Problems In Mathematics Education Research Articles

Intelligent tutoring systems work as a math gap reducer in 6th grade after-school program

Achievement gaps have been long-lasting problems in mathematics education. Racial/ethnic gaps, gender gaps, and differences between school socioeconomic status are three well-known contributors to gaps in achievement. This study explored the effect of an intelligent tutoring system, the Assessment and LEarning in Knowledge Spaces (ALEKS) system, on reducing such gaps in an after-school program. The study was conducted with a sample of 6th grade student volunteers who were randomly assigned to one of two after-school conditions (ALEKS versus comparable teacher-led mathematics teaching). In the teacher-led condition, White males and females and African American males and females coming from schools of two levels of socioeconomic status performed differently on the math state test. In contrast, in the ALEKS condition, students with different individual differences performed similarly on the state test. These findings provide encouragement for the use of computer technology assistance to aid in the education of disadvantaged students in math.

GENERAL TASKS OF MATHEMATICAL EDUCATION DEVELOPMENT

The paper discusses basic implementation aspects of the Mathematical Education Development Concept, adopted by the Russian Government in 2013. According to the above document, the main problems of mathematical education include: low motivation of secondary and higher school students for studying the discipline, resulted from underestimation of mathematical knowledge; and outdated educational content, overloaded by technical elements. In the author’s opinion, a number of important new mathematical fields, developed over the last years, - the graph theory, discrete mathematics, encoding theory, fractal geometry, etc – have a large methodological and applied educational potential. However, these new subdisciplines have very little representation both in the secondary and higher school mathematical curricula. As a solution for overcoming the gap between the latest scientific achievements and pedagogical practices, the author recommends integration of the above mentioned mathematical disciplines in educational curricula instead of some outdated technical issues. In conclusion, the paper emphasizes the need for qualified mathematical teachers’ training for solving the problems of students’ motivation development and content updates.

Developing shift problems to foster geometrical proof and understanding

Meaningful learning of formal mathematics in regular classrooms remains a problem in mathematics education. Research shows that instructional approaches in which students work collaboratively on tasks that are tailored to problem solving and reflection can improve students’ learning in experimental classrooms. However, these sequences involve often carefully constructed reinvention route, which do not fit the needs of teachers and students working from conventional curriculum materials. To help to narrow this gap, we developed an intervention—‘shift problem lessons’. The aim of this article is to discuss the design of shift problems and to analyze learning processes occurring when students are working on the tasks. Specifically, we discuss three paradigmatic episodes based on data from a teaching experiment in geometrical proof. The episodes show that is possible to create a micro-learning ecology where regular students are seriously involved in mathematical discussions, ground their mathematical understanding and strengthen their relational framework.

The Mathematics of Mathematics Houses (The Snaky Connection)

from scientists, historians, anthropologists, and others. T he first mathematics house in Iran was established in Isfahan in 1999 to inform the young students in this great historical and cultural city about the history, the beauty, the importance, and the applications of mathematics. It did this by familiarizing these young people with various mathematical sciences beyond the classroom, through observations, collaborations, and so forth, including teamwork with their teachers or other scholars. The house is financially supported by the municipal council of Isfahan. The activities of the Isfahan house are colorfully recounted on its lively webpage, http://www.mathhouse. org/; see also nms.lu.lv/mcg_10/2day-12/Ali_Rejali.ppt, which is the PowerPoint presentation by my colleague A. Rejali of the Isfahan University of Technology, who played a key role in establishing the Isfahan house. In the years after the first house opened in 1999, local authorities, with the advice and the help of mathematicians, have opened houses in Tabriz, Kerman, Zanjan, and other towns in Iran. These houses are supported by the municipal councils of the cities, or by the office of the ministry of education, or by both. In a few special cases, the houses are also supported by the private sector. There is no doubt that in the long run these houses will have an impact on mathematics education in Iranandwill assist the school system in raising the interest of Iranian students in mathematics. The schools and universities in different cities of Iran are usually busywith their routines and are not expected to have a serious impact on the mathematics awareness of the public, but the mathematics houses, in collaboration with the Iranian Mathematical Society, can have a natural and key role in increasing the public understanding of and appreciation for mathematics. (See [4], [1] for more details about the mathematics houses in Iran.) One of the main activities pursued by those in the Isfahan Mathematics House (IMH), which is being emulated in other mathematics houses in Iran, is for the leaders to invite prominent scholars fromboth inside the country and fromabroad to deliver popular talks about mathematics to general audiences, including mathematicians, teachers, students, and laypeople. This provides a good opportunity for the young students to meet some well-known mathematicians, which is very exciting for the students. Past invitees from abroad include Y. Dodge (University of Neuchâtel, Switzerland), who spoke on p and random-number generators; S. Gazor (Queen’s University, Canada) on psycho-acoustics; K. Salamatian (Paris VI, France) on internet measurement; A. Enayat (American University, USA) on a gift from Cantor’s heaven; J. Vaananen (Helsinki University, Finland) on logic and mathematics; M. Andler (Universite de Versailles-Saint-Quentin and Animath, France) on current problems in mathematics education in France; G. Frey (Duisburg-Essen University, Germany) on number theory and coding; J.-M. Deshouillors (Universite de Bordeaux 1, France) on prime numbers yesterday and today Submissions may be uploaded to Editorial Manager (see instructions for authors), or sent directly to the Marjorie Senechal, mi.editor1@gmail.com

“Nadie se Puede Sentar Aquí”: Dos Perspectivas sobre Cómo los Problemas de Matemáticas en Contexto Median las Discusiones de Grupo de Resolución de Problemas

Este estudio examina cómo un grupo de estudiantes de álgebra bilingües discuten sobre dos problemas de texto presentados en términos de contextos “de la vida real.” Usando las lentes de la acción mediada (Wertsch, 1998), el análisis revela dos maneras distintas en las que los problemas contextualizados influyen sobre el razonamiento matemático del grupo. En uno de los problemas, el contexto afrontaba maneras particulares de interpretar las inscripciones dadas, cosa que tuvo tanto beneficios, como costes. En el otro problema, la terminología de una historia no familiar pareció dificultar el razonamiento matemático del grupo. Estas dos formas de contexto mediado se discuten a la luz de la investigación actual en el uso de problemas de la vida real en educación matemática.Palabras Clave: discusiones matemáticas, mediación, problemas de texto, álgebra, discusiones de grupo.

Some Classes of Differential Equations that are Convertible to Homogenous Equation

Abstract As known, differential equations has great importance in education of physics, chemistry and, engineering along it's great importance in education of mathematics. Also, when the insolvability of differential equations with exact methods in most situations is taken into account, it can be said that, the enlargement of the class of differential equations which can be solved by exact methods is one of the current problems of mathematics education and, applied mathematics. This ar ticle is devoted to, two types of first-order differential equations, which can be converted to homogeneous equations with replacement depending on the situation are examined.

The problems of mathematics education at secondary schools and gymnasia

The article reviews the ties between secondary schools/gymnasia and universities, and also discusses complementary mathematics education. Major attention is directed to the general mathematics curricula of general education and secondary education. A proposal of developing an integral mathematics education curriculum for gymnasium as well as withdrawing the state school graduation curriculum (by organising the examination under the general mathematics education curriculum) has been put forward.

DIAGNOSTICO DE HABILIDADES y CONOCIMIENTOS DE MATEMÁTICAS EN ALUMNOS DE SEXTO GRADO DE PRIMARIA

The teaching of mathematics is an important component of contemporary education and one to which behavior analysis can make a strong contribution. Four problems in mathematics education can be identified: 1. the correspondence between natural and technicallanguage. 2. the morphology of the responses being used. 3. the conditions for transfer; and 4. The availability of effective methods for teaching mathematics. The arithmetic and reading competencies of sixth grade children were assessed and then their performance was compared using implicit and explicit performance criteria. The childrens' performance was better when explicit criteria were specified. The results suggest that student performance in mathematics could be improved if more traditional teaching methods based upon implicit criteria were replaced by more behavioral approaches involving explicit criteria. In addition, such explicit criteria also might facilitate the transfer of skills to new learning situations.

Chinese upper elementary school mathematics teachers’ attitudes towards the place and value of problematic word problems in mathematics education

Word problems play a crucial role in mathematics education. However, the authenticity of word problems is quite controversial. In terms of the necessity of realistic considerations to be taken into account in the solution process, word problems have been classified into two categories: standard word problems (S-items) and problematic word problems (P-items). S-items refer to those problems involving the straightforward application of one or more arithmetical operations with the given numbers, whereas P-items call for the use of real-world knowledge and real-life experience in the problem-solving process. This study aims to explore how Chinese upper elementary school mathematics teachers think of the place and value of P-items in the elementary mathematics curriculum.

Using components of mathematical ability for initial development and identification of mathematically promising students

Kruteskii's work on the mathematical abilities of school children is a seminal work on the nature of mathematical ability. However, the task of developing methods for the practical application of his work is still a significant problem in mathematics education. The authors have developed a practical application of Kruteskii's approach to the important problem of initially developing components of mathematical ability in student and thereafter identifying mathematically promising students. Examples of problems that were designed to develop ability to generalize, flexibility and reversibility of mental processes are presented. A practical guide for determining the level of development of components of mathematical abilities in individual students, in terms of specified observables, is presented as a set of structured reference tables. The authors set out a practical application protocol that combines use of the tables and sets of specially developed problems for initial development of mathematical abilities prior to identification of mathematically promising students in the general classroom. A significant motivation for this work is the desire to avoid time-consuming and resource intensive practices such as interviews and summer schools which therefore have been used successfully because these practices are now out of reach for all but very wealthy countries or highly ideologically driven systems. On the other hand, special examinations heavily depend on the level of preparedness of the students for the particular examination, and therefore some students with high abilities but with fewer opportunities to prepare could be overlooked.

Analysis of Socially Open-end Problems in Mathematics Education from the Perspective of Values

Analysis of Socially Open-end Problems in Mathematics Education from the Perspective of Values

The onto-semiotic approach to research in mathematics education

In this paper we synthesize the theoretical model about mathematical cognition and instruction that we have been developing in the past years, which provides conceptual and methodological tools to pose and deal with research problems in mathematics education. Following Steiner’s Theory of Mathematics Education Programme, this theoretical framework is based on elements taken from diverse disciplines such as anthropology, semiotics and ecology. We also assume complementary elements from different theoretical models used in mathematics education to develop a unified approach to didactic phenomena that takes into account their epistemological, cognitive, socio cultural and instructional dimensions.

How Fast Do Trees Grow? Using Tables and Graphs to Explore Slope

Slope is one of the most important mathematical concepts that students encounter in middle school and high school. The concept of slope “weaves its way through algebra, geometry, trigonometry, and calculus” (Anderson and Nelson 1994, p. 27), yet research with high school students shows that they can often calculate slope but are unable to interpret its meaning (Newburgh 2001; Stump 2001). This is a familiar problem in mathematics education; students learn a formula for solving a particular type of problem without conceptually understanding the relevant mathematical ideas. One way to enhance students' understanding of slope is to introduce it conceptually in middle school (Beckmann and Rozanski 1999), with the understanding that this conceptual foundation will provide a basis for the formal definition of slope to be introduced later on. In this article, we describe two related lessons for sixth-grade students that were designed to accomplish this goal.

From the 1980s: President's Annual Address: 58th Annual Meeting

The main focus of the president's address is communicating recommendations for school mathematics summarized in the document “An Agenda for Action”. It defines three major problems and presents analysis of a set of recommendations on how to improve the situation. Recommendations covers eight major categories, from “Problem solving” to “Public support for mathematics instruction”. It is noted that problem in mathematics education can only be solved by the cooperation of all sectors of our society.

The functional use of a mathematical sign

The question of how a mathematics student at university-level makes sense of a new mathematical sign, presented to her or him in the form of a definition, is a fundamental problem in mathematics education. Using an analogy with Vygotsky's theory (1986, 1994) of how a child learns a new word, I argue that a learner uses a new mathematical sign both as an object with which to communicate (like a word is used) and as an object on which to focus and to organise her or his mathematical ideas (again as a word is used) even before she or he fully comprehends the meaning of this sign. Through this sign usage, I claim that the mathematical concept evolves for that learner so that it eventually has personal meaning, like the meaning of a new word does for a child; furthermore, because the usage is socially regulated, I claim that the concept evolves for the learner so that its usage concurs with its usage in the mathematical community. In line with Vygotsky, I call this usage of the mathematical sign before mature understanding, ‘functional use’. I demonstrate ‘functional use’ of signs (manipulations, imitations, template-matching and associations) through an analysis of an interview in which a mathematics university student engages with a ‘new’ mathematical sign, the improper integral, using pedagogically designed tasks and a standard Calculus textbook as resources.

Problems of Mathematics Education in Germany (III) : TIMSS Report and Educational Reform

Problems of Mathematics Education in Germany (III) : TIMSS Report and Educational Reform

Relating Geometry and Algebra in the Pascal Triangle, Hexagon, Tetrahedron, and Cuboctahedron Part I: Binomial Coefficients, Extended Binomial Coefficients and Preparation for Further Work

Click to increase image sizeClick to decrease image size Additional informationNotes on contributorsPeter HiltonPeter Hilton (marge@math.binghamton.edu) is Distinguished Professor of Mathematics Emeritus at the State University of New York at Binghamton, and Distinguished Professor of Mathematics at the University of Central Florida at Orlando. His principal research interests are in algebraic topology, homological algebra and group theory; and he has long taken a close interest in problems of mathematical education, having been Chairman of the United States Commission on Mathematics Instruction. He has been First Vice President of the MM. He and Jean Pedersen have published four books and over 100 articles together since they began their collaboration in 1978, and are currently writing their fifth book.Jean PedersenJean Pedersen (jpedersen@scu.edu) is a Professor of Mathematics at Santa Clara University. She began her real study of mathematics with George Pólya in 1969, visiting him and his wife, Stella, weekly at their home from then until his death in 1985. Her main mathematical interests are polyhedral geometry, number theory and combinatorics. In 1978 she was asked by the MM to arrange for Peter Hilton and George Pólya to present a special session on the teaching of mathematics. The rest (see above) is history! She is a past Governor of the Northern California section of the MM and, in 1997, she received the Section's award for Distinguished Teaching.

The role of open-ended problems in mathematics education

Open-ended problems have become a popular educational tool in mathematics education in recent years. Since mathematical research is nothing but a daily confrontation with open-ended problems, the introduction of this type of problems to the classroom brings mathematical education one step closer to real mathematics. The appearance of these problems in secondary education is therefore a welcome sight from a mathematical standpoint. More than this is true, however. While these problems may represent something of a pedagogical innovation to the professional educators, the fact is that many mathematicians have made use of them in their teaching all along and do not regard their presence in the classroom as any kind of departure in educational philosophy. For example, I myself have often given such problems in my homework assignments and exams. Nevertheless, I have chosen to take up this topic for discussion here because, after having reviewed a limited amount of curricular materials for mathematics in the schools, I could not help but notice that they pose certains hazards in practice. These hazards include the possibility of misinforming the students about the very nature of mathematics itself. To avoid meaningless generalities, I have se-

The potential of case studies of exemplary mathematics teaching

Because past research often highlights the problems of mathematics education, case studies of exemplary teachers were conducted in order to emphasize positive aspects and to stimulate and improve mathematics education. Observations of two primary mathematics teachers nominated as exemplary by their peers provided some marked contrasts. One teacher subscribed to a constructivist philosophy, provided students with opportunities for active mental engagement and had an energetic monitoring style which ensured high levels of time on task. The other teacher emphasized whole‐class activities and gave students limited opportunities to learn in meaningful ways. This teacher's style, however, was undergoing changes which were facilitated by the support of the researchers.

Kognitionstheoretische Modelle und mathematische Lernprozesse

The intention is to check to what extend models of cognitive science can help us to describe, to explain or to understand pupils’ mathematical behaviour in a more appropriate way. To this purpose, at first such models (as e.g. “semantic networks” or “production systems”) are described in more detail. In the main part it is discussed which problems in mathematics education call for explanations using results from cognitive psychology, and which answers can be given; i.e. it is investigated how useful models of cognitive science are in research on mathematics education. Finally, more recent developments are discussed, as for instance the significance of expert knowledge, intelligent tutoring systems, metacognition, and cognitive strategies and structures.