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Fostering conceptual understanding in mathematics classrooms is an important goal in mathematics education. To support this goal, we need to be able to diagnose and assess the extent to which students have conceptual understanding. In this study we employed a problem-posing task and a problem-solving task in order to diagnose and assess preservice teachers' mathematical understanding of fraction division. The results of the study show that although over 99% of the preservice teachers could correctly perform fraction division, they were much less likely to exhibit conceptual understanding of fraction division either through a problem-solving task involving graphical representation or through a problem-posing task. However, engaging in problem posing appears to more likely than making a graphical representation to elicit preservice teachers' conceptual understanding. Moreover, a conceptual cue about the meaning of fraction division appears to greatly increase the likelihood that preservice teachers will exhibit conceptual understanding of fraction division in their posed problems and generate conceptually based diagrams of fraction division. The findings highlight the usefulness of problem-posing tasks for diagnosing and assessing preservice teachers' mathematical understanding.

In this paper we discuss students' opportunities to learn to pose mathematical problems, based on a historical analysis of problem posing in the area of number and algebra in six series of Chinese primary school mathematics textbooks published since the 1950s. We examine changes in the proportion and distribution of the problem-posing tasks, and in the presentation of the problem-posing tasks. Our results show a decreasing number of problem-posing tasks as grade level increases, even though problem posing has become more important in mathematics education in China during the last 70 years. This study also provides a variety of examples of problem-posing tasks which could serve as a reference for teachers in other countries in designing and employing problem-posing tasks in the classroom.

The aim of the present study was to determine the binding mechanisms between zein and folic acid in an ethanol – water solution. Fluorescence spectroscopy demonstrated that folic acid quenched the fluorescence intensity of zein by both dynamic and static fluorescence quenching mechanisms, with static quenching playing a prominent role. The binding constants (Ka) of the zein-folic acid complex at 292, 302, and 312 K were evaluated to be 5.97 × 105, 3.00 × 105 and 1.54 × 105 L/mol, respectively. The process of folic acid binding zein was driven by ∆H0 = –51.24 kJ/mol, ∆S0 = –64.90 J/mol•K. Van der Waals forces and hydrogen bonding primarily governed the formation of the zein-folic acid complex. Confirmation of the complex formation was obtained via UV-visible absorption spectroscopy, Fourier transform infrared spectroscopy, and circular dichroism spectroscopy, which also revealed alterations in the secondary structure of zein upon binding to folic acid. Measurements of particle size and zeta potential demonstrated an enhancement in the stability of the complex system. Scanning electron microscopy and transmission electron microscopy showed the complex to possess a spherical morphology, with significant changes in the zein's morphology following its binding to folic acid. Additionally, zein increased the photostability of folic acid against UV light radiation. Molecular docking and molecular dynamics simulations were used to investigate the binding mechanisms involved further, and the results effectively elucidated the observed experimental phenomena. This research establishes a significant theoretical foundation for the utilization of zein as a system for delivering and safeguarding folic acid. [ABSTRACT FROM AUTHOR]

Students in Shanghai ranked at the top in mathematics on the past two assessments of the Program for International Student Assessment (PISA). However, even though Asian students in general, and Chinese students in particular, ranked at the top in mathematics, we know little about Shanghai students' subjective well-being (SWB). This paper reports two studies that investigated the SWB of elementary and middle school students in Shanghai, as well as their mathematics performance. It is found that the mean scores of elementary school students on all scales of SWB are significantly higher than those of middle school students, representing a large drop for students when moving from elementary to middle school. Furthermore, students' mathematics performance is moderately correlated with their SWB. And for Grade 6, students' SWB affects their mathematics performance, especially from academic self-concept, attentiveness in the classroom, and relationship with teachers.

Problem posing has long been recognized as a critically important teaching method and goal in the area of mathematics education. However, few studies have used problem posing to assess in-service teachers' mathematical understanding. The present study investigated in-service teachers' mathematical understanding of fraction division, which is often considered challenging content in elementary school, from three angles: computation, drawing, and problem posing. Two studies involving 66 and 193 primary and middle school teachers were conducted to reveal the in-service teachers' mathematical understanding and whether drawing and problem posing affected each other. Although the in-service teachers rarely had the opportunity to pose mathematical problems in their daily teaching, they were able to pose mathematical problems in this study. In addition, problem-posing tasks were more useful in diagnosing the in-service teachers' conceptual understanding than were computation or drawing. Thus, problem posing seems to have contributed to their conceptual understanding of fraction division on the drawing task. [ABSTRACT FROM AUTHOR]