HOPE Reflection P4 – Technology

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.

Technology Lesson Plan and Reflection Questions

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).

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Micro-Teaching Reflection

Micro-Teaching Lesson Plan

[1] O1 – Offer an organized curriculum aligned to standards and outcomes. This program standard means that teachers will be thinking critically when writing lesson plans and will make sure that students are learning relevant material which meet state and national requirements. In teaching, curriculum should be easy to follow for maximum student understanding. [2] The attached document is lesson plan for my micro teaching lesson presented to the MTMS Cohort. The accompanying picture is a sample of student work from the micro teaching lesson. This lesson plan demonstrates my understanding of planning collaborative learning and inquiry based learning activities. Asking good questions and facilitating a collaborative learning environment increases student engagement and ultimately increases learning (Borich, 2014).Micro-Teaching Student Sample Work

[3] Within the lesson plan, I include questions which help students engage with the lesson and informally assess understanding. Students were also encouraged to work in groups where they could discuss their misunderstandings. The lesson clearly states the Common Core State Standards in Mathematics and the lesson aligns the learning activity with the learning target which helps students learn math concepts prescribed by the standard. [6] After teaching the lesson, I reflected on improvements I could make to improve the lesson or better achieve the learning targets. I would scaffold the learning more, my understanding of vocabulary relating to sets and subsets is strong, yet often times students do not have such deep understanding. I worked to scaffold the lesson with some vocabulary, although, if I were to teach this same lesson again, I would use direct instruction to introduce vocabulary and concepts and then use the activity to help improve understanding by allowing structured freedom. I would conclude by providing more independent practice. [5] The result for the student is that when lessons are highly organized and scaffolded well, their learning improves. The student will retain more taught information if we guide them towards independent thinking. [4] In summary, by constructing this lesson, I learned about scaffolding well, using student inquiry when teaching a lesson and the possible challenges associated with gauging student learning. [Extra Learning] An additional learning point during creating the lesson is how easy it can become for teachers to use powerpoint slides to dominate classroom instruction and how dangerous it is to overload students with words on slides.

Reference List:

Borich, G. D. (2014). Effective Teaching Methods: Research-Based Practice (8th ed.). Upper Saddle River, NJ.: Pearson Education, Inc.