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1.
Stephan Ramon Garcia 《PRIMUS》2017,27(8-9):856-868
Abstract

A second course in linear algebra that goes beyond the traditional lower-level curriculum is increasingly important for students of the mathematical sciences. Although many applications involve only real numbers, a solid understanding of complex arithmetic often sheds significant light. Many instructors are unaware of the opportunities afforded by the early introduction of complex arithmetic. Most elementary properties of complex numbers have immediate matrix analogues and many important theorems can be deduced, or at least postulated, from the basics of complex arithmetic alone.  相似文献   

2.
Abstract

Quantitative Reasoning for Business is a two-semester sequence that serves as an alternative to elementary and intermediate algebra for first-year business students with weak mathematical preparation. Students who take the sequence have been retained at a higher rate and demonstrated a larger reduction in math anxiety than those who take the traditional developmental courses. We share the challenges that led to our choices in adopting and modifying inquiry-based instruction in order to serve our population.  相似文献   

3.
Abstract algebra courses tend to take one of two pedagogical routes: from examples of mathematics structures through definitions to general theorems, or directly from definitions to general theorems. The former route seems to be based on the implicit pedagogical intention that students will use their understanding of particular examples of an algebraic structure to get a sense of those properties which form the basis of the fundamental definitions. We will explain the transition from examples to abstract algebra as a series of shifts of attention and in this paper we will use a case study to examine the initial shift, which we will call apprehending a structure, and examine how one student came to apprehend the structure of the commutative ring Z99.  相似文献   

4.
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   

5.
Jenna Van Sickle 《PRIMUS》2015,25(8):600-613
Abstract

This paper outlines the experience of a university professor who implemented flipped learning in two sections of college algebra courses for two semesters. It details how the courses were flipped, what technology was used, advantages, challenges, and results. It explains what students do outside of class, what they do inside class, and discusses what students thought of the course based on surveys and course evaluations. It also compares results on a similar final exam to those of a control group.  相似文献   

6.
H. Hirst  K. Palmer 《PRIMUS》2019,29(9):950-964
Abstract

The authors describe working with partner disciplines during the process of updating mathematics courses for the general education quantitative literacy requirement. The conversations resulted in significant changes to the business calculus course and a rich listing of applications to be incorporated into the college algebra course from technical fields such as industrial design, exercise science, and building science.  相似文献   

7.
William C. Bauldry 《PRIMUS》2018,28(5):425-437
The standard technique taught in calculus courses for partial fraction expansions uses undetermined coefficients to generate a system of linear equations; we present a derivative-based technique that calculus and differential equations instructors can use to reinforce connections to calculus. Simple algebra shows that we can use the derivative to calculate coefficients, reinforcing calculus connections. For irreducible quadratic factors, the simple derivative formula with complex arithmetic gives the coefficients, helping students gain facility with complex numbers. For higher multiplicity factors, we can use higher derivative formulas taken from the Laurent expansion. We conclude with examples of using the technique in different courses, highlighting precalculus and calculus classes.  相似文献   

8.
Abstract

Using six waves of data (Grades 7–12) from the Longitudinal Study of American Youth, the author examined the effects of different mathematics course work (pre-algebra, geometry, calculus) on subsequent achievement in, and attitude toward, mathematics, with partial adjustment for student background characteristics. Results showed that in the early grades of high school, algebra courses significantly affected mathematics achievement. Mathematics course work, however, did not play a significant role in mathematics achievement in the middle grades of high schools. There was a “harvest” of significant course-work indicators in the later grades of high school; every advanced mathematics course affected mathematics achievement. Many course-work effects were substantial even after accounting for variables such as prior mathematics achievement and socioeconomic status.  相似文献   

9.
Abstract

In this paper we address practical questions such as: How do symbols appear and evolve in an inquiry-oriented classroom? How can an instructor connect students with traditional notation and vocabulary without undermining their sense of ownership of the material? We tender an example from linear algebra that highlights the roles of the instructor as a broker, and the ways in which students participate in the practice of symbolizing as they reinvent the diagonalization equation A = PDP?1.  相似文献   

10.
Frank A. Farris 《PRIMUS》2017,27(8-9):827-844
Abstract

The domain-coloring algorithm allows us to visualize complex-valued functions on the plane in a single image—an alternative to before-and-after mapping diagrams. It helps us see when a function is analytic and aids in understanding contour integrals. The culmination of this article is a visual discovery and subsequent proof of the Argument Principle, which relates the count of poles and zeros of a meromorphic function inside a contour to the accumulated change in argument of the function around the contour. Throughout, I offer connections to standard learning goals of courses in complex variables.  相似文献   

11.
Background: This exploratory study is part of a larger-scale research project aimed at building theoretical and practical knowledge of complex systems in students and teachers with the goal of improving high school biology learning through professional development and a classroom intervention.

Purpose: We propose a model of adaptive expertise to better understand teachers’ classroom practices as they attempt to navigate myriad variables in the implementation of biology units that include working with computer simulations, and learning about and teaching through complex systems ideas.

Sample: Research participants were three high school biology teachers, two females and one male, ranging in teaching experience from six to 16 years. Their teaching contexts also ranged in student achievement from 14–47% advanced science proficiency.

Design and methods: We used a holistic multiple case study methodology and collected data during the 2011–2012 school year. Data sources include classroom observations, teacher and student surveys, and interviews. Data analyses and trustworthiness measures were conducted through qualitative mining of data sources and triangulation of findings.

Results: We illustrate the characteristics of adaptive expertise of more or less successful teaching and learning when implementing complex systems curricula. We also demonstrate differences between case study teachers in terms of particular variables associated with adaptive expertise.

Conclusions: This research contributes to scholarship on practices and professional development needed to better support teachers to teach through a complex systems pedagogical and curricular approach.  相似文献   

12.
Abstract

This study reports the academic benefits of peer tutoring in algebra for middle school students. A total of 380 students enrolled in grades 7th and 8th participated in the study. Two peer tutoring sessions took place during each week (10?weeks). Interactions between peers lasted 20 to 25?minutes for each session. The typology of tutoring was fixed and same-age. A pretest posttest with control group design was used. Statistical significant improvements were reported in the academic achievement variable after the implementation of the peer tutoring program for 7th and 8th grade courses separately and altogether. Over 87% of the students in the experimental group improved their marks. The overall effect size for the experience was reported to be medium (Hedge’s g?=?0.48). The main conclusion of this study is that fixed and same-age peer tutoring in algebra may be very beneficial for middle school students.  相似文献   

13.
Background: In developed countries, it is challenging for teachers to select pedagogical practices that encourage students to enrol in science and technology courses in upper secondary school.

Purpose: Aiming to understand the enrolment dynamics, this study analyses sample-based data from Finland’s National Assessment in Science to determine whether pedagogical approaches influence student intention to enrol in upper secondary school physics courses.

Sample: This study examined a clustered sample of 2949 Finnish students in the final year of comprehensive school (15–16 years old).

Methods: Through explorative factor analysis, we extracted several variables that were expected to influence student intention to enrol in physics courses. We applied partial correlation to determine the underlying interdependencies of the variables.

Results: The analysis revealed that the main predictor of enrolment in upper secondary school physics courses is whether students feel that physics is important. Although statistically significant, partial correlations between variables were rather small. However, the analysis of partial correlations revealed that pedagogical practices influence inquiry and attitudinal factors. Pedagogical practices that emphasise science experimentation and the social construction of knowledge had the strongest influence.

Conclusions: The research implies that to increase student enrolment in physics courses, the way students interpret the subject’s importance needs to be addressed, which can be done by the pedagogical practices of discussion, teacher demonstrations, and practical work.  相似文献   


14.
Abstract

This article presents research on persistence among at-risk students using network analysis following multiple linear regression (MLR). Data on a population of enrolled undergraduate students at an urban-serving university over several years (P?=?35,239) is tested using multiple linear regression. Variables interacting at different dimensions of the model are analyzed using IBM SPSS Neural Networks (2017) and Cytoscape (2018) to show network linkages. While variables may not be significant in MLR models where anomalies are ruled out, network analysis takes these anomalies into account and reveals complex layers of interactions between and among variables. Findings show that loans of any kind contribute to attrition while financial aid of any kind contributes to persistence and offsets attrition from loans.  相似文献   

15.
Abstract

In this paper, we describe how we integrated complex analysis into the second semester of a geometry course designed for preservice secondary mathematics teachers. As part of this inquiry-based course, the preservice teachers incorporated their geometric understanding of the arithmetic of complex numbers and complex-valued functions to create a game using Geometer’s Sketchpad. We detail a game created by a pair of preservice teachers that exemplifies their creativity and knowledge of complex-valued functions. Given inquiry-based courses have inherent challenges we also present projects that were not as exemplary.  相似文献   

16.
Three groups of students at Illinois State University (of respective sizes 235, 157, and 397) were used as subjects to determine which factors were significant predictors of success in the first course in calculus. The second and third groups were used to provide replications of the initial study. Academic independent variables considered were: ACT scores, high school rank, high school GPA, high school algebra grades, and the score from an algebra pretest. Biographical independent variables considered were: sex, birth order, family size, and high school size. The dependent variable was a function of the student’s course grade in the first semester of calculus. The use of stepwise and all-subsets regression procedures on the three groups revealed in each case that the best combination of predictors consisted of the algebra pretest and high school rank. From this result, the investigators concluded that the combination of algebraic skills, as represented by the score on the algebra pretest, and long-term perseverence and competitiveness, as measured by high school rank, play a significant role in the prediction of achievement in the first semester of calculus.  相似文献   

17.
Constant solutions to Yang-Baxter equation are investigated over Grassmann algebra for the case of 6-vertexR-matrix. The general classification of all possible solutions over Grassmann algebra and particular cases with 2,3,4 generators are studied. As distinct from the standard case, whenR-matrix over number field can have a maximum 5 nonvanishing elements, we obtain over Grassmann algebra a set of new full 6-vertex solutions. The solutions leading to regularR-matrices which appear in weak Hopf algebras are considered.  相似文献   

18.
ABSTRACT

Sixty accredited MSW programs were surveyed to determine whether there were significant differences between those programs offering discrete ethics courses and those not doing so on a number of ethics education related variables. Results suggest virtually no significant differences on the variables examined, with the exception that programs offering discrete courses more often expose students to literature on the broad topic of moral philosophy. Also examined was the extent to which all of the programs surveyed were following the pedagogical recommendations of the ethics education literature reviewed. The results suggest that many MSW programs are not following these recommendations in a number of respects. The implications of these findings are discussed, and specific suggestions are offered for those faculty concerned with the ethics component of their course offerings.  相似文献   

19.
Abstract

Using national longitudinal data, the authors investigated factors related to student learning or growth in statistics, algebra, and geometry in middle school and high school. The authors used hierarchical linear models to model variation in student rate of growth with factors associated with student characteristics and instructional and environmental factors. In addition, the authors designed the study to identify factors that differentially affect student growth at different levels of secondary school (middle school vs. high school) and for different mathematical content areas (statistics, algebra, geometry). Results indicated substantial growth in all 3 content areas in both middle school and high school. Factors related to student learning were identified and found to differ by level of secondary school and content area.  相似文献   

20.
论述了线性空间的直和分解思想在数学中和在学生学习过程中所处的地位;并论述了直和分解思想对学习本课程和后继课程以及对培养学生思维能力方面所起的重要作用．  相似文献   

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