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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.

The 3C-like protease (also known as Mpro) plays a key role in SARS-CoV-2 replication and has similar substrates across mutant coronaviruses, making it an ideal drug target. We synthesized 19 thiazolidinedione derivatives via the Knoevenagel condensations and Mitsunobu reactions as potential 3C-like protease inhibitors. The activity of these inhibitors is screened in vitro by employing the enzymatic screening model of 3C-like protease using fluorescence resonance energy transfer. Dithiothreitol is included in the enzymatic reaction system to avoid non-specific enzymatic inhibition. Active inhibitors with diverse activity are found in this series of compounds, and two representative inhibitors with potent inhibitory activity are highlighted.

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.

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.

Healing of the tendon-to-bone interface remains a challenge in clinical practice due to its unique gradient structure. Despite substantial efforts to reproducing the transitional structure from mineralized to nonmineralized tissue, successful regeneration of tendon-to-bone interface through tissue engineering approaches remains rare. To maximally simulate the four distinct zones of the tendon-to-bone interface, a novel three-dimensional (3D) hydroxyapatite (HA) gradient scaffold with spatial mineral distribution is implemented through a combined strategy of electrospinning and traditional textile manufacturing. Our results showed that the scaffold allows sustained release of Ca ions from each segment in a gradient manner. Besides, this scaffold is structurally anisotropic with excellent mechanical properties. In vitro study demonstrated that the mineralized segments boosted the proliferation of mouse embryo osteoblast precursor cells (MC3T3-E1) cells and promoted osteogenic differentiation of rat bone marrow stem cells (rBMSCs), while nonmineralized segment improved the tenocytes differentiation of rBMSCs. Moreover, the HA gradient scaffold was able to spatially guide the differentiation of rBMSCs, leading to the formation of neotissue with structural, biochemical, and biomechanical characteristics similar to that of the tendon-bone insertion site. Overall, this study introduces an approach to inducing targeted and localized stem cell differentiation for tissue engineering applications, and the HA gradient scaffold holds enormous potential for tendon-to-bone tissue regeneration.