The paper is an exposure to the latest practices of questioning in teaching and learning math (TLM) on the basis of psychological-semiotic approach. Emphasis is placed on the degree of semantic support of the expected answer when formulating educational questions. The paper explored: whether teachers are able to distinguish between types of questions and to use them in sync with didactic purpose; what types of questions teachers consider to be the most effective; what factors influence this process. To achieve these goals, survey-based research was conducted among 173 high school mathematics teachers across Ukraine. The research proved that, in their majority, teachers are able to correctly distinguish among the types of the questions offered. According to the teachers, questions with full semantic support for the answer are less useful in TLM. The study showed teachers’ lack of ability to identify the goals of the questions. There has been revealed a gap between the teachers’ attitude to the expedience of using questions with several possible answers and the practice of their implementation in TLM. The study yielded 35 variables characterizing the current status of the problem. They were optimized to 13 factors. It was stated that questioning should comply with the content of educational material, and the questions formulated with the use of topical vocabulary known to the students are viewed as most cost-effective. The research revealed the significant impact of the number of questions that teachers or students ask. The factor of primary importance appears to be that of time.
Students' mastering the art of proof is one of the most important educational results of teaching Mathematics in the secondary school. The study shows that there are significant challenges, gaps, and weaknesses in the practice of teaching reasoning and proving. The goal of the research is to determine the way of using traditional teaching practices to present reasoning and proving, the way of organizing the review and mastery of the theorem proofs. In addition, the obvious and hidden factors affecting the students' productivity in these activities were identified. To study the problem, a survey that involved 136 Mathematics teachers across Ukraine was carried out. A standard close-ended questionnaire was developed. Factor analysis was used to analyze the results of the survey. The important factors determining the time efficiency when a teacher organizes teaching and learning of a theorem proof, were discovered. The analysis of the factors and numerical loadings of variables forming them, result in the conclusions presented in this paper.
This empirical study determines the obvious and hidden factors that affect the Ukrainian Mathematics teachers to use Project-Based Learning and Teaching (PBL and PBT) Mathematics. A survey of 126 practicing Mathematics teachers was conducted using a Standard closed ended questionnaire. The study confirms that modern Mathematics teachers believe that it is impossible to teach Mathematics for modern students without using PBL and PBT. On the one hand, teachers demonstrate their beliefs in these educational techniques. On the other hand, the survey reveals hidden factors that are inhibitory in the practice of PBL and PBT Mathematics. The study shows the following statistically confirmed factors in teachers' beliefs concerning the use of PBL and PBT Mathematics: Content-Technological Factor; Result & Age Factor; Factor of the Target Audience on the expediency of using PBL and PBT Mathematics; Teacher's Overload Factor; Praxeological Factor; Locality Factor; Teacher's Awareness Spectrum Factor. The previous assumption that the experience of a Mathematics teacher is an influential factor in the use of PBL and PBT has not been statistically confirmed. The results show that an influential factor is the Locality Factor. So, it's important if a teacher teaches Mathematics in a city or a village. Its origins (genesis and causes) and the consequences of this factor influence on educational processes in Ukraine need more detailed study.
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