Final Post...Final Project

Link to Technology Integration Matrix

                Information is all around our students, and it is important for them to be able to critically analyze and interpret what they read and see. This lesson, about developing a line of best fit, does just that, with a new-found leaning toward technological literacy. In redeveloping this lesson plan, I believe it now hits all essential aspects of literacy (access, analyze, evaluate, communicate and produce) and does so with an appropriate level of technology.

                This lesson for eighth-grade begins with a “Do Now” activity projected on the SmartBoard that will address the first part of the first mathematics standard regarding creating scatter plots. It will be a list of data with an independent and dependent variable and students will have to plot the points on a sheet of graph paper. One student would come up to the SmartBoard to plot their points as a solution to this activity. The “access” part of this standard comes from familiarizing students with the many data sets made available from Iowa State University located here. I would ask students to pick a data set they are interested in viewing as a class (being sure to avoid the three data sets they will explore later in class), and we would create an Excel spreadsheet where we could create a table and scatter plot. We would then look at the data from the perspective of correlations and open up a discussion of what a positive, negative or no correlation data set would look like.

                I would then transition into the main part of the lesson, which is determining a line of best fit. I would use a SmartBoard presentation with student interaction and questioning throughout. The presentation would focus on the plot of one data set consisting of about 10 points. On the SmartBoard, I would draw about three or four different “lines of best fit” on the same scatter plot (two terrible fits, one okay fit and one great fit) and generate a list of criteria the students come up with for what makes a line a “good fit”. As a class, we would then estimate two points that fall on the line to generate an equation for this “informal” line of best fit. I would then put another data set on the board and have one student come up to draw what they would consider to be the line of best fit. Another student would come up to the board and be asked if they agree or disagree with the line. If they disagree, they would draw another line. If they agreed, they would estimate two points and generate an equation for the line.

At the conclusion of this part of the lesson, I would end with showing students how to perform a more formal linear regression on both their calculators (using a virtual calculator on SmartBoard) and in Microsoft Excel. By this point, the mathematics standard is more than met because students are familiar with and have created informal lines of best fit. The technology encourages critical thinking because there is clearly more than one way to attempt a problem such as this, and each one uses a different form a technology. It will be up to the student to determine, from the knowledge they acquired during this lesson, which method is most appropriate for them. All of these techniques, both the formal and informal, would be integrated together in the evaluation, communication and production piece of this lesson.

                The final task I would give students is group work in the form of a performance task, which would conclude this lesson and be assigned for homework either as a long-term group project or take up another class period or two as an in-class project. Performance tasks are often underused in mathematics classes, but as I have learned more about them since I first wrote this lesson plan, I think they can serve as a great, interdisciplinary way to bring technology into the classroom. Not only do they serve as a way to evaluate understanding of the mathematics concepts, but can be a great way to judge student knowledge of technologies needed to be successful in the 21^st century, particularly in the workplace. The premise of this performance task would be that students will be serving as data analysts for a client of a consulting firm and must perform several types of linear regressions discussed in class in order to advise of any relationships in the data and predict any future outcomes. Students will be directed to one of three Iowa State University links that have real-life data sets in them which can be used for linear regressions. They are: catalog print run versus orders, poverty, unemployment, murder rate, gas consumption versus local conditions. After choosing one of those data sets, they will be given instructions that are specific to their data set. However, the first step, regardless of data set, will be to identify an example of who may have provided that data (i.e.- an example of a business, community, etc.) in order to determine who they are serving as consultants to. Students would then perform a linear regression (the exact variables for each data set they would be focusing on would be outlined in the data-specific worksheet) by hand, with Excel and in the TI-83 calculator, keeping track of the equations of the lines and how closely they fit the actual data set. Students would then produce a written paper in Microsoft Word that includes all of the linear regressions (noting which is most appropriate) and an analysis of correlations, predictions of future outcomes and any other information students deem useful regarding recommendations for improving the data (if improvement is necessary). They would also be required to develop a strong argument using research (internet database, journals, etc.) as to why any potential relationships in the data exist. Additionally, the document would have to include any Excel charts and graphs they created with the appropriate and necessary labels and explanations.

                I strongly believe that this new and improved lesson effectively and appropriately uses technology and improves the technological literacy of students in the class. Each of the standards is clearly reached because of the strategies employed and the specific technologies that thoughtfully and fully support each of them. I included standards outside of the required mathematics and NET-S because I firmly believe that educators must prepare students to enter life as a productive member of society through the all-important 21^st Century Life Skills. Those standards serve as a great way to bring mathematics and NET-S standards to life in a way that is relevant to students.