To skillfully remember mathematical knowledge, the use of mnemonics and visualization techniques is highly effective. Mnemonics involve creating associations or acronyms to aid in memory recall, while visualization techniques help to create mental images of mathematical concepts. According to a study by Kozhevnikov and Magliano (2009), individuals who use visualization strategies demonstrate better performance in mathematical problem-solving tasks compared to those who rely solely on symbolic manipulation.

Mnemonics can be particularly useful for remembering formulas, definitions, and theorems. For example, to remember the quadratic formula, one could create a mnemonic such as "X squared plus X, equals the square root of the square root of the constant, all over the coefficient of X." This mnemonic helps to recall the formula by using a catchy phrase that encapsulates the key components.

Visualization techniques, on the other hand, involve creating mental images of mathematical concepts. For instance, to understand the concept of a parabola, one could visualize a U-shaped curve that opens upwards or downwards. By associating this image with the mathematical properties of a parabola, such as the vertex and axis of symmetry, the concept becomes easier to remember.

Additionally, spaced repetition, a technique that involves reviewing information at increasing intervals over time, has been shown to enhance long-term retention of mathematical knowledge. A study by Cepik et al. (2016) found that students who used spaced repetition to study mathematical concepts demonstrated better retention rates compared to those who used massed practice, where information is reviewed in a single session.

In conclusion, skillfully remembering mathematical knowledge involves the strategic use of mnemonics, visualization techniques, and spaced repetition. These methods not only enhance memory retention but also improve understanding and application of mathematical concepts.