“Craindre l’erreur et craindre la vérité est une seule et même chose. Celui qui craint de se tromper est impuissant à découvrir. C’est quand nous craignons de nous tromper que l’erreur qui est en nous se fait immuable comme un roc. Car dans notre peur, nous nous accrochons à ce que nous avons décrété “vrai” un jour, ou à ce qui depuis toujours nous a été présenté comme tel. Quand nous sommes mus, non par la peur de voir s’évanouir une illusoire sécurité, mais par une soif de connaître, alors l’erreur, comme la souffrance ou la tristesse, nous traverse sans se figer jamais, et la trace de son passage est une connaissance renouvelée.”
RÉCOLTES ET SEMAILLES
Réflexions et témoignage sur un passé de mathématicien
par Alexandre GROTHENDIECK
Fatuité et Renouvellement
2. Erreur et découverte
https://webusers.imj-prg.fr/~leila.schneps/grothendieckcircle/RetSbis.pdf#I2
“Fear of error and fear of truth are one and the same thing. He who fears error is powerless to discover. It’s when we fear being wrong that the error within us becomes immovable as a rock. For in our fear, we cling to what we once thought “true”, or to what has always been presented to us as true. When we are moved, not by the fear of seeing an illusory security vanish, but by a thirst for knowledge, then error, like suffering or sadness, passes through us without ever becoming fixed, and the trace of its passage is renewed knowledge.”
HARVESTS AND SOWINGS
The life of a mathematician
Reflections and bearing witness
by Alexandre GROTHENDIECK
https://ps.ucw.cz/grothendieck/deepl/d_1_part1.pdf
“Récoltes et Semailles” (“Reapings and Sowings”) is an autobiographical and philosophical work by the renowned mathematician Alexander Grothendieck. Written in the 1980s, it serves as a deeply introspective and critical reflection on his life, work, and the world of mathematics. The book is divided into several parts, combining personal anecdotes, critiques of the mathematical community, and explorations of broader philosophical and spiritual themes…
https://rlchapman.com/content/ai008.asp
Alexander Grothendieck, later Alexandre Grothendieck in French, 28 March 1928 – 13 November 2014), was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory, and category theory to its foundations, while his so-called “relative” perspective led to revolutionary advances in many areas of pure mathematics. He is considered by many to be the greatest mathematician of the twentieth century.
https://en.m.wikipedia.org/wiki/Alexander_Grothendieck
Although error avoidance during learning appears to be the rule in American classrooms, laboratory studies suggest that it may be a counterproductive strategy, at least for neurologically typical students. Experimental investigations indicate that errorful learning followed by corrective feedback is beneficial to learning. Interestingly, the beneficial effects are particularly salient when individuals strongly believe that their error is correct: Errors committed with high confidence are corrected more readily than low-confidence errors. Corrective feedback, including analysis of the reasoning leading up to the mistake, is crucial. Aside from the direct benefit to learners, teachers gain valuable information from errors, and error tolerance encourages students’ active, exploratory, generative engagement. If the goal is optimal performance in high-stakes situations, it may be worthwhile to allow and even encourage students to commit and correct errors while they are in low-stakes learning situations rather than to assiduously avoid errors at all costs.
An unwarranted reluctance to engage with errors may have held back American education. The behavioral and neurological data reviewed here indicate that, as long as one is not amnesic, making errors can greatly facilitate new learning. Errors enhance later memory for and generation of the correct responses, facilitate active learning, stimulate the learner to direct attention appropriately, and inform the teacher of where to focus teaching. The concern that errors might evoke dysfunctional emotional reactions appears to be exaggerated. Of course, sensitive handling of errors and avoiding gratuitous punishments—verbal or otherwise—is essential. The research reviewed here suggests that teachers and learners alike should be encouraged to be open to mistakes and to actively use them in becoming prepared for the test that counts.
Success Is Failure Inside Out!
Think like a mathematician and learn from your previous mistakes. In order to do so, I would suggest that you keep a record or journal of the patterns of errors. Mathematics requires a lot of practice, review the concepts that caused you grief from previous tests. Keep all of your marked test papers, this will assist you to prepare for ongoing summative tests. Diagnose problems immediately! When you are struggling with a specific concept, don’t wait to get assistance (that’s like going to the doctor three days after breaking your arm) get immediate help when you need it, if your tutor or instructor isn’t available - take the initiative and go online, post to forums or look for interactive tutorials to guide you through.
Remember, problems can be your friends!
https://www.thoughtco.com/learning-from-math-mistakes-2312578
Myths and Misconceptions
None of the following is true!
- You’re born with a math gene, either you get it or you don’t.
- Math is for males, females never get math!
- It’s hopeless, and much too hard for average people.
- If the logical side of your brain isn’t your strength, you’ll never do well in math.
- Math is a cultural thing, my culture never got it!
- There’s only one right way to do math.