Open Access. Powered by Scholars. Published by Universities.®
- Discipline
- Keyword
-
- Correlation (2)
- Kendall (2)
- Rank statistics (2)
- 3-manifolds (1)
- Absolute value (1)
-
- Autism Spectrum Disorder (1)
- Autism Spectrum Quotient (1)
- Calculus (1)
- Chromatic number (1)
- Classical regression (1)
- Combinatorics (1)
- Computer (1)
- Confidence intervals; Hypothesis testing; Robust estimates; Simple linear regression (1)
- Correlation coefficient (1)
- Covariation (1)
- Density parameter estimation (1)
- Department history (1)
- Eating Disorder (1)
- Eating Disorder Examination Questionnaire (1)
- Geometric topology (1)
- Gini (1)
- Girth (1)
- Graph theory; extremal numbers; hypergraphs (1)
- Greatest Deviation (1)
- Greatest deviation correlation coefficient (1)
- HIERARCHICAL (1)
- Hydrology (1)
- Hyperbolic geometry (1)
- Kalman Filter (1)
- Knapsack (1)
- Publication Year
- Publication
- Publication Type
Articles 31 - 60 of 426
Full-Text Articles in Mathematics
Editorial: All Good Things Come In Three, Bharath Sriraman
Editorial: All Good Things Come In Three, Bharath Sriraman
The Mathematics Enthusiast
No abstract provided.
Linking Pre-Service Teachers’ Questioning And Students’ Strategies In Solving Contextual Problems: A Case Study In Indonesia And The Netherlands, Rahmah Johar, Sitti Maesuri Patahuddin, Wanty Widjaja
Linking Pre-Service Teachers’ Questioning And Students’ Strategies In Solving Contextual Problems: A Case Study In Indonesia And The Netherlands, Rahmah Johar, Sitti Maesuri Patahuddin, Wanty Widjaja
The Mathematics Enthusiast
This study examined the relationship between teachers’ questioning techniques and students’ strategies in solving contextual mathematical problems. This case study was undertaken with one pre-service teacher (and 22 Year 4 students) from Indonesia and one pre-service teacher (and 25 Year 4 students) in the Netherlands. Both pre-service teachers assigned the same problems to their students and these problems were novel for the students in both countries. The lessons were observed by the first author and video recorded for data analysis. Qualitative data analysis was undertaken through within-case and cross-case analysis. The findings suggest that the contextual problems, the way pre-service …
Subtraction Involving Negative Numbers: Connecting To Whole Number Reasoning, Laura Bofferding, Nicole Wessman-Enzinger
Subtraction Involving Negative Numbers: Connecting To Whole Number Reasoning, Laura Bofferding, Nicole Wessman-Enzinger
The Mathematics Enthusiast
In this article, we explore how students attempt to bridge from their whole number reasoning to integer reasoning as they solve subtraction problems involving negative numbers. Based on interviews with students ranging from first graders to preservice teachers, we identify two overarching strategies: making connections to known problem types and leveraging conceptions of subtraction. Their initial connections suggest that rather than identifying the best instructional models to teach integer concepts, we should focus on identifying integer instructional models that build on the potentially productive connections that students’ already make; we propose an example of one such form of instruction.
Students’ Reactions To Reform Mathematics Pedagogy In A Postsecondary Remedial Mathematics Course, Luke Smith, W. Gary Martin, Anna Wan, Gilbert Duenas
Students’ Reactions To Reform Mathematics Pedagogy In A Postsecondary Remedial Mathematics Course, Luke Smith, W. Gary Martin, Anna Wan, Gilbert Duenas
The Mathematics Enthusiast
The students in this study were enrolled in a remedial mathematics course at a small 4-year university and were taught according to the reform pedagogical principles advocated by NCTM, AMATYC, and MAA. Since most of the students had not been previously exposed to these teaching methods, this study obtained students’ reactions (n = 22) to the course through an anonymous, free-response (not multiple choice) survey at the end of the course. Surveys from students in two equivalent “traditional” lecture courses (n = 44) were also analyzed and served as a baseline by which to gauge students’ responses from the reform …
On Mathematics With Distinction, A Learner-Centered Conceptualization Of Challenge And Choice-Based Pedagogies, Boris Koichu
On Mathematics With Distinction, A Learner-Centered Conceptualization Of Challenge And Choice-Based Pedagogies, Boris Koichu
The Mathematics Enthusiast
The main argument of this article is that “challenging mathematics for all” can be more than just a nice slogan, on condition that all students are empowered to make informed choices of: a challenge to be dealt with, a way of dealing with the challenge, a mode of interaction, an extent of collaboration, and an agent to learn from. Pedagogies supporting such choices are called choice-based pedagogies. The article begins from a theoretical discussion of the relationships between the notions ‘mathematics with distinction,’ ‘giftedness’, ‘challenge’ and ‘choice’. As a result, the learner-centered conceptualization of mathematical challenge is proposed. Then two …
A 21st Century Economic, Educational And Ethical Mathematics Curriculum Policy, Glen S. Aikenhead
A 21st Century Economic, Educational And Ethical Mathematics Curriculum Policy, Glen S. Aikenhead
The Mathematics Enthusiast
Reformulating a mathematics curriculum is a political act, contextualized by economic, educational and ethical considerations, among others. This article represents a political rendition of a rationale to update the Saskatchewan, Canada, curriculum so it harmonizes with a cultural understanding of school mathematics (Ernest, 1988). By revisiting the 19th century definition of school mathematics that we generally follow today, its economic, educational and ethical consequences seem contrary to the expectations of 21st century Saskatchewan.The article’s point form organization, uninterrupted by the appearance of references, conforms to the genre of submissions to government committees. However, footnotes will clarify information for readers unfamiliar …
Counting Subgraphs In F-Free Graphs, Cory T. Palmer
Counting Subgraphs In F-Free Graphs, Cory T. Palmer
University Grant Program Reports
During the funded period I continued what had been a preliminary investigation into a generalization of the central theory of extremal graph theory. With the help of funding from the UGP grant I was able to cover the travel expenses for several very productive visits.
Editorial, Bharath Sriraman
The Secret Life Of 1/N: A Journey Far Beyond The Decimal Point, Christopher Lyons
The Secret Life Of 1/N: A Journey Far Beyond The Decimal Point, Christopher Lyons
The Mathematics Enthusiast
The decimal expansions of the numbers 1/n (such as 1/3 = .03333..., 1/7 = 0.142857...) are most often viewed as tools for approximating quantities to a desired degree of accuracy. The aim of this exposition is to show how these modest expressions in fact have much more to offer, particularly in the case when the expansions are infinitely long. First we discuss how simply asking about the period (that is, the length of the repeating sequence of digits) of the decimal expansion of 1/n naturally leads to more sophisticated ideas from elementary number theory, as well as to …
The History Of Algorithmic Complexity, Audrey A. Nasar
The History Of Algorithmic Complexity, Audrey A. Nasar
The Mathematics Enthusiast
This paper provides a historical account of the development of algorithmic complexity in a form that is suitable to instructors of mathematics at the high school or undergraduate level. The study of algorithmic complexity, despite being deeply rooted in mathematics, is usually restricted to the computer science curriculum. By providing a historical account of algorithmic complexity through a mathematical lens, this paper aims to equip mathematics educators with the necessary background and framework for incorporating the analysis of algorithmic complexity into mathematics courses as early on as algebra or pre-calculus.
Integral Of Radical Trigonometric Functions Revisited, Natanael Karjanto, Binur Yermukanova
Integral Of Radical Trigonometric Functions Revisited, Natanael Karjanto, Binur Yermukanova
The Mathematics Enthusiast
This article revisits an integral of radical trigonometric functions. It presents several methods of integration where the integrand takes the form 1+/- sin x or 1+/- cos x. The integral has applications in Calculus where it appears as the length of cardioid represented in polar coordinates.
Mathematical Problem-Solving Via Wallas’ Four Stages Of Creativity: Implications For The Undergraduate Classroom, Milos Savic
Mathematical Problem-Solving Via Wallas’ Four Stages Of Creativity: Implications For The Undergraduate Classroom, Milos Savic
The Mathematics Enthusiast
The central theme in this article is that certain problem-solving frameworks (e.g., Polya, 1957; Carlson & Bloom, 2005) can be viewed within Wallas’ four stages of mathematical creativity. The author attempts to justify the previous claim by breaking down each of Wallas’ four components (preparation, incubation, illumination, verification) using both mathematical creativity and problem-solving/proving literature. Since creativity seems to be important in mathematics at the undergraduate level (Schumacher & Siegel, 2015), the author then outlines three observations about the lack of fostering mathematical creativity in the classroom. Finally, conclusions and future research are discussed, with emphasis on using technological advances …
Plato On The Foundations Of Modern Theorem Provers, Ines Hipolito
Plato On The Foundations Of Modern Theorem Provers, Ines Hipolito
The Mathematics Enthusiast
Is it possible to achieve such a proof that is independent of both acts and dispositions of the human mind? Plato is one of the great contributors to the foundations of mathematics. He discussed, 2400 years ago, the importance of clear and precise definitions as fundamental entities in mathematics, independent of the human mind. In the seventh book of his masterpiece, The Republic, Plato states “arithmetic has a very great and elevating effect, compelling the soul to reason about abstract number, and rebelling against the introduction of visible or tangible objects into the argument” (525c). In the light of this …
Aesthetics In School Mathematics: A Potential Model And A Possible Lesson, Hartono Tjoe
Aesthetics In School Mathematics: A Potential Model And A Possible Lesson, Hartono Tjoe
The Mathematics Enthusiast
Earlier studies on improving classroom practice in mathematics have suggested a closer attention to nurturing an aesthetic appreciation for mathematics in students’ learning experiences. Recent evidence nonetheless reveals little indication of its presence. This article offers a potential model of the case for aesthetics in school mathematics. Central to this model is the harmonious hierarchy of necessity, existence, and uniqueness without any of which the case for aesthetics in student learning might be suboptimal, if not untenable. This article offers an example of the proposed model using a possible lesson designed to engage students aesthetically in the learning of mathematics. …
Assessing Mathematical Knowledge For Teaching: The Role Of Teaching Context, Geoffrey Phelps, Heather Howell
Assessing Mathematical Knowledge For Teaching: The Role Of Teaching Context, Geoffrey Phelps, Heather Howell
The Mathematics Enthusiast
Assessments of mathematical knowledge for teaching (MKT), which are often designed to measure specialized types of mathematical knowledge, typically include a representation of teaching practice in the assessment task. This analysis makes use of an existing, validated set of 10 assessment tasks to both describe and explore the function of the teaching contexts represented. We found that teaching context serves a variety of functions, some more critical than others. These context features play an important role in both the design of assessments of MKT and the types of mathematical knowledge assessed.
Guest Editorial: Mathematical Knowledge For Teaching: Developing Measures And Measuring Development, Reidar Mosvold, Mark Hoover
Guest Editorial: Mathematical Knowledge For Teaching: Developing Measures And Measuring Development, Reidar Mosvold, Mark Hoover
The Mathematics Enthusiast
No abstract provided.
Interview Prompts To Uncover Mathematical Knowledge For Teaching: Focus On Providing Written Feedback, Yeon Kim
The Mathematics Enthusiast
One area of study that has been gathering enthusiastic attention and interest is mathematical knowledge for teaching (MKT). How to research MKT, however, is still unsettled despite the plethora of unexamined areas of practice. As one of ways to unearth and measure MKT, this study uses interview prompts designed to providing written feedback, as a target area of practice. This study specifies in what ways the interview prompts are used in order to provide a comprehensive method to researching MKT. From interviews across professional communities with different kinds of mathematical expertise, the author develops a conceptual model based on the …
Why Defining The Construct Matters: An Examination Of Teacher Knowledge Using Different Lenses On One Assessment, Chandra H. Orrill, Allan S. Cohen
Why Defining The Construct Matters: An Examination Of Teacher Knowledge Using Different Lenses On One Assessment, Chandra H. Orrill, Allan S. Cohen
The Mathematics Enthusiast
What does it mean to align an assessment to the domain of interest? In this paper, we analyze teachers’ performance on the Learning Mathematics for Teaching assessment of Proportional Reasoning. Using a mixture Rasch model, we analyze their performance on the entire assessment, then on two different subsets of items from the original assessment. We consider the affordances of different conceptualizations of the domain and consider the implications of the domain definition on the claims we can make about teacher performance. We use a single assessment to illustrate the differences in results that can arise based on the ways in …
Tme Volume 13, Numbers 1 And 2
Knowledge For Equitable Mathematics Teaching: The Case Of Latino Ells In U.S. Schools, Aaron T. Wilson
Knowledge For Equitable Mathematics Teaching: The Case Of Latino Ells In U.S. Schools, Aaron T. Wilson
The Mathematics Enthusiast
This paper reports the exploration of an aspect of knowledge needed for equitable mathematics teaching. Pedagogical Content Knowledge for Teaching Mathematics to English Language Learners (PCK-MELL) was proposed as a theoretical knowledge construct, a subdomain of MKT, and the construct was investigated through a process of survey instrument development and administration. The survey contained items intended to measure teachers’ knowledge of the obstacles encountered by ELLs in math classes, of the resources that ELLs draw upon, and of instructional strategies for teaching ELLs. Analysis of middle school mathematics teachers’ responses (N = 42) offered insights into how to improve the …
Making Progress On Mathematical Knowledge For Teaching, Mark Hoover, Reidar Mosvold, Deborah L. Ball, Yvonne Lai
Making Progress On Mathematical Knowledge For Teaching, Mark Hoover, Reidar Mosvold, Deborah L. Ball, Yvonne Lai
The Mathematics Enthusiast
Although the field lacks a theoretically grounded, well-defined, and shared conception of mathematical knowledge required for teaching, there appears to be broad agreement that a specialized body of knowledge is vital to improvement. Further, such a construct serves as the foundation for different kinds of studies with different agendas. This article reviews what is known and needs to be known to advance research on mathematical knowledge for teaching. It argues for three priorities: (i) finding common ground for engaging in complementary studies that together advance the field; (ii) innovating and reflecting on method; and (iii) addressing the relationship of such …
Use Of Mathematical Tasks Of Teaching And The Corresponding Lmt Meaures In The Malawi Context, Mercy Kazima, Arne Jakobsen, Dun N. Kasoka
Use Of Mathematical Tasks Of Teaching And The Corresponding Lmt Meaures In The Malawi Context, Mercy Kazima, Arne Jakobsen, Dun N. Kasoka
The Mathematics Enthusiast
We discuss the adaptation and piloting of the previously developed U.S.-specific measures of mathematical knowledge for teaching to the Malawi context. The purpose is to produce measures that can be used to evaluate changes in mathematical knowledge for teaching gained through primary teacher education, thus informing teacher educators on the most effective evidence-based practices. By interviewing 14 teachers, we first examine whether the 16 recurrent mathematical tasks of teaching tasks identified in the U.S. are applicable to the Malawi context. This is followed by the discussion of the adaptability of the U.S. developed number concept and operations LMT measures. Next, …
In-Service Teachers' Reasoning About Scenarios Of Teaching Mathematics To English Language Learners, Sultan Turkan
In-Service Teachers' Reasoning About Scenarios Of Teaching Mathematics To English Language Learners, Sultan Turkan
The Mathematics Enthusiast
The student population in the U.S. and worldwide is becoming increasingly diverse, creating a need to support all learners, especially linguistically and culturally diverse subpopulations such as English language learners (ELLs). From a social equity standpoint, the need to support these learners is critical especially in mathematics classrooms. In the U.S, the demand for mathematics teachers who are adequately prepared to teach ELLs has in fact risen. Yet, little is known about what knowledge base is essential to teach mathematics to ELLs. Driven by the need to explore this knowledge base, in this paper I explore what is involved in …
What Does It Take To Develop Assessments Of Mathematical Knowledge For Teaching?: Unpacking The Mathematical Work Of Teaching, Sarah Kate Selling, Nicole Garcia, Deborah L. Ball
What Does It Take To Develop Assessments Of Mathematical Knowledge For Teaching?: Unpacking The Mathematical Work Of Teaching, Sarah Kate Selling, Nicole Garcia, Deborah L. Ball
The Mathematics Enthusiast
In the context of the increased mathematical demands of the Common Core State Standards and data showing that many elementary school teachers lack strong mathematical knowledge for teaching, there is an urgent need to grow teachers’ MKT. With this goal in mind, it is crucial to have research and assessment tools that are able to measure and track aspects of teachers’ MKT at scale. Building on the concept of “mathematical tasks of teaching” (Ball et al., 2008), we report on a new framework that unpacks the mathematical work of teaching that could serve as a scaffold for item writers who …
Teachers And Their Educators - Views On Contents And Their Development Needs In Mathematics Teacher Education, Mika Koponen, Mervi A. Asikainen, Antti Viholainen, Pekka E. Hirvonen
Teachers And Their Educators - Views On Contents And Their Development Needs In Mathematics Teacher Education, Mika Koponen, Mervi A. Asikainen, Antti Viholainen, Pekka E. Hirvonen
The Mathematics Enthusiast
Finland has scored well in international assessments (e.g. PISA, TIMSS), and the pressure to attain excellent scores has activated a drive toward even more effective mathematics teacher education. This article presents the results of a qualitative assessment of the mathematics teacher education provided by the University of Eastern Finland. In this study, the views held by practicing teachers (N=101) and teacher educators (N=19) are compared so that the outstanding development needs of mathematics teacher education in terms of their contents can be revealed. The data was gathered via an electronic survey and was mainly analyzed using data-driven methods. In addition, …
Problems In The Theory Of Extremal Graphs And Hypergraphs, Cory T. Palmer
Problems In The Theory Of Extremal Graphs And Hypergraphs, Cory T. Palmer
University Grant Program Reports
Objective: Investigate the tree packing conjecture from graph theory and extremal numbers for hypergraphs.
Guest Editorial: Risk – Mathematical Or Otherwise, Egan J. Chernoff
Guest Editorial: Risk – Mathematical Or Otherwise, Egan J. Chernoff
The Mathematics Enthusiast
No abstract provided.
What Can Education Learn From Real-World Communication Of Risk And Uncertainty?, David Spiegelhalter, Jenny Gage
What Can Education Learn From Real-World Communication Of Risk And Uncertainty?, David Spiegelhalter, Jenny Gage
The Mathematics Enthusiast
Probability is a difficult topic to teach, not least because it is rather unclear what it actually means. Modern risk communication has tackled general public incomprehension of probability statements by using the metaphor of ‘expected frequencies’ – for example, “of 100 people like you, we would expect 10 to have a heart attack or stroke in the next 10 years.” We show how these ideas can be taken into the classroom as the basis for teaching probability, using frequency tree diagrams as the fundamental representation. Empirical frequency trees can be used to summarise a series of classroom experiments, and then …