Secondary Level Mathematics Research Articles

Teachers’ beliefs about the discipline of mathematics and the use of technology in the classroom

In the article, three Danish secondary level mathematics teachers’ beliefs about the use of technological tools in the teaching of mathematics and their beliefs about mathematics as a scientific discipline are identified and classified - and the process also aspects of their beliefs about the teaching and learning of mathematics. The potential relationships between these sets of beliefs are also explored. Results show that the teachers not only manifest different beliefs about the use of technology and mathematics as a discipline, but that one set of beliefs can influence the other set of beliefs. The article concludes with a discussion of the research findings and their validity as well as their implications for both practice and research in mathematics education.

Trends in basic mathematical competencies of beginning undergraduates in Ireland, 2003–2013

Deficiencies in beginning undergraduate students’ basic mathematical skills has been an issue of concern in higher education, particularly in the past 15 years. This issue has been tracked and analysed in a number of universities in Ireland and internationally through student scores recorded in mathematics diagnostic tests. Students beginning their science-based and technology-based undergraduate courses in the University of Limerick have had their basic mathematics skills tested without any prior warning through a 40 question diagnostic test during their initial service mathematics lecture since 1998. Data gathered through this diagnostic test have been recorded in a database kept at the university and explored to track trends in mathematical competency of these beginning undergraduates. This paper details findings surrounding an analysis of the database between 2003 and 2013, outlining changes in mathematical competencies of these beginning undergraduates in an attempt to determine reasons for such changes. The analysis found that the proportion of students tested through this diagnostic test that are predicted to be at risk of failing their service mathematics end-of-semester examinations has increased significantly between 2003 and 2013. Furthermore, when students' performance in secondary level mathematics was controlled, it was determined that the performance of beginning undergraduates in 2013 was statistically significantly below that of the performance of the beginning undergraduates recorded 10 years previously.

Why new mathematics teachers do or don’t use practices emphasized in their credential program

A major research concern for teacher education is the impact of university credentialing programs on K-12 teaching and the disjuncture between university-promoted practices and what teachers actually do in their classrooms. In particular, mathematics-credential programs typically promote reform-oriented methods, while mathematics teaching in the US remains largely traditional. Proposed explanations for the limited uptake of university-promoted mathematics-teaching methods have included new teachers’ struggle to bridge the “two worlds” of the university and school, the relative difficulty of reform-oriented teaching, and the failure of the standard teacher-preparation model that teaches general pedagogical concepts prior to specific teaching tools and practices. In this study, interviews of 19 first- through 4th-year secondary-level mathematics teachers—graduates of a single credential program—investigated the factors, internal and external to the credential program, that these teachers perceived to support or impede their implementation of certain university-taught practices. The findings are used to examine previously proposed explanations for limited uptake, and recommendations are made for credential programs and employing schools.

Teachers’ Mathematical Knowledge, Cognitive Activation in the Classroom, and Student Progress

In both the United States and Europe, concerns have been raised about whether preservice and in-service training succeeds in equipping teachers with the professional knowledge they need to deliver consistently high-quality instruction. This article investigates the significance of teachers’ content knowledge and pedagogical content knowledge for high-quality instruction and student progress in secondary-level mathematics. It reports findings from a 1-year study conducted in Germany with a representative sample of Grade 10 classes and their mathematics teachers. Teachers’ pedagogical content knowledge was theoretically and empirically distinguishable from their content knowledge. Multilevel structural equation models revealed a substantial positive effect of pedagogical content knowledge on students’ learning gains that was mediated by the provision of cognitive activation and individual learning support.

Curriculum-Based Measurement for Mathematics at the High School Level

The purpose of this article is to explore the research and developmental needs for curriculum-based measurement (CBM) at the secondary level (9th through 12th grades) for mathematics. Much has been accomplished empirically on the validity, reliability, and utility of CBM as an assessment measure in mathematics at the elementary level. Encouragingly, a few CBM mathematics studies are beginning to emerge at the early (preschool through 1st grades) and middle school levels (6th through 8th grades); however, only one study exists on the use of CBM as an assessment tool for secondary-level mathematics courses. First, the author discusses the current mathematics predicament of secondary students with and without disabilities and their teachers. She then, within the different educational settings (general education, inclusion, resource, self-contained) available at the secondary level, discusses the types of CBM research (technical adequacy, instructional utility) needed.

Pedagogical content knowledge and content knowledge of secondary mathematics teachers.

Drawing on the work of L. S. Shulman (1986), the authors present a conceptualization of the pedagogical content knowledge and content knowledge of secondary-level mathematics teachers. They describe the theory-based construction of tests to assess these knowledge categories and the implementation of these tests in a sample of German mathematics teachers (N=198). Analyses investigate whether pedagogical content knowledge and content knowledge can be distinguished empirically, and whether the mean level of knowledge and the degree of connectedness between the two knowledge categories depends on mathematical expertise. Findings show that mathematics teachers with an in-depth mathematical training (i.e., teachers qualified to teach at the academic-track Gymnasium) outscore teachers from other school types on both knowledge categories and exhibit a higher degree of cognitive connectedness between the two knowledge categories.

Challenges Associated with Developing Discursive Classrooms in High-Poverty, Rural Schools

That teacher was discussing the challenges associated with initiating mathematical discourse with his Navajo students. Although he is interested in developing a classroom in which students regularly share their mathematical thinking with one another, such a discursive classroom may in fact be incongruent with the students' culture. This example demonstrates one of many issues that impede secondary-level mathematics teachers in their efforts to negotiate toward a classroom in which students' ideas are valued and frequently solicited.

Characterizing Students’ Understandings of Mathematical Proof

For many secondary-level mathematics teachers and students, the notion of mathematical proof often conjures up images of mathematical rigor in the form of two-column proofs. Yet in recent years, many mathematics educators have been reexamining the nature of mathematical proof in the secondary curriculum.

Up the Creek with a Paddle

Do I have to know how to do any math for geography?” Although Luke was hoping to find a niche where he needed as little mathematics as possible, his question brought to mind all the practical mathematics that I had used in college geography projects. I was motivated to develop an extended hands-on project for my eighth-grade mathematics classes in which they were to determine the probability that a local creek would flood. This project can be easily adapted to almost any secondary-level mathematics class.

Technology Tips: Evaluating Mathematics Videotapes for Use in the Classroom

One type of technology that is not used to its fullest potential in mathematics classrooms is video technology. Students today, however, have learned from television since they were toddlers. They are constantly exposed to a variety of multimedia entertainment, from computer-animated movies to music television to interactive software and games. Secondary-level mathematics teachers should consider mathematics videotapes to be an important enhancement to their overall instructional program. This article presents selection criteria for teachers to use when reviewing video materials for classroom use and provides an annotated bibliography of available video material.

Eight Methods To Evaluate and Support Reform in the Secondary-Level Mathematics Classroom

An evaluation plan using eight methods—teacher demographic/attitude/behavior questionnaire, focus groups, content knowledge, work sample analysis, teaching logs, videotapes of classrooms, accomplishments and presentations, and action research thesis development—has been effective in assessing a complex project. "Using Computer Visualization in Teaching Secondary Mathe matics (Viz-Math)," a National Science Foundation-funded master's degree program, has been both intensive and extensive in enhancing teachers' mathematics content; in implementing classroom-reformed pedagogy, curriculum, and technology; in requiring classroom research; and m training teachers as change agents. The evaluation methods explored the project's goals in multiple ways to provide a triangulation of findings.

A Matrix Application Technique for Secondary Level Mathematics

Imagine how often we need the equation of a line through two points. Or perhaps it is the equation for a parabola through three noncollinear points that we seek. A single method will allow us to determine these linear and quadratic functions and those of degrees greater than 2! Based on matrices and their inverses, the mechanics of the method are often developed in secondary level mathematics classes.

Course in Applications of Secondary Level Mathematics for 7th-12th Grade Mathematics Teachers, Oregon State University, Corvallis, Oregon.

Course in Applications of Secondary Level Mathematics for 7th-12th Grade Mathematics Teachers, Oregon State University, Corvallis, Oregon.