Characters of Feigin-Stoyanovsky's type subspaces of level one modules for affine Lie algebras of types Aℓ(1)A_\ell^{(1)} and D4(1)D_4^{(1)}

We use combinatorial description of bases of Feigin-Stoyanovsky's type subspaces of standard modules of level 1 for affine Lie algebras of types $A_\ell^{(1)}$ and $D_4^{(1)}$ to obtain character formulas. These descriptions naturally lead to systems of recurrence relations for which we also find solutions

Presentations of Feigin-Stoyanovsky\u27s type subspaces of standard modules for affine Lie algebras of type (C_l^{(1)})

Feigin-Stoyanovsky\u27s type subspace (W(Λ)) of a standard g-module (L(Λ)) is a (g_1)-submodule of (L(Λ)) generated by the highest-weight vector (v_Λ), where (g_1) is a certain commutative subalgebra of (g). Based on the description of basis of (W(Λ)) for of type (C_l^{(1)}), we give a presentation of this subspace in terms of generators and relations (W(Λ)≃ U(g_1^-)/J)

Particle basis of Feigin-Stoyanovsky\u27s type subspaces of level one tildemathfrakslell+1(C)tilde{mathfrak{sl}}_{ell+1}(C)-modules

We construct particle basis for Feigin-Stoyanovsky\u27s type subspaces of level $1$ standard $tilde{mathfrak{sl}}_{ell+1}(C)$-modules. From the description we obtain character formulas

Ciljevi postignuća u matematici budućih osnovnoškolskih učitelja i njihov pristup učenju i poučavanju matematike

In Croatia, as in many other countries, primary education teachers are trained as generalists and mathematics is only one of several different subjects that they teach, so when choosing their profession they are not necessarily drawn by their interest in becoming a mathematics teacher. Still, it is very important that they have a positive attitude towards mathematics and are motivated to teach it to their students. The aim of this study was to explore whether pre-service teachers with different achievement goal profiles have different beliefs about mathematics and teaching and learning mathematics. The participants were 325 pre-service primary education students. The research was conducted in three waves, during the students’ first, third and fifth year of study. In their first year of studies, we collected data on the achievement goals in mathematics that they had in high school, and selfefficacy in mathematics. Epistemic beliefs, subjective value of mathematics and mathematics anxiety were assessed at all measurement points. In their third and fifth year of study, we also collected data on the participants’ mathematics teaching efficacy beliefs and, in their fifth year, beliefs on teaching and learning mathematics. The results of the cluster analysis showed that we could group pre-service primary education teachers into three groups according to the profiles of their achievement goals in high school: (1) all goals high, (2) all goals low, (3) mastery orientation. The results showed differences between the groups in terms of motivation for learning mathematics at the beginning of their studies. However, these differences tend to be less prominent over time. At the end of their studies, they do not differ in their mathematics teaching efficacy beliefs or their beliefs about teaching and learning mathematics.U Hrvatskoj, kao i u mnogim drugim zemljama, osnovnoškolski učitelji korisnici su generaliziranoga obrazovanja i Matematika je samo jedan od nekoliko različitih predmeta koje poučavaju, tako da ih pri odabiru profesije nužno ne privlači interes da budu učitelji matematike. Ipak, njihov pozitivan stav prema matematici i motivacija za poučavanje učenika matematici vrlo su važni. Cilj je ovoga istraživanja ispitati imaju li učitelji s različitim profilima ciljeva postignuća različita uvjerenja o matematici i poučavanju i učenju matematike. U istraživanju je sudjelovalo 325 studenata, budućih učitelja primarnoga obrazovanja. Istraživanje je provedeno u tri ciklusa: tijekom prve, treće i pete godine studija ispitanika. Na prvoj godini studija prikupljali smo podatke o ciljevima postignuća u matematici koje su sudionici imali u srednjoj školi i o samoučinkovitosti u matematici. Epistemološka uvjerenja, subjektivnu vrijednost matematike i tjeskobu procjenjivali smo u svim ciklusima mjerenja. Na trećoj i petoj godini studija sudionika također smo prikupljali podatke o njihovim uvjerenjima o učinkovitosti u poučavanju matematike i, na petoj godini, uvjerenja o poučavanju i učenju matematike. Rezultati klaster analize pokazali su da se budući učitelji, studenti primarnoga obrazovanja, mogu grupirati u tri skupine prema profilima ciljeva postignuća u srednjoj školi: (1) svi visoki ciljevi, (2) svi niski ciljevi i (3) orijentacija prema vještini. Dobiveni rezultati pokazali su razlike između skupina s obzirom na motivaciju za učenje matematike na početku studija. Ipak, te su razlike manje uočljive tijekom vremena. Na kraju studija sudionici se ne razlikuju u svojim uvjerenjima o učinkovitosti u poučavanju matematike niti u svojim uvjerenjima o učenju matematike