InTasc #4
The teacher understands the central concepts, tools of inquiry, and structures of mathematics and creates learning experiences that make these aspects of mathematics accessible and meaningful for learners to assure mastery of the content.
Number Talk - Isosceles Triangles (Key Questions)
Number talks are short, 5–10-minute tasks that involve a problem posed to students meant to elicit specific strategies and to get students to explain their reasoning. These problems typically have more than one correct answer or more than one solution method and require the use of mental math rather than pencil and paper. This number talk asked students to find possible side lengths for an isosceles triangle given the total perimeter. It called on their knowledge of isosceles triangles, perimeter, and mental math and reasoning skills. The highlighted section is the key questions used to connect the students’ strategies to prior knowledge and learning targets and to get students to a deeper understanding of their and their classmates’ solutions.
This artifact demonstrates how teachers can create learning experiences that make math accessible and meaningful to assure mastery of the content. Rather than explicitly teaching the procedure, the question is posed to the class, and students must construct their own strategy and apply it to the problem, making the task a more meaningful experience. The key questions make the math more accessible by making their thinking visible to the rest of the class and helping them to think about their own reasoning. Students that had difficulty with the problem can hear how others made sense of it and learn from each other. This helps to ensure mastery from the whole class rather than just a handful that share the responses.
These types of activities are some of the most interesting for me as a math teacher. Getting to see how students make sense of a new problem, communicate their ideas, and build off each other gives me an opportunity to assess students on the process standards of problem solving, reasoning, and communication. Students often have new ways of thinking about the problems that I had not anticipated or spark entirely new discussions. In this number talk, one student proposed the idea that all three sides could have the same length which led to a lengthy and fascinating discussion of whether that met the conditions of the problem.
Praxis 5165 Score Report
The Praxis 5165 is the content knowledge exam for secondary math teachers. It is designed to measure competency for teaching math courses ranging from middle school to advanced high school courses, including calculus. This means assessing both mathematical and pedagogical knowledge and skills. The report shows a score of 197 out of 200, well above the qualifying score of 159, demonstrating a high level of content knowledge.
A score of 197 out of 200 shows that a teacher understands the central concepts and structures of mathematics. This score is well above the average range of 150 to 184. The score breakdown in section 3 shows high marks in each category meaning content knowledge preparedness to teach at all levels of secondary math.
The score exemplifies the time and effort put into my B.S. in mathematics. This included courses in Math for Secondary Teachers I and II which went further in depth into secondary math concepts and pedagogy. While I have been in an M.A.Ed. program for just under a year, I have spent much longer preparing to be the best math teacher I can be and this exam serves as confirmation of my content mastery.
Professional Practice Reflection
This reflection was an assignment in Teaching in Middle and Secondary Schools I to create an annotated bibliography on a specific topic in math education. I chose to focus on instruction for English language learners (ELL) in the math classroom. Three articles were selected, synthesized, and evaluated for their value to teaching. The articles describe strategies and frameworks for direct literacy instruction and designing tasks to support ELLs’ mathematics and language development.
This reflection demonstrates understanding of creating learning experiences that make math accessible and meaningful to assure mastery through willingness to learn new strategies and to take on the dual role as teachers of both mathematics and language. Through connecting new mathematical concepts and skills to prior knowledge in students’ native language as discussed in the artifact, the content becomes more meaningful and accessible. Doing so helps to ensure mastery for students learning math in a second language.
Classrooms across the country have become more linguistically diverse than ever and pre-service teachers should be prepared to meet the needs of the wide range of English proficiency they may encounter. ELLs are often placed in general education classrooms taught entirely in English before their language proficiency has reached a level comparable to that of their native speaking peers. Even ELLs with higher proficiency might have more difficulty with reading and writing and still need to constantly transfer knowledge back and forth between different linguistic and cultural contexts. Having strategies and frameworks in place helps to ease transfer of knowledge and development of language.