Lecture method may work very well for some subjects but not all the time in a Mathematics classes.
Engaging students by constantly asking them some questions is a nice method but only when the explanation and the questions are Mathematical. Reasoning and justifying are good habits of mind but they are only productive if they are based on mathematical theories.Creating a productive classroom discussion is probably the most difficult part of Mathematics teaching. I suggest five methods for moving beyond Lecture methods in teaching Mathematics.
I have always tried to practice these methods in my own teaching whether with students or with teachers and I have found them very useful
1. Predict the Pupils’ Responses of Mathematics
All the teachers should know about each and every student how he/she is going to react to the instructional tasks(s) that they are asked to work on.
Predicting students’ responses involves developing considerable expectations that what strategy will a certain student adopt to solve a particular problem. What mistakes he/she can do, what right steps he/she can take and how those strategies might get related to the Mathematical ideas, practices, and procedures, that the teacher would like his/ her pupils to know.
2.Observing Pupils’ Responses

Teachers should pay close attention to the Mathematical thinking in which the students are engaged as they work on a problem during the phase of exploration. This is usually done by roaming around the students in the classroom while they work. The goal of observing is to identify the Mathematical learning potential of the methods adopted by the students.
This way may quickly enable us to gauge that which student’s idea can be shared with the whole class during the discussion phase.
3. Intentionally Choosing Student’s Responses for Public Display

If the teacher has observed the class closely then he/she will be able to select a student to show his work. This way teacher can display a certain piece of Mathematical work. Generally, teachers call on specific students to show their work as the discussion proceeds. Or, a teacher might say”How many of you are done with it” and after this, select a particular student that he or she knows is one of several who has a right idea to share with the class.

4. Intentionally Sequencing Student Responses

After demonstrating one student’s work, the teacher can now decide about how to sequence other students’ presentations. By making right choices about the order of students’ work, a teacher can achieve his/her’s maximum academic goals. He/she can tell the students what to do, how to do and what mistakes can be avoided.

5. Bridging Student Responses  
Teachers can help students make bridges among the Mathematical ideas that are showing in the strategies and representations that they use.They can help students understand what concept they should apply, why they should apply and what are the results of using wrong methods. This way they can know about their possible errors and avoid them


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