Level of competence on the concept of basis of vector space using SOLO taxonomy

Author(s):  
Verónica VALENZUELA-GONZÁLEZ ◽  
Andrés HERNÁNDEZ-QUINTANA ◽  
Alberto CAMACHO-RÍOS

The purpose of this research paper is to determinate the level of competence on the concept of basis of a vector space on college level students who finished the Linear Algebra course, providing complementary information to the various studies from a different perspective through the SOLO taxonomy (Structure of the Observed Learning Outcome). An instrument was designed to address the concept of basis from different perspectives and difficulty degrees; it was applied through individual video-recorded interviews. Their answers were analyzed, and it was found that they average level 3 (multistructural) of the taxonomy: the students know the basis definition from an algorithmic or methodological perspective, and they can reproduce some procedures, but they are unable to understand the basis concept.

Author(s):  
Siti Fatimah

SOLO Taxonomy is one of the frameworks used in analyzing the quality of responses in problem solving. This research aim to analyze the student’s responses level in doing problem solving item based on SOLO Taxonomy overviewed from motivation to learn. The research method used in this study was a qualitative research with the data sources of this study were 75 students period 2016/2017. The results of the study showed that student’s responses in doing problem solving wave concept at prestructural level is 62,17%, Unistructural Level is 27,63%, Multistructural level is 58,22%, Relasional level is 48,50%, and Extended Abstract level is 37,82%; Motivation to learn’s student high category are better at responding to answer item based SOLO Taxonomy than motivation to learn’s students low category.Keywords: Student’s reponses; SOLO Taxonomy; Motivation to Learn


1990 ◽  
Vol 16 (1) ◽  
pp. 1-17 ◽  
Author(s):  
J. J. Dongarra ◽  
Jeremy Du Croz ◽  
Sven Hammarling ◽  
I. S. Duff

Author(s):  
Siti Fatimah

SOLO Taxonomy is one of the frameworks used in analyzing the quality of responses in problem solving. This research aim to analyze the student’s responses level in doing problem solving item based on SOLO Taxonomy overviewed from motivation to learn. The research method used in this study was a qualitative research with the data sources of this study were 75 students period 2016/2017. The results of the study showed that student’s responses in doing problem solving wave concept at prestructural level is 62,17%, Unistructural Level is 27,63%, Multistructural level is 58,22%, Relasional level is 48,50%, and Extended Abstract level is 37,82%; Motivation to learn’s student high category are better at responding to answer item based SOLO Taxonomy than motivation to learn’s students low category.Keywords: Student’s reponses; SOLO Taxonomy; Motivation to Learn


Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 3031-3043
Author(s):  
O.R. Dehghan

The study of linear functionals, as an important special case of linear transformations, is one of the key topics in linear algebra and plays a significant role in analysis. In this paper we generalize the crucial results from the classical theory and study main properties of linear functionals on hypervector spaces. In this way, we obtain the dual basis of a given basis for a finite-dimensional hypervector space. Moreover, we investigate the relation between linear functionals and subhyperspaces and conclude the dimension of the vector space of all linear functionals over a hypervector space, the dimension of sum of two subhyperspaces and the dimension of the annihilator of a subhyperspace, under special conditions. Also, we show that every superhyperspace is the kernel of a linear functional. Finally, we check out whether every basis for the vector space of all linear functionals over a hypervector space V is the dual of some basis for V.


2020 ◽  
Vol 69 (4/5) ◽  
pp. 253-268
Author(s):  
Abbas Doulani ◽  
Sepideh Sahebi ◽  
Mohammad Karim Saberi

Purpose The purpose of this study is to carry out the demographic evaluation and analysis of the entrepreneurial orientation of librarians in Iranian public libraries using the Lumpkin and Dess model. Design/methodology/approach In this study, a structured questionnaire of entrepreneurial orientation was used. The research population consisted of 5,000 librarians of Iranian public libraries who were selected using Krejcie and Morgan table (95% confidence level and p-value of 5%) and stratified the random sampling method. A total of 365 individuals were selected as the study sample. Data were analyzed by SPSS software using descriptive statistics (frequency, percent, mean, standard deviation and standard error mean) as well as inferential statistics (Pearson correlation, one-sample t-test, independent samples t-test and ANOVA. Findings The results showed that the mean level of entrepreneurial orientation of librarians was 2.92 with an average level (µ = 3). Librarians were at an average level (µ = 3) in terms of components of innovativeness (2.98), risk-taking (2.93) and proactiveness (3.02). The status of the autonomy component (2.53) was at an undesirable level (3 < µ), and only the competitive aggressiveness status (3.12) was at the desirable level (3 < µ). The analysis of the librarian’s entrepreneurial orientation based on demographic characteristics indicated that the male librarian’s entrepreneurial orientation was higher than the female librarian’s (p-value = 0.039). Meantime, librarians with library and information science degrees have less entrepreneurial orientation than the librarians with other (non-librarian and information science) degrees (p-value = 0.01). Also, the higher the librarian’s degree, the lower their entrepreneurial orientation will be (p-value = 0.000). In addition, there was no significant relationship between librarians’ age (p-value = 0.14), marital status (p-value = 0.15) or work experience (p-value = 0.388) and their entrepreneurial orientation. Practical implications Entrepreneurial orientation is one of the significant concepts in entrepreneurship of organizations. Accordingly, studying the concept of entrepreneurial orientation and formulating an appropriate strategy is of great importance in improving the performance of libraries because libraries can be more useful and appealing to library members by enhancing the entrepreneurial orientation of librarians, delivering new, unique and tailor-made services to users’ needs. Originality/value Not much research has been carried out on entrepreneurship in library and information sciences. To the best of the authors’ knowledge, this is the first study to examine the entrepreneurial orientation of librarians based on their demographic characteristics.


Author(s):  
William A. Adkins

This paper is concerned with studying hereditary properties of primary decompositions of torsionR[X]-modulesMwhich are torsion free asR-modules. Specifically, if anR[X]-submodule ofMis pure as anR-submodule, then the primary decomposition ofMdetermines a primary decomposition of the submodule. This is a generalization of the classical fact from linear algebra that a diagonalizable linear transformation on a vector space restricts to a diagonalizable linear transformation of any invariant subspace. Additionally, primary decompositions are considered under direct sums and tensor product.


1997 ◽  
Vol 23 (3) ◽  
pp. 379-401 ◽  
Author(s):  
Iain S. Duff ◽  
Michele Marrone ◽  
Giuseppe Radicati ◽  
Carlo Vittoli

Author(s):  
Nicolas H. Christianson ◽  
Ann Sizemore Blevins ◽  
Danielle S. Bassett

Knowledge is a network of interconnected concepts. Yet, precisely how the topological structure of knowledge constrains its acquisition remains unknown, hampering the development of learning enhancement strategies. Here, we study the topological structure of semantic networks reflecting mathematical concepts and their relations in college-level linear algebra texts. We hypothesize that these networks will exhibit structural order, reflecting the logical sequence of topics that ensures accessibility. We find that the networks exhibit strong core–periphery architecture, where a dense core of concepts presented early is complemented with a sparse periphery presented evenly throughout the exposition; the latter is composed of many small modules each reflecting more narrow domains. Using tools from applied topology, we find that the expositional evolution of the semantic networks produces and subsequently fills knowledge gaps, and that the density of these gaps tracks negatively with community ratings of each textbook. Broadly, our study lays the groundwork for future efforts developing optimal design principles for textbook exposition and teaching in a classroom setting.


1987 ◽  
Vol 22 (3) ◽  
pp. 2-14 ◽  
Author(s):  
Jack Dongarra ◽  
Jeremy Du Croz ◽  
Iain Duff ◽  
Sven Hammarling

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