One of the aims of mathematics according to the CAPS document, is “deep conceptual understanding in order to make sense of mathematics”. What does deep conceptual understanding mean? A. Learners remember every step of the calculation methods and find the right answer B. Learners get very good marks in their tests and examination. C. Learners can make meaningful connections between different mathematical ideas D. Learners know when to use a rule to solve the problem

Deep conceptual understanding in mathematics means that learners grasp the underlying principles, relationships, and structures of mathematical ideas, rather than just memorizing procedures or facts. It involves understanding why mathematical concepts work and how they connect to other concepts.

Let's evaluate the options:

• A. Learners remember every step of the calculation methods and find the right answer: This describes procedural fluency, which is important, but not necessarily deep conceptual understanding. It focuses on how to do something, not why.
• B. Learners get very good marks in their tests and examination: Good marks can be achieved through various means, including rote learning, and do not inherently guarantee deep conceptual understanding.
• C. Learners can make meaningful connections between different mathematical ideas: This accurately describes deep conceptual understanding. It means understanding the relationships between concepts, seeing the bigger picture, and being able to apply knowledge flexibly in new situations.
• D. Learners know when to use a rule to solve the problem: This indicates some level of understanding and strategic competence, but it doesn't fully encompass the "deep" aspect, which involves understanding the underlying reasons for the rule and its connections to other mathematical ideas.

Therefore, the option that best describes deep conceptual understanding is C.

The correct option is C.
$\boxed{\text{C. Learners can make meaningful connections between different mathematical ideas}}$