Expository Teaching Methods in Math


Mathematics instruction, like other forms of educational teaching, has undergone significant changes in the early part of the 21st century. These changes have affected education levels from preschool to college and subjects as far ranging as art and physics. Though there has been a shift away from traditional education methods such as exposition to more student-led approaches such as constructivist learning, there is still an important place for the expository form of teaching in math education.

Paradigm Shift

  • Exposition, from the latin expositorius, means to explain. Just as the word suggests, this method involves telling or lecturing about math concepts. This traditional teaching methodology has been used for hundreds of years, but as long ago as the late 19th century, American philosopher John Dewey started questioning the success of lecture-style teaching and learning. In its place, he suggested a more pragmatic, hands-on learning approach. More than 100 years later, a paradigm shift has taken place in education, with many educators advocating for hands-on learning.

Expository Teaching

  • Using an expository teaching method, a teacher uses his knowledge to explain or tell about the subject or concept being learned. The teacher lectures, and the students listen and take notes as needed. A good expository teacher will have a firm grasp of the subject and an organized approach to revealing it in a logical sequence for the students. While this method might encourage a static classroom environment, it doesn't have to be that way. A good teacher will encourage questioning and stimulate discussion.


  • Many educational philosophers believe students learn metaphorically, which means they learn a new concept by understanding how it relates to something they already know. Proponents of expository methodology believe that learning is based on connecting new information with already learned concepts. Therefore, the teacher organizes and presents information in a sequence that begins with a foundation students already have.

    For example, students who are comfortable with addition can move on to understanding multiplication as repeat addition. Only after they understand it as repeat addition do they come to know what multiplication is. Similarly, an instructor must tie addition to counting before attempting to teach young children how to add two numbers. Because educators must connect new knowledge to old, an expository teacher needs to organize information tightly so as not to confuse students with extraneous information and must sequence carefully so that each new step builds upon the one presented before. Most importantly, leave time for questions. Students need time to resolve things they are confused about and teachers need this feedback to know whether students grasped the lesson before any measures of evaluation take place. Expository-based educators believe that students learn best by having information presented to them rather than trying to discover it for themselves.

Pros and Cons

  • Expository teaching is a time-efficient way to communicate knowledge. Because discovery takes time, presenting the information is a more efficient approach, and therefore, a teacher has more time to communicate more information to students. Because the teacher is the class expert in the subject, knowledge will be transmitted correctly. A teacher can listen to students during questions and discussion and adjust, reiterate or move forward as needed.

    On the other hand, there are some drawbacks to this approach. A poor or lazy teacher may let class become a one-sided communication. Many people have been in the unfortunate position of listening to a speaker drone on with little care or interest in student or audience feedback. Though this is not a good expository teaching method, it can happen. Because students are being told the lesson rather than participating in a hands-on way, learning may be more superficial, with students holding on to knowledge only long enough to perform successfully on any measures of evaluation.


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