Background I am working from the New York State Teacher Certification Examinations (NYSTCE) standards, Field 005: Mathematics. This week, we will be discussing a topic from Competency 0005 - Geometry and Measurement. Within this Competency, I have chosen the following performance indicator: "Understands the Pythagorean theorem and its converse (including proofs) and applies the theorem to solve problems in two and three dimensions and in the coordinate plane." Here are the NY State Common Core Learning Standards for Mathematics which align with my selected topic: My goal is to provide students with an geometric proof of the Pythagorean Theorem. The theorem is often taught using algebra alone despite it being one of the most fundamental geometric theorems. To be clear, I have not invented this geometric proof, nor did I create the activity I am working through here. I first discovered it from Eddie Woo's video , though I imagine that he discovered the activity elsewhere. R...

Background I am working from the New York State Teacher Certification Examinations (NYSTCE) standards, Field 004: Mathematics. This week, we will be discussing a topic from Competency 0004 - Calculus. Within this Competency, I have chosen the following performance indicator: "applies techniques of differentiation and integration (e.g., product rule, chain rule, u-substitution)." There are no NY State Common Core Learning Standards for Mathematics which align with my selected topic. Regardless, I am choosing to focus on the "power rule." This is a common differentiation technique used in all calculus courses. My goal is to create an engaging activity for students to practice using the power rule. For reference, here is the power rule:

Background I am working from the New York State Teacher Certification Examinations (NYSTCE) standards, Field 004: Mathematics. This week, we will be discussing a topic from Competency 0003 - Functions. Within this Competency, I have chosen the following performance indicator: "analyzes arithmetic and geometric sequences both recursively and with an explicit formula, translates between the two forms, and uses them to model situations."  For simplicity, I will only focus on arithmetic sequences, though the activity can easily be modified to focus on geometric sequences as well. Here are the NY State Common Core Learning Standards for Mathematics which align with my selected topic: My goal is to design a creative activity which requires students to create their own arithmetic sequences rather than solving pre-written problems. It will be assumed that students already understand the basics of arithmetic sequences including the recursive and explicit formulas. This activity could ...

Background I am working from the New York State Teacher Certification Examinations (NYSTCE) standards, Field 004: Mathematics. This week, we will be discussing a topic from Competency 0002 - Algebra. Within this Competency, I have chosen the following performance indicator: "solves systems of linear and quadratic equations using a variety of methods."  More specifically, I will be focusing on the discriminant of the quadratic formula. Here are the NY State Common Core Learning Standards for Mathematics which align with my selected topic: My goal is to create an engaging activity for students to practice working with quadratic equations. More specifically, the activity will require students to work with the discriminant of the quadratic formula. It will be assumed that students already understand how to use the quadratic formula as well as how to calculate the discriminant of a quadratic equation. For reference, the discriminant is highlighted in orange below. For referenc...

Hello everyone! This is my first blog post, a very exciting time indeed. My name is Foster Harlfinger, and I am a 5th year student in Fordham's 5-year education program. Last year, I received my Bachelor's Degree in Math, and I will graduate with a Masters Degree in Teaching Adolescent Mathematics in Spring 2022. I am currently acting as a student teacher at West Bronx Academy for the Future in a 9th grade geometry class. I have not had any experience teaching in front of a classroom, but I worked as a one-on-one math tutor with an organization in the Bronx and as a homework grader for Fordham's math department for several years. My first official teaching year should begin in Fall 2022.