Education Commons^™

Parts Of The Whole: Why I Teach This Subject This Way, Dorothy Wallace

Numeracy

The importance of mathematics to biology is illustrated by search data from Google Scholar. I argue that a pedagogical approach based on student research projects is likely to improve retention and foster critical thinking about mathematical modeling, as well as reinforce quantitative reasoning and the appreciation of calculus as a tool. The usual features of a course (e.g., the instructor, assessment, text, etc.) are shown to have very different purposes in a research-based course.

A Quantitative Reasoning Approach To Algebra Using Inquiry-Based Learning, Victor I. Piercey

Numeracy

In this paper, I share a hybrid quantitative reasoning/algebra two-course sequence that challenges the common assumption that quantitative literacy and reasoning are less rigorous mathematics alternatives to algebra and illustrates that a quantitative reasoning framework can be used to teach traditional algebra. The presentation is made in two parts. In the first part, which is somewhat philosophical and theoretical, I explain my personal perspective of what I mean by “algebra” and “doing algebra.” I contend that algebra is a form of communication whose value is precision, which allows us to perform algebraic manipulations in the form of simplification and solving …

Developing Teacher Competencies For Problem-Based Learning Pedagogy And For Supporting Learning In Language-Minority Students, Peter Rillero, Mari Koerner, Margarita Jimenez-Silva, Joi Merritt, Wendy J. Farr

Interdisciplinary Journal of Problem-Based Learning

Teachers need to be able to design and implement problem-based learning (PBL) experiences to help students master the content and the processes in new mathematics and science education standards. Due to the changed population of learners within schools, it is also critically important that teachers in the elementary grades have the abilities to work effectively with English language learners (ELL). This article discusses the implementation of a major initiative by our teachers college to achieve both of these goals through Problem-Based Enhanced Language Learning (PBELL), which combines PBL, enhanced opportunities for language, and ELL methods. The implementation began with a …

Problem-Based Learning In K–8 Mathematics And Science Education: A Literature Review, Joi Merritt, Mi Yeon Lee, Peter Rillero, Barbara M. Kinach

Interdisciplinary Journal of Problem-Based Learning

This systematic literature review was conducted to explore the effectiveness of problem-based and project-based learning (PBL) implemented with students in early elementary to grade 8 (ages 3–14) in mathematics and science classrooms. Nine studies met the following inclusion criteria: (a) focus on PBL, (b) experimental study, (c) kindergarten to grade 8 level, and (d) focus on mathematics or science content. For these studies, we examined: the definitions of PBL used, the components of PBL explicitly identified as salient to student learning, and the effectiveness of PBL. This review found that although there is no consistent definition of PBL, PBL is …

"Returning To The Root" Of The Problem: Improving The Social Condition Of African Americans Through Science And Mathematics Education, Vanessa R. Pitts Bannister, Julius Davis, Jomo Mutegi, Latasha Thompson, Deborah Lewis

Catalyst: A Social Justice Forum

The underachievement and underrepresentation of African Americans in STEM (Science, Technology, Engineering and Mathematics) disciplines have been well documented. Efforts to improve the STEM education of African Americans continue to focus on relationships between teaching and learning and factors such as culture, race, power, class, learning preferences, cultural styles and language. Although this body of literature is deemed valuable, it fails to help STEM teacher educators and teachers critically assess other important factors such as pedagogy and curriculum. In this article, the authors argue that both pedagogy and curriculum should be centered on the social condition of African Americans – …

The History Of American Mathematics Education, Rivka Schreier

The Touro Teacher

The author discusses the history of mathematics education in the United States.

Dramathizing Functions: Building Connections Between Mathematics And Arts, Gunhan Caglayan

Journal of Humanistic Mathematics

This article focuses on connections between mathematics and performance arts (drama). More specifically we offer an exposition of a segment of college algebra mathematics (an introduction to functions), with an approach primarily emphasizing the aesthetic aspects of mathematical learning, teaching, and performing.

What If?: Mathematics, Creative Writing, And Play, Emily Clader

Journal of Humanistic Mathematics

Mathematics can inform creative writing by suggesting structures for it to follow, as well as by providing the imaginative impetus for common rules to be broken. In a workshop co-taught by the author, a class of sixth-grade students explored this interplay as they produced fractal-inspired poetry and geometry-inspired fiction. This article describes the form and results of the workshop in the context of a broader discussion of the influence of mathematics upon literature.

The Role Of Sequence In The Experience Of Mathematical Beauty, Leslie Dietiker

Journal of Humanistic Mathematics

In this article, I analyze the aesthetic dimensions of a sequence of mathematical events found in an unusual first grade lesson in order to demonstrate how sequencing may affect an individual’s experience of mathematical beauty. By approaching aesthetic as a sense or felt quality of an experience in context (Sinclair, 2001, 2011), this analysis explains how sequence can affect the way mathematical objects or actions are experienced by an individual. Thus, rather than questioning whether or in what ways a set of mathematical objects are beautiful or not, this paper addresses under what conditions is the mathematics in play beautiful. …

Exploring Quality Teaching In The Online Environment Using An Evidence-Based Approach, Elena Prieto-Rodriguez, Jennifer Gore, Kathryn Holmes

Australian Journal of Teacher Education

Online learning is increasingly ubiquitous in higher education. However, research regarding online teaching often focuses on the affordances of the online environment rather than on the quality of pedagogy. In this paper we consider how online learning could be enhanced using rich pedagogical models that are consistent with a wealth of existing knowledge on pedagogy for face-to-face settings. To do so, we apply an established framework, the Quality Teaching model, to explore pedagogy in the online environment and illustrate its potential benefits using a case study of 60 students in a tertiary mathematics teacher education program. We conclude that the …

Mathematics For What? High School Students Reflect On Mathematics As A Tool For Social Inquiry, Anastasia Brelias

Democracy and Education

This study examines high school students’ views of mathematics as a tool for social inquiry in light of their classroom experiences using mathematics to explore social issues. A critical theoretical perspective on mathematics literacy is used to ascertain the ways in which their views challenge or affirm the dominant image of mathematics in society. The study concludes that mathematics applications addressing social justice issues are promising vehicles for developing students’ appreciation of mathematics as a social problem-solving tool, an awareness of its limitations, and a healthy skepticism toward its uses.

I Know How To Add Them, I Didn't Know I Had To Add Them, Jyoti R. Jhagroo

Australian Journal of Teacher Education

Abstract: Ten non-English speaking immigrant students shared their lived experiences in their secondary school mathematics classrooms in New Zealand. Through the voices of these students some understandings of the challenges they experienced as second language learners are brought to the fore. The students’ perspectives of the language-related challenges that they faced, how they made sense of learning in an environment where the medium of instruction was dissimilar to their first language, and the impact that language-related challenges may have had on their perceptions of their ability in their new environment compared to their home country, form the basis of this …

What Is So Negative About Negative Exponents?, Geoffrey D. Dietz

Journal of Humanistic Mathematics

While teaching college-level mathematics (from College Algebra to Calculus to Abstract Algebra), I have observed that students are often uncomfortable using negative exponents in calculations. I believe the fault partially lies in the manner in which negative exponents are taught in Algebra 1 or Algebra 2 courses, especially in rigid instructions always to write answers using only positive exponents. After reviewing a sample of algebra texts used in the United States over the last two centuries, it appears that while attitudes toward negative exponents have varied from author to author over time, the current trend is to declare explicitly that …

Parts Of The Whole: The Educational Sieve, Dorothy Wallace

Numeracy

This essay argues that the structure of course prerequisites affects retention of students in a course of study. The same argument suggests that the structure of degree requirements, including quantitative reasoning courses, affects retention in college. In particular, the same set of courses required in a rigid sequence will cause more students to exit the program early than if the same courses were offered in a flexible order.

Changing The Order Of Mathematics Test Items: Helping Or Hindering Student Performance?, Kristin T. Kennedy, Allison G. Butler

Journal of Humanistic Mathematics

This paper recounts an experiment by a mathematics professor who primarily teaches mathematics majors. The main question explored is whether the ordering of the questions makes a difference as to how students perform in a test. More specifically we focus here on the following research questions:\ (1) Does arranging a math test with easy-to-hard items versus hard-to-easy items impact student performance? and (2) If so, does item order impact male and female mathematics majors and non-majors in unique ways? We examine data collected over multiple semesters with several different classes. We find that for most of the mathematics students who …

Parts Of The Whole: When Variation Is The Goal, Dorothy Wallace

Numeracy

The goals of higher education are a population of extreme variability in expertise, a diffusion of specialized knowledge across disciplinary boundaries, and production of strong K-12 teachers. Promoting these three goals has implications at all granularities, from the pedagogy of an individual college professor to the incentives and policies that shape systemic change.

A Mathematician Weighs In On The Evolution Debate, Kris H. Green

Journal of Humanistic Mathematics

There are a variety of reasons underlying the lack of public acceptance for the theory of evolution in the United States. An overlooked cause is related to problems with the mathematics curriculum in the K-12 setting. In this essay, we examine this relationship and propose changes to the mathematics curriculum that could improve mathematical thinking while also providing a basis for understanding theories, like evolution, that are poorly understood.

Review Of Calculation Vs. Context: Quantitative Literacy And Its Implications For Teacher Education By Bernard L. Madison And Lynn Arthur Steen (Editors), Maura B. Mast

Numeracy

Madison, Bernard L. and Steen, Lynn Arthur (Eds.). Calculation vs. Context: Quantitative Literacy and Its Implications for Teacher Education. (Washington, DC: Mathematical Association of America, 2009). 197 pp. Softcover. ISBN 978-0-88385-908-7. Available free on the MAA website at http://www.maa.org/ql/calcvscontext.html

The papers in Calculation vs. Context discuss the role of quantitative literacy in the K-12 curriculum and in teacher education. The papers present a varied set of perspectives and address three themes: the changing environment of education in American society; the challenges, and the necessity, of preparing teachers to teach quantitative literacy and of including quantitative literacy in the K-12 education; …

The Implementation Of Radical Constructivism Within The Urban Mathematics Classroom, Randy Lattimore

Trotter Review

One of the most serious problems in mathematics education continues to be the dismal statewide mathematics proficiency test performance of African-American students in urban schools. It has been argued that one of the best ways to improve performance is by connecting the pedagogy of mathematics to the lives and experiences of these students. Although many theories have been implemented in the urban mathematics classroom to assist African-American students in developing and increasing conceptual understanding, members of the urban mathematics education community should take a closer, more serious look at the implementation of radical constructivism within urban mathematics classrooms.

A number …

Project Mime: Reshaping Mathematics Education In Secondary Schools, Joseph A. Meyinsse

Trotter Review

For a number of years the movement to reform the content and processes of mathematics education has gained momentum. At this time the consensus of professional thought based on student performance is that the old methods of teaching based on performance objectives have failed. As a result, these must be replaced from kindergarten through college by methods which emphasize hands-on activities and thereby actively involve the learner in the educational process and which promote the development of higher order cognitive skills. It is also the consensus that this process will develop students who are mathematically and scientifically literate and who …

Black Underrepresentation In Science And Technology, Robert C. Johnson

Trotter Review

The United States is experiencing a crisis in the training of scientific and technical personnel. A recent report from the National Science Foundation (NSF) indicates that the number of U.S. citizens earning science and engineering doctorates has decreased nearly 5% since 1980. The National Research Council's study of the adequacy of research support for the mathematical sciences in the United States reveals that not only has the production of Ph.D.s in mathematics declined since 1969-70, but the percentage of U.S. citizens receiving those degrees fell during the last decade from 78% of all mathematics Ph.D.s to only 61% of all …