共查询到11条相似文献，搜索用时 843 毫秒
1.
Inspired by the relation between the algebra of complex numbers and plane geometry, William Rowan Hamilton sought an algebra of triples for application to three-dimensional geometry. Unable to multiply and divide triples, he invented a non-commutative division algebra of quadruples, in what he considered his most significant work, generalizing the real and complex number systems. We give a motivated introduction to quaternions and discuss how they are related to Pauli matrices, rotations in three dimensions, the three sphere, the group SU(2) and the celebrated Hopf fibrations. 相似文献
2.
李森林 《湖南城市学院学报》1988,(5)
In this paper,we shall apply the theory of nilpotent radical toderive Some results about ideals of a three-dimensional associatvealgebra over a field F and of an associative ring of order P~3 where Pis a prime.These results are useful in studying the structure of thealgebra and the ring. THEOREM 1.Let A be a three-dimensional associative algebraover a field F,N(A)the nilpotent radical of A.If N(A)≠O,then 相似文献
3.
Sarah E. Wright 《PRIMUS》2015,25(8):627-640
AbstractThis paper describes the linear algebra class I taught during Spring 2014 semester at Adelphi University. I discuss the details of how I flipped the class and incorporated elements of inquiry-based learning as well as the reasoning behind specific decisions I made. I give feedback from the students on the success of the course and provide my own reflections of the semester. Examples of some of the materials used are provided in the Appendix. 相似文献
4.
AbstractIn this article we describe a partially flipped Introductory Linear Algebra course developed by three faculty members at two different universities. We give motivation for our partially flipped design and describe our implementation in detail. Two main features of our course design are team-developed preview videos and related in-class activities. We share quantitative data and qualitative lessons learned related to our project. 相似文献
5.
Giang-Nguyen T. Nguyen 《Community College Journal of Research & Practice》2013,37(8):693-707
This paper examines data from a larger study that focused upon students’ experiences and motivations in a college algebra course. The study revealed that students failed this course because of various factors and continued to view this course as a “gatekeeper” class. Through a stepwise multiple regression, the analysis of the ARCS instrument showed that Attention, Relevance, and Confidence were strong predictors of Satisfaction in the course. 相似文献
6.
Algebraic competence is a major determinant of college access and career prospects, and equal sign knowledge is taken to be foundational to algebra knowledge. However, few studies have documented a causal effect of early equal sign knowledge on later algebra skill. This study assessed whether second-grade students’ equal sign knowledge prospectively predicts their fourth-grade algebra knowledge, when controlling for demographic and individual difference factors. Children (N = 177; Mage = 7.61) were assessed on a battery of tests in Grade 2 and on algebraic knowledge in Grade 4. Second-grade equal sign knowledge was a powerful predictor of these algebraic skills. Findings are discussed in terms of the importance of foregrounding equal sign knowledge to promote effective pedagogy and educational equity. 相似文献
7.
S. Aslι Özgün-Koca 《Journal of Mathematics Teacher Education》2010,13(1):49-71
Although growing numbers of secondary school mathematics teachers and students use calculators to study graphs, they mainly
rely on paper-and-pencil when manipulating algebraic symbols. However, the Computer Algebra Systems (CAS) on computers or
handheld calculators create new possibilities for teaching and learning algebraic manipulation. This study investigated the
views of Turkish prospective secondary mathematics teachers on the use of advanced calculators with CAS in algebra instruction.
An open-ended questionnaire and group interviews revealed prospective teachers’ views and beliefs about when and why they
prefer three possible uses of CAS—black box, white box, or Symbolic Math Guide (SMG). The results showed that participants
mainly preferred the white box methods and especially SMG to the black box method. They suggested that while the black box
method could be used after students mastered the skills, the general white box method and SMG could be used to teach symbolic
manipulation. 相似文献
8.
《Journal of research on educational effectiveness》2013,6(2):111-148
Abstract Expanded instructional time has become increasingly popular as a strategy to improve the academic outcomes of low-skilled students, particularly in the 9th grade. We evaluate the efficacy of a double-period algebra policy initiated in the Chicago Public Schools in 2003. This policy required all students with 8th-grade test scores below the national median to enroll in a support algebra course in addition to regular algebra in the 9th grade. Using regression discontinuity combined with interrupted time series designs, and instrumental variable models, we show the effects of the policy on students' grades, failure rates and test scores in 9th-grade algebra and 10th-grade geometry. Providing support courses improved algebra test scores for the target population but only modestly affected grades and failure rates. Students with very low initial abilities benefited less than students close to the national median. The policy also led schools to track algebra classes by students' entering math skills. As a result, it affected academic outcomes among students not targeted by the policy; test scores among high-ability students improved whereas their grades declined. 相似文献
9.
John Paul Cook 《PRIMUS》2015,25(3):248-264
AbstractThis paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context, identifying patterns, and venturing conjectures. A sequence of open-ended instructional tasks that aim to capitalize on students’ prior experiences with equation solving is provided along with notes and sample student responses for prospective instructors. 相似文献
10.
Mark D. Reckase Raven McCrory Robert E. Floden Joan Ferrini-Mundy Sharon L. Senk 《Educational Assessment》2013,18(4):249-267
Numerous researchers have suggested that there are multiple mathematical knowledge and skill areas needed by teachers in order for them to be effective teachers of mathematics: knowledge of the mathematics that are the goals of instruction, advanced mathematics beyond the instructional material, and mathematical knowledge that is specific to what is needed to teach students. The research reported here is about the development of a test of teachers’ knowledge in these three areas related to the teaching of algebra. The test development process is described and the results of several analyses are reported that had the goal of checking whether valid inferences can be made about the hypothesized components of teacher knowledge. 相似文献
11.
白鸿武 《咸阳师范学院学报》2001,16(4):80-80
举例说明了P.J.Hilton及U.Stammbacb的<A course in Homological Algebra>中命题7.7中的结论并非普遍成立. 相似文献