An Advanced Mathematics Program for Middle School Teachers

The Conference Board of the Mathematical Sciences (CBMS), National Council of Teachers of Mathematics, and other organizations recommend twenty-one credits of mathematics coursework for prospective middle school teachers, beginning with a foundation based on mathematics for the elementary school curriculum, and followed by advanced courses directly addressing middle school mathematics. Three simultaneous factors—the emergence of the Interdisciplinary Liberal Studies Program at James Madison University, the release of CBMS guidelines, and a statewide focus on a critical shortage of qualified middle school teachers—provided an immediate audience for new upper-division courses built around the guidelines in probability/statistics, algebra, geometry, and calculus/analysis. We will discuss our experience with course planning and adaptation of other programs

English only for science and maths

Most ot the courses offered at Universiti Putra Malaysia (UPM) will be taught in English beginning, 2005, in line with the Government's policy to teach mathematics and science based courses in the language

Comparing Recent High School Graduates Placed in Developmental and College-Level Mathematics Courses

The purpose of this study was to determine any significant differences among recent high school graduates placed in developmental and college-level mathematics courses. The focus of the investigation was on students’ high school course-taking patterns in mathematics and their attitudes and beliefs towards mathematics. High school location was also considered. The study was conducted at two community colleges in east Tennessee. Students placed in both developmental and college-level mathematics courses completed surveys at the beginning of the fall semester 2006. Four scales of the Fennema-Sherman Mathematics Attitudes Scales (1976), along with the Indiana Mathematics Belief Scales (Kloosterman & Stage, 1992), were used to assess students’ attitudes and beliefs towards mathematics. Data analysis was limited to recent high school graduates (students who graduated from high school in the spring of 2006) who were taking a mathematics course for the first time in college. No significant differences were found among rural and non-rural recent high school graduates with regard to mathematics course-taking patterns in high school and attitudes and beliefs towards mathematics. Furthermore, rural students were no more likely to be placed in developmental mathematics courses upon entering college than were non-rural students. Significant differences were found among students placed in developmental and college-level mathematics courses. Students placed in developmental mathematics courses took significantly fewer mathematics courses in high school than did students placed in college-level mathematics courses. In addition, students placed inSignificant differences were found among students placed in developmental and college-level mathematics courses. Students placed in developmental mathematics courses took significantly fewer mathematics courses in high school than did students placed in college-level mathematics courses. In addition, students placed in developmental mathematics courses were less likely to have taken a course beyond Algebra II or Geometry in high school than were students placed in college-level mathematics courses. Students placed in developmental mathematics courses had significantly less confidence and effectance motivation in mathematics than did students placed in college-level mathematics courses. Also, students placed in developmental mathematics courses had a significantly lower belief in the usefulness of mathematics than did students placed in college-level mathematics courses. Finally, students placed in developmental mathematic courses had a significantly lower belief in their ability to solve time-consuming mathematics problems and in that it is not always possible to solve word problems using simple, step-by-step procedures than did students placed in collegelevel mathematics courses

Concordance between introductory university mathematics courses and the program of pre-university studies: A view from the perspectives of content and academic performance

This article reports data about academic achievement in introductory university level mathematics courses taught by the Department of Mathematics at the Universidad Nacional de Costa Rica and the concord¬ance between the contents of these courses and those of pre-university (secondary education) programs. Information was collected by analyzing grades from introductory university mathematics courses for all programs of study in the period 2011-2016, the courses offered, and the program of studies in mathemat¬ics in secondary education. This was done to determine academic performance and to make comparisons between introductory mathematics courses at university level and the program of mathematics studies in secondary education, to stimulate revision and updating of the courses and generate recommenda¬tions. The results show that there are high failure and dropout rates in most introductory university-level mathematics courses, and that there are differences between the content that students study in secondary education and the content of introductory mathematics courses offered by the Universidad Nacional; prior knowledge is therefore relevant for academic achievement in introductory university mathematics courses. In addition, the data collected on content and aspects of methodology and evaluation show important differences in the way mathematical contents are addressed at each level. This implies that analysis of the contents of these courses should be carried out and strategies should be created, to guarantee a minimum level of prior knowledge in students when beginning the study of these subjects at university level

Problem-posing as a didactic resource in formal mathematics courses to train future secondary school mathematics teachers

Beginning university training programs must focus on different competencies for mathematics teachers, i.e., not only on solving problems, but also on posing them and analyzing the mathematical activity. This paper reports the results of an exploratory study conducted with future secondary school mathematics teachers on the introduction of problem-posing tasks in formal mathematics courses, specifically in abstract algebra and real analysis courses. Evidence was found that training which includes problem-posing tasks has a positive impact on the students’ understanding of definitions, theorems and exercises within formal mathematics, as well as on their competency in reflecting on the mathematical activityPeer Reviewe

An Investigation of First-time College Freshmen and Relationships Among Mathematical Mindset, Identity, Self-efficacy, and Use of Self-regulated Learning Strategies

Students experience great social and academic challenges during their first semester of college and for many, the completion of required mathematics courses is one of those challenges. This study investigated the relationship of first-time college freshmen’s mathematics course enrollment, gender, and high school mathematics course experience to their mathematical mindset, identity, self-efficacy, and use of self-regulated learning strategies in mathematics courses. Two forms of a researcher-developed survey instrument were administered to students enrolled in three mathematics courses at a Midwestern public research university to examine the differences among those constructs at the beginning and end of the Fall 2018 semester. A multivariate analysis of variance on the data from 299 participants at the beginning of the semester indicated significant differences in students’ mathematical identity and self-efficacy scores. Calculus I students reported significantly higher mathematical identity scores than Intermediate Algebra students, and students who had taken mathematics courses beyond Algebra 2 in high school had significantly higher mathematical identity and self-efficacy scores than those who had not. A multivariate analysis of variance on the data from 176 participants at the end of the semester found marginally significant differences in Intermediate Algebra and Calculus I students’ mathematical identity scores. There were no significant gender differences identified for any of the constructs nor any significant differences in students’ mathematical mindset or use of self-regulated learning strategies scores at the beginning or end of the semester, and no significant differences in mathematical self-efficacy were identified at the end of the semester. Multiple linear regression analyses indicated that college mathematics course enrollment contributed significantly to mathematical mindset, identity, and use of self-regulated learning strategies, and high school mathematics course experience contributed significantly to mathematical identity and self-efficacy. Mathematical self-efficacy scores decreased over the course of the semester for all 68 of the participants who took both surveys; a repeated measures analysis of variance revealed statistically significant differences for males, Intermediate Algebra students, and those who had taken advanced mathematics courses in high school. No statistically significant differences were identified among two-time participants with regard to mathematical mindset, identity, or use of self-regulated learning strategies

Mathematics Tracking: Policy Brief

Tracking is a long-standing practice in schools. Students are often placed in tracks beginning in upper elementary or middle school. The tracks in which students are placed in earlier grades set them up for the mathematics courses they are able to take in high school. The number of mathematics tracks for students can differ from school to school, but the policy of having mathematics tracks is common throughout schools in the United States. This policy brief will discuss the arguments for and against mathematics tracking policies, implications for educators and policymakers, and future directions

Attitudes towards mathematics in pre-service teacher training: a comparative study between spain and portugal focusing on anxiety

This article is part of a larger project - Attitudes towards Sciences and Mathematics - involving several Ibero-American countries. In this paper, we analyze attitudes related to anxiety towards mathematics in two studies with Spanish and Portuguese pre-service teachers. The participants of the first study (N = 186) are Spanish pre-service teachers at the beginning of the mathematics curricular units of their courses, and Portuguese preservice teachers at the beginning of professional master's degree courses; the participants of the second study (N = 229) are the same Spanish pre-service teachers and Portuguese pre-service teachers at entry into higher education. The Modified Auzmendi Questionnaire was used to research the association between anxiety and gender, stage of education and country. An association between anxiety and country was found in the first study, Spanish pre-service teachers showing greater anxiety. At entry into higher education (second study), no significant difference in level of anxiety was found across the two countries. We concluded that further cross-country comparative research is needed to examine the stability of those findings, and whether the pedagogies used throughout teacher training contribute to the increase or decrease of anxiety towards mathematics

Ode to Applied Physics: The Intellectual Pathway of Differential Equations in Mathematics and Physics Courses: Existing Curriculum and Effective Instructional Strategies

The purpose of this thesis is to develop a relationship between mathematics and physics through differential equations. Beginning with first-order ordinary differential equations, I develop a pathway describing how knowledge of differential equations expands through mathematics and physics disciplines. To accomplish this I interviewed mathematics and physics faculty, inquiring about their utilization of differential equations in their courses or research. Following the interviews I build upon my current knowledge of differential equations in order to reach the varying upper-division differential equation concepts taught in higher-level mathematics and physics courses (e.g., partial differential equations, Bessel equation, Laplace transforms) as gathered from interview responses. The idea is to present a connectedness between the simplest form of the differential equation to the more complicated material in order to further understanding in both mathematics and physics. The main goal is to ensure that physics students aren’t afraid of the mathematics, and that mathematics students aren’t without purpose when solving a differential equation. Findings from research in undergraduate mathematics education and physics education research show that students in physics and mathematics courses struggle with differential equation topics and their applications. I present a virtual map of the various concepts in differential equations. The purpose of this map is to provide a connectedness between complex forms of differential equations to simpler ones in order to improve student understanding and elevate an instructor’s ability to incorporate learning of differential equations in the classroom