We offer this synthesized framework as a tool to reveal mathematical activity in a non-formal making-space. In particular, we connect research at different grain sizes to illustrate and explain how ...mathematics plays a crucial, if often implicit, role in making activities. We begin by describing the Approximate Number System and the Ratio-Processing System, and explaining how those systems connect to both embodied cognition and Thompson’s (1994) conceptualization of quantities. Then, we examine how prediction and anticipation relate, with a particular emphasis on how social feedback guided the emergent mathematical activity. We offer this framework as a way to perceive, account for, and understand the multi-layered nature of experiencing mathematical activities.
Parents' high academic expectations are positively associated with young children's mathematical abilities. However, minimal attention has been devoted to whether, and how, different ways of ...conveying the performance targets would result in different outcomes.
The current study investigated whether and how parents' perfectionistic strivings and concerns were associated with young children's mathematical abilities through home mathematical activities, children's approach motivation to learn mathematics, and children's avoidance motivation to learn mathematics.
Participants included 211 kindergarteners in Hong Kong and their parents.
Data were collected through individual child tests and parent questionnaires.
Structural equation modelling revealed that parents' perfectionistic strivings had a direct positive link with children's mathematical abilities, an indirect link via approach motivation to learn mathematics, and an indirect link via home mathematical activities, and then approach motivation. Parents' perfectionistic concerns had a direct negative link with children's mathematical abilities, an indirect link via approach motivation to learn mathematics, and an indirect link via avoidance motivation to learn mathematics.
Early childhood practitioners are recommended to raise parents' awareness of how to communicate high-performance targets to children in a constructive manner.
The continuous exploration of mathematics as a human activity triggers the need to research ethnomathematics. This study aimed to identify ethnomathematics in the manufacture of indigenous fish traps ...(Bubu) from Bintan Regency. This ethnography study uses direct observation, interviews, and documentation. The researcher acts as the main instrument. The data were analyzed using the Spradley analysis technique, namely domain, taxonomic, componential, and cultural theme analysis. Data reduction, data presentation, and conclusions were carried out for each analysis. The results show that there are mathematical activities in designing, counting, and measuring length dimensions in Bubu's making. In these activities, there are mathematical concepts, including three-dimensional figures, the net of three-dimensional figures, curves, odd numbers, sequences with their attributes, bilateral symmetry, symmetry axes, figurative numbers, the congruence of plane figures, and length measurements with non-standardized units. These results showed that the Bubu maker already had a geometric sense through the symmetrical concept that became the basis for two activities such as counting and measuring, similar to the results of ethnomathematical research on the Yupiaq Eskimo community in Alaska and the Carolina Islanders in Micronesia. This study provides ideas to utilize everyday phenomena in teaching mathematics as a starting point prior to learning mathematics more formally.
Children's numeracy competencies are not only relevant for their academic achievement, but also later in life. The development of early numeracy competencies is influenced by children's learning ...environment. Here, the home numeracy environment (HNE) and parent's own beliefs about mathematics play an important role for children's numeracy competencies. However, only a few studies explicitly tested these associations separately for mothers and fathers. In our study, we assessed mothers' and fathers' mathematical gender stereotypes, self-efficacy and their beliefs on the importance of mathematical activities at home, and tested their associations with parents' numeracy activities and children's numeracy competencies in a sample of
= 160 children (
= 80 girls) with an average age of
= 59.15 months (
= 4.05). Both, fathers and mothers regarded boys as being more competent in mathematics than girls. Fathers when compared to mothers reported a greater mathematical self-efficacy. Further, only mothers' self-efficacy was associated with the frequency of numeracy activities with the study child. In contrast, only fathers' beliefs on the importance of mathematics was associated with their numeracy activities which, in turn, predicted children's numeracy competencies. However, the non-invariant constructs and varying results lead to the question whether a revision of existing scales assessing parental beliefs and home numeracy activities is needed to investigate differences of mothers and fathers and their potential associations with children's numeracy outcomes.
Bu çalışmada ortaokul 7. sınıf matematik ders kitaplarında yer verilen etkinliklerin matematiksel potansiyel düzeyleri incelenmiştir. Çalışmada doküman incelemesi yöntemi kullanılmıştır. Doküman ...olarak Milli Eğitim Bakanlığı Talim ve Terbiye Kurulu (MEB-TTK) tarafından ders kitabı olarak okutulması için onay verilen iki kitap seçilmiştir. Bu kitaplar A ve B kitabı olarak isimlendirilmiştir. A kitabında 36 ve B kitabında ise 13 etkinliğe yer verilmiştir. Kitaplarda yer verilen etkinliklerin matematiksel potansiyel düzeyleri derinlik, matematiksel odak ve komplekslik bileşenlerine göre betimsel olarak analiz edilmiştir. Etkinlikler bu bileşenlerin her birine göre çok düşük (0 puan), düşük (1 puan), orta (2 puan) ve yüksek (3 puan) olmak üzere dört düzeye göre puanlanmıştır. Derinlik bileşeni kapsamında her iki kitapta yer verilen etkinliklerin ağırlıklı olarak orta ve yüksek puanlı etkinlikler olduğu gözlenmiştir. Matematiksel odak bileşeni kapsamında B kitabında yer verilen etkinliklerin A kitabındaki etkinliklere göre daha yüksek puanlı etkinlikler olduğu görülmüştür. Her iki kitapta da özellikle komplekslik bileşeni düzeyleri düşük çıkmıştır. Veri analizlerinden elde edilen bulgular incelenen her iki ders kitabında yer verilen etkinliklerin matematiksel potansiyel bileşenleri kapsamında farklı öğrenme fırsatları sunduklarını göstermiştir. Ayrıca her iki kitapta yer verilen ve aynı kazanıma yönelik olan bazı etkinliklerin aynı bağlama sahip olmalarına rağmen matematiksel potansiyel bileşenleri özelinde farklı puan dağılımlarına sahip olabildikleri görülmüştür.
This study aims to examine the level of mathematical potential in the activities included in the 7th grade mathematics textbooks used in secondary schools. The study utilizes the document analysis method to achieve this objective. The dataset for the study comprises activities from two textbooks (called Book A and B) approved by the Ministry of National Education. A total of 36 activities from Book A and 13 activities from Book B were analyzed using deductive content analysis technique. The mathematical potential of the activities were examined based on three components: depth, mathematical focus, and complexity. Each component was assessed and scored at four levels: very low (0 points), low (1 point), medium (2 points), and high (3 points). The findings revealed that activities in both books received predominantly medium and high scores in terms of the depth component. However, activities in Book B scored higher than those in Book A in terms of the mathematical focus component. The results highlighted differences in the learning opportunities provided by the textbooks through the prescribed mathematical activities. It was observed that both books had significant deficiencies, particularly in the complexity component. Furthermore, even though activities in both books shared the same context, it was found that certain activities for the same gains had different score distributions in terms of the mathematical potential components. The findings underscore the need for improvement in the complexity aspect of the activities and highlight the variations in the mathematical potential across different textbooks, despite similar contexts.
Although it is a challenge for primary school teachers, real-context estimation problems can be used as an introduction to mathematical modeling. With this aim, we designed a two-phase activity: in ...the first phase, 224 prospective teachers developed individual action plans to solve a sequence of real-context estimation problems in the classroom; in the second phase, they completed the solution of the same problems working in groups in the real location where the four problems were contextualized. A comparative study showed that, in the second phase, prospective teachers were able to adapt their solutions to contextual features detected in situ that had not been anticipated in the action plans developed during the first phase. Two-phase modeling activities, which permit a comparison of different perspectives on problems, facilitate the experience of collaborative work. These activities could be incorporated into prospective teachers’ initial training as a useful resource for improving their problem-solving expertise.
•This study allows us to establish a teaching methodology proposal for teacher training on the teaching of mathematical modeling based on promoting adaptive expertise by confronting them with a sequence of Fermi problems.•Prospective teachers are confronted with the problems in a specific way: it is necessary that the problems to be tackled can be solved using a variety of strategies and that these can be refined to high levels of accuracy in the results.•It is important that each participant faces the problems individually to generate a plan of action, this activity allows each one to contribute an initial version of the resolution strategy to be constructed and to later compare it with those of the other participants.
Although research on mathematics education incorporating humor generally expects humor to improve students’ emotional experiences in mathematics learning and provides multiple ways to interpret word ...problems, this study examined the cognitive role of humor in authentic mathematical activities, wherein more general mathematical problems are generated from relatively particular ones. Particularly, this study clarified the cognitive role of humor in mathematics lessons that intentionally incorporate humor in secondary education. We applied the incongruity theory of humor as a theoretical framework and analyzed eighth-grade students’ mathematical activities for ascertaining the sum of interior angles of polygons. We observed that students themselves discovered that different initial assumptions led to the same mathematical conclusion. We found that the incorporation of humor into mathematics education has at least three effects, wherein humor 1) guarantees freedom of thinking in solving mathematical problems; 2) updates didactical contracts between teachers and students; and 3) enhances students’ critical thinking skills. Thus, we concluded that humor contributes to the realization of students’ authentic mathematical activities. As an implication for future mathematics education research, we point out the necessity of exploring how classroom cultures for connecting humor with mathematics might emerge.
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