Mathematics Commons^™

Enhancing Statistics Instruction In Elementary Schools: Integrating Technology In Professional Development, Maria Meletiou-Mavrotheris, Efi Paparistodemou, Despina Stylianou

The Mathematics Enthusiast

The research discussed in this article comes from an ongoing multifaceted program for the teaching and learning of early statistical reasoning in Cyprus. The initial stage of the program was concerned with the design of a line of instructional materials for the development of statistical reasoning. Central to this design was the functional integration with existing core curricular ideas of the recently developed dynamic statistics software Tinkerplots@, which provides young students with the opportunity to model and investigate real world problems of statistics. Next, professional development seminars for the teaching of statistics with the use of Tinkerplots® were designed and …

Teaching Statistics Must Be Adapted To Changing Circumstances: A Case Study From Hungarian Higher Education, Andras Komaromi

The Mathematics Enthusiast

Teaching statistics can bring up difficulties of various types for the teacher. Some of these are independent of the environment, i.e. they could occur at any place and time; some are specifically conditional on the surrounding circumstances. This paper presents an example for both of these kinds from the practice of two Hungarian teachers.

Calculating Dependent Probabilities, Mike Fletcher

The Mathematics Enthusiast

In the 2004 European soccer competition France were one of the favourites to win the World Cup and Thierry Henry, their star forward, was one of the favourites to be top goal scorer. Bookkeepers were offering odds of 4 :1 on France winning the competition and odds of 8: 1 on Thierry Henry being the top scorer. A large number of punters went into betting shops in the United Kingdom and made a single bet that France would win the competition and that Thierry Henry would be top scorer. The counter clerks in the betting shops accepted the bets and …

Teacher Knowledge And Statistics: What Types Of Knowledge Are Used In The Primary Classroom?, Tim Burgess

The Mathematics Enthusiast

School curricula are increasingly advocating for statistics to be taught through investigations. Although the importance of teacher knowledge is acknowledged, little is known about what types of teacher knowledge are needed for teaching statistics at the primary school level. In this paper, a framework is described that can account for teacher knowledge in relation to statistical thinking. This framework was applied in a study that was conducted in the classrooms of four second-year teachers, and was used to explore the teacher knowledge used in teaching statistics through investigations. As a consequence, descriptions of teacher knowledge are provided and give further …

Comparision Of High Achievers With Low Achievers: Discussion Of Juter’S (2007) Article, T. P. Hutchinson

The Mathematics Enthusiast

The use of questionnaires and interviews to compare the responses to a mathematical task of high achievers with low achievers has limitations. The partial information that they have provides a way of comparing high and low achievers. Some references are given here to relevant task formats and theories. An example is given of how examinees’ performance with unusual task formats (specifically, answer-until-correct) may be analysed to throw light on the mathematical description of partial information.

A Trailer, A Shotgun, And A Theorem Of Pythagoras, William H. Kazez

The Mathematics Enthusiast

Counselor: Please tell the Court your name.

Expert Witness: My name is Will Kazez

Counselor: No, no, no! Your name is…

This is not a good start. I am not naturally a nervous person. I have survived teaching calculus to a large class that included the entire freshman football team of the University of Pennsylvania, but I've never been an Expert Witness. Even though I'm confident of the mathematics, I'm not sure I like the idea of being cross-examined. But still, I'm just rehearsing my testimony with the lawyer, and even if I've got my own name a little wrong, …

Statistics Teaching In An Agricultural University: A Motivation Problem, Klara Lokos Toth

The Mathematics Enthusiast

There are many teaching methods and there are various teaching materials even in one university, not to mention different universities specialising in different disciplines. So I cannot talk about Hungarian method in general, but about my experience in teaching statistics. I teach statistics on several levels (BSc, MSc, PhD) and in different faculties (Agriculture and environmental Sciences, Economic and Social Sciences) and in different forms. I find different problems according to the faculties and forms. In this paper I focus on only one of them, which is the most important for me.

To Publish Or Not To Publish?- That Is The (Editorial) Question, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

What Makes A “Good” Statistics Student And A “Good” Statistics Teacher In Service Courses?, Sue Gordon, Peter Petocz, Anna Reid

The Mathematics Enthusiast

Statistics is taught within a diverse array of disciplines and degree programs at university. In recent research we investigated international educators’ ideas about teaching and learning ‘service’ statistics. This paper investigates what these educators think are important attributes, knowledge and skills for learners and teachers of statistics. Results show that educators are in agreement about qualities of ‘good’ statistics students, such as curiosity and critical thinking. An emerging issue was the role mathematics plays in learning statistics as a service subject with some academics postulating mathematics as the basis of statistical learning, others proposing it has limited or little importance …

Students’ Conceptions About Probability And Accuracy, Ignacio Nemirovsky, Mónica Giuliano, Silvia Pérez, Sonia Concari, Aldo Sacerdoti, Marcelo Alvarez

The Mathematics Enthusiast

College students’ conceptions about probability and accuracy were explored. Both qualitative and quantitative analyses were done by means of two tests applied at two different moments. We show the results referring to the beliefs and conceptions about probability, margin for error, accuracy, certainty, truth and validity. Previous misconceptions about science may cause difficulties in the interpretation of scientific models. So, to find out students’ beliefs about science and technology, a Likert scale type test was made and presented to part of the sample. Although most of the people who answered the survey accredited the incidence of probability in the results …

Undergraduate Student Difficulties With Independent And Mutually Exclusive Events Concepts, Adriana D'Amelio

The Mathematics Enthusiast

The concepts of disjunctive events and independent events are didactical ideas that are used widely in the classroom. Previous observations of attitudes in assessments given to students at university level who attended the introductory Statistics course helped to detect the confusion between disjunctive and independent events, and indicate the spontaneous ideas that students tend to elaborate about both concepts in different situations in which these appear. However the didactical relation between these ideas and their formal definitions is not known in detail. In this work, we analyze students’ misconceptions, their persistence, and the process by which the student confronts his …

For The Rest Of Your Life, Mike Fletcher

The Mathematics Enthusiast

‘For the Rest of Your Life’ is a new TV game show. Contestants play to win money every month. This can be for as little as one month or, if every one of their guesses is correct, for the rest of their lives.

Learning, Participation And Local School Mathematics Practice, Cristina Frade, Konstantinos Tatsis

The Mathematics Enthusiast

This paper reports on a study whose aim was to examine students’ learning in terms of participation in collective mathematical discussions. Our basic theoretical assumptions are based on a combination of situated learning perspectives and a framework that links social and psychological approaches of mathematical activity and learning. The research was carried out in a Year-8 classroom (students were aged 12 to 13), and the mathematical subject under investigation was area measurement. Data are presented to illustrate possible correspondences between ‘signs’ of learning and ‘local’ changes of participation. We conclude by discussing some pedagogical implications resulting from the study.

If A.B = 0 Then A = 0 Or B = 0?, Cristina Ochoviet, Asuman Oktaç

The Mathematics Enthusiast

We present a study carried out in Uruguay, with secondary school students and tertiary level mathematics students, concerning the zero-product property. In our research we observed that when early secondary and late secondary school students have to solve equations of the form (ax + b)(cx + d) = 0, they do not always apply the property, even when it is the only available tool and have received specific instruction on its application to the resolution of equations of this type. We also detected an error that students make when they have to verify the solutions of this type of equations. …

The Origins Of The Genus Concept In Quadratic Forms, Mark Beintema, Azar Khosravani

The Mathematics Enthusiast

We present an elementary exposition of genus theory for integral binary quadratic forms, placed in a historical context.

The Impact Of Undergraduate Mathematics Courses On College Student’S Geometric Reasoning Stages, Nuh Aydin, Erdogan Halat

The Mathematics Enthusiast

The purpose of this study is to investigate possible effects of different college level mathematics courses on college students’ van Hiele levels of geometric understanding. Particularly, since logical reasoning is an important aspect of geometric understanding, it would be interesting to see whether there are differences in van Hiele levels of students who have taken non-geometry courses that emphasize or focus on logic and proofs (Category I) and those that don’t (Category II). We compared geometric reasoning stages of students from the two categories. One hundred and forty nine college students taking various courses from the two categories have been …

Elementary School Pre-Service Teachers’ Understandings Of Algebraic Generalizations, Jean E. Hallagan, Audrey C. Rule, Lynn F. Carlson

The Mathematics Enthusiast

It is critical for all students to learn algebra, including the ability to generalize, to function in our increasingly complex world. This pretest/intervention/posttest study of preservice elementary teachers (N = 63) in their math methods course assessed their knowledge of writing and applying algebraic generalizations using instructor-made rubrics along with analysis of work samples and reported insights. Initially, although most subjects could solve a specific case, they had considerable difficulty determining an algebraic rule. After a problemsolving- based teaching intervention, students improved in their ability to generalize, however, they encountered more difficulty with determining the algebraic generalization for items arranged …

A Longitudinal Study Of Student’S Representations For Division Of Fractions, Sylvia Bulgar

The Mathematics Enthusiast

The representations that students use as part of their mathematical problem solving can provide us with a window into their grasp of the concepts they are exploring and developing. In this paper, the author indicates how these representations can evolve over time and enrich the understanding of division of fractions, often thought to be the most difficult of elementary school mathematical topics. The results of this research suggest that when appropriate problems are provided for students, in a meaningful context, they can demonstrate understanding of division of fractions that is durable over time, and that they are able to flexibly …

Catch Me If You Can!, Steve Humble

The Mathematics Enthusiast

Learning mathematics outside the classroom is not enrichment, it is at the core of empowering an individuals understanding of the subject.

The three activities described in this article can all be used outside the classroom in a maths lesson. Teaching mathematical concepts in this way engages and reinforces learning. It puts the ideas learnt into a setting and allows time for those ideas to be developed without any of the maths hang-ups which can occur in the classroom. By taking maths beyond the classroom, we can more clearly illustrate the connections between the real world and what they are studying …

Fostering Connections Between The Verbal, Algebraic, And Geometric Representations Of Basic Planar Curves For Student’S Success In The Study Of Mathematics, Margo F. Kondratieva, Oana G. Radu

The Mathematics Enthusiast

We discuss the significance of making connections between the verbal, algebraic, and geometric representations of basic mathematical objects for students’ understanding of mathematical instructions. Our survey of 499 students enrolled in a precalculus university course reveals that such connections are not always present, even if the objects themselves are familiar to the students. We stress that the ability of making these connections needs to be specifically addressed in teaching mathematics at various levels. A proper attention to the matter contributes to the formation of students’ mathematical background, which makes a difference for their success in study of calculus, in particular.

How To Increase Mathematical Creativity- An Experiment, Kai Brunkalla

The Mathematics Enthusiast

Creativity is an integral part of mathematics. In this article I examine the increase in awareness of creativity in mathematics using Fröbel’s blocks in a college classroom. A majority of students found the introduction of the “gifts” of the founder of Kindergarten to a college geometry classroom enhancing their interest in mathematics. They judged the wooden blocks helpful in their understanding of geometry. The students showed increased awareness of creativity in mathematics.

Korean Teachers’ Perceptions Of Student Success In Mathematics: Concept Versus Procedure, Insook Chung

The Mathematics Enthusiast

This article examines the Korean classroom teachers’ beliefs about mathematics education in elementary schools. Their perceptions about contributing factors to Korean students’ high achievement scores in international comparative studies in the area of mathematics are explored. Elementary classroom teachers were surveyed using the researchermade questionnaire (Teacher Perception about Mathematics Curriculum) and 141 teachers completed the questionnaire. The data collected was analyzed by a descriptive analysis. The results reveal that the majority of classroom teachers agreed that real life applications, processing skills, using concrete instructional manipulatives, and conceptual knowledge are very important in teaching children mathematics. Most of teachers participating in …

Book X Of The Elements: Ordering Irrationals, Jade Roskam

The Mathematics Enthusiast

Book X from The Elements contains more than three times the number of propositions in any of the other Books of Euclid. With length as a factor, anyone attempting to understand Euclidean geometry may be hoping for a manageable subject matter, something comparable to Book VII’s investigation of number theory. They are instead faced with a dizzying array of new terminology aimed at the understanding of irrational magnitudes without a numerical analogue to aid understanding. The true beauty of Book X is seen in its systematic examination and labeling of irrational lines. This paper investigates the early theory of irrationals, …

Tme Volume 6, Numbers 1 And 2

The Mathematics Enthusiast

No abstract provided.

The Brachistochrone Problem: Mathematics For A Broad Audience Via A Large Context Problem, Jeff Babb, James Currie

The Mathematics Enthusiast

Large context problems (LCP) are useful in teaching the history of science. In this article we consider the brachistochrone problem in a context stretching from Euclid through the Bernoullis. We highlight a variety of results understandable by students without a background in analytic geometry. By a judicious choice of methods and themes, large parts of the history of calculus can be made accessible to students in Humanities or Education.

How Can Science History Contribute To The Development Of New Proposals In The Teaching Of The Notion Of Derivatives?, Arnaud Mayrargue

The Mathematics Enthusiast

The 18th century was a milestone for the incorporation of mathematics into physics. By this time already seen in Newton’s work, we know that a great deal of progress had found the light of day concerning the relationship between physics and mathematics, particularly as the latter began to deal with universal gravitation and optics. Based on his theory of monochromatic light, which used mathematics to describe optical phenomena, Newton became interested in the behavior of the various colors which, according to him, compose white light. Furthermore, toward the end of the 17th century, scientists had a remarkable mathematical tool at …

"Obeying A Rule": Ludwig Wittgenstein And The Foundations Of Set Theory, Giorgio T. Bagni

The Mathematics Enthusiast

In this paper we propose some reflections on Wittgenstein’s ideas about grammar and rules; then we shall consider some consequences of these for the foundations of set theory and, in particular, for the introduction of major concepts of set theory in education. For instance, a community of practice can decide to follow a particular rule that forbids the derivation of arbitrary sentences from a contradiction: since, according to Radford’s perspective, knowledge is the result of thinking, and thinking is a cognitive social praxis, the mentioned choice can be considered as a form of real and effective knowledge.

Introduction To Thinking As Communicating, Anna Sfard

The Mathematics Enthusiast

This book is a result of years-long attempts to change my own thinking about thinking, a task seemingly as improbable as breaking a hammer by hitting it with itself. In this unlikely undertaking, I have been inspired by Lev Vygotsky, the Byelorussian psychologist who devoted his life to “characterizing the uniquely human aspects of behavior,”2 and by Ludwig Wittgenstein, the Austrian-British philosopher who insisted that no substantial progress can be made in this kind of endeavor unless the ways we talk, and thus think, about uniquely human “forms of life” undergo extensive revisions.

Mathematics For Middle School Teachers: Choices, Successes, And Challenges, Linda Martin, Kristin Umland

The Mathematics Enthusiast

The opportunities for mathematics department faculty from institutions of higher education (IHEs) to work with middle school mathematics teachers are on the rise; the U.S. Department of Education has allocated almost $800 million for mathematics and science partnerships since 2004 that require collaboration between faculty from IHEs departments of arts and sciences and school districts. Changes in credentialing requirements due to the No Child Left Behind Act of 2001 mean that middle school mathematics teachers must take more mathematics content courses, yet current offerings for teachers in many mathematics departments typically focus on elementary or high school mathematics and often …

Main Points Of Objections To The "No Child Left Behind", Mike O'Lear, Bettina Dahl

The Mathematics Enthusiast

Adequate Yearly Progress (AYP):

--The guidelines fail to distinguish between successful schools and unsuccessful schools

--Between schools under-performing in just one area vs. schools likely to need a complete overhaul

--Does not give credit for student growth toward a high standard

--Need to establish AYP levels which make a distinction between struggling schools and those needing only limited assistance