demonstraatiohanteet

Demonstraatiohanteet is a term used in Finnish mathematics education to describe didactic devices that illustrate the structure and reasoning of mathematical proofs. The concept refers to cues, prompts, or exemplars that help learners understand how a proof proceeds, what assumptions are involved, and what conclusions follow from them.

Definition and forms: Demonstraatiohanteet can take several forms, such as partially worked proofs, lemmas, skeleton outlines of a proof, or carefully chosen examples that illuminate critical steps without giving away the entire argument. They are intended to make the logical flow more transparent and to highlight common inference patterns used in proofs.

Purpose and context: The aim is to support students in recognizing the structure of arguments, to reduce cognitive load, and to scaffold the transition from concrete cases to abstract reasoning. The use of demonstraatiohanteet is discussed in Finnish pedagogy and mathematics education literature, often within broader discussions of proof pedagogy and inquiry-based learning.

Considerations: While they can facilitate understanding, critics caution that too much scaffolding may impede independent reasoning or overemphasize specific proof routes. Effective use typically involves balancing guided demonstrations with opportunities for students to construct or critique arguments themselves.

See also: mathematical proof, pedagogy, scaffolding, worked example, proof by example.