Stepping beyond high school mathematics: a case study of high school women

The Summer Explorations and Research Collaborations for High School Girls (SEARCH) Program, held annually since 2004 at Mount Holyoke College in the US, was created for talented high school girls to explore mathematics beyond that taught in high school. Our study, which focuses on factors that facilitate or inhibit the pursuit of higher level mathematics by girls, is centered on the 2006 SEARCH Program. We present a combination of qualitative and quantitative data drawn from student journals written during SEARCH, program evaluations written at the end of SEARCH, post-program interviews, and comparisons with two peer group samples. From this data we point to important factors, such as developing a mathematical voice, gaining a broader view of advanced mathematics, being challenged in a supportive atmosphere, and having a positive stance toward risk-taking, that may help to maintain the interest of talented girls in advanced mathematical studies.     

Mathematical Readiness of Entering College Freshmen: An Exploration of Perceptions of Mathematics Faculty

The National Council of Teachers of Mathematics has set ambitious goals for the teaching and learning of mathematics that include preparing students for both the workplace and higher education. While this suggests that it is important for students to develop strong mathematical competencies by the end of high school, there is evidence to indicate that overall this is not the case. Both national and international studies corroborate the concern that, on the whole, US 12th grade students do not demonstrate mathematical proficiency, suggesting that students making the transition from high school to college mathematics may not be ready for its rigors. In order to investigate mathematical readiness of entering college students, this study surveyed mathematics faculty. Specifically, faculty members were asked their perceptions of average entering students' readiness related to relevant mathematical skills and concepts, and the importance of the same skills and concepts as foundations for college mathematics. Results demonstrated that the faculty perceived that average freshman students are generally not mathematically prepared; further, the skills and concepts rated as highly important — namely, algebraic skills and reasoning and generalization — were among those rated the lowest in terms of student competencies.     

Comparing adult mathematical literacy with PISA students: results of a pilot study

In Germany, very little empirical data about the mathematical competence of adults is available. The aim of this study is to test the level of mathematical competence in an adult sample. For this purpose, a mathematics test was constructed using the PISA mathematics framework as a guideline. The test consisted of fourteen public items from the mathematics test in PISA 2000. The study was implemented by carrying out house visits (Germany). The sample was comprised of 64 adults (90% women, age: 41 years). The test results were scaled in the metric of PISA 2000. Compared with the average German student competencies in PISA 2000, the average competency in the adult sample was on the same level as the fifteen-year-old comprehensive secondary school student (at a German Gymnasium). Further analysis shows that the mathematics competency level in the adult sample is positively connected to the individual vocational education degree.     

The near-peer mathematical mentoring cycle: studying the impact of outreach on high school students’ attitudes toward mathematics

College students may be seen as near-peers to high school students and high school students are often able to see themselves in the college students who are but one step ahead. This nearness in maturity and educational level may place college students in a particularly powerful position when it comes to reaching out to high school students to promote higher education in math and science. In this study college students gave dynamic mathematics outreach presentations, MathShows, to minority and low-income high school students in a mid-sized public school district on the U.S. border with Mexico. The study investigated the impacts of this sort of outreach work on high school students’ attitudes towards mathematics using a mathematics attitudes survey. Results, obtained from N = 306 participants, showed statistically significant improvements in almost all components of mathematical attitudes, with less of an effect on the component of self-confidence in doing mathematics. Differences in impacts by specific student subgroups are all discussed.     

Shortcomings of Mathematics Education Reform in The Netherlands: A Paradigm Case?

This article offers a reflection on the findings of three PhD studies, in the domains of, respectively, subtraction under 100, fractions, and algebra, which independently of each other showed that Dutch students' proficiency fell short of what might be expected of reform in mathematics education aiming at conceptual understanding. In all three cases, the disappointing results appeared to be caused by a deviation from the original intentions of the reform, resulting from the textbooks' focus on individual tasks. It is suggested that this “task propensity”, together with a lack of attention for more advanced conceptual mathematical goals, constitutes a general barrier for mathematics education reform. This observation transcends the realm of textbooks, since more advanced conceptual mathematical understandings are underexposed as curriculum goals. It is argued that to foster successful reform, a conscious effort is needed to counteract task propensity and promote more advanced conceptual mathematical understandings as curriculum goals.     

Reading mathematics for understanding—From novice to expert

As students progress through the college mathematics curriculum, enter graduate school and eventually become practicing mathematicians, reading mathematics textbooks and journal articles appears to become easier and leads to increased proficiency and understanding. This study was designed to begin to understand how mathematically more advanced readers read for understanding in mathematical exposition as it appears in textbooks compared to first-year undergraduate students. Three faculty members and three graduate students participated in this study and read from a first-year graduate textbook in an area of mathematics unfamiliar to each of them. The observed reading strategies of these more mathematically advanced readers are compared to observed reading strategies of first-year undergraduate students from an earlier study. The reading methods of the faculty level mathematicians were all quite similar and were markedly different from those that have been identified for undergraduate students, as well as from those used by the graduate students in this study. A Mathematics Reading Framework is proposed based on this study and previous research documenting the strategies that first-year undergraduate students use for reading exposition in their mathematics textbooks.     

Not from Nowhere History and Philosophy behind Mathematical Education

In this paper I discuss some of the historical and philosophical aspects of mathematical education, especially in foundational subjects where many of the principal issues seem to lie. Historical examples are chosen from the calculus, mathematical analysis, set theory and logic, but the philosophical points discussed also apply to other branches of mathematics.

The paper falls into four parts, which are alternately mainly historical and philosophical. The first part is motivated partly by problems arising in school mathematics (although the subject matter is treated from a more advanced viewpoint), and the second attempts to develop some general methodological considerations. The third part is relevant mainly to university mathematics, while the final part contains a number of broad conclusions, including the question of the role of the history of mathematics in mathematical education.     

Post-primary students’ images of mathematics: findings from a survey of Irish ordinary level mathematics students

A questionnaire survey was carried out as part of a PhD research study to investigate the image of mathematics held by post-primary students in Ireland. The study focused on students in fifth year of post-primary education studying ordinary level mathematics for the Irish Leaving Certificate examination – the final examination for students in second-level or post-primary education. At the time this study was conducted, ordinary level mathematics students constituted approximately 72% of Leaving Certificate students. Students were aged between 15 and 18 years. A definition for ‘image of mathematics’ was adapted from Lim and Wilson, with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. A questionnaire was composed incorporating 84 fixed-response items chosen from eight pre-established scales by Aiken, Fennema and Sherman, Gourgey and Schoenfeld. This paper focuses on the findings from the questionnaire survey. Students’ images of mathematics are compared with regard to gender, type of post-primary school attended and prior mathematical achievement.     

Gender differences in the mathematics achievements of German primary school students: results from a German large-scale study

In Germany, national standards for mathematics for the end of primary school were established in 2004. In the present study, data were collected to evaluate these standards, and were used to compare the mathematical skills of girls and boys. Many studies have shown that gender differences are strongest at the highest levels of education. The findings from primary school are less consistent. Thus, in our study we analyzed achievement differences in a sample of approximately 10,000 third and fourth graders, representative of the German elementary school population. Gender-specific competencies were compared in the different content domains, both for the general mathematical competence, and for the cognitive levels of the tasks. Overall, boys outperformed girls, but substantial variation was found between the content domains and general mathematical achievement. Differences were higher in grade three than in grade four. The proportion of boys in the classroom did not appear to affect the individual level of performance. Analysis of the items on which boys or girls clearly outperformed each other reproduced a pattern of specific item characteristics predicting gender bias consistent with those reported in previous studies in other countries.     

在军事院校大一新学员高等数学的教学中融入数学文化的思考与体会

军事院校的高等数学的教学有其固有的特点,大学数学的部分内容进入中学课堂,对高等数学的教学产生了一定的积极影响,在此过渡基础上军校的高等数学的教学中融入数学文化,不仅增强了趣味性有利于克服脱节现象,而且在教学内容、教学理念、教学方法上也得到衔接与提升,有助于培养军事院校大学生的综合素质与创新能力.     

数学建模对高职数学基础课程改革的推动作用

针对高职办学定位和生源基础,开发高职专业案例,将数学建模思想融入常规教学,创新高职数学教学模式,在数学建模活动的普及中破除"数学无用"的偏见、降低高职学生对学数学的心理畏惧。对大数据时代进一步扩大数学建模对高职数学课程改革的影响力提出了关注数据处理、开发共享资源和引领高职本科数学教学方向等对策建议。     

中学数学教学内容改革对高等数学教学影响的客观分析及对策

大学数学的部分内容进入中学课堂是大势所趋,对大学高等数学的教学产生了一定的积极影响.在此基础上的高等数学教学改革不仅需要重视传统,更需要重视教学内容、教学理念、教学方法上的提升与创新.     

Comparisons of Success and Retention in a General Chemistry Course Before and After the Adoption of a Mathematics Prerequisite

This study of the relationships between mathematical ability and success and retention in a general chemistry course was conducted at an open‐enrollment university whose mission is to provide a quality education to a culturally and economically diverse student body. We studied the correlation between the demonstrated level of mathematical ability and success in chemistry and the correlation between the demonstrated level of mathematical ability and retention in chemistry. After the chemistry department implemented a mathematics prerequisite for the chemistry course, data were examined to compare success and retention prior to and after the adoption of the prerequisite. Analysis showed that success and retention in chemistry increased after the adoption of the mathematics prerequisite.     

Mathematics on the Playground

Non‐traditional forms of instruction provide exciting and engaging opportunities for mathematics education. This article proposes the use of mathematicalfigures painted on the school playground as an environment to support mathematical teaching, learning, and understanding. Teachers plan mathematics lessons to take advantage of the playground figures and present new topics, reinforce current topics, and review previous topics. Figures were chosen to support mathematical concepts required by the curriculum and state and national standards. The intentional blank portions of the playground figures allowed for adjustment of lesson activities to meet different grade level and individual student needs, as well as making the figures interactive with the use of sidewalk chalk. A teacher handbook suggests activities for each figure by grade level, and teachers often create their own ideas for using the figures. Students like the change of perspective and teachers feel that such lessons help to raise standardized test scores because the information is better retained. The lessons addressed multiple learning styles, help with vocabulary for English Language Learners, and infuse higher thinking levels into lessons.     

The Influences of Three Interventions on Prospective Elementary Teachers' Beliefs About the Knowledge Base Needed for Teaching Mathematics

To meet the challenge to reform mathematics education, effective opportunities to learn are needed to promote prospective elementary school teachers' development of the knowledge base that supports teaching for mathematical proficiency. This article describes three professional development interventions and their influence on prospective teachers' beliefs about mathematics, how children learn mathematics, and mathematics teaching. The three interventions consisted of problem‐solving journals, structured interviews, and peer teaching that were integrated in a PreK‐6 mathematics methods course. Results of precourse and postcourse survey data are included that measured 24 prospective teachers' beliefs about the knowledge base needed to teach elementary school mathematics. Data indicated that using these interventions and other course experiences facilitated change in the prospective teachers' beliefs, with a shift toward reform‐oriented mathematics education perspectives.     

高师本科数学分析教学改革的研究与实践

以信息社会为特征的新世纪开始提出扫“数学盲”的历史任务 ,而脱盲的标志则是要懂得微积分基础 [1 ] ,然微分与积分是数学分析的主体的结构 .因此 ,2 1世纪的大学数学教育应该搞好数学分析课程的改革与建设 ,开展教学研究 .本文将给出我们在数学分析教学改革的研究与实践 [1 - 3] 的一系列的做法 ,以便请教于同行     

Relationships Between Student,Teacher, and School Characteristics and Mathematics Achievement

A variety of factors contributes to student achievement in mathematics, including but not limited to student behaviors and student, teacher, and school characteristics. The purpose of this study was to explore which of these factors have an impact on student mathematics achievement. The target population for this study was North Carolina Algebra II students. Analyses of variance models were examined for group differences and a Three‐level Hierarchical Linear Modeling method was employed to examine individual predictors of student achievement in mathematics. Statistically, significant differences were found between students of different ethnicities, socioeconomic statuses (SES), and parental education levels. No gender effects were statistically significant. All teacher‐level variables investigated were found to be statistically significant, impacting student achievement in mathematics. School size and SES were not found to significantly contribute to student achievement. More research on the relationships between these factors shown to make statistically significant differences on mathematics achievement is needed to further explain several phenomena that this research reveals.     

Mathematics-related teaching competence of Taiwanese primary future teachers: evidence from TEDS-M

This paper draws on data from the international TEDS-M study, organized by the IEA, and utilizes a conceptual framework describing the Taiwanese perspective of mathematics and mathematics teaching competences (MTCs) with regard to investigating the uniqueness and patterns of Taiwanese future primary teacher performance in the international context. The framework includes content-oriented and thought-oriented categories of mathematics competence. The latter category contains subcategories adopted and revised from (3rd Mediterranean conference on mathematical education. Hellenic Mathematical Society, Athens, 2003) the competence approach by Niss. Hsieh’s (Research on the development of the professional ability for teaching mathematics in the secondary school level (3/3). Taiwan: National Science Council, 2009) model is also adopted and revised to serve as an analytical framework, including four categories relating to MTCs, representations, language, and misconceptions or error procedures. This paper shows that in thought-oriented mathematics competences Taiwan and Singapore share a unique pattern of higher percent correct in competences related to formalization, abstraction, and operations in mathematics than in those related to the way of thinking, modelling and reasoning in and with mathematics. The paper also addresses weak teaching competences claimed in domestic studies, which conflict with the TEDS-M results. Namely, in contrary to the international trend, Taiwanese future primary teachers are weak at judging mathematics competences required by students to learn mathematical concepts or solve problems, and superior at diagnosing and dealing with student misconceptions and error procedures.     

Progressive, classical or balanced— A look at mathematical learning environments in Swiss-German lower-secondary schools

In a national supplement to TIMSS, lower-secondary school teachers (N=102) and their students (N=975) reported on mathematics instruction by means of a teacher questionnaire (teaching-learning methods, instructional sub-goals, facilitated student activities, achievement assessment, teacher role) and a student questionnaire (teachers' instructional proficiency, classroom climate). A cluster analysis performed on the ratings of teaching-learning methods yielded a solution with three clusters referred to as progressive, classical, and balanced learning environment. Cluster-related differences in facilitated student activities, achievement evaluation and preferred teacher role were found but not in instructional sub-goals. Students from different learning environments equally approved teachers' instructional proficiency and classroom climate and also had similar TIMSS mathematics scores. The results of this study provide empirical evidence that in addition to classical teacher-centered learning environments there seem to exist more diversified and studentcentered learning environments that address the needs for students to direct their own learning, communicate and work with others, and develop ways of dealing with complex problems. In line with the research literature it was also found that high mathematics achievement is not restricted to a certain type of learning environment.     

数学建模对高中生构建数学底层思维的作用及其教学实施建议

数学底层思维即用数学的眼光观察世界、用数学的思维分析世界以及用数学的语言表达世界,是人们面对自然和社会中纷繁多样的现象和问题时,所展现的自发的、不依赖监督的、融汇数学学科核心素养的思维方式.作为国家高中新课程标准中数学六大核心素养之一的数学建模,是培养学生数学底层思维的良好载体,对人才培养和社会发展均起到良好的促进作用.本文主要阐述了数学建模对高中生构建数学底层思维的作用,并结合教学实例给出教学实施建议.