Critical areas of mathematics for Czech pupils based on TIMSS 2007 data

Cílem empirické studie je popsat kritická místa matematiky základní školy, jak je lze vysledovat z výsledků našich žáků 8. ročníků v TIMSS 2007, a identifikovat pravděpodobné příčiny jejich obtížnosti. V první části je stručně uveden kontext výzkumu – mezinárodní srovnávací výzkumy v matematice a možnosti sekundární analýzy jejich dat. Ve druhé části podrobně popisujeme metodologii výzkumu. Analyzovali jsme data z tzv. almanachů TIMSS (výsledky našich žáků na úrovni konkrétních úloh a odpovědi učitelských dotazníků). K interpretaci možných příčin jsme používali také kurikulární dokumenty a analýzu zřejmě nejpoužívanější řady učebnic matematiky pro základní školy. Stanovili jsme kritérium, podle něhož je možné rozhodnout, zda je výkon našich žáků u dané úlohy pod jejich standardem, přičemž jsme vycházeli z porovnání jejich průměrné úspěšnosti s průměrnou úspěšností mezinárodního souboru. Tak byly identifikovány tzv. slabé a velmi slabé úlohy. Ty byly rozděleny do tří oblastí, které tedy můžeme považovat za místa, která jsou v matematice pro české žáky kritická: Algebra (s podoblastmi Funkce, Substituce, Rovnice a nerovnice, Výrazy), Posloupnosti, Obrazce a tělesa. U každé z těchto oblastí jsou prezentovány slabé a velmi slabé úlohy spolu s nástinem povahy obtíží, které při jejich řešení čeští žáci zřejmě měli, a jejich možných příčin. Ukazuje se, že je nutné získat ještě hlubší vhled do problematiky pomocí klinických rozhovorů přímo se žáky. To bude předmětem dalších článků. The goal of the empirical study is to describe critical areas of primary mathematics as can be found from the Czech Grade 8 pupils’ results in TIMSS 2007 and to identify possible causes of their difficulty for pupils. In the first part, a research background is briefly given – international comparative research in mathematics and possibilities of the secondary analyses of its data. The second part describes methodology in detail. We analysed data from so called TIMSS almanacs (results of Czech pupils at the level of concrete mathematical items from TIMSS and answers of the teacher questionnaire). To interpret possible causes we also used curricular documents and the analysis of the apparently most used primary mathematics textbooks. We set up a criterion for deciding whether the Czech pupils’ results for the given item is below their standard which we determined by comparing their average success rate with that of the international sample. Thus so called weak and very weak items were identified. They were divided into three areas which can be considered critical areas for Czech pupils: Algebra (with subareas of Functions, Substitution, Equations and inequalities, Expressions), Sequences, Shapes and solids. For each of the areas, weak and very weak items are presented together with their results and an outline of the nature of their difficulty for Czech pupils and possible causes of Czech pupils’ failure to solve them. It transpires that it is necessary to get a deeper insight into the nature of problems by clinical interviews with pupils. This will be a topic of further articles

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