Throughout my thematic unit, the chosen universal subject is Algebra. Because many subjects in mathematics correlate and interconnect among each other, the choice to select Algebra was both for the numerous and diverse pragmatic applications to real life situations and my personal high proficiency and comfortability with the subject.  As a teacher, it is vital to fully understand a subject that he or she is teaching to students. In the thematic unit, I chose lessons in which students will build connections with previous concepts to master novel mathematical ideas. For example, before students were taught how to multiply binomials using the “FOIL” method, they were taught the properties of exponents and steps to factor polynomials. Also, students can make connections in the lesson on solving radical equations by understanding previous topics such as properties of exponents and solving two step equations. This scope and sequence is fundamental in scaffolding, linking old and new ideas, and understanding mathematics.

 At times, the standards did not include these types of connections that are necessary for students to understand prior concepts to new ones, especially those that require remediation. Professional judgment from the teacher is required in making decisions on whether to add old concepts into the lesson plan in order to encourage students to make these connections or remediate these concepts in order to understand newer ideas. For example, the lesson on solving radical equations assumed that students understood the order of operations and certain mathematical terminology like coefficients, constants, etc. but the reality is that some students did not understand these concepts. It was my professional judgment as a pre-service teacher to include them in the lesson to satisfy student’s needs in the subject.

One of the concepts of learning through problem solving is the idea of creating a classroom where discussions and debates on mathematics is encouraged. One of the ways in doing so is to have students participate by working out problems on the board and having other students see if their answers are correct or if their mathematical logic was pointed in the right direction. This type of classroom is not engendered overnight. These lesson plans in the subject of Algebra are supposed to raise student’s mastery in logic, critical thinking, and understanding by linking previous concepts to new ideas. It encourages students to think outside the box by learning different solving methods and strategies during the classroom discussions. The fundamental idea of a teacher’s high expectations when creating lesson plans is to have students build their problem-solving skills with increasing difficulties as they progress from one lesson plan to the next.

This assignment has benefited me by demonstrating the im