Answer to Question #116853 in Geometry for Pappu Kumar Gupta

Question

The ability to observe patterns and make a conjecture based on these patterns is an
important aspect of mathematical learning. Describe two distinct activities that would
help your students to develop this ability.

Answer 1

A conjecture is a mathematical process that involved identifying patterns, formulating claims. a conjecture is defined as a reasoned hypothesis has not yet been proved. Conjectures arise when one notices a pattern that holds for many cases.

The conjecturing problem-solving process involves observing a finite number of cases, analyzing the problem structures, examining cases, developing a conjecture about the solution, and then proving that conjecture is true.

The two distinct activities that would help students to develop the ability to conjecture are:

Communication 

A teacher should be able to communicate with the student in a comfortable manner. The teacher should Critically Observe each student to know their methods of apprehension to patterns and seeing connections.

the teacher can make the students understand more by giving a follow-up lesson and assignment

The act of critical reasoning of a pattern before jumping to a conclusion is required by all students.

Representation 

The teacher should be able to illustrate a pattern using different representations. There are different ways students can understand a pattern. The different ways of representation in school may include; oral and written, mathematical symbols, contexts, pictures, and Developing visual imagery.