COLLEGE ALGEBRA STUDENTS�� ATTITUDES TOWARD MATHEMATICS IN THEIR CAREERS

The purpose of this study was to identify the degree to which college algebra students’ value mathematical skills in their prospective careers. A survey was administered to N = 144 students in 6 college algebra classes at a mid-sized doctoral granting university. Students in half the classes completed a data analysis project, and half of the students planned to major in a business-related degree. Logistic regression suggested that students held mostly positive attitudes about the value of mathematics in their career, with business students expressing more positive attitudes than those reported by non-business students. Unexpectedly, those who completed the data analysis project expressed less positive attitudes on 6 of the 20 survey items.     

记叙文教学提高初中生审美素养的作用探析

初中阶段的学生正处于世界观和审美观发展的阶段,这时需要充分利用作文课堂教学来提高他们的审美素养。在作文教学中,记叙文处于基础地位,从感知、运思和写作三个阶段出发,记叙文训练可以有效培养学生的审美观察、想象、分析、逻辑和组织能力,从整体上提高他们的审美素养。     

The effects of high school math curriculum on college attendance: Evidence from the NLSY97

Using a sample of youth who graduated from high school in the late 1990s and early 2000s, this paper examines the impact of high school math curriculum on the decision to go to college. Results that control for unobserved differences between students and their families suggest that a more rigorous high school math curriculum is associated with a higher probability of attending college and of attending a 4-year college. The household fixed effect results imply that students who take an advanced academic math curriculum in high school (algebra II or precalculus, trigonometry, or calculus) are about 17 percentage points more likely to go to college and 20 percentage points more likely to start college at a 4-year school by age 21 compared to those students whose highest math class was algebra I or geometry.     

Applying effective instructional strategies for teaching dyslexic students in a remedial college algebra course

For many secondary and postsecondary students with dyslexia, passing required algebra courses presents a formidable challenge. Although dyslexic students do have specific and sometimes severe learning deficits that can affect their chances of success in algebra, they can succeed if given appropriate and effective instruction that meets their special and individual needs. This article briefly describes the application of effective instructional practices to the teaching of remedial algebra that have been used with dyslexic students in the University of Wisconsin Oshkosh Project Success program.     

Revitalizing Algebra: the effect of the use of a cognitive tutor in a remedial course

This study investigated the effect of instruction with a cognitive tutoring software system in a remedial algebra course. The performance on algebra tasks of students who attended the experimental (cognitive tutor) and a control class was compared. The results indicated that the two groups of students were equally proficient with respect to algebraic manipulation skills. However, students who attended the experimental algebra section performed significantly better in problem solving than students in the control section. This finding suggested that the use of the cognitive tutor (a) improved students' problem‐solving abilities; (b) fostered student development of richer concepts of variable and function; and (c) improved students' procedural abilities in approaching and carrying through mathematical analyses of relatively complex situations.     

小学生关系性思维的测试与分析

代数思维被认为是数学的“核心思想”,关系性思维与“代数思维”密切相关。有研究表明,有意识地培养学生的关系性思维,有助于学生从算术学习过渡到代数学习。文章对小学生关系性思维的特点进行了分析,并借助测试工具,对四、五、六年级小学生解决“23＋15=26＋口”这样的等式问题的思维方式进行了研究。这次测试反映出,小学生在解决上述等式问题时所表现出的关系性思维水平,并不因年级的升高表现更优。     

Learning the Unwritten Rules: Working Class Students in Graduate School

While researchers have begun to examine the experiences of working class students in undergraduate education more closely, we know less about the experiences of working class students in graduate school. Through a nationwide survey of graduate students enrolled in Ph.D. programs in Sociology, we examined the extent to which working class students face greater challenges or barriers in completing their degrees compared to their middle class peers. We found working class students to be comparatively disadvantaged in academic integration and financial support. We discuss the implications of these findings for improving the graduate school experiences of working class students.     

Geometry of spin: Clifford algebraic approach

Spin is a fundamental degree of freedom of matter and radiation. In quantum theory, spin is represented by Pauli matrices. Then the various algebraic properties of Pauli matrices are studied as properties of matrix algebra. What has been shown in this article is that Pauli matrices are a representation of Clifford algebra of spin and hence all the properties of Pauli matrices follow from the underlying algebra. Clifford algebraic approach provides a geometrical and hence intuitive way to understand quantum theory of spin, and is a natural formalism to study spin. Clifford algebraic formalism has lot of applications in every field where spin plays an important role.     

“Double-Dose” Algebra as an Alternative Strategy to Remediation: Effects on Students' Academic Outcomes

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.     

The effect of primary school mergers on academic performance of students in rural China

We examine the impact of primary school mergers on academic performance of students using a dataset that we collected using a survey designed specifically to examine changes in the academic performance of students before and after their schools were merged. We use difference-in-differences and propensity score matching approaches and demonstrate that overall the primary school merger has not harmed the academic performance of students, as some have claimed. We do find, however, that the timing of mergers matter; when students are older (e.g., the fourth grade) their grades rise after merging. The grades of younger students, however, fall.     

矩阵乘积的精彩——贯穿于《线性代数》始终的矩阵乘积的教学方法探讨

探讨了在《线性代数》教学过程中关于矩阵乘积的问题。首先是矩阵乘法引入时要注意的问题,其次是在矩阵分块以后探讨矩阵乘积的规律,然后是用内积的观点来看待矩阵的乘积。这样从多个侧面引导学生去理解矩阵的乘积可以开阔他们的视野,提高他们分析问题和解决问题的能力。     

Secondary School Students’ Errors in the Translation of Algebraic Statements

In this article, we present the results of a research study that explores secondary students’ capacity to perform translations of algebraic statements between the verbal and symbolic representation systems through the lens of errors. We classify and compare the errors made by 2 groups of students: 1 at the beginning of their studies in school algebra and another 1 completing their studies on algebra in compulsory education. This comparison allows us to detect errors which require specific attention in instruction due to its persistence and to identify errors that disappear as students advance in their study of algebra. The results and conclusions have a pedagogic value to inform instruction and also lead to backed conjectures and research questions to push forward research on student’s translation capacity and students’ knowledge of algebraic symbolism.     

The Micropolitics of Educational Inequality: The Case of Teacher–Student Assignments

Politics of education researchers have long recognized the role of micropolitics in school decision-making processes. We argue that investigating micropolitical dynamics is key to an important set of school decisions that are fundamental to inequities in access to high-quality teachers: assignments of teachers and students to classrooms. Focusing on the intraorganizational political power of experienced teachers, our analysis of survey and administrative data from a large urban district suggests that more experienced teachers have more influence over which students are assigned to their classrooms. By a variety of measures, we also find that more experienced teachers are assigned fewer disadvantaged students, on average, a pattern inconsistent with goals of ameliorating educational inequality by matching more qualified teachers with the students who need them most.     

Embedded Mathematics in Chemistry: A Case Study of Students’ Attitudes and Mastery

There are many factors that shape students’ attitudes toward science, technology, engineering and mathematics. This exploratory study of high school students examined the effect of enriching chemistry with math on chemistry students’ attitudes toward math and careers involving math. To measure student attitudes, a survey was administered before and after the 18-week chemistry class; results from the chemistry class were compared to survey results from students in an elective science class that did not emphasize mathematics. At the end of the 18-week period, only the chemistry students exhibited more positive views toward their abilities in mathematics and careers that involve mathematics, as compared to their views at the outset of the course. To ensure that chemistry mastery was not hindered by the additional emphasis on math, and that mastery on state end-of-course examinations reflected knowledge acquired during the math-intensive chemistry class, a chemistry progress test was administered at the start and end of the term. This exploratory study suggests that emphasizing mathematical approaches in chemistry may positively influence attitudes toward math in general, as well as foster mastery of chemistry content.     

高职医学生实习前就业相关问题的探索——以襄阳职业技术学院为例

目的了解医学类专业学生对就业问题的看法,以利于进行针对性的就业指导。方法对襄阳职业技术学院2011级845名大学生（男593人、女252人）,分三个专业（临床347人、护理372人、药学126人）进行匿名问卷调查,进行χ2检验分析。结果药学类、临床类专业的大学生对自己第一份工作的薪酬期望都在2 000元左右,护理类的学生在2 000-3 000元之间,三个专业之间具有较高统计学差异（χ2=88.292,P=0.000）;就业指导方面：48.7%大学生认为成功就业的重要因素是就业出路指导（招聘信息的提供）,27.9%的被调查者选择了个人素质能力的培养,13.5%的选择了应试技巧训练,具有较高统计学差异（χ2=38.967,P=0.000）;就业时工作地域的取向调查结果表明：大多数学生选择了中小城市,排列第二的是经济发达城市;同中有异的是护理学生选择经济发达城市较多,临床学生选择基层乡镇的较多,具有较高统计学差异（χ2=51.950,P=0.000）;学生就业失败时取向调查结果表明：排列顺序为大部分选择继续求职（48.9%）、继续求学（20.3%）、自主创业（14.0%）,少部分选择普通打工（11.0%）,但是临床类学生首选继续求学,护理与药学类学生首选继续求职,选择自主创业的临床与护理类学生也为数不少,具有较高统计学差异（χ2=106.560,P=0.000）;就业地点与恋爱关系遇到可能冲突时的选择调查结果表明：排列顺序为大部分选择以自己为主（58.7%）、爱情至上（21.8%）、具有较高统计学差异（χ2=106.560,P=0.000）。结论社会应当视解决学生就业为头等大事,根据专业性质不同,针对性地提供招聘就业信息,培训应聘技巧和素质能力,指导学生根据学历现状选择就业地点与工资水平,及时提高学历,树立正确的就业观和恋爱观。     

Algebra slaves and agents in a Logo-based mathematics curriculum

For many students the ideas and methods of algebra appear obscure and mysterious, their sense and purpose unclear, and their applicability to anything genuinely real or interesting very remote. Students often fail to acquire an understanding of the key concepts, despite their inherent simplicity. Even when they gain the notion of variables, expressions and equations, students often lack the strategic knowledge required to motivate and direct the global planning and detailed execution of an attack on a problem. These conceptual and strategic difficulties are compounded by the needs for precise performance of the arithmetic and symbolic operations required in manipulating expressions. Extended operations like subtracting an expression from both sides of an equation or expanding a product of three terms, are very difficult for beginning students. Their buggy performance in carrying out the detailed manipulative work greatly confounds and frustrates their acquisition and assimilation of the most important and central ideas.In an effort to confront these difficulties and show how they can be overcome, we are developing a Logo-based introductory algebra course for sixth graders. Our approach has three major components: work on Logo programming projects in algebraically rich contexts whose content is meaning ful and compelling to students, the use of algebra microworlds with concrete iconic representations of formal objects and operations, and the introduction of the algebra workbench, an expert instructional system to aid students in performing extended algebraic operations.The algebra workbench will employ a set of powerful symbolic manipulation tools for performing the standard manipulations of high school algebra. It will have two main modes of use: demonstration mode, which uses an expert tutor program to solve algebra problems incrementally, explaining its strategy and its step by step operations in straightforward terms along the way; and practice mode, in which the student tries to solve a problem with the assistance of the tutor, which performs the operations requested by the student at each step and which can be called at any point to advise the student of the correctness of a step, to perform or explain any step, to evaluate the student's solution, or to perform a problem that she poses.These powerful aids make it possible to effectively separate out the difficulties in performing the formal and manipulative aspects of algebra work from those encountered in learning the central conceptual and strategic content. Distinctly different kinds of instructional tools and activities-Logo programming, expert tutors, or algebra microworlds-can thus be brought to bear where each is most appropriate and effective.     

Teaching Algebra to Students with Learning Difficulties: An Investigation of an Explicit Instruction Model

Abstract. Thirty‐four matched pairs of sixth‐ and seventh‐grade students were selected from 358 participants in a comparison of an explicit concrete‐to‐representational‐to‐abstract (CRA) sequence of instruction with traditional instruction for teaching algebraic transformation equations. Each pair of students had been previously labeled with a specific learning disability or as at risk for difficulties in algebra. Students were matched according to achievement score, age, pretest score, and class performance. The same math teacher taught both members of each matched pair, but in different classes. All students were taught in inclusive settings under the instruction of a middle school mathematics teacher. Results indicated that students who learned how to solve algebra transformation equations through CRA outperformed peers receiving traditional instruction on both postinstruction and follow‐up tests. Additionally, error pattern analysis indicated that students who used the CRA sequence of instruction performed fewer procedural errors when solving for variables.     

Keep DRAGging ON: Is solving more problems in DragonBox 12+ associated with higher mathematical performance during the COVID-19 pandemic?

Prior research has shown that game-based learning tools, such as DragonBox 12+, support algebraic understanding and that students' in-game progress positively predicts their later performance. Using data from 253 seventh-graders (12–13 years old) who played DragonBox as a part of technology intervention, we examined (a) the relations between students' progress within DragonBox and their algebraic knowledge and general mathematics achievement, (b) the moderating effects of students' prior performance on these relations and (c) the potential factors associated with students' in-game progress. Among students with higher prior algebraic knowledge, higher in-game progress was related to higher algebraic knowledge after the intervention. Higher in-game progress was also associated with higher end-of-year mathematics achievement, and this association was stronger among students with lower prior mathematics achievement. Students' demographic characteristics, prior knowledge and prior achievement did not significantly predict in-game progress beyond the number of intervention sessions students completed. These findings advance research on how, for whom and in what contexts game-based interventions, such as DragonBox, support mathematical learning and have implications for practice using game-based technologies to supplement instruction.

Practitioner notes

What is already known about this topic

• DragonBox 12+ may support students' understanding of algebra but the findings are mixed.
• Students who solve more problems within math games tend to show higher performance after gameplay.
• Students' engagement with mathematics is often related to their prior math performance.

What this paper adds

• For students with higher prior algebraic knowledge, solving more problems in DragonBox 12+ is related to higher algebraic performance after gameplay.
• Students who make more in-game progress also have higher mathematics achievement, especially for students with lower prior achievement.
• Students who spend more time playing DragonBox 12+ make more in-game progress; their demographic, prior knowledge and prior achievement are not related to in-game progress.

Implications for practice and/or policy

• DragonBox 12+ can be beneficial as a supplement to algebra instruction for students with some understanding of algebra.
• DragonBox 12+ can engage students with mathematics across achievement levels.
• Dedicating time and encouraging students to play DragonBox 12+ may help them make more in-game progress, and in turn, support math learning.

     

Evolution of a teaching approach for beginning algebra

The article reports aspects of the evolution of a teaching approach over repeated trials for beginning symbolic algebra. The teaching approach emphasized the structural similarity between arithmetic and algebraic expressions and aimed at supporting students in making a transition from arithmetic to beginning algebra. The study was conducted with grade 6 students over 2 years. Thirty-one students were followed for a year, and data were analysed as they participated in the three trials conducted that year. Analysis of students’ written and interview responses as the approach evolved revealed the potential of the approach in creating meaning for symbolic transformations in the context of both arithmetic and algebra as well as making connections between arithmetic and symbolic algebra. Students by the end of the trials learnt to use their understanding of both procedures and a sense of structure of expressions to evaluate/simplify expressions and reason about equality/equivalence of expressions both in the arithmetic and the algebraic contexts.     

Worth Knowing: Talmud Study and the Intellectual Values of High School Students at Liberal Jewish Day Schools

ABSTRACT

What do Jewish day school students believe constitutes good understanding and worthwhile learning in the context of their encounter with rabbinic texts in the classroom? This article shares findings from an interview study of Jewish day school students in grades 9 through 12 regarding their attitudes toward the study of Talmud. I argue that high school students’ estimations of the value of Talmud study are shaped, not only by individually held tastes, talents, and commitments, but also by a set of shared intellectual values. These values, related to their beliefs about the purposes of learning and what good learning should accomplish for the learner, develop in the context of their schools and communities and frame how students set goals for and assess their own understanding of Talmud.