Evidence 1. Praxis II Score ReportThis evidence is my passing score on the Praxis II Exam. This relates to Standard 4, Content Knowledge, because it clearly shows that I have an understanding of the central concepts and structures of the mathematics courses I am teaching.
This knowledge allows me to fully explain concepts within this subject area to my students in a clear and concise manner. I also have the background knowledge to appropriately select resources and materials for my class that will aid my students in developing an understanding of the mathematics content. My mathematics knowledge, which is shown in my passing score, allows me to flexibly and confidently teach concepts that create meaningful learning experiences for students. My understanding allows me to modify instruction easily to make topics relevant to students’ lives and experiences without losing the accuracy of the content. In addition, I know how to refocus students’ attention as necessary by making connections within the mathematics content to assure mastery of the content. |
Evidence 2. Factoring out the Greatest Common Factor Lesson PlanIn this lesson, I introduced my students to factoring out the greatest common factor of a polynomial expression using Algeblocks. This was the first of a series of lessons on factoring polynomials. My goal was to help students connect their understanding of multiplying binomials with Algeblocks to factoring. In this lesson, students were given polynomial expressions that they made a rectangular model for, with one side length of the model being the greatest common factor of the polynomial. This helped students understand factors as the side lengths of area models. As the lesson progressed, students moved from the geometric models to the algebraic methods for factoring out the greatest common factor and the class discussed how these representations were related.
This lesson relates to Standard 4 because I created a learning experience that made factoring accessible and meaningful for learners to assure mastery of the content. This was accessible to all students because in previous classes, they had been introduced to Algeblocks and understood how to make area models. I was having students use appropriate materials for mathematics that they were all familiar with to then make connections to a new concept. This was a meaningful lesson because I encouraged students’ academic curiosity and critical thinking. Students were given various polynomials and once they identified the greatest common factor, they had to work with a partner to determine how to set up their area model in a way that showed this factor. This was a challenging task, but the students did a great job working with one another and trying various solutions. This evidence is important to me because I created the investigation entirely from scratch. I had many resources for writing lessons on factoring using Algeblocks, but there was not much on factoring out the greatest common factor. I wanted the lessons in this unit to correlate and build upon one another, so I wrote this lesson with Algeblocks so that students understood to look for factors of a polynomial in the side lengths of a rectangular area model. This is a big part of factoring with Algeblocks and this lesson helped them get a head start in working with the concepts. This lesson was entirely inquiry based and I think the students enjoyed a more creative learning experience. |
Evidence 3. "Restaurant Math" Lesson PlanTo teach students about markups, tax, and tip, I had them running through a real-world scenario where they were ordering a meal at a restaurant and then calculating their final bill after both tax and tip were applied to the cost of their meal. Students were allowed to pick the type of meal and restaurant they were ordering from and I had them visit real online restaurant menus. Each of the restaurants were local places that I knew at least some of the students had been to or heard of before. Students worked with a partner to decide upon the items they were ordering and then calculating their final bill.
This relates to Standard 4 because I used my knowledge of the central mathematics concepts I was teaching to design a learning experience that was accessible and meaningful for learners. My ability to apply the concepts to a real-world setting shows that I can explain the subject area in a way that the students understand and that I can modify instruction to make topics relevant to students’ lives and experiences. During this lesson, students were focused and interested in deciding upon a meal. I had students who went with a practical approach and ordered an appetizer, and two main courses for their pair, while another group ordered fancy sodas and a handful of desserts. Both groups of students still got the same mathematical experience out of the lesson, which shows that I can engage and maintain students’ attention and that I encourage diverse perspectives. This evidence is important to me because it was exciting to see how excited and involved the students got in the lesson. This particular Math 8 class has a lot of students who really do not like math class and it can be a challenge to prepare lessons that will engage them and motivate them to do work. During this lesson, I had a student exclaim, “Wait, we can actually use this math in our lives!” What a rewarding thing to hear as a teacher! I also was very proud of the connections my students were making between their own experiences and the mathematics. One student shared with her partner, “Oh, I’ve been here before, I don’t like it that much because it is always a really long wait. We wouldn’t tip them this much.” |
Evidence 4. Relations and Functions with Dr. SeussIn this lesson, I read “The Sneetches” by Dr. Seuss to my students. I also had the option to play a recording of the book with an animated video if the book was not available. In this story, there is a machine that changes characteristics of the Sneetches that live by the beaches. After reading the story, the students each made their own machine, and I selected which students would share their work based on what representation they used and whether there were multiple outputs for the same input in their machine. This led into a class discussion on relations and which relations qualified as a function, with a card sort on functions.
This relates to Standard 4 because I used appropriate literature to create a meaningful learning environment for students. My understanding of the mathematics content in this lesson allowed me to encourage students’ academic curiosity and modify instruction to make topics relevant to students’ lives. In addition, the card sort shows that I check for student understanding with review activities during lessons to assure mastery of the content. This evidence is important to me because it was a challenging lesson to put together. Writing questions that would help students make connections from the literature to the mathematics content took some time, but I was confident in the final product. In addition, anticipating student solutions for an open ended task such as this was not easy, but I think that my outline of possible solutions and what the teacher should be looking for shows that I understand how to keep the lesson focused on the mathematical content I am teaching. |