Svrha rada je dvostruka (1) prikaz manje poznatog razvojno-psihologijskog postupka mjerenja kvantitativno-relacijskog (K-R) prosuđivanja te njegovo psihometrijsko vrednovanje na hrvatskom uzorku djece i adolescenata, (2) testiranje hipoteza vezanih uz razvojne osobitosti K-R prosuđivanja, prvenstveno proizašlih iz Trirazinske teorije razvijajućeg uma A. Demetrioua i suradnika (Demetriou i Raftopoulos, 1999; Demetriou, Christou, Spanoudis, i Platsidou, 2002). Na uzorku od 420 učenika (197 ženskih) jedne osnovne škole i gimnazije Grada Zagreba (prosječno 84 učenika 2., 3., 5. i 7. razreda osnovne i 3. razreda srednje škole) primijenjena je papir-olovka baterija zadataka K-R prosuđivanja, sastavljena od tri vrste zadataka - omjerno prosuđivanje, aritmetika i algebra – podijeljenih u četiri razvojne razine. Metrijske osobine K-R baterije su vrlo dobre: (1) osjetljivost na cijelom uzorku sudionika je visoka jer prosječni indeks težine 35 zadataka iznosi 0,52 (s time da očekivano raste od najniže do najviše školske dobi), a Ferguson Δ iznosi 0,98; (2) pouzdanost izračunata na izvornim rezultatima je visoka (Cronbach α = 0,92, split-half = 0,95), dok je uz kontrolu varijance školske dobi dobra (Cronbach α = 0,73, split-half = 0,82); (3) Konstruktna valjanost je vrlo dobra (sa i bez kontrole varijance školske dobi dobivena je faktorska struktura koja odražava temeljne odrednice konstrukcije i primjene instrumenta – vrstu i razinu zadataka, te vrijeme primjene – i objašnjava 38 do 50% varijance rezultata), sadržajna valjanost visoka, a kriterijska prihvatljiva (korelacije s ocjenama iz matematike iznosi 0,45). Potvrđen je porast K-R prosuđivanja sa školskom dobi i opadanje rezultata s porastom razvojne razine zadataka, a razlike u rješivosti tri vrste zadataka u skladu su s očekivanjima (najprije se usvaja aritmetika, potom omjerno prosuđivanje i na kraju algebra). Spolne razlike nisu potvrđene, a svi interakcijski efekti spola, dobi i razvojne razine zadataka na Q-R prosuđivanje objašnjivi su teorijskim modelima kognitivnog razvoja i prethodnim istraživanjima.The objectives of the study were: (1) to give an overview of a less known developmental-psychological method of measuring quantitative-relational (Q-R) thought and it’s psychometric validation on a Croatian sample of children and adolescents; (2) to investigate hypotheses on developmental specificities of Q-R thought derived from a Three-level theory of the developing mind by A. Demetriou and colleagues (Demetriou i Raftopoulos, 1999; Demetriou et al., 2002). A pen-and-paper battery of Q-R thought tasks was administered on a sample of 420 children (197 females) in one elementary and one high school in Zagreb (84 pupils on average in 2nd, 3rd, 5th and 7th grade in elementary and 3rd grade of high school). The battery included three types of tasks – proportional reasoning, arithmetic and algebra - divided into four developmental levels. The psychometric properties of Q-R battery are very good: (1) discriminability on the whole sample is high since the average index of difficulty of 35 tasks is 0.52 (it increases as a function of school age as expected), and Ferguson’s Δ is 0,98; (2) reliability on original scores is high (Cronbach α = 0.92, split-half = 0.95), and when the variance of school age is controlled, the reliability is good (Cronbach α = 0.73, split-half = 0.82); (3) construct validity is very good (factor analysis, on raw data and data with the school age variance controlled, yields the structure that reflects basic determinants of construction and application of the instrument – type and developmental level of tasks and the time of completion – and accounts for 38% - 50% of the variance), content validity is high and criterion validity is acceptable (correlations with mathematic grades are 0.45). The increase of Q-R thought with school age and decrease of results with increased developmental level of tasks was confirmed. Moreover, differences in performance in three types of tasks were as expected – arithmetic is acquired first, then relational thinking and lastly algebra. Furthermore, the analysis showed no gender differences, while all interaction effects of gender, school age and developmental level of tasks on Q-R thought are explainable in terms of theoretical models of cognitive development and previous research in this field
