Examining Problem-Solving and Problem-Posing Skills of Pre-Service Mathematics Teachers: A Qualitative Study

The aim of this study is to examine the problem-solving processes and problem-posing skills of pre-service mathematics teachers, which consists of four stages (understanding the problem, preparing a plan for the solution, applying the plan, evaluating) defined by Polya (1997) with the progressive scoring scale based on the alternative assessment approach. Qualitative research approach has been adopted in the study. Participants of the study consist of 71 pre-service teachers studying at the department of primary education mathematics teaching at the education faculty of a state university in the Southeastern Anatolia region of Turkey. Since the problem solving and problem posing behaviors of the participants were examined separately in the study, the gradual scoring scale developed by Baki (2008) was used. As a result of the analysis, it was determined that the participants showed the highest performance in the category of understanding the problem, and the lowest performance in the category of evaluation and problem posing. It was determined that participants who failed in the problem posing phase either wrote the same problem or could not write a problem. Another result reached in the study is that the participants had difficulties in expressing the operations in mathematical language.

Examining Problem-Solving and Problem-Posing Skills of Pre-Service Mathematics Teachers: A Qualitative Study

The aim of this study is to examine the problem-solving processes and problem-posing skills of pre-service mathematics teachers, which consists of four stages (understanding the problem, preparing a plan for the solution, applying the plan, evaluating) defined by Polya (1997) with the progressive scoring scale based on the alternative assessment approach. Qualitative research approach has been adopted in the study. Participants of the study consist of 71 pre-service teachers studying at the department of primary education mathematics teaching at the education faculty of a state university in the Southeastern Anatolia region of Turkey. Since the problem solving and problem posing behaviors of the participants were examined separately in the study, the gradual scoring scale developed by Baki (2008) was used. As a result of the analysis, it was determined that the participants showed the highest performance in the category of understanding the problem, and the lowest performance in the category of evaluation and problem posing. It was determined that participants who failed in the problem posing phase either wrote the same problem or could not write a problem. Another result reached in the study is that the participants had difficulties in expressing the operations in mathematical language.

Effectiveness of a numeracy intelligent tutoring system in kindergarten: A conceptual replication

Intelligent Tutoring Systems are a genre of highly adaptive software providing individualized instruction. The current study was a conceptual replication of a previous randomized control trial that incorporated the intelligent tutoring system Native Numbers, a program designed for early numeracy instruction. As a conceptual replication, we kept the method of instruction, the demographics, the number of kindergarten classrooms (n = 3), and the same numeracy and intrinsic motivation screeners as the original study. We changed the time of year of instruction, changed the control group to a wait-control group, added a maintenance assessment for the first group of participants, and included a mathematical language assessment. Analysis of within- and between-group differences using repeated measures ANOVA indicated gains of numeracy were significant only after using Native Numbers (Partial Eta Square = 0.147). Results of intrinsic motivation and mathematical language were not significant. The effect size of numeracy achievement did not reach that of the original study (Partial Eta Square = 0.622). Here, we compared the two studies, discussed plausible reasons for differences in the magnitude of effect sizes, and provided suggestions for future research.

Exploring the Educational Value of Mathematical Beauty and Effective Ways of Discovering Mathematical Beauty

The precision of mathematical reasoning, the abstractness of mathematical language, the profundity of mathematical thought and method, as well as the excessive formalization of mathematics teaching have formed an impassable gap, hindering students in approaching mathematics. This has concealed the beauty of mathematics and the light of mathematical culture. However, if students are able to cross this gap, they would find that mathematics is a vast world full of vitality, imagination, wisdom, poetry, and beauty. The pursuit of mathematical beauty is one of the motivations for scientists to research this field. Experiencing mathematical beauty is of great significance to students’ learning and growth. In teaching, the value of mathematical beauty is explored, such as stimulating emotions, opening up to the truth, and cultivating goodness. Several effective ways are suggested in this article to guide students to discover the mathematical beauty in life while finding it in problem-solving methods and exploring it in knowledge systems.

Elements of Group Theory

The mathematical language which encodes the symmetry properties in physics is group theory. In this chapter we recall the main results. We introduce the concepts of finite and infinite groups, that of group representations and the Clebsch–Gordan decomposition. We study, in particular, Lie groups and Lie algebras and give the Cartan classification. Some simple examples include the groups U(1), SU(2) – and its connection to O(3) – and SU(3). We use the method of Young tableaux in order to find the properties of products of irreducible representations. Among the non-compact groups we focus on the Lorentz group, its relation with O(4) and SL(2,C), and its representations. We construct the space of physical states using the infinite-dimensional unitary representations of the Poincaré group.

FUTURE TEACHERS’ STUDYING THE SCIENTIFIC LANGUAGE OF PHYSICS AND MATHEMATICS: PROBLEMS AND PROSPECTS

Математический язык является основой таких дисциплин, преподаваемых в вузах, как математика и физика. Особое внимание следует обратить на подготовку будущих учителей математики и физики. Как показывает практика, в процессе подготовки студентов по обозначенным специальностям большинство трудностей связано именно с обеспечением надлежащих условий по усвоению учащимися языка предметной области. Настоящее исследование обращено к общетеоретическому и практическому раскрытию проблемы практического перевода задач на язык математической теории и, напротив, проведение обратного перевода. Статья также посвящена особенностям овладения технологиями прочного усвоения математического языка студентами, что должно стать залогом достижения конкретных практических результатов в будущей педагогической деятельности. Студент должен не только овладеть навыком решения математических и физических задач, но и уметь объяснять подробности их решения на математическом языке и раскрывать учащимся особенности построения математической задачи как на языке предметной лексики, так и при помощи стандартных формулировок, лексики и синтаксиса. В рамках исследования было проведено анкетирование, направленное на определение уровня владения математическим языком среди студентов первого и последнего курса, проходящих обучение по направлению подготовки «Педагогическое образование», с целью разработки системы упражнений, направленных на облегчение процесса усвоения математического языка. The mathematical language is the basis of university mathematics and physics. Special attention is to paid when training future teachers of mathematics and physics. As practice shows, in the process of preparing students for the considered specialties, most difficulties are associated precisely with the provision of appropriate conditions for the assimilation of the language of the subject area by students. The present study is to consider theoretical and practical aspects of the problem of practical interpretation of problems into the language of mathematical theory and vice versa. The article is also devoted to the peculiarities of mastering solid assimilation of the mathematical language by students, which should be the key to achieving specific practical results in future pedagogical activities. Since the student must not only master the skill of solving mathematical and physical problems, but also be able to explain the details of the solution in mathematical language and reveal to pupils the peculiarities of making a mathematical problem, both in the language of subject vocabulary and using standard phrases, vocabulary and syntax. As part of the study, a questionnaire was conducted to determine the level of proficiency in the mathematical language among first and last year “Pedagogical Education” training program students in order to develop a system of exercises aimed at facilitating the process of mastering the mathematical language.