Science and Mathematics Education Commons^™

Simple Statements, Large Numbers, Shana Streeks

MAT Exam Expository Papers

Large numbers are numbers that are significantly larger than those ordinarily used in everyday life, as defined by Wikipedia (2007). Large numbers typically refer to large positive integers, or more generally, large positive real numbers, but may also be used in other contexts. Very large numbers often occur in fields such as mathematics, cosmology, and cryptography. Sometimes people refer to numbers as being “astronomically large”. However, it is easy to mathematically define numbers that are much larger than those even in astronomy. We are familiar with the large magnitudes, such as million or billion. In mathematics, we may know a …

Teaching Mathematics: Using Research-Informed Strategies, Peter Sullivan

Australian Education Review

AER 59 reviews research into aspects of mathematics teaching, focusing on issues relevant to Australian mathematics teachers, to those who support them, and also to those who make policy decisions about mathematics teaching. It was motivated by and draws on the proceedings of the well-attended and highly successful ACER Research Conference Teaching mathematics? Make it count: What research tells us about effective mathematics teaching and learning, held in Melbourne in August 2010.

Section 2 describes the goals of teaching mathematics and argues that a practical orientation should be the focus of mathematics teaching in the compulsory years, and outlines …

Five Processes Of Mathematical Thinking, Toni Scusa

Summative Projects for MA Degree

My research project was to investigate key processes of mathematical thinking in my seventh grade mathematics classroom. Its purpose was to see whether I could affect the quality of student mathematical thinking and solution writing by teaching students five key processes of mathematical thinking I had identified, and by providing students with opportunities to evaluate sample student solutions using traits describing these processes. Every two weeks, students attempted solutions for a given problem and rated their work according to the specific characteristics identified as key to mathematical thinking. Every other week I gave the class sample student work at varied …

Five Key Ingredients For Improving Student Motivation, Caro C. Williams-Pierce

Mathematics and Statistics Faculty Scholarship

Motivation is probably the most important factor that educators can target in order to improve learning. Numerous cross-disciplinary theories have been postulated to explain motivation. While each of these theories has some truth, no single theory seems to adequately explain all human motivation. The fact is that human beings in general and students in particular are complex creatures with complex needs and desires. With regard to students, very little if any learning can occur unless students are motivated on a consistent basis. The five key ingredients impacting student motivation are: student, teacher, content, method/process, and environment. The focus of this …

Constructivist And Behaviorist Approaches: Development And Initial Evaluation Of A Teaching Practice Scale For Introductory Statistics At The College Level, Rossi A. Hassad

Numeracy

This study examined the teaching practices of 227 college instructors of introductory statistics from the health and behavioral sciences. Using primarily multidimensional scaling (MDS) techniques, a two-dimensional, 10-item teaching-practice scale, TISS (Teaching of Introductory Statistics Scale), was developed. The two dimensions (subscales) are characterized as constructivist and behaviorist; they are orthogonal. Criterion validity of the TISS was established in relation to instructors’ attitude toward teaching, and acceptable levels of reliability were obtained. A significantly higher level of behaviorist practice (less reform-oriented) was reported by instructors from the U.S., as well as instructors with academic degrees in mathematics and engineering, whereas …

The Importance Of Using Manipulatives In Teaching Math Today, Joseph M. Furner, Nancy L. Worrell

Transformations

This paper explores the research and use of mathematics manipulatives in the teaching of mathematics today during an age of technology and standardized testing. It looks at the drawbacks and cautions educators as they use math manipulatives in their instruction. It also explores some cognitive concerns as a teacher goes about teaching with math manipulatives. The paper shares many commonly used math manipulatives used in today’s classrooms and matches them up to some of the Common Core Math Standards that are taught today in classrooms in the USA and around the world.

Class Notes For Math 871: General Topology, Instructor Jamie Radcliffe, Laura Lynch

Math Department: Class Notes and Learning Materials

Topics include: Topological space and continuous functions (bases, the product topology, the box topology, the subspace topology, the quotient topology, the metric topology), connectedness (path connected, locally connected), compactness, completeness, countability, filters, and the fundamental group.

Struggling Learners Of Mathematics: An Investigation Of Their Learning Through Reform-Based Instruction, Jennifer Pothast

Dissertations and Theses @ UNI

The purpose of this study was to explore mathematics instruction which implements reform-based problems within a traditionally taught classroom and its effect on struggling learners of mathematics. The reform-based problems implemented during the course of this study dealt with area and perimeter concepts at the fifth grade level. For this study, struggling learners of mathematics were defined as students scoring below the 40th percentile on the mathematics subtests of the Iowa Test of Basic Skills. The regular classroom teacher taught all lessons during the unit of instruction, while the researcher collected data from students using multiple methods: pretests and posttests, …

Palindromes, Stephanie Fuehrer

MAT Exam Expository Papers

A palindrome is a word or phrase that reads the same forward and backward, such as the word “level” and the phrase “Madam, I’m Adam.” Numbers whose digits read the same forward and backward are also called palindromes, such as the numbers 22, 1234321, and 2002. Palindromic phrases can also occur in number form, for example the Universal day of Symmetry: 8:02 P.M. on February 20, 2002. If one were to look at the time on a twenty-four hour clock, it would read 20:02; the date can be read as the twentieth day of the second month, which also represents …

La Diversidad De Los Análisis De Diversidad La Diversidad De Los Analisis De Diversidad [The Diversity Of Diversity Analyses], Victor D. Carmona-Galindo, Tizziana V. Carmona

Biology Faculty Works

There is a lack of consistency with respect to the use of the terms like species richness, diversity and biodiversity, which extends to the analysis of diversity indices and the merit of using diversity indices in the evaluation (comparison and contrast) of biological communities. The purpose of this article is to provide working definitions for these terms and cite examples from the primary literature that demonstrate the utility of estimating richness, evaluating proportional abundance patterns, as well as comparing indices of diversity and similarity to study patterns of biological organization at different ecological scales. Additionally, we provide a manual in …