Mathematical learning material:

A. helps teachers in demonstrating the formulae.

B. helps students in self-learning.

C. helps teachers in providing instructions.

D. develops learning environment in the class.

Choose the correct option:

The correct option is B and D.

Mathematical learning materials (such as manipulative objects, charts, geometry sets, and interactive aids) play a crucial role in modern student-centered pedagogy. Let us evaluate each statement to understand why options B and D form the correct combination:

Analysis of Statements:

Statement A: "helps teachers in demonstrating the formulae."
While learning materials can aid illustration, relying on materials strictly to demonstrate or memorize abstract mathematical formulas reflects a teacher-centric, rote-learning approach. Hence, this is not the primary learner-centered purpose of teaching-learning materials (TLMs).

Statement B: "helps students in self-learning."
Hands-on mathematical materials allow students to explore, experiment, discover concepts independently, and build concrete understandings of abstract mathematical ideas. Thus, TLMs directly support self-learning and learner autonomy.

Statement C: "helps teachers in providing instructions."
Using materials purely to issue instructions or deliver traditional lectures does not maximize the pedagogical value of TLMs. Mathematics education emphasizes active student engagement over passive reception of instructions.

Statement D: "develops learning environment in the class."
Interactive mathematical materials foster an engaging, rich, and collaborative classroom environment where students actively construct knowledge rather than remaining passive listeners.

Conclusion:

Since statements B (helps students in self-learning) and D (develops learning environment in the class) represent the true educational benefits of mathematical learning materials, the correct option is B and D.