Pedagogy

Improving language competencies involves developing skills in reading, writing, listening, and speaking.
- Competitive exams: Primarily for assessment, not a direct tool for effective utilization by a teacher to improve competencies on a daily basis, though they can motivate.
- Laboratory: Typically associated with science subjects for experiments, not directly for language competency development, unless it's a language lab (which is a specialized form of resource).
- Play ground: Important for physical development and social skills, can offer informal language use, but not a structured resource a teacher "utilizes effectively" for targeted language competency improvement.
- Library: A library is a rich resource of books, magazines, and other reading materials.
Effective utilization of a library by a teacher involves encouraging reading habits, providing access to diverse texts, storytelling sessions, book discussions, etc.
These activities directly contribute to vocabulary building, comprehension, an understanding of grammar and sentence structure, and fostering a love for language.
Therefore, a library is the most suitable resource among the options for a teacher to utilize effectively to improve language competencies of children.

The question asks for a strategy to make children solve mathematics problems "firstly," implying foundational or initial approaches to build confidence and understanding before moving to more complex written problems.
- (1) working problems: This refers to solving written problems, which is usually a later stage after foundational understanding is built.
- (2) oral maths: Engaging in oral mathematics (mental math, verbal problem-solving, quick recall of facts) helps build number sense, quick thinking, and understanding of basic operations without the immediate pressure of written calculations.
It can make mathematics more accessible and less intimidating initially.
- (3) reading tables: Memorizing and reciting multiplication tables is a part of mathematical skills, but "reading tables" by itself might not be the primary strategy to start solving problems.
It's a tool.
- (4) dictation: While math problem dictation can be an activity, it's more about transcribing than the initial engagement with problem-solving concepts.
Oral maths (mental math, verbal problem solving) is an excellent strategy to introduce children to mathematical problem-solving.
It helps them to think about numbers and operations in a flexible way, builds confidence, and prepares them for more formal written problem-solving.
It can make the initial engagement with mathematics more interactive and less dependent on just written skills.
If "firstly" means the very first approach to math, oral math is often highly recommended.