Mathematics is a subject which encompasses a variety of facts, theorems, procedures, and skills. The way in which they are presented has an immense effect on the way learners perceive mathematics. Teachers have the opportunity to introduce learners to the excitement, challenges, and wonder that mathematics has to offer through their lessons. While it is the responsibility of the teacher to adhere to district and statewide requirements for curriculum, they are also accountable for guiding the students to make connections, discoveries, and to further question their mathematical findings.
To fully understand and appropriately apply the content in mathematics, the course design must be filled with exploring, questioning, collaboration with peers, and discussion. In order for students to feel confident in executing these skills, a positive learning environment must be established. Students must feel encouraged to take risks, ask questions, make mistakes, and decide on the next course of action when their original path does not lead them to the expected answer. This inquisitive atmosphere will instill in students that the process of solving a problem is as important to their educational journey as the final answer.
Since the five strands of mathematical proficiency according to the National Research Council include conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition, there is no single instructional method that should be utilized in mathematics classroom. A variety of instructional models, such as direct instruction, cooperative learning, problem-based learning, and inquiry-based lessons, should be employed strategically in order to convey content in a way that will best reach the learners. Engaging activities that include real-world applications and technology should be included in the course in order to create a purpose for learning the content and help the students connect the mathematics to their own lives. Students should be given the opportunity, when appropriate, to construct knowledge on their own or with their peers through cooperative, project-based, and/or inquiry learning models. This approach to teaching and learning encourages a change in the traditional roles of both teacher and student. The student is accountable for their own learning journey and the teacher acts as a guide. This method allows the students to build on their prior knowledge and make connections to the content, both important for the level of retention of the new material. In mathematics, unlike most other courses, the learning is linear. The students must build upon prior knowledge in order to understand the new topics. Student-centered instruction in mathematics classrooms also allows for the differentiation of instruction to best serve the needs of all students. Students build off of their own prior knowledge, learn in the style that they prefer, and have the ability to learn at their own pace. With the guidance of the teacher, activities can be scaffolded to help each learner construct the necessary knowledge.
Since learning in mathematics depends on the understanding of the previous topics, assessment should be the driving force behind the instructional decisions that teachers makes for their students. Both formal and informal assessments should be utilized often in order to monitor student learning. This should occur through a variety of methods, such as observation, questioning, projects, presentations, portfolios, and formal tests and quizzes. Based on the data a teacher collects from the assessments, decisions can be made for future lessons.
Mathematics is an abstract language to students that include numbers, letters, and symbols. Students must be encouraged to communicate their mathematical ideas with the teacher and their peers. This sharing of ideas leads the students to learning language and material, building analytical and problem-solving skills, and achieving confidence in their mathematical abilities.
Due to the abstract nature of mathematics, the teachers of the subject must show excitement and enthusiasm for the field. As the expert in the classroom, a teacher must guide students to find the value in learning math. They must be flexible and creative in order to present the content to students in a way that will help them thrive.