The+Power+of+Authentic+Data

Presenter: **Patrick Galuska** Time: **10:30 - 11:15** Room: **275** Contact: **pgaluska@wssd.k12.pa.us** __Description of Presentation__ ==Mathematics shouldn't be bound within the pages of a textbook. Learn how your students can use 21st century tools to collect, analyze, and interpret REAL data in every lesson. == Audience: All high school mathematics teachers.


 * = **Gapminder World** ||= **Google Forms** ||
 * = [[image:Picture_1.png width="368" height="257"]] ||= media type="custom" key="3083734" ||
 * = **Dynamic Geometry Software** ||= **Google Spreadsheets** ||
 * = [[image:fountain.png width="492" height="401"]] ||= [[image:Picture_5.png]] ||

Links [|Gapminder World] [|Geogebra] [|Google Forms] [|Mathematica Player] [|Mathematica Applets]


 * Blog for "The Power of Authentic Data"**__

Introduction of the topic with an example from a textbook of a table of data to be used for analysis. The numbers were something like several temperatures and the corresponding "cricket chirps" associated with that temperature. The example was chosen to illustrate that examples from our typical textbooks are not interesting to students.

From there we looked at the website gapminderworld.org. The first example chosen was life expectancy. The website showed the life expectancy for most major nations of the world in an interactive graph. Patrick showed that the website could show data for many countries at once over time. It could also show one particular country over time. You can even track one country over several years with a lineplot - type display. There are many different types of data to view and manipulate. We looked at oil consumption, children per woman, and many more. The data is from the U.N. and is accurate from 1900 on.

Next we looked at a Google form. The form is located on this page on the top right. Patrick described an introduction to a problem for which students could enter information and be involved in solving the problem. For example, with the form above, the problem could be that the Athletic Director has to order jerseys for the basketball team, but the coach does not know the players' heights. However, he does have a list of their shoe sizes. Thus it is the problem for the class to use their shoe sizes to look for a relation between shoe size and height, and thus give the A.D. a good idea of how tall the basketball players might be.

Once the data is entered into the Google form, the teacher can then access the results of the students' entries on a Google document. The document is a spreadsheet of the information that has been entered. After this, the data can be exported to a Microsoft Excel file and be further analyzed with that program to draw a trend line and find the equation of best fit.

After that, Patrick showed a model of the "3 Door Problem" on Google Docs. This example demonstrated that data does not always need to be exported to be analyzed. Google Docs can be used in many cases just like Excel. He demonstrated the use of a formula to find the mean of a set of data.

Next he demonstrated the use of a free program called Geogebra (linked above). With Geogebra, he demonstrated an activity in which he inserted a picture that he had taken of some shelves. He then posed the question, "Did the people who installed these shelves do a good job of making them parallel?" This question would then be up to the students to use the program to answer the question. By knowing the properties of parallel lines with transversals, the students can give an informal proof of this by drawing lines and a transversal over the shelves in the picture and then measuring the angles with the program.

A second example used a picture of a dartboard. Many example questions were posed such as the two that follow. What is the area of the dartboard? What is the probability of hitting a certain part of the dartboard? This type of activity could go in to many different directions.

Thirdly, he showed a picture of stairs. The problem then posed was, "The slope of the stairs, by regulation, may not be more than 1.5. Do these stairs meet the regulated slope for public buildings?" Geogebra can be used to make these calculations as well.

Finally, with the time we had remaining, Patrick showed us Mathmatica Player (linked above), and Mathmatica Applets (also linked above). This player is a free version of the type of activities shown in an earlier session about Gadgets. The applets are not all as good as most of the Gadgets, but many are very good. The files are not large, and if the student laptops have the Mathematica Player loaded on them, then students can access shared applets and use them to explore different ideas in class. The page that he showed us with High School level applets showed that there were at least 290 of them.

Overall, this session showed many ways to bring students' surroundings into the classroom and explore them using the same properties and methods that they'd learn in a "traditionally taught" math class. When students feel connected to the problems they are working on, they are much more engaged and interested. They begin to want to solve problems, because the problems relate to their lives, not predict how many times a cricket will chirp at 57 degrees Fahrenheit...

Great Presentation, Patrick! Thank you!