Development Of Mathematical Knowledge Research Articles

Formation and development of mathematical literacy in the context of evaluative – Study tasks of PISA

To identify the level of education of schoolchildren in different countries of the world, the OECD conducts international studies in the field of education. Comparative results of these studies make it possible to determine the effectiveness of national educational systems contributing to adapting programs for modernization and reform of educational systems. This study aims to develop mathematical literacy among 15-year-old students of the Republic of Kazakhstan by developing the basic skills of the 21st century in solving practice-oriented problems. An experimental study was conducted to determine teachers' attitudes toward the formation of mathematical literacy among schoolchildren. The study involved 32 teachers. The Analysis of the results of the survey revealed that the majority of teachers had a negative attitude towards the formation of mathematical literacy among schoolchildren, substantiating their points of view by the fact that the formation and development of mathematical knowledge and skills by itself contributed to the development of skills in the 21st century. Only 11% of teachers could accurately indicate those tasks, out of the seven tasks presented for consideration, in the solution of which schoolchildren had shown critical, systemic thinking. An analysis of geometry textbooks used in schools of the Republic of Kazakhstan showed that out of the total number of educational tasks studied in geometry lessons, the share of practice-oriented tasks comprised less than 3%. Based on the results of the experimental study, it is concluded that it is necessary to develop appropriate methodological approaches that contribute to the formation of mathematical literacy among schoolchildren using the learning tasks of the school geometry course.

New Objects, Questions, and Methods in the History of Mathematics

This article sums up recent developments in the history of mathematics. The range of mathematics considered has considerably broadened, expanding well beyond the traditional field of original research. As new topics have been brought under consideration, methodologies borrowed from neighboring academic fields have been fruitfully put into use. In the first section, we describe how well-known questions—about the concept of proof and the nature of algebra—have been reconsidered with new questions and analytical concepts. We then sketch up some of the new research topics, among others the history of mathematical education, the inclusion of actors previously neglected, and the prominent role of bureaucracies in the cultural development of mathematics. The last section briefly retraces the development of the Zilsel thesis as a case study illustrating the previous points. Introduced in the mid-20th century, the theory that early modern craftsmen once played a decisive role in the mathematization of nature has recently led to very diverse fruitful studies about the nature and development of mathematical knowledge.

Investigating the effect of computer-supported instruction on students’ understanding of different representations of two-variable inequalities

ABSTRACT : The topic of inequalities is one of the fundamental subject areas for the development of mathematical knowledge. Although there is a considerable body of research focused on one-variable inequalities, studies that investigate students’ performance on two-variable inequalities are scarce. With this in mind, the aim of this study is twofold: first, it provides an account of the difficulties that students face in interpreting and constructing different representations of two-variable inequalities; and second, it investigates the effectiveness of a computer-supported teaching sequence aimed at developing students’ understanding of different representations of two-variable inequalities. The participants in the study were 33 elementary mathematics teacher candidates. The data were gathered via a test implemented as a pre- and post-test. The main finding of the study was that students had difficulty in establishing the link between the coordinates of the points in a solution set and the algebraic representation of a two-variable inequality. Moreover, it was found that the students were not able to correctly use and interpret the logical connectives in compound inequalities. The comparison of the pre- and post-test scores indicated that the designed instructional sequence was beneficial for supporting students in understanding the different representations of two-variable inequalities.

Digital technology in learning mathematical literacy, can it helpful?

Literacy is a critical skill and is quite a concern in the world of education, especially mathematics education in the 21st century. Literacy in mathematics illustrates how a student identifies and understands the problems in which mathematics he has learned plays a role in all aspects of life. On the other hand, the 21st-century digital era demands the realm of education to be able to utilize ICT (Information and communication technologies) in the learning process, not least in mathematics. Digital technology, as a tool that is believed to make a significant contribution to the development of education, is also a challenge in its application, especially concerning the development of mathematical knowledge and skills, mathematical literacy. A question that arises is, can the use of digital technology develop mathematical literacy in the process of learning mathematics? If the answer can, then how should such integration be carried out. This article aims to provide an overview of the answers to these questions by giving an overview of the importance of mathematical literacy and digital technology in developing mathematical literacy.

THE DEVELOPMENT OF WRITTEN COMMUNICATION TRANSVERSAL COMPETENCY IN THE EDUCATION IN MATHEMATICS FOR GRADES 1-4

Communicational transversal competency represents an important part of the mathematical knowledge, skills and competencies in the process of students’ development in Grade 1-4.
 The creation and formation of communicational transversal competency helps to put students into an active cognitive position in the course of pedagogical interactions in mathematics classes. Further, creation of communicational transversal competencies develops not only students’ analytic – synthetic activity during the process of solving different types of mathematical tasks but also their creative thinking.
 This longitudinal research presents some theoretical concepts related to the transversal communicational competency and to its development during the educational process in mathematics in Grade 1-4.
 During this empirical study a completely new methodology system of work was developed with the purpose to facilitate development of mathematical knowledge, skills and competencies including the communicational transversal competency. The new system was tested and applied during the compulsory, additional and extended classes in mathematics in Grade 1-4 and consequently was improved after the performance of entry and intermediate diagnostic. Also, this article presents some of the mathematical tasks included in the tests.
 The researcher studied the objectiveness, the validity and the reliability of the diagnostic tools developed for the purpose as well as the tasks included in the tests in respect of their difficulty and separating force. 
 The presented results of the experimental work were processed using mathematics-statistics methods.

Bilangan Bulat dan Kekeliruan dalam Operasi Matematika

The challenge of Mathematics education is to find and choose learning models that are easy to understand, arousing, challenging to get involved in and eventually make students understand easily. This paper intends to be a bridge in the process of teaching and learning of integers and mathematical fallacies that often occur in mathematical operations. Integers play an important role in the development of mathematical knowledge and the use of these numbers enables the current generation to build space satellites and investigate the structure of the universe. Integers often look very simple but are actually very difficult to solve. On the other hand, carelessness in completing mathematical operations often results to fallacies that can cause ridiculousness. This paper is trying to review these two problems in an easy and fun way.

The learning of differential calculus mediated by the platform Khan-academy

Through the most recent years Information and Communication Technologies (ICT) have been positioned as powerful and revitalizing mechanisms in the educational processes. Therefore, this study measures the incidence of a digital platform by the learning of real functions with a view of identifying didactic strategies that contributes to the strengthening and development of mathematical knowledge in reference to the variational thought. The original random sample was primary conformed by students of second semester at a technological academic formation of an institution of higher education based on Santander-Colombia (N = 176). The respective quantitative study is being considering by the correlation type, with the proper use of the Spearman’s correlation coefficient and descriptive statistics. The used program to realize this kind of analysis was the statistical software SPSS. So far at this point the results shows that the average academic performance on the partial of functions evidenced was 2.61 with standard deviation (SD)0.92, meanwhile in another way by the independent work that is being taken in the Khan-Academy’s platform scored 3.72 with a (SD) 0.2. Besides, it can be said that the bivariate correlation coefficient shown a substantial relation of 0.846 with a significance level of 1%. in all the process the conclusions that can be considered, it can be affirmed the strong relation between the study variables, denoting in fact that the correlation coefficient showed a clear association between the variables.

Spontaneous focusing on quantitative relations as a predictor of rational number and algebra knowledge

Spontaneous Focusing On quantitative Relations (SFOR) has been found to predict the development of rational number conceptual knowledge in primary students. Additionally, rational number knowledge has been shown to be related to later algebra knowledge. However, it is not yet clear: (a) the relative consistency of SFOR across multiple measurement points, (b) how SFOR tendency and rational number knowledge are inter-related across multiple time points, and (c) if SFOR tendency also predicts algebra knowledge. A sample of 140 third to fifth graders were followed over a four-year period and completed measures of SFOR tendency, rational number conceptual knowledge, and algebra knowledge. Results revealed that the SFOR was relatively consistent over a one-year period, suggesting that SFOR is not entirely context-dependent, but a more generalizable tendency. SFOR tendency was in a reciprocal relation with rational number conceptual knowledge, each being uniquely predictive of the other over a four-year period. Finally, SFOR tendency predicted algebra knowledge three-years later, even after taking into account non-verbal intelligence and rational number knowledge. The results of the present study provide further evidence that individual differences in SFOR tendency may have an important role in the development of mathematical knowledge, including rational numbers and algebra.

Fostering and supporting the coordinated use of digital technologies in mathematics learning

The wide use of different digital technologies in social and daily activities has been transforming ways in which people interact and communicate. To what extent can the coordinated use of several digital technologies foster and enhance students' development of mathematical knowledge? What kind of reasoning do problem solvers construct as a result of using several digital technologies to represent, explore and solve a mathematical problem? Addressing these questions led us to outline a framework that aims to characterise ways in which multiple purpose technologies and ad hoc technologies can be used in problem solving approaches. In particular the construction of dynamic models of tasks or problems plays a crucial role in looking for mathematical relationships and novel approaches to solve those problems.

Examination of the Mathematical Problem-Solving Beliefs and Success Levels of Primary School Teacher Candidates Through the Variables of Mathematical Success and Gender

Since the 1970s, developments in the field of social psychology have brought the concepts of cognition and belief into question; research that had been performed on the concept of belief in the 1980s especially gained importance and were applied to different disciplines such as psychology, political science, anthropology, and educational sciences (Thompson, 1992). Belief can be defined as feeling that something is good, right, or valuable, (Merriam-Webs ter, 2014), or as being bonded with an idea in the heart, (Turk Dil Kurumu, 2011, p. 1186). As in the scope of educational sciences, many researchers have defined the concept of belief in different ways. According to Pajares (1992) for example, belief means the choices and behaviors of people based on their life experiences. For Richardson (1996), beliefs are the assumptions and thought patterns that individuals develop due to conditions in their life. Thompson (1992) defined belief as a diagram of the emotions, value judgments, and past experiences of an individual. Schoenfeld (1998) defined belief as the experiences and understandings of individuals coded into mental diagrams. Deryakulu (2004, p. 260) defined belief as the internal acceptance or statements assumed to be right by an individual that determine how one perceives, intends, and acts towards every event, fact, person, or object. As can be gathered from these opinions, there is not a common, agreed-upon definition regarding the concept of belief in terms of the educational literature. In terms of mathematical education, it has been evaluated that many researchers point out mathematical belief and its importance with the concept of problem-solving (Bishaw, 2010; De Corte & Opt Eynde, 2002; Philipp, 2007; Raymond, 1997; Schoenfeld, 1992; Silver 1985; Thompson, 1985, 1992). In this scope, Raymond (1997) defines mathematical belief as value judgements towards mathematics that an individual has obtained from past experiences. Pehkonen and Torner (2003) define mathematical belief as an individual understanding of the mathematical world while identifying mathematical tasks alongside this. Again, Ernest (1989) defines mathematical belief as the concepts, ideologies, values, and philosophies of an individual on life and mathematics. Dede and Karakuc (2014) define it as the psychological understandings and mental structures of an individual that are shaped from past experiences. Mathematical belief is also handled as the sum of value judgments and subjective approaches that an individual has developed due to their past experiences in this study.When evaluating the concept of in terms ofwords, many sources define problem as acondition that needs to be solved but whose solution is not known directly from daily life (Blum & Niss, 1991; Polya 1990, Van De Walle, Karp, & Bay-Williams, 2013). Mathematically, problems should need a solution; having made no preparations for finding the solution, there should be attempts at solving it (Jonassen, 2000; Reys, Suydam, Lindquist, & Smith, 1998; Schoenfeld, 1992; Van De Walle, 2007). Based on this, problem solving is the period of completing facts or complicated situations by checking over different ways of obtaining solutions (NCTM, 2000; Schoenfeld, 1992). Since problem solving is a basic part of mathematical learning, it is also an important area in the development of mathematical knowledge and thought processes of students (Ho, 2009; Lester, Garofalo, & Kroll, 1989; Malloy, 2002; NCTM, 2000; Reys et al, 1998; Schoenfeld, 1992; Thompson, 1985). The development of problem-solving skills is an important skill that needs to be developed slowly and continuously from kindergarten to higher education (Van De Walle, 2007). Many researchers that have examined the stages of problem solving emphasize the importance of internal and external factors in problem solving (Jonassen, 2000; Smith, 1991). In this scope, external problems are reasons that originate from the problem itself, such as the structure of the problem, its complexity, abstractness, and presentation. …

Understanding the evolution of mathematics performance in primary education and the implications for STEM learning: A Markovian approach

National reports have documented deficiencies in the vertical alignment of mathematical learning in K-12 education. Many students fail to master requisite concepts before advancing to more complex ideas, leaving them ill-prepared to succeed in higher level Science, Technology, Engineering, and Mathematics (STEM) coursework. In this paper, we model elementary and middle school students’ performance in mathematics over time as a stochastic process to forecast their proficiency by the eighth grade. We conduct an extensive examination of tens of thousands of student records and extract useful information. We use this data to present a longitudinal analysis of student performance on the North Carolina End-of-Grade mathematics exam and use Markov chain models to probabilistically characterize the movement of students’ scores from one grade level to the next. This work is the first step in developing a framework to forecast individual students’ development of mathematical knowledge over time.

Development of Mathematical Knowledge in Young Children: Attentional Skill and the Use of Inversion

The principle of inversion, that a + b − b must equal a, is a fundamental property of arithmetic, but many children fail to apply it in symbolic contexts through 10 years of age. We explore three hypotheses relating to the use of inversion that stem from a model proposed by Siegler and Araya (2005). Hypothesis 1 is that greater calculational skill is related to greater use of inversion. Hypothesis 2 is that greater attentional skill is related to greater use of inversion. Hypothesis 3 is that the relation between attentional skill and the use of inversion is particularly strong among children with high skill in calculation. We found suggestive evidence for Hypothesis 2 and clear evidence for Hypothesis 3, indicating that for children who are strong at calculation, attentional flexibility is related to use of inversion.

Teaching pre-school Mathematics and influences by the kindergarten school social context: A preliminary study

The empirical material of this preliminary study was drawn from the recording and analysis of teaching activities used during the implementation of the new pre-school Greek curriculum in sixteen classes of public kindergartens. More specifically, according to the opinion of the kindergarten teachers about the social backgrounds of the majority of their students, 8 kindergartens belonged in a middle-class social context and 8 in a working-class social context. Research findings showed variations in the pedagogical practices in those two types of kindergartens. Variations were observed in the choices made by pre-school teachers in the development of mathematical knowledge in the classroom, in the ways that teachers and students interact during the teaching process, in the organization of the classroom, and in the application of evaluative rules and teaching strategies for teaching mathematics.

The Early Childhood Mathematics Education Revolution

Research Findings: We are in the midst of a revolution. Prior to the onset of the 21st century, mathematics education in the United States was deemphasized (Geary, 1996), and mathematics as an instructional subject has traditionally been considered above the preschool and kindergarten levels. However, the old regime—the knowledge and philosophies that governed mathematics and early childhood education theory in the last century—has been overthrown. Today, developmental psychologists have begun to map out the specific pathways of mathematical knowledge development from birth to age 8. We now know that prior to elementary school, young children engage in surprisingly complex intuitive mathematical thinking in the areas of number, geometry, measurement, algebraic thinking, and data analysis (for reviews, see T. C. Cross, T. A. Woods, & H. Schweingruber,2009; J. Sarama & D. H. Clements, 2009). With increased recognition of the importance of early mathematics for later academic success, early childhood mathematics education is now a national priority. Practice or Policy: This article discusses the history, research, and political impetus for the shift in paradigm; the current status of the early childhood mathematics education movement; and the implications for young children and teachers in the United States.

La alfabetización matemática y su relación con el intercambio comercial, la escolaridad elemental y el trabajo

En este artículo abordo algunos aspectos de la adquisición del conocimiento y las herramientas matemáticas elementales en diferentes contextos: la educación básica de personas jóvenes y adultas, algunas actividades laborales que no requieren una escolaridad importante, y la experiencia de intercambio comercial que se desarrolla en la cotidianeidad. Mi intención es contribuir a la reflexión sobre los aportes de la educación básica, la experiencia cotidiana y el trabajo a la alfabetización matemática de las personas. Para ilustrar mis afirmaciones, tomo como centro la noción de proporcionalidad. Esta noción cruza la educación básica, es fundamento de la matemática más avanzada y, también, es instrumento de trabajo e interacción en distintos ámbitos de la actividad social. Adelanto que, en México, el sistema educativo para jóvenes y adultos incumple en buena medida un compromiso fundamental: lograr que las personas se apropien de herramientas simbólicas que potencien su pensamiento y su forma de vinculación con el mundo. En cambio, algunas actividades laborales y comerciales contribuyen al desarrollo de conocimientos y habilidades útiles para resolver problemas matemáticos que el propio contexto plantea. Este tipo de aprendizaje, no debe empero olvidarse, es un aprendizaje situado cuyos límites conviene también señalar.

Adding support to maths

The majority of teaching assistants support numeracy lessons daily, making use of quality strategies to promote numeracy development, vital to children’s progress. As any teaching assistant knows, however, there are many factors that have to be taken into account to create a quality learning activity – grouping, how the activity relates to the learning styles of the children, the resources, level of engagement, how well they know the children and the teaching assistant’s personal confidence in maths – to name but a few. The ability to focus on the development of mathematical knowledge, skills and understanding, along with individual progress, can be a challenge, but is certainly not impossible. One of the first priorities is to take notice of children’s individual targets and personal interests and to get an idea of how much they enjoy maths. This can be done through discussions with the class teacher and becoming involved in the work that is going on behind the scenes in terms of the planning and assessment. The greater involvement you can have, the more you will understand the teacher’s thinking behind each activity and the better you will be able to support the children. To provide the teacher with further accurate feedback, which will assist in informing future planning, I would recommend keeping a record of the children’s participation and progress during activities. This will also assist you in recognising patterns in the types of activities that really engage the children and allow them to achieve the learning outcomes successfully and with apparent ease and enjoyment. The Primary Framework for Mathematics is also a great starting point to find out what is expected of the children during each year group and the progression expected. By looking at the framework you will also gain a better idea of the rationale behind the teacher’s planning and how they have interpreted the curriculum into a structure that is meaningful and purposeful to the children. Before supporting learning activities within a topic, it is advisable to carry out some research on the common misconceptions associated with that area. These misconceptions are often very simple to rectify, however, they often go unnoticed by teaching assistants because they are not sure what they are looking for and how they should respond. An example of a common misconception children have is writing the number ‘three thousand and two’ as 3,0002 instead of 3,002. Other misconceptions include counting each object more than once when learning one-to-one correspondence (one number relates to one object), or starting to measure a line from the end of the ruler and not the ‘0’ mark. Mathematical understanding and misconceptions may be due to the age and developmental stage of the children. Some further reading into Jean Piaget’s stages and conservation tasks can be incredibly useful in helping teaching assistants to understand why it is important that when children are adding two sets of counters these remain in the position that the child counted them. Once moved, the child may need to count them again as the movement has caused them to think that the quantity has changed. The same principle applies when moving liquid from one size of container to another, and to anything else that can change in appearance, such as modelling dough. The most important aspect of supporting numeracy is to enjoy it – if you can demonstrate a genuine enthusiasm for the topic you are delivering, this will have a hugely positive impact on the children. Of course, as we all know, when children really enjoy what they are learning and feel confident enough to take risks without worrying about getting it ‘wrong’, that is when the real learning takes place. PTU top tips

Improving the Teaching of Engineering Mathematics using Action Research

Our experience showed that students will struggle with new concepts in Engineering Mathematics and faced difficulties with the need to use various mathematical techniques to solve problems. Thus, we embarked on a study to improve our teaching and students’ learning. We designed teaching strategies to support students’ development of mathematical knowledge and problem solving as well as communication and team working skills. We used an action research perspective as various methods within this stance can ensure flexibility in responding to the dynamics of interaction between the teachers and the students. This paper will present an account of our study and highlight various issues in the use of action research.

Saúde e números: uma parceria de sucesso

Perante a recente inserção da Educação de Jovens e Adultos na rede federal de Educação Profissional e Tecnológica, por meio da implantação do PROEJA - Programa de Integração à Educação Básica na Modalidade Educação de Jovens e Adultos nos Institutos Federais de Educação, Ciência e Tecnologia, percebeu-se a necessidade de investigar as possibilidades da construção de um material didático para ensino de Matemática para um curso de Agente Comunitário de Saúde nesta modalidade. Este artigo apresenta resultado de uma pesquisa de mestrado: o Caderno Temático Saúde e Números, composto por 10 unidades e um projeto interdisciplinar, cuja finalidade é proporcionar ao estudante o desenvolvimento dos conhecimentos matemáticos de forma interdisciplinar, permitindo uma formação integral do cidadão. Além disso, espera-se que os professores possam, a partir deste, produzir seu próprio material didático.

The Innateness Hypothesis and Mathematical Concepts

In historical claims for nativism, mathematics is a paradigmatic example of innate knowledge. Claims by contemporary developmental psychologists of elementary mathematical skills in human infants are a legacy of this. However, the connection between these skills and more formal mathematical concepts and methods remains unclear. This paper assesses the current debates surrounding nativism and mathematical knowledge by teasing them apart into two distinct claims. First, in what way does the experimental evidence from infants, nonhuman animals and neuropsychology support the nativist hypothesis? Second, granting that infants have some elementary mathematical skills, does this mean that such skills play an important role in the development of mathematical knowledge?

Middle School Immigrant Students Developing Mathematical Reasoning in Spanish and English

Language is the means through which mathematics is learned and mathematical reasoning is developed and expressed. Students' development of mathematical knowledge is dependent upon their codevelopment of language competencies. This study sought to understand the intersection of language acquisition and mathematical reasoning in a multigrade, dual-language mathematics classroom. The focal research question was: In what ways do immigrant middle-school students use L1 and L2 to communicate and to reason mathematically? The students who participated were first- and second-generation immigrants from Mexico. Data included (1) ethnographic field notes, (2), videotape and audiotape of small-group work, (3) interviews with the bilingual mathematics teacher, and (4) student work. Findings suggest that (1) nonroutine mathematical problem posing is useful for eliciting productive talk and encouraging reasoning; and (2) when given the opportunity, ELLs are likely to draw productively upon their linguistic resources in L1 and L2 to support high-level mathematical reasoning.