We have always believed in the concept of “less is more, slow is fast.” This idea has been increasingly accepted in the field of mathematics education, and it is equally profound in the journey of teenagers learning C++ programming.
Many parents and students think that learning programming means quickly mastering all the syntax of C++ and then solving a large number of problems. This falls into the trap of “fast is slow.”
For example, when students learn about functions and recursion, if they only mechanically memorize templates without understanding the principles of the stack and recursive thinking, they will be at a loss when faced with complex recursive problems. At this point, slowing down and using a simple Fibonacci sequence or the Tower of Hanoi problem to let students truly experience the process of recursion is much more effective than rushing to the next knowledge point.
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Case 1: The “Fast” and “Slow” of Digit Separation The teacher quickly explained how to separate the digits of an integer using
<span>/10</span>and<span>%10</span>. The students understood, but when the problem changed to determining whether a number is a Narcissistic number, problems arose. The “fast” students might immediately start writing but forget that a temporary variable is needed in the loop to avoid altering the original number, which could lead to an infinite loop or incorrect results. In contrast, the “slow” students would first work through the process on paper, understanding why a temporary variable is necessary and the relationship between digit separation, loops, and conditional statements. This “slow” process enables them to quickly solve future problems involving digit sums and palindromic numbers. -
Case 2: The “Fast” and “Slow” of Prime Number Determination Students quickly learn to determine prime numbers by looping up to
<span>n-1</span>. This is very “fast.” However, when the problem’s data range increases, requiring the determination of many primes or a single very large number, the program becomes too slow to run due to inefficiency. If we had initially “slowed” down and not been satisfied with just “getting it done,” but instead guided students to think: Do we really need to loop to n-1? Can we optimize? Through exploration, they would discover that it is sufficient to loop up to<span>sqrt(n)</span>. This “slow” exploratory process not only solves a specific problem but also cultivates the core thinking of algorithm optimization, which is the true foundation for being “fast” in competitive programming. -
Case 3: The “Fast” and “Slow” of Palindrome Determination There are two mainstream approaches to determining palindromes: one is to convert to a string and use two pointers for comparison; the other is to separate the digits to construct the reverse number and compare it with the original number. “Fast” teaching might only cover one method, leading students to memorize it. However, when the problem changes to determining if a string is a palindrome or finding the closest palindromic prime, students who only remember one method may get stuck. “Slow” teaching would guide children to understand both methods, comparing their similarities, differences, and applicable scenarios. This “slow” thinking about the essence of the problem equips students with the ability to quickly adapt when facing new variations.
The “Three Talks and Three Not Talks” Principle
Three Talks:
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Talk about the essential understanding of core concepts
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Talk about the fundamental reasons for common mistakes
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Talk about the development of algorithmic thinking
Three Not Talks:
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Do not talk about things that students can understand by consulting materials
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Do not talk about advanced features that are not needed at this stage
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Do not talk about complex techniques that exceed students’ cognitive levels
From “Understanding” to “Application” Gap
In programming education, the biggest challenge is not whether the teacher can teach, but whether the students can convert “understanding” into “application”.
A typical example: students find bubble sort very simple when the teacher explains it, but when they try to write the code themselves, they encounter numerous bugs. At this point, it is necessary to slow down the pace, allowing students to debug hands-on, observing the changes in the array after each loop, and understanding the underlying ideas of the algorithm.
Currently, the trend in competitions and assessments is to emphasize skills over rote problem-solving, and the trend in problem design also confirms the idea that “slow is fast.” Competition problems increasingly focus on assessing students’:
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Reading comprehension skills — understanding complex problem descriptions
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Abstract modeling skills — transforming problems into computational models
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Algorithm design skills — not just memorizing algorithms
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Debugging and troubleshooting skills — one of the core abilities in programming
Students who rely on rote problem-solving and memorizing templates often perform poorly when faced with novel, on-the-spot analysis problems. In contrast, those with a solid foundation and critical thinking skills, even if they have solved fewer problems, can adapt effectively to changes.
So should we still practice problems? Yes, we should! However, we must recognize that: one problem with multiple solutions is better than ten problems with one solution: exploring multiple solutions to a single problem yields greater benefits than solving ten similar problems.
Conclusion
On the path of learning C++ programming and competitive programming, what we need is not a rush for success, but a steady and deep understanding. When students truly grasp the essence of each concept and cultivate the ability to think independently and solve problems quickly, their progress will exceed everyone’s expectations. Slow is for a more solid foundation; less is for a deeper understanding.