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A basic question is whether "learning by heart" is helpful for learning math.
Do we not want to understand rather than just recite? My own experience is to see students who know how to remember things, do better also in problem solving. I myself can do math better in areas, where I have learnt it by heart. The mantra in math education has been for decades that "learning by heart is bad". I recommend students to ignore this dogma but not tell the teachers ... Again, why do I think that memory is important? Because I believe in knowledge and more importantly about techniques, which includes ways to think, ways to work, ways to solve problems, ways to ask questions etc. This is all knowledge. Without knowledge, problem solving is very hard. Knowledge is the soil on which new ideas can flourish. Here are some earlier writings addressing this:
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Mathematics Far from Pointless: Memorization Facilitates Problem SolvingTranslated automatically:Some people love it, others hate it: memorization. It can be helpful for both groups - when used correctly. The small multiplication table, the large multiplication table: memorization is disliked and considered outdated. But even in modern education, it still has value, as a new study shows. 7 times 6 is 42. 7 times 7 is 49. 7 times 8 is 56... Still remember it? Many people stop at the large multiplication table - some even stumble over the small one. Unlike in the past, these number sequences are no longer taken for granted as basic knowledge, even though they are still drilled in elementary school. Memorization is not only unpopular; it is literally seen as "old school." Shouldn't memorization be replaced by a deeper, conceptual engagement with mathematics? And aren't multiplication tables redundant in an age of calculator apps? A research team from several U.S. Universities has re-examined these questions. Their findings, drawn from cognitive development research, have been published in the journal Psychological Science in the Public Interest. The study, titled "What the Science of Learning Teaches Us About Arithmetic Fluency," [PDF] aims to show how children"s arithmetic skills can be best supported. Arithmetic fluency is generally defined as the ability to solve mathematical problems quickly and accurately. The researchers propose an expanded definition of fluency that includes not just the automatic recall of facts like 6 * 8 = 48, but also the recognition and use of numerical relationships to solve problems. Parents can influence their children's cognitive development much more than many realize. But the educational zeal of some mothers and fathers often does more harm than good. What truly matters in developing a child"s intellect"and why it"s so important to support their interests and hobbies. Nevertheless, the researchers do not argue against memorization"on the contrary: it is an important part of the learning process. Those who have automated certain arithmetic procedures and facts can better focus on the underlying concepts and thus develop a deeper understanding of mathematics. The researchers advocate for an evidence-based cycle in the classroom through which children can learn most effectively: First, present the facts (e.g., the multiplication table), along with a conceptual foundation. Then, a short phase of practice, including memorization, helps internalize the facts. Finally, students should return to discussion and reflect on what they've learned to deepen their understanding. "We want to make clear: educators do not have to choose between brief practice sessions and in-depth classroom discussions," says lead author Nicole McNeil. Short exercises reinforce facts in memory. Discussions help integrate those facts into a broader knowledge network. This combination gives children the fluency they need to succeed. |