In this paper, we construct combinatorial bases of Feigin–Stoyanovsky’s type subspaces of standard modules for level k affine Lie algebra Cℓ(1). We prove spanning by using annihilating field xθ(z)k+1 ...of standard modules. In the proof of linear independence, we use simple currents and intertwining operators whose existence is given by fusion rules.
Different kinds of resources, material and non-material, are used and developed with the aim of being part of an effective mathematics education. As a non-material resource, time seems to be of great ...importance to teachers and students. The aim of the present study is to focus on teachers’ views about time as a resource and its interactions with other resources in mathematics education. For this purpose, a large-scale examination of teachers’ opinions was undertaken, combining qualitative and quantitative methods, and involving teachers from different school levels. The results show that teachers highly value time as a resource, although with clear differences among primary, middle, and higher grade teachers. The participants of all levels complained to a great extent about not having as much time as they need for geometry topics, problem solving, and teamwork. On the other hand, the results show that textbooks and technology as material resources save teachers and students time, making lesson preparation and enactment more efficient, particularly in lower grades. The insight gained into teachers’ views about time, together with the literature review, indicate the importance of non-material resources within the discussion of resources.
Let
be an affine Lie algebra of the type
. Suppose we are given a ℤ-gradation of the corresponding simple finite-dimensional Lie algebra =
−1
⊕
0
⊕
1
; then we also have the induced ℤ-gradation ...of the affine Lie algebra
Let L(Λ) be a standard module of level 1. Feigin-Stoyanovsky's type subspace W(Λ) is the
-submodule of L(Λ) generated by the highest-weight vector v
Λ
,
We find a combinatorial basis of W(Λ) given in terms of difference and initial conditions.
The aim of the study was to explore pre-service primary school teachers' motivational beliefs about mathematics in the light of the expectancy-value theory. We wanted to find out to what extent the ...motivational beliefs of pre-service teachers are related to their previous experiences in mathematics and to their engagement in learning mathematics and mathematics anxiety. The participants were 237 pre-service primary school teachers in their first year of study. They completed a mathematics exam and a questionnaire on their motivational beliefs (self-efficacy and subjective value), previous experiences in mathematics (level of high school math program, mathematics competencies, epistemic beliefs and achievement goals during high school), engagement and mathematics anxiety. The results of hierarchical regression analyses show that previous experiences with mathematics are important predictors of self-efficacy and subjective value. Furthermore, motivational beliefs are significant predictors of the pre-service teachers' engagement in learning mathematics and mathematics anxiety, along with their previous experiences with mathematics. The results are in line with the expectancy- -value theory and indicate that it is important to foster the development of adaptive beliefs about mathematics during the initial education of pre-service teachers.
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 self-efficacy 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.Key words: achievement goals; mathematics education; motivation; teacher education; teachers’ beliefs---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 samo-učinkovitosti 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.Ključne riječi: ciljevi postignuća; matematičko obrazovanje; motivacija; obrazovanje učitelja; uvjerenja učitelja
In this paper, we construct combinatorial bases of Feigin–Stoyanovsky’s type subspaces of standard modules for level
k
affine Lie algebra
C
ℓ
(
1
)
. We prove spanning by using annihilating field
x
θ
...(
z
)
k
+
1
of standard modules. In the proof of linear independence, we use simple currents and intertwining operators whose existence is given by fusion rules.
The aim of the study was to explore pre-service primary school teachers' motivational beliefs about mathematics in the light of the expectancy-value theory. We wanted to find out to what extent the ...motivational beliefs of pre-service teachers are related to their previous experiences in mathematics and to their engagement in learning mathematics and mathematics anxiety. The participants were 237 pre-service primary school teachers in their first year of study. They completed a mathematics exam and a questionnaire on their motivational beliefs (self-efficacy and subjective value), previous experiences in mathematics (level of high school math program, mathematics competencies, epistemic beliefs and achievement goals during high school), engagement and mathematics anxiety. The results of hierarchical regression analyses show that previous experiences with mathematics are important predictors of self-efficacy and subjective value. Furthermore, motivational beliefs are significant predictors of the pre-service teachers' engagement in learning mathematics and mathematics anxiety, along with their previous experiences with mathematics. The results are in line with the expectancy- -value theory and indicate that it is important to foster the development of adaptive beliefs about mathematics during the initial education of pre-service teachers.
PDF
