> real world questions are asked for which they need to find a solution, and where they need to explain how they found it.
This could be fun if the questions are predictable enough, but typically in my own early education 'word problems' just ended up being computation problems with the single extra step of translating the question into one of a very small handful of known formulas.
> mathematical formulas are already taught to 7-8 year olds
That's great, but applying memorized formulas is still just computation.
> How can it be thought in a less boring way, i do not immediately see it.
Mathematics is the work mathematicians do. That work is fundamentally creative: it's about exploring, defining, and constructing abstract structures and conducted through writing. Mathematics as it's taught before college is typically presented almost exclusively as a mere instrument in service of engineering or the empirical sciences. This is like teaching physics purely as a parade of unexplained facts about past results and never giving students a chance to conduct experiments!
There should be way less emphasis on the notion of a single track of linear progress from arithmetic to calculus. Formulas should be derived by students rather than just presented to them for memorization. Formal logic should be introduced about as early as arithmetic; first-order logic certainly isn't any more complicated than addition and multiplication. Teachers should prove the principles they expect students to rely on. Mathematical topics which do not require great facility with engineering computations (e.g., calculus, linear algebra, trigonometry), like propositional logic, discrete math, and basic geometry, should be used as opportunities to get students reading and writing proofs for themselves in multiple mathematical contexts as early as possible.
The more students have a sense of the foundations of what they're learning, the more meaningful it can be to them. The more deeply they understand their formulae, the less memorization is required. And the sooner they engage with proofs, the sooner they have a chance to engage with mathematical as a creative and collaborative process.
This could be fun if the questions are predictable enough, but typically in my own early education 'word problems' just ended up being computation problems with the single extra step of translating the question into one of a very small handful of known formulas.
> mathematical formulas are already taught to 7-8 year olds
That's great, but applying memorized formulas is still just computation.
> How can it be thought in a less boring way, i do not immediately see it.
Mathematics is the work mathematicians do. That work is fundamentally creative: it's about exploring, defining, and constructing abstract structures and conducted through writing. Mathematics as it's taught before college is typically presented almost exclusively as a mere instrument in service of engineering or the empirical sciences. This is like teaching physics purely as a parade of unexplained facts about past results and never giving students a chance to conduct experiments!
There should be way less emphasis on the notion of a single track of linear progress from arithmetic to calculus. Formulas should be derived by students rather than just presented to them for memorization. Formal logic should be introduced about as early as arithmetic; first-order logic certainly isn't any more complicated than addition and multiplication. Teachers should prove the principles they expect students to rely on. Mathematical topics which do not require great facility with engineering computations (e.g., calculus, linear algebra, trigonometry), like propositional logic, discrete math, and basic geometry, should be used as opportunities to get students reading and writing proofs for themselves in multiple mathematical contexts as early as possible.
The more students have a sense of the foundations of what they're learning, the more meaningful it can be to them. The more deeply they understand their formulae, the less memorization is required. And the sooner they engage with proofs, the sooner they have a chance to engage with mathematical as a creative and collaborative process.