Numbers, variables, and all the various mathematical operations are conceptual. That is, they exist and are carried out on an intellectual level. Critical thinking skills help a math teacher understand this conceptual relationship, and therefore aids in lectures and explanations. This is especially true when it comes to students who have trouble grasping mathematical concepts, as these students require more extensive explanations. Critical thinking skills also allow a math teacher to abstract from mathematical concepts, which helps when creating metaphoric explanations such as story problems.
Some types of math problems require extensive critical thinking to solve. In the cases such as word problems, students are often required to apply their mathematical knowledge to a real-world scenario. A math teacher must have developed critical thinking skills, both to create and successfully teach such critical thinking problems. Even if the problem requires relatively simple math operations, students who have trouble understanding mathematics on the conceptual level may need thorough critical explanations of how the math operations apply to the word scenario.
Critical thought must be utilized by teachers during interaction with students. Every student brings a different perspective to the classroom, which means each student learns in a different way. Critical thinking is necessary to fully explain some of the questions students may struggle with. Critical thinking skills help a teacher understand the student's perspective, which is very useful in explaining the concept in different ways so all students fully understand the material.
Most mathematical concepts require the practice of example problems to work with and fully understand the concept. Critical thinking skills help a math teacher come up with lecture material that explains the concepts in the simplest way possible. For example; a teacher may include real-world examples of the math concepts in action. Another method is to illustrate the concepts, such as with a drawing or diagram. All of these lecture materials require critical thought to create and teach successfully.