*Philosophy of Teaching and Learning Mathematics*

*Philosophy of Teaching and Learning Mathematics*

There are two primary actions that take place in the classroom: the teaching of mathematics and the learning of mathematics. An effective teacher not only has effective teaching practices but also is also able to present the information so that students are continuously learning. Teaching math requires developing goals that will focus learning, being able collect and utilize evidence of student thinking, and promoting equity within the classroom. Learning math requires that the teacher implements appropriate tasks, poses meaningful questions, and allows for productive struggle. Teachers ultimately guide student learning.

Effective teachers develop goals that align with the common core to guide lesson planning. Clearly stated learning goals help students make connections between activities and the math within these activities. Goals help define the purpose of the lesson as well as pushes students towards progress.

Along with developing focused learning goals to guide lesson planning, teachers also need to take in consideration the work of the students when creating these lesson plans. Teachers should use student work as evidence of student learning. Useful evidence should require a high level of cognitive demand in which students need to explain, represent, and/or justify their understanding of mathematical concepts. It is important that teachers can identify where students are in the learning process, so they can build lessons that help students move on to the next level of critical thinking.

The tasks chosen for a lesson are of extreme importance when learning mathematics. These tasks should be motivating, promote reasoning and problem solving, and be of high cognitive demand. Tasks should be of some difficulty to students. If a student does not find the task to be struggling, then the student is not learning. At the first signs of struggle, teachers should support students rather than jump in to tell them the solution.

Here is where productive struggle becomes important in the learning process. First and foremost, I think it is important that the students understand it is ok to struggle and make mistakes. In order for a teacher to handle student struggle most efficiently, the teacher should anticipate where students would struggle. By anticipating the struggle, the teacher is able to come up with questions and techniques of handling the situation.

Meaningful discourse is a great way to correct misconceptions and help promote productive struggle. To help facilitate meaningful discourse, the teacher should asks questions that focus student thinking rather than funnel student thinking. Focusing student thinking allows the teacher to have insight to what the student is actually thinking rather than leading to a desired answer. Along with these focusing questions, the teacher should probe students to explain and clarify.

Developing learning goals, efficiently using student evidence to guide instruction, creating meaningful tasks, promoting productive struggle, and raising purposeful questions move students from having surface procedural knowledge to having conceptual knowledge and procedural fluency. Through these teaching practices, mathematics can be effectively taught and learned.

Effective teachers develop goals that align with the common core to guide lesson planning. Clearly stated learning goals help students make connections between activities and the math within these activities. Goals help define the purpose of the lesson as well as pushes students towards progress.

Along with developing focused learning goals to guide lesson planning, teachers also need to take in consideration the work of the students when creating these lesson plans. Teachers should use student work as evidence of student learning. Useful evidence should require a high level of cognitive demand in which students need to explain, represent, and/or justify their understanding of mathematical concepts. It is important that teachers can identify where students are in the learning process, so they can build lessons that help students move on to the next level of critical thinking.

The tasks chosen for a lesson are of extreme importance when learning mathematics. These tasks should be motivating, promote reasoning and problem solving, and be of high cognitive demand. Tasks should be of some difficulty to students. If a student does not find the task to be struggling, then the student is not learning. At the first signs of struggle, teachers should support students rather than jump in to tell them the solution.

Here is where productive struggle becomes important in the learning process. First and foremost, I think it is important that the students understand it is ok to struggle and make mistakes. In order for a teacher to handle student struggle most efficiently, the teacher should anticipate where students would struggle. By anticipating the struggle, the teacher is able to come up with questions and techniques of handling the situation.

Meaningful discourse is a great way to correct misconceptions and help promote productive struggle. To help facilitate meaningful discourse, the teacher should asks questions that focus student thinking rather than funnel student thinking. Focusing student thinking allows the teacher to have insight to what the student is actually thinking rather than leading to a desired answer. Along with these focusing questions, the teacher should probe students to explain and clarify.

Developing learning goals, efficiently using student evidence to guide instruction, creating meaningful tasks, promoting productive struggle, and raising purposeful questions move students from having surface procedural knowledge to having conceptual knowledge and procedural fluency. Through these teaching practices, mathematics can be effectively taught and learned.