P4 – Practice the integration of appropriate technology with instruction. This means that the teacher is actively using the tools within the classroom to extend student knowledge. The technology used may not be the most modern or advanced, but it must be accessible for students in the future and commonly used within STEM fields. Since the students at my school are highly interested in Math, Science and Technology, the utility of this skill is for engineering tasks and aviation are highly relevant to the task.
The evidence presented is a lesson plan that integrates the use of a graphing calculator to solve for unknown coefficients of a polynomial when given a set of points. Even advanced technology and regression techniques in computers cannot solve for a polynomial that is greater than degree 5 without significant algebra manipulation. Students are confronted with this realization and are directed to create a system of linear equations and are guided to use prior knowledge of matrix operations to solve for the polynomial coefficients. After the lesson plan, there is a set of reflection questions for the teacher and responses which help justify many of the decisions made throughout the lesson. In this commentary I explain the benefit of using a graphing calculator (as opposed to any other form of technology) to help students make connections form mathematical concepts.
The technology lesson plan meets the program standard because it differentiates for different groups of learners and their experience with a graphing calculator. This tool is most appropriate because ALL STUDENTS have a Texas Instruments graphing calculator (or may borrow one from the class set). Additionally, the use of this type of technology is relevant to students who will continue into college when solving systems of equations are important. To relate this to student learning, many engineer students or those interested in design must learn how to create a polynomial function to fit points on a line. Some students in my class are also taking a class in engineering when they use CAD computer design. The computer automates the mathematical process and this lesson connects the computer process to the math behind the computer.
In creating this lesson, I was able to be highly reflective of the lesson that I was designing. During my internship, I am continuously working to differentiate instruction. In creating this lesson, I was able to challenge advanced students and also support students with another piece of material to help them grasp the mathematical procedure. If I were to do this activity again, I would want to show students another type of technology to accomplish the same task, such as a computer programming language or other online tool. Another way I would like to change this activity would be to have less direct instruction and create a more engaging lesson that would lead students to arrive at the conclusion that matrix operations would be the solution to the problem encountered within the lesson (not being able to model a fifth order polynomial with calculator regression).