--- title: "Meaning & Key Takeaway of: The presentation of mathematics in…" description: "\"The presentation of mathematics in schools should be psychological and not systematic. The teacher, so to speak, should be a diplomat. He must take acc..." image: "https://sms4smile.com/quotes/i/ff4/felix-klein-38045_abstract_the-presentation-of-mathematics-in-schoo_1939549.png" --- # The presentation of mathematics in schools should be… ![“The presentation of mathematics in schools should be psychological and not systematic. The teacher, so to speak, should be a diplomat. He must take account of the psychic processes in the boy in order to grip his interest, and he will succeed only if he presents things in a form intuitively…” quote by Felix Klein](https://sms4smile.com/quotes/i/ff4/felix-klein-38045_abstract_the-presentation-of-mathematics-in-schoo_1939549.png) [Download](https://sms4smile.com/quotes/i/ff4/felix-klein-38045_abstract_the-presentation-of-mathematics-in-schoo_1939549.png) [Open image](https://sms4smile.com/quotes/i/ff4/felix-klein-38045_abstract_the-presentation-of-mathematics-in-schoo_1939549.png) > “The presentation of mathematics in schools should be psychological and not systematic. The teacher, so to speak, should be a diplomat. He must take account of the psychic processes in the boy in order to grip his interest, and he will succeed only if he presents things in a form intuitively comprehensible. A more abstract presentation is only possible in the upper classes.” [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Mathematics teaching should be intuitive, considering students’ psychology, not purely systematic; abstract methods suit higher levels. **In simple terms:** Teach math intuitively, respecting student psychology; abstract later. Key Takeaway Adapt teaching to learners’ mental processes. Themes education psychology pedagogy Mood thoughtful instructive Type pedagogical philosophical When to use this quote - classroom instruction - teacher training - curriculum reform - student mentorship Key Concepts cognitive development curriculum design Questions to Reflect On - How can teachers balance intuition and rigor? - When is abstraction appropriate? A Different Perspective May limit exposure to formal rigor early on. ★ ★ ★ ★ ★ No ratings yet [Abstract](https://sms4smile.com/quotes/about/abstract/) [Boys](https://sms4smile.com/quotes/about/boys/) [Class](https://sms4smile.com/quotes/about/class/) [Diplomats](https://sms4smile.com/quotes/about/diplomats/) [Education](https://sms4smile.com/quotes/about/education/) [Interest](https://sms4smile.com/quotes/about/interest/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Order](https://sms4smile.com/quotes/about/order/) [Presentation](https://sms4smile.com/quotes/about/presentation/) [Process](https://sms4smile.com/quotes/about/process/) [Psychics](https://sms4smile.com/quotes/about/psychics/) [Psychological](https://sms4smile.com/quotes/about/psychological/) [School](https://sms4smile.com/quotes/about/school/) [Teacher](https://sms4smile.com/quotes/about/teacher/) [Upper class](https://sms4smile.com/quotes/about/upper-class/) ## Related quotes > [I have a class prejudice - against the upper class, which is foolish.](https://sms4smile.com/quotes/miriam-margolyes/i-have-a-class-prejudice-against-the-upper-class-which-is-foolish/) [Miriam Margolyes](https://sms4smile.com/quotes/author/miriam-margolyes/) > [So often in English fiction, people are either upper-class twits, or else they're knockabouts, less than human.](https://sms4smile.com/quotes/justin-cartwright/so-often-in-english-fiction-people-are-either-upper-class-twits-or/) [Justin Cartwright](https://sms4smile.com/quotes/author/justin-cartwright/) > [The piano is just a different animal. It's expensive, it's big, it's heavy, and it doesn't fit in the mix easily. Everyone grew up…](https://sms4smile.com/quotes/ben-folds/the-piano-is-just-a-different-animal-it-s-expensive-it-s-big-it-s/) [Ben Folds](https://sms4smile.com/quotes/author/ben-folds/) > [I grew up in a wealthy upper-class household in Jamaica, which was run along militaristic lines by my mother, Gloria.](https://sms4smile.com/quotes/lady-colin-campbell/i-grew-up-in-a-wealthy-upper-class-household-in-jamaica-which-was-run/) [Lady Colin Campbell](https://sms4smile.com/quotes/author/lady-colin-campbell/) > [When I first left drama school, I was too posh for the working-class parts and not posh enough for the upper-class roles. You know…](https://sms4smile.com/quotes/ben-chaplin/when-i-first-left-drama-school-i-was-too-posh-for-the-working-class/) [Ben Chaplin](https://sms4smile.com/quotes/author/ben-chaplin/) > [There were a lot of upper-class or royal roles and I felt like I was always searching for other stuff.](https://sms4smile.com/quotes/harris-dickinson/there-were-a-lot-of-upper-class-or-royal-roles-and-i-felt-like-i-was/) [Harris Dickinson](https://sms4smile.com/quotes/author/harris-dickinson/) > [I'm interested in illuminating the enormous disparity between vast poverty and the tiny upper class... This vast inequity is unfair by definition, and I…](https://sms4smile.com/quotes/nick-mcdonell/i-m-interested-in-illuminating-the-enormous-disparity-between-vast/) [Nick McDonell](https://sms4smile.com/quotes/author/nick-mcdonell/) > [In the United States, the working class are Democrats. The middle class are Republicans. The upper class are Communists.](https://sms4smile.com/quotes/whittaker-chambers/in-the-united-states-the-working-class-are-democrats-the-middle-class/) [Whittaker Chambers](https://sms4smile.com/quotes/author/whittaker-chambers/) > [And that's where I think vulnerability comes in - the fact that we're figuring out that there is strength in actually being vulnerable to…](https://sms4smile.com/quotes/rege-jean-page/and-that-s-where-i-think-vulnerability-comes-in-the-fact-that-we-re/) [Rege-Jean Page](https://sms4smile.com/quotes/author/rege-jean-page/) > [I was born in Paris in 1950. I had a strict upper-class Catholic education but I never really fitted in the system and revolted…](https://sms4smile.com/quotes/francois-gautier/i-was-born-in-paris-in-1950-i-had-a-strict-upper-class-catholic/) [Francois Gautier](https://sms4smile.com/quotes/author/francois-gautier/) > [“We spend to pretend that we’re upper-class. And when the dust clears—when bankruptcy hits or a family member bails us out of our stupidity—there’s…](https://sms4smile.com/quotes/j-d-vance/we-spend-to-pretend-that-we-re-upper-class-and-when-the-dust-clears/) [J.D. Vance](https://sms4smile.com/quotes/author/j-d-vance/) > [Tomorrow everybody - or practically everybody - will have had the education of the upper class of yesterday, and will expect equivalent opportunities. That…](https://sms4smile.com/quotes/peter-drucker/tomorrow-everybody-or-practically-everybody-will-have-had-the/) [Peter Drucker](https://sms4smile.com/quotes/author/peter-drucker/) > [How shall we ever know if it's morning if there's no servant to pull up the blinds?](https://sms4smile.com/quotes/james-m-barrie/how-shall-we-ever-know-if-it-s-morning-if-there-s-no-servant-to-pull/) [James M. Barrie](https://sms4smile.com/quotes/author/james-m-barrie/) > [The American middle class always wants to be upper class and is scared to death of being lower class. It's a highly mobile group…](https://sms4smile.com/quotes/sloan-wilson/the-american-middle-class-always-wants-to-be-upper-class-and-is/) [Sloan Wilson](https://sms4smile.com/quotes/author/sloan-wilson/) > [While some multimillionaires started in poverty, most did not. A study of the origins of 303 textile, railroad and steel executives of the 1870s…](https://sms4smile.com/quotes/howard-zinn/while-some-multimillionaires-started-in-poverty-most-did-not-a-study/) [Howard Zinn](https://sms4smile.com/quotes/author/howard-zinn/) ## More by Felix Klein > [Every one who understands the subject will agree that even the basis on which the scientific explanation of nature rests is intelligible only to…](https://sms4smile.com/quotes/felix-klein/every-one-who-understands-the-subject-will-agree-that-even-the-basis/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) > [It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations.](https://sms4smile.com/quotes/felix-klein/it-is-well-known-that-the-central-problem-of-the-whole-of-modern/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) > [Mathematics in general is fundamentally the science of self-evident things.](https://sms4smile.com/quotes/felix-klein/mathematics-in-general-is-fundamentally-the-science-of-self-evident/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) > [The developing science departs at the same time more and more from its original scope and purpose and threatens to sacrifice its earlier unity…](https://sms4smile.com/quotes/felix-klein/the-developing-science-departs-at-the-same-time-more-and-more-from/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) > [The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal…](https://sms4smile.com/quotes/felix-klein/the-teacher-manages-to-get-along-still-with-the-cumbersome-algebraic/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) > [Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions.](https://sms4smile.com/quotes/felix-klein/everyone-knows-what-a-curve-is-until-he-has-studied-enough/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) > [Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.](https://sms4smile.com/quotes/felix-klein/thus-in-a-sense-mathematics-has-been-most-advanced-by-those-who/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) > [Regarding the fundamental investigations of mathematics, there is no final ending ... no first beginning.](https://sms4smile.com/quotes/felix-klein/regarding-the-fundamental-investigations-of-mathematics-there-is-no/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) > [Projective geometry has opened up for us with the greatest facility new territories in our science, and has rightly been called the royal road…](https://sms4smile.com/quotes/felix-klein/projective-geometry-has-opened-up-for-us-with-the-greatest-facility/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) > [The greatest mathematicians, as Archimedes, Newton, and Gauss, always united theory and applications in equal measure.](https://sms4smile.com/quotes/felix-klein/the-greatest-mathematicians-as-archimedes-newton-and-gauss-always/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) > [Among mathematicians in general, three main categories may be distinguished; and perhaps the names logicians, formalists, and intuitionists may serve to characterize them.](https://sms4smile.com/quotes/felix-klein/among-mathematicians-in-general-three-main-categories-may-be/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) [Explore all 12 Felix Klein quotes ](https://sms4smile.com/quotes/author/felix-klein/) ## More Abstract quotes > [Love is like that, fragile and light. No wonder it rests upon our hearts in intangible moments, bids us follow fleeting thoughts and ideas…](https://sms4smile.com/quotes/anonymous/love-is-like-that-fragile-and-light-no-wonder-it-rests-upon-our/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [Wisdom is the abstract of the past, but beauty is the promise of the future.](https://sms4smile.com/quotes/anonymous/wisdom-is-the-abstract-of-the-past-but-beauty-is-the-promise-of-the/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [Where human eyes have never seen, where human beings have never been, I build a world of abstract dreams, and I wait for you.](https://sms4smile.com/quotes/sun-ra/where-human-eyes-have-never-seen-where-human-beings-have-never-been-i/) [Sun Ra](https://sms4smile.com/quotes/author/sun-ra/) > [A little too abstract, a little too wise, It is time for us to kiss the earth again, It is time to let the…](https://sms4smile.com/quotes/robinson-jeffers/a-little-too-abstract-a-little-too-wise-it-is-time-for-us-to-kiss-the/) [Robinson Jeffers](https://sms4smile.com/quotes/author/robinson-jeffers/) > [“Happy is very abstract, you can't touch it.”](https://sms4smile.com/quotes/julius-veal/happy-is-very-abstract-you-can-t-touch-it/) [Julius Veal](https://sms4smile.com/quotes/author/julius-veal/) > [Abstract Expressionism was invented by New York drunks.](https://sms4smile.com/quotes/joni-mitchell/abstract-expressionism-was-invented-by-new-york-drunks/) [Joni Mitchell](https://sms4smile.com/quotes/author/joni-mitchell/) > [The more horrible this world (as today, for instance), the more abstract our art, whereas a happy world brings forth an art of the…](https://sms4smile.com/quotes/paul-klee/the-more-horrible-this-world-as-today-for-instance-the-more-abstract/) [Paul Klee](https://sms4smile.com/quotes/author/paul-klee/) > [Describing comic sensibility is near impossible. It's sort of an abstract silliness, that sometimes the joke isn't the star.](https://sms4smile.com/quotes/dana-carvey/describing-comic-sensibility-is-near-impossible-it-s-sort-of-an/) [Dana Carvey](https://sms4smile.com/quotes/author/dana-carvey/) > [For people of color - especially African Americans - the idea that racist cops might frame members of their community is no abstract notion,…](https://sms4smile.com/quotes/tim-wise/for-people-of-color-especially-african-americans-the-idea-that-racist/) [Tim Wise](https://sms4smile.com/quotes/author/tim-wise/) > [The word of the Lord never comes to us as an opinion, no attempt is made to support it by argument, it comes as…](https://sms4smile.com/quotes/anthony-w-ivins/the-word-of-the-lord-never-comes-to-us-as-an-opinion-no-attempt-is/) Anthony W. Ivins > [A mobile is an abstract sculpture made chiefly out of sheet metal, steel rods, wire and wood. Some or all of these elements move,…](https://sms4smile.com/quotes/alexander-calder/a-mobile-is-an-abstract-sculpture-made-chiefly-out-of-sheet-metal/) [Alexander Calder](https://sms4smile.com/quotes/author/alexander-calder/) > [I'm this superphilosophical kind of person. Stuck in a prison of abstract ideas and overpowering emotions, I have this personality that makes it really…](https://sms4smile.com/quotes/natsuo-kirino/i-m-this-superphilosophical-kind-of-person-stuck-in-a-prison-of/) [Natsuo Kirino](https://sms4smile.com/quotes/author/natsuo-kirino/) > [Future lawyers should be more aware that law is not a system of abstract logic, but the web of arrangements, rooted in history but…](https://sms4smile.com/quotes/felix-frankfurter/future-lawyers-should-be-more-aware-that-law-is-not-a-system-of/) [Felix Frankfurter](https://sms4smile.com/quotes/author/felix-frankfurter/) > [The trouble is that when you read criticisms about the other films that I've made you get the impression that they're all about themes,…](https://sms4smile.com/quotes/michael-haneke/the-trouble-is-that-when-you-read-criticisms-about-the-other-films/) [Michael Haneke](https://sms4smile.com/quotes/author/michael-haneke/) > [Painting is... a richer language than words... Painting operates through signs which are not abstract and incorporeal like words. The signs of painting are…](https://sms4smile.com/quotes/jean-dubuffet/painting-is-a-richer-language-than-words-painting-operates-through/) [Jean Dubuffet](https://sms4smile.com/quotes/author/jean-dubuffet/) [Browse all 1,403 Abstract quotes ](https://sms4smile.com/quotes/about/abstract/) ```json { "@context": "https://schema.org", "@graph": [ { "@type": "Quotation", "text": "The presentation of mathematics in schools should be psychological and not systematic. The teacher, so to speak, should be a diplomat. He must take account of the psychic processes in the boy in order to grip his interest, and he will succeed only if he presents things in a form intuitively comprehensible. 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