Acquisition Of Mathematical Concepts Research Articles

The Impact of the Madrasati Platform Experience on Acquiring Mathematical Concepts and Improving Learning Motivation from the Point of View of Mathematics Teachers

Abstract The objective of this research is to examine the impact of the Madrasati platform experience on acquiring mathematical concepts, and improving learning motivation from the point of view of mathematics teachers. To achieve the objective of the research, the researchers relied on the descriptive approach in its survey style. The sample of the study consisted of 613 mathematics teachers in the Kingdom of Saudi Arabia, and the study tool (questionnaire) was distributed to them. These data were processed through the use of quantitative methods and measures, such as the statistical packages program SPSS. The main results were as follows. First, there was a moderate level of agreement among participants regarding the impact of the experience of using the Madrasati platform. Second, there was a much stronger level of agreement regarding the degree to which using the Madrasati platform enabled students to acquire mathematical concepts. Third, there was almost universal agreement among participants that using the platform enhanced students’ motivation to learn. Fourthly, the participants perceived there to be an extremely strong relationship between enhanced motivation to learn and the acquisition of mathematical concepts. The researchers recommend that students and mathematics teachers should continue to use the Madrasati platform in the everyday school environment.

"Now I Get It!": Eureka Experiences During the Acquisition of Mathematical Concepts.

Many famous scientists have reported anecdotes where a new understanding occurred to them suddenly, in an unexpected flash. Do people generally experience such "Eureka" moments when learning science concepts? And if so, do these episodes truly vehicle sudden insights, or is this impression illusory? To address these questions, we developed a paradigm where participants were taught the mathematical concept of geodesic, which generalizes the common notion of straight line to straight trajectories drawn on curved surfaces. After studying lessons introducing this concept on the sphere, participants (N = 56) were tested on their understanding of geodesics on the sphere and on other surfaces. Our findings indicate that Eureka experiences are common when learning mathematics, with reports by 34 (61%) participants. Moreover, Eureka experiences proved an accurate description of participants' learning, in two respects. First, Eureka experiences were associated with learning and generalization: the participants who reported experiencing Eurekas performed better at identifying counterintuitive geodesics on new surfaces. Second, and in line with the firstperson experience of a sudden insight, our findings suggest that the learning mechanisms responsible for Eureka experiences are inaccessible to reflective introspection. Specifically, reports of Eureka experiences and of participants' confidence in their own understanding were associated with different profiles of performance, indicating that the mechanisms bringing about Eureka experiences and those informing reflective confidence were at least partially dissociated. Learning mathematical concepts thus appears to involve mechanisms that operate unconsciously, except when a key computational step is reached and a sudden insight breaks into consciousness.

THE USE OF GAME METHODS AND TECHNIQUES IN TEACHING ELEMENTARY MATHEMATICS TO PRESCHOOL CHILDREN

The article gives a definition of the concept of “plot-didactic game”, characterizes such games, taking into account their use in the process of forming elementary mathematical representations, provides a brief description of games aimed at mastering the program material in the section “Formation of elementary mathematical representations”. In addition, the role of such games in the acquisition of mathematical concepts by preschool children is revealed.

أثر استخدام التطبيقات الرياضية الذکية على اکتساب المفاهيم الرياضية لدى طلبة الصف الرابع الأساسي ذوي صعوبات التعلم الحسابية في الأردن

هدفت هذه الدراسة إلى التعرف على أثر استخدام التطبيقات الرياضية الذکية على اکتساب المفاهيم الرياضية لدى طلبة الصف الرابع الأساسي ذوي صعوبات التعلم الحسابية في المدارس الحکومية في الأردن، تکونت عينة الدراسة من (50) طالبة وطالبا من طلبة الصف الرابع في خمس مدارس حکومية تابعة لمديرية التربية والتعليم في محافظة عمان في العام الدراسي( 2021/2022)، حيث جرى توزيعهم عشوائيا في مجموعة تجريبية ومجموعة ضابطة، ولتحقيق أهداف الدراسة تم بناء اختبار في المفاهيم الرياضية، کما جرى بناء تصميم تطبيق رياضي ذکي خاص بالطلبة ذوي صعوبات التعلم متعلق بالوحدة الأولى من کتاب الفصل الدراسي الأول للصف الرابع الابتدائي، وتم التحقق من صدق أدوات الدراسة وثباتها، وتوصلت الدراسة الى نتائج أهمها: وجود فروق ذات دلالة احصائية بين أفراد المجموعتين التجريبية والضابطة لصالح المجموعة التجريبية. This study aimed to identify the effect of using smart mathematical applications on the acquisition of mathematical concepts among fourth-grade students with arithmetic learning difficulties in government schools in Jordan. The study sample consisted of (50) fourth-grade students in five government schools affiliated to the Directorate of Education In Amman Governorate in the academic year (2022/2021). Where they were assigned equally in an experimental group and a control group, and to achieve the objectives of the study, a test on mathematical concepts was built, and the design of a smart mathematical application for students with learning difficulties related to the first unit of the first semester book of the fourth grade of primary school was built, and the validity of the study tools was verified. The study found the most important results, the most important of which is that there are statistically significant differences between the members of the experimental and control groups in favor of the experimental group.

The effect of Peer Teaching Strategy on the acquisition of some by mathematical concepts Special Education pupils

The current research amides know the effect of peer teaching strategy on the acquisition of mathematical concepts. To achieve the aim of this research ,the researcher put two null hypotheses .The first ,There is no statistically significant difference at the level of (0.5)between the average of the grades of experimental group that used peer tutoring and that of the control group that used traditional method in the acquisition of some mathematical concepts in the post- test phase according to sex variable. The sample included all special education pupils at Nineveh center for the year 2011/2012. The researcher used the experimental design with two equal groups. The sample consisted of (12) male and female pupils divided in two groups ;the experimental with(6)pupils , (3) males and (3) females who used peer to touring and the other control group of (6) pupils with(3) males and (3)females that used traditional method .Equivalence process in clouded 'time age measured in month and the academic achievement of the parents'. The researcher made a test to acquire mathematical concepts. After doing surface validity ,the test in its final image was adopted. Stability was done using re-test reaching (0.82).The researcher applied the test to measure the acquisition of math metical concepts .After applying the tools, the data were treated statistically .The results showed; 1-There is a statistically significant difference at the level of (0.5)between the means of the experimental group that used peer tutoring and the one of the control group that used traditional method on the acquisition of some mathematical concepts in post test 2- There is no statistically significant difference at the level of (0.5), between the means of the experimental group that used peer to tutoring the average of the control group that used the traditional method in acquiring some mathematical concepts in post test according to sex variable. Given the results mentioned above, the researcher recommends the use of using peer tarring strategy in the acquisition of mathematical concepts due to its positive effect in developing class interaction between the pupils of special education The researcher suggests using a similar study to know the effect of using peer tutoring stretchy on learning some materials or initiate a study about the effect of using peer tutoring to ring strategy on some variables like social interaction and the stage.

The Impact of the Learning Learning Strategy on the Acquisition of Mathematical Concepts in Measurement and Evaluation in Students of the Faculty of Education / Ibn Rushd for Human Sciences

   The present study aimed at :   The Impact of the Learning Strategy in the Acquisition of Mathematical Concepts in Measurement and Evaluation in Students of the Faculty of Education / Ibn Rushd for Human Sciences To achieve the research objective, the following zero hypotheses were formulated: 1- There are no statistically significant differences at the level of significance (0.05) between the average score of the students of the experimental group who study according to the strategy of the learning process, and the average score of the students of the control group who study according to the usual method of acquiring mathematical concepts. 2- There are no statistically significant differences at the level of (0,05) between the average of the students of the experimental group who are studying according to the strategy of the learning process and the average score of the students of the control group who study according to the usual method of acquiring mathematical concepts.   The current research sample is 80 students, 40 students, 40 students, 2018-2019, English / Faculty of Education, Ibn Rushd School of Humanities, Baghdad University    To achieve the research objective, the researcher conducted the following - The construction of a post-writing achievement test consisting of (20) test paragraphs and after verifying the validity of the test and its stability and conducting the necessary statistical analysis.    The researchers used a set of statistical tools, including Pearson correlation coefficient, square Kaye, the equation of the effectiveness of the wrong alternatives, and the testing of the two independent samples.      After processing the data statistically, the results were as follows: There are statistically significant differences in the post-achievement test for the experimental group and at the level of significance (0,05).     In the light of the results, the researchers recommended a number of recommendations and proposals.

The Challenge of Modeling the Acquisition of Mathematical Concepts.

As a full-blown research topic, numerical cognition is investigated by a variety of disciplines including cognitive science, developmental and educational psychology, linguistics, anthropology and, more recently, biology and neuroscience. However, despite the great progress achieved by such a broad and diversified scientific inquiry, we are still lacking a comprehensive theory that could explain how numerical concepts are learned by the human brain. In this perspective, I argue that computer simulation should have a primary role in filling this gap because it allows identifying the finer-grained computational mechanisms underlying complex behavior and cognition. Modeling efforts will be most effective if carried out at cross-disciplinary intersections, as attested by the recent success in simulating human cognition using techniques developed in the fields of artificial intelligence and machine learning. In this respect, deep learning models have provided valuable insights into our most basic quantification abilities, showing how numerosity perception could emerge in multi-layered neural networks that learn the statistical structure of their visual environment. Nevertheless, this modeling approach has not yet scaled to more sophisticated cognitive skills that are foundational to higher-level mathematical thinking, such as those involving the use of symbolic numbers and arithmetic principles. I will discuss promising directions to push deep learning into this uncharted territory. If successful, such endeavor would allow simulating the acquisition of numerical concepts in its full complexity, guiding empirical investigation on the richest soil and possibly offering far-reaching implications for educational practice.

Collaborative work as a learning strategy to teach mathematics incorporating robotics using led godt education system and fischertechnik in seventh graders at the school Isidro Caballero Delgado in Floridablanca Santander Colombia

This article describes the impact of collaborative work to teach Mathematics in Seventh graders (70 students) at the school Isidro Caballero Delgado, Ocaña, Colombia. Led godt education system and fischertechnik allowed a great interaction and participation and provided the tools to incorporate robotics in the classroom. Moreover, these tools are used as a learning strategy to achieve understanding and analysis in the solving problems teaching math. Students became more critical and responsible facing daily solutions and a better understanding of basic problems of geometry, math and statistics. Students also learnt about and improved interpersonal abilities and improved social interaction. It also allowed making learning effective creating a better environment to improve the acquisition of mathematical concepts.

Building Blocks of Mathematical Learning: Virtual and Tangible Manipulatives Lead to Different Strategies in Number Composition

Multiple kinds of manipulatives, as traditional, virtual or technology-enhanced tangible objects, can be used in primary education to support the acquisition of mathematical concepts. They enable playful experiences and help children understand abstract concepts, but their connection with cognitive development is not totally clear. It is also not clear how virtual and physical materials influence the development of different strategies for solving instructional tasks. To shed light on these issues, we conducted a 13-day intervention with 64 children from first grade, divided into three groups: Virtual Interaction (VI), Tangible Interaction (TI), and Control Group (CO). The VI group played a fully digital version of a mathematics videogame BrUNO and the manipulation of virtual blocks took place on the tablet screen. The TI group played the same videogame with digitally augmented tangible manipulatives. Finally, the CO group continued with their classroom curricular activities while we conducted the training, and only participated in the pre- and post-test evaluations. Our results highlighted that the use of tangible manipulatives may improve children’s mathematical abilities. Of most interest, we recorded children’s actions during all the training activities, which allowed us to achieve a refined analysis of participants’ operations while solving a number composition task. We explored the differences between the use of virtual and tangible manipulatives and the strategies employed. We observed that the TI group opted for a greater number of blocks in the number composition task, whereas the VI group favoured solutions requiring fewer blocks. Interestingly, those children whose improvement in mathematics were greater were the ones employing a greater number of blocks. Our results suggest that tangible interactive material increases action possibilities and may also contribute to a deeper understanding of core mathematical concepts.

The Effect of Using the Frayer Teaching Model in Acquiring Mathematical Concepts among the Seventh Grade Students

The current research aim to identify the effect of using the Frayer teaching model in acquiring mathematical concepts among the seventh grade students.To achieve this goal, the two researchers used the experimental method. The experiment was applied to a sample of 62 students  from the seventh  grade who were selected intentionally from(bjara) intermediate School which is located in the center of Dohuk  governorate for the academic year (2017-2018) and then distributed randomly to two equal groups, one of which is experimental, consisting of (31) students who studied using the Frayer teaching model, and another  group consists of (31) students studied using the usual method, The results of the study  were analyzed using the arithmetic mean and the T-test for two independent samples. The results were as follows: There is a statistically significant difference between the scores of the two research groups. Thus, the students who study according to the frayer model are superior to the students who study according to the usual method in the test of mathematical concepts. There is no statistically significant difference between the scores of the research students in the experimental group according to gender variables and in the mathematical concepts test. In the experimentation of student-centered teaching models in the acquisition of mathematical cocepts. The study came out with a set of conclusions, recommendations and suggestions. Keywords: Frayer Model, Acquisition of Mathematical Concepts.

استخدام موقع ماثلتیکس (Mathletics) فی تعْلِیم وتعلُّم الریاضیَّات وأثره على إکتساب الطالبات للمفاهیم الریاضیة

هدف البحث إلى معرفة واقع استخدام موقع ماثلتيکس (Mathletics) في تعليم وتعلم الرياضيات من وجهة نظر المعلمات والطالبات، کما هدف إلى التعرف على أثر استخدام موقع الماثلتيکس على اکتساب طالبات الصف الثالث المتوسط بالمدينة المنورة للمفاهيم الرياضية، وتحقيقا لهدف البحث استخدم المنهج الوصفي والمنهج شبه التجريبي، کما استخدمت مجموعة من الأدوات شملت: استبانة واقع استخدام موقع الماثلتيکس في تعليم الرياضيات من وجهة نظر المعلمات، واستبانة واقع استخدام موقع الماثلتيکس في تعلم الرياضيات من وجهة نظر الطالبات، واختبار اکتساب المفاهيم الرياضية وفقا لأنموذج فراير في وحدة الجذرية والمثلثات. وحللت البيانات باستخدام اختبار (ت) للعينات المستقلة، واختبار (ت) للعينات المرتبطة، واختبار مان وتني، واختبار کرسکال ويلز، وحساب مربع إيتا لمعرفةحجم الأثر، وتوصل البحث إلى النتائج التالية: يوجد فرق دال إحصائيا عند مستوى الدلالة (0.05 ≥ α) بين: (1) متوسطات تقديرات المعلمات لواقع استخدامهن لموقع الماثلتيکس تعزى لمتغير عدد سنوات الخبرة في التدريس لصالح السنوات الأکثر؛ (2) متوسطات تقديرات المعلمات لواقع استخدامهن لموقع الماثلتيکس تعزى لمتغير المؤهل العلمي لصالح مؤهل الدبلوم؛ (3) متوسطات تقديرات المعلمات لواقع استخدامهن لموقع الماثلتيکس تعزى لمتغير نوع المؤهل لصالح الغير تربوي؛ (4) متوسطات تقديرات الطالبات لواقع استخدامهن لموقع الماثلتيکس تعزى للمرحلة الدراسية لصالح المرحلة الابتدائية؛ (5) متوسطي درجات مجموعتي البحث التجريبية والضابطة في التطبيق البعدي لاختبار إکتساب المفاهيم الرياضية لصالح طالبات المجموعة التجريبية؛ (6) متوسطي درجات المجموعة التجريبية في التطبيقين القبلي والبعدي لاختبار إکتساب المفاهيم الرياضية لوحدة المعادلات الجذرية والمثلثات بالصف الثالث المتوسط لصالح التطبيق البعدي. بينما لا يوجد فرق دال إحصائيا عند مستوى الدلالة (0.05 ≥ α) بين متوسطات تقديرات المعلمات لواقع استخدامهن لموقع الماثلتيکس تعزى لمتغير المرحلة التدريسية. Abstract: Using Mathletics Website In Teaching And Learning Mathematics And its Impact On The Students’ Acquisition Of The Mathematical Concepts The research aimed at finding out the use of Mathletics website in teaching and learning mathematics from the point of view of teachers and students. Likewise, it aimed at knowing the impact of using Mathletics website on the third intermediate class students’ acquisition of mathematical concepts in the radical equations units and trigonometry compared to the traditional way. To achieve the goal of the research, the descriptive and the quasi-experimental approaches have been used in addition to a set of tools including: applying a questionnaire about using Mathletics website in teaching mathematics from the teachers’ point of view on a random, and applying a questionnaire about using Mathletics website in teaching mathematics from the students’ point of view on a random, and the test of mathematical concepts acquisition according to Frayer model in the radical equations unit and trigonometry, that has been prepared by the researcher. The data were analyzed using the t-test for the independent samples, the t-test for the paired samples, the test of Mann-Whitney, the test of Kruskal-Wales and calculate the square Eta to know how much it the impact, the outcome of the research was the following: There is a statistically significant difference at the level of function (α ≤ 0.05) between: (1) the average scores of the teachers, who used Mathletics website, are attributable to the variable of number of years of experience in teaching, with the result being in favor of the higher number of years; (2) the average scores of the teachers who used Mathletics website are attributable to the variable of the educational qualification, with the result being in favor of the diploma; (3) the average scores of the teachers who used Mathletics website are attributable to the variable of the type of educational qualification, with the result being in favor of the non-educational; (4) the average scores of the students who used Mathletics website are attributable to the variable of the educational stage, with the result being in favor of the elementary stage; (5) the average scores of the experimental and control groups in the post application of the test of the acquisition of the mathematical concepts are in favor of the experimental group students; (6) The average scores of the experimental group in the pre- and post-application of the test of the acquisition of the mathematical concepts of “radical equations and trigonometry” in the third intermediate class are in favor of the post-application. While there is no statistically significant difference at the level of function (α ≤ 0.05) between the average scores of the teachers who used Mathletics website are attributable to the variable of the teaching stage.

Computational thinking and mathematics using Scratch: an experiment with sixth-grade students

ABSTRACTThe potential benefits from the introduction of programming environments such as Scratch for learning mathematics has reactivated research in this area. Nonetheless, there are few studies which attempt to analyse their influence at the stage of Primary Education. We present the results of a quasi-experimental piece of research with sixth-grade students which studies the influence of Scratch both on the acquisition of mathematical concepts, and on the development of computational thinking. The experiment consisted of two different phases, a programming phase linked to the instruction in Scratch and focused on the acquisition of basic concepts of computational thinking (sequences, iterations, conditionals, and events-handling), and a mathematical phase completely oriented towards the resolution of mathematical tasks. In particular, the mathematical phase focused on word problems whose resolution involves the use of the least common multiple and the greatest common divisor. In order to evaluate the aims of the study, results from tests before and after instruction, both in computational thinking and in the mathematical standards, were compared. The results seem to indicate that Scratch can be used to develop both students’ mathematical ideas and computational thinking.

The Effectiveness of Teaching Geometry to Enhance Mathematical Understanding in Children with Down Syndrome

ABSTRACTIt is widely known that people with Down syndrome have difficulties transitioning from a basic understanding of counting and cardinality to more advanced arithmetic skills. This is commonly addressed by resorting to the mechanical use of algorithms, which hinders the acquisition of mathematical concepts. For this reason some authors have recently proposed a shift in the focus of learning from arithmetic to more fertile fields, in terms of understanding. In this paper we claim geometry fits this profile, especially suited for initiating children with Down syndrome into mathematics. To support this we resort to historical, epistemological, and cognitive reasons: the work of Séguin and his intuition on the central role of geometry in the development of abstract thinking in the so-called idiot children, the ideas of René Thom about the role of continuum intuition in the emergence of conscious thinking, and finally the two strengths people with Down syndrome display: visual learning abilities and interest in abstract symbols. To support these ideas we present the main findings of qualitative research on elementary mathematics teaching to a group of seven children (3–8) with Down syndrome in Spain. The didactic method used, naturally enhance their naïve geometrical conceptions.

The Effect of Using the Generative Model on the Acquisition of Mathematical Concepts and Problem Solving for 7th Grade Students in Light of their Logical Thinking

The Effect of Using the Generative Model on the Acquisition of Mathematical Concepts and Problem Solving for 7th Grade Students in Light of their Logical Thinking

Teaching strategies of mathematical generalizations and their effects on students of 12th grade in the State of Kuwait: تدريس استراتيجيات التعميمات الرياضية وآثار استخدامها لدى طلاب الصف الثاني عشر بدولة الكويت

This study aimed at knowing the use of the strategies "Text - direct example - indirect example - proof", "text - proof - direct example - indirect example" in the teaching of mathematical generalizations in grade 12 students, The sample was randomized to a first experimental group of 37 students and a second experimental group of 40 students and a group of 40 students. The researcher prepared an educational material for mathematical generalizations by calculating mathematics book for the twelfth grade for the academic year 2016/2017. Shall be of (28) paragraphs, and the validity of the test was confirmed by presenting it to a committee of arbitrators, and calculating the correlation coefficient of each paragraph with the total score of the test. The results of the study were statistically significant at (0.01> α) between both the experimental group and the control group for the benefit of the two experimental groups. (24.75) compared to (19.05) for the control. In the light of the previous results, the researcher recommended enriching the mathematics curriculum with direct examples and indirect examples in terms of quantity and type. And provide a guide for the mathematics teacher that includes a variety of ideas for direct examples and indirect examples in triangulation, to help communicate mathematical generalizations and to adopt effective teaching methods and strategies that facilitate students' acquisition of mathematical concepts and generalizations.

The Effectiveness of an E-Book on Developing Mathematical Thinking Skills and Acquisition of Mathematical Concepts among 5th Graders in Gaza

This study aimed to investigate the effectiveness of using an ebook on Developing Mathematical Thinking Skills and Acquisition of Mathematical Concepts Among 5th Graders in Gaza. The researchers adopted the experimental approach. The Quasi Experimental Design ( pre-post test for two groups) is adopted in the study, The sample of the study included (70) students from Bet Lahya Elementary School during the second term(2013-2014). The study sample consists of two classes have been randomly selected from the school 5th grade classes, one of them (36 students) has been chosen as experimental group and the other(34 students) as control group. Two tools were used, Mathematical thinking test and Mathematical Concepts Acquisition Test. The results revealed that there were statistically significant difference at (α = 0.05) between the scores means of the experimental group and control group in mathematical thinking skills test in favor of the experimental group. Moreover there are also significant differences at (α = 0.05) between the scores mean of the experimental group and control group in Acquisition of Mathematical Concepts in favor of experimental group. η2 and d values which were calculated, indicated to large effectiveness of the used e-book on developing mathematical thinking skills and acquisition of mathematical concepts of 5 Graders in Gaza.

Integration of the development of mathematical concepts and music education in preschool education by means of songs

Starting from the fact that in early education the process of learning should be understood in its totality, as a system of activities in which the subject fields are interwoven and woven into every segment of a child's life together with other children and adults in preschool, the authors of the work point out the integration of the development of mathematical concepts and music education. Music education is viewed as a context which can contribute to the acquisition of mathematical concepts, and to that effect they mention the (touching points) parallels between the content of music education and the content of preschool mathematical education by means of using songs. In that context, they point out the importance and role songs have in the total development of children, in the development of their music abilities, and especially in the context of the development of mathematical concepts. Using concrete examples of songs, they point out their possible function in the development of beginner mathematical concepts, and in musical education in the framework of preschool education.

Ensino da matemática a alunos com deficiência intelectual na educação de jovens e adultos

A inclusão de jovens e adultos com deficiência intelectual na EJA representa tanto um avanço quanto um desafio frente ao processo ensino-aprendizagem; e, quando tratamos da adaptação curricular para o ensino de Matemática a este alunado, estamos diante da construção de novas possibilidades educacionais. Este estudo teve como objetivo conhecer as práticas do professor da EJA para o ensino de saberes matemáticos ao aluno jovem e adulto com deficiência intelectual, e intervir junto ao docente sobre possíveis estratégias que seriam então adotadas. Para isso, utilizou-se como referência metodológica a abordagem qualitativa com foco na pesquisa-intervenção. O estudo foi realizado em uma sala da EJA, na qual participaram uma professora e cinco estudantes, dois destes com deficiência intelectual. Foram realizadas observações em sala e intervenções mediante aplicação de atividades diferenciadas com foco no ensino desses saberes. Por intermédio dessa pesquisa, verificou-se que estratégias tais como jogos podem efetivamente auxiliar na aquisição de conceitos matemáticos. Assim, espera-se que este estudo desperte reflexões entre os pesquisadores dos campos da Educação Matemática e da Educação Especial e destaque, desse modo, a necessidade de trabalhos diferenciados e colaborativos com o ensino de saberes matemáticos para esse alunado em específico.

Incomplete understanding of complex numbers Girolamo Cardano: a case study in the acquisition of mathematical concepts

In this paper, I present the case of the discovery of complex numbers by Girolamo Cardano. Cardano acquires the concepts of (specific) complex numbers, complex addition, and complex multiplication. His understanding of these concepts is incomplete. I show that his acquisition of these concepts cannot be explained on the basis of Christopher Peacocke’s Conceptual Role Theory of concept possession. I argue that Strong Conceptual Role Theories that are committed to specifying a set of transitions that is both necessary and sufficient for possession of mathematical concepts will always face counterexamples of the kind illustrated by Cardano. I close by suggesting that we should rely more heavily on resources of Anti-Individualism as a framework for understanding the acquisition and possession of concepts of abstract subject matters.

The Hidden Treasure: The Role of Darts in Acquisition of Mathematical Concepts

This study set out to explore the role of darts in acquisition of mathematical concepts. A case study was carried out in Mucheke Suburb, Masvingo Province, in Zimbabwe. Twenty participants (18 males and 2 females) from two teams in Masvingo District Darts Association were purposely selected to take part in the study. The researchers used interviews and participant observation to gather data since they also play for one of the teams studied. This study found out that darts are very useful in facilitating the acquisition of cognitive skills like addition, subtraction, multiplication and division. Players also acquire skills in carrying out combined operations and idiosyncratic algorithms. Besides acquiring cognitive skills, players also acquire psychomotor skills which improve their precision in target hitting. In the process of play, the researchers noted that individuals’ emotional skills develop as evidenced by virtues of tolerance, cooperation and acceptance of criticism. Irrespective of these benefits, the researchers noted that darts still remain a hidden treasure since they are mostly played in pubs with limited access to children and most of those who do not take alcohol. Arising from the findings were recommendations that, women and children should be given access to play darts since they are useful in mathematics education as well as human development.