possible, (and maybe even probable,) that a shareware program would not work as well as one might hope. It will be important to test all programs before using them in the classroom. In addition, it is important to make sure that the sources from which shareware is downloaded are reliable. It would not be beneficial to the classroom if the shareware program being used contained a virus that damaged the classroom computer. It is also possible that the projector may fail, in which case, the entire planning and preparation revolving around the proposed demonstration was for naught. After all, how helpful is a visual demonstration without the visual. Because technology failures can, (and in so many case are likely,) to happen, it is important to plan for such failures by preparing for the worst. If a projector did happen to fail, or a program did not run as planned, the teacher would more than likely need to resort to the use of a traditional whiteboard to demonstrate how manipulating different variables would look graphically.
In the end, technology is a double-edged sword. Relying on its use is an excellent way to save time. Demonstrating numerous different ways that a line can be affected by changes in variables would be a much slower process using a whiteboard. By using web manipulators and a projector, a teacher could demonstrate all the major graphical changes of a linear equation in only a fraction of the time. However, the danger that technology may not work will always loom. But when you consider that using a whiteboard takes the same amount of time whether or not technology is used, it does not make sense to avoid its use. If it works, great; you have just saved precious class time. If it doesn’t work, class time is not truly lost; it is just converted to a slower activity.
The unit that we’ll be exploring as we attempt to incorporate technology will revolve around the use of a basic linear equation of the form y = mx+b. The goal in using technology with this topic will revolve around manipulating equation data to demonstrate for students in real-time how changing different variables of the basic equation translates into changes of the graphical representation of the equation. This will primarily be done using both a projector, access to the internet, and a web manipulative program. Web manipulatives are available through the internet and can commonly be found through shareware. A simplistic program will suffice for manipulation of variables and demonstrating in real-time what different variable changes will look like. For instance, if we were to manipulate the “b” variable in our equation and made it larger, we could demonstrate for our students how the line shifts vertically along the y-axis of our graph. Likewise, if we make the “m” variable in our equation negative, students will be able to see that the graphic representation of the line is reflected across the y-axis. Once students have been allowed to watch these real-time changes of variables, then we can switch our focus to a traditional whiteboard for the duration of the lesson. In my mind, this is where a SmartBoard could come into play, if one was available. However, since I cannot truly justify the cost of a SmartBoard when a traditional whiteboard will suffice, there is simply no utility in purchasing one. Students can demonstrate their knowledge of variable manipulation on a whiteboard, which will sufficiently wrap up the use of technology for this particular topic.
It should be noted that the use of a web manipulative may not be flawless in its design. Relying on technology at any point can cause major slowdowns during class lectures due to technology failures that can occur. For instance, it is entirely possible, (and maybe even probable,) that a shareware program would not work as well as one might hope. It will be important to test all programs before using them in the classroom. In addition, it is important to make sure that the sources from which shareware is downloaded are reliable. It would not be beneficial to the classroom if the shareware program being used contained a virus that damaged the classroom computer. It is also possible that the projector may fail, in which case, the entire planning and preparation revolving around the proposed demonstration was for naught. After all, how helpful is a visual demonstration without the visual. Because technology failures can, (and in so many case are likely,) to happen, it is important to plan for such failures by preparing for the worst. If a projector did happen to fail, or a program did not run as planned, the teacher would more than likely need to resort to the use of a traditional whiteboard to demonstrate how manipulating different variables would look graphically.
In the end, technology is a double-edged sword. Relying on its use is an excellent way to save time. Demonstrating numerous different ways that a line can be affected by changes in variables would be a much slower process using a whiteboard. By using web manipulators and a projector, a teacher could demonstrate all the major graphical changes of a linear equation in only a fraction of the time. However, the danger that technology may not work will always loom. But when you consider that using a whiteboard takes the same amount of time whether or not technology is used, it does not make sense to avoid its use. If it works, great; you have just saved precious class time. If it doesn’t work, class time is not truly lost; it is just converted to a slower activity.
Tuesday, August 26, 2008
Teacher Websites
As part of my Ed Tech assignment, I looked for and found three separate websites that can serve as resources for student teachers and professional teachers.
The first website is www.pbs.org/teachers which is a resource that allows teachers access to different online training courses. It also gives teachers information concerning different lesson plans, and provides examples from that other professionals have used in their classrooms.
The second website is teacher.net which is a forum for teachers that can post issues/concerns/problems related to the teaching field. Other teachers can then reply to these posts with possible solutions. It allows teachers to connect with one another and share their knowledge and experience.
The third website is www.lessonplanpage.com. Much like the PBS website, this website provides numerous examples of lesson plans appropriate for different subjects and grade levels.
Go ahead and visit these pages, hopefully they will provide a resource for us all in the future.
The first website is www.pbs.org/teachers which is a resource that allows teachers access to different online training courses. It also gives teachers information concerning different lesson plans, and provides examples from that other professionals have used in their classrooms.
The second website is teacher.net which is a forum for teachers that can post issues/concerns/problems related to the teaching field. Other teachers can then reply to these posts with possible solutions. It allows teachers to connect with one another and share their knowledge and experience.
The third website is www.lessonplanpage.com. Much like the PBS website, this website provides numerous examples of lesson plans appropriate for different subjects and grade levels.
Go ahead and visit these pages, hopefully they will provide a resource for us all in the future.
Monday, August 25, 2008
Ed Tech
This is my first official post on the web! I hope to use this blog in the future as an information resource for both parents and students. I will use it to post daily class lesson summaries and important reminders of upcoming deadlines and homework assignments. I think that this will serve as an effective way for parents to stay up to date on the information that their children are learning in my classroom and also will aid parents in holding their students accountable to their homework obligations.
I'm excited to learn more about using the internet in the classroom and I invite comments and suggestions to help me make this blog successful.
I'm excited to learn more about using the internet in the classroom and I invite comments and suggestions to help me make this blog successful.
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