Reflection/Summary
Katherine Huffman

Our unit focuses on the concept of least squares.  We have attempted to find a way to make an investigation of the topic that will be both interesting and beneficial for the students.  We have created a survey for the students to complete that focuses on information that they will hopefully find interesting.  We have the students measure their own height, arm span, foot length, and hand length, as well as that of their family and friends in an attempt to make the material being covered appear more pertinent to their lives.  It is important to provide students with an activity that they will find interesting because when students are interested in something they are more likely to learn.  The use of technology in this unit also helps to generate students interest.  I have found that most students are more willing to be actively involved in the learning process when they are not just sitting in the typical classroom filled with desks and chairs.  The opportunity to do their own investigations and use technology will help to promote students interest in the material being covered and give them a deeper understanding of the concepts.

This unit implements Fathom2 as well as the TI-83+ calculator.  Fathom2 is a very useful program because it so easily analyzes data and is such an easy program for the students and teachers to use.  I found the survey feature of Fathom2 to be extremely useful.  Not only is it a quick and easy way to collect data, but it is easy to create the survey itself.  The option to mount the survey on your personal webpage is one of the best features I found.  This makes it extremely easy to use as a classroom tool.  The students can simply go to the teachers webpage and take the survey.  The data is immediately uploaded to the Fathom2 survey webpage and can easily be downloaded into Fathom2 where the students can manipulate the data to investigate multiple statistical concepts.

The ability to impose a movable line onto scatter plots is also a helpful tool in our lesson.  This ability allows students to make a line of best fit using their eye and then compare it to the actual line of least squares that Fathom will provide for them.  The students can also impose squares to help them understand the concept of line of least squares, as well as the reason for its name.  However, Fathom is not the only method students have for finding the equation for the line of least squares.  I think it is important for students to understand the procedure that the computer and calculators use.  For this reason, we included a lesson in which the students take a very small data set and find the equation for the line of least squares for that data set.  This will help the students to have a deeper understanding of the line of least squares as well as ideas associated with the concept such as correlation.  The students can then see how they can verify their computations using the calculator.

I found Fathom2 to be a very useful program and was surprised at how easily I was able to use the program.  This project helped me to see that Fathom2 would be a useful tool in the classroom.  It is not a difficult program for the students to use or understand and it will help them to have a deeper understanding of the material being covered because they are allowed to manipulate data as well as see multiple examples in a very short amount of time.  I believe that our unit could easily be implemented in the classroom and would be excited to use these lessons in my classroom in the future.