Mathematical learning: New perspectives and challenges

Understanding of the base-10 structure of multi-digit numbers is one of the critical aspects in early mathematics learning. It has been documented that children from different countries vary in their use of base-10 representations. Questions concerning potential sources of this variability have been debated for decades. One commonly posited explanation is that some languages provide explicit cues about the structure of multi-digit numbers, facilitating the development of base-10 representations. In the present study, we tested this view against an alternative view, positing that variability in children’s learning of numeric structure may reflect differences in their experiences with numbers. The study examined kindergartners and first-graders from four countries: Taiwan, South Korea, the USA, and Russia. Results showed that the use of base-10 representations by American first-graders increased dramatically over the last decades, following changes in curricular guidelines. First-graders across the four countries showed some differences in performance (however, not consistent with the language account), whereas kindergartners performed comparably despite the differences in their languages. The results suggest that the nature of early math instruction may be critical for children’s developing understanding of numeric structure.

The goal of the present study was to describe the organization of a guided activity for problem solution in primary school. The method, which was applied to mathematical problems, allowed us to propose a specific orientation for the proper solution of arithmetic problems by pupils. The study was based on the activity-theory approach applied to the process of teaching and learning. It was carried out with pupils in the second grade of a private school in the city of Puebla (Mexico). The method was used in the classroom during 30 school sessions of 1 hour per day. The methodology of formative experiment was used in the study. Qualitative analysis of the pedagogical process of teaching and learning was conducted. The results show that, after participation in the formative process, the schoolchildren became able to identify essential elements, data, and all relationships among them in order to solve mathematical problems. At the end of the program the verbal external level was raised for the process of orientation and the solution of problems together with the ability to use logarithms independently. We conclude that orientation, as a guided form of activity in primary school, is essential for the development of the ability to analyze problems.

The present study examined the extent to which college students’ academic mindsets predicted their persistence when solving challenging math problems. The study included an experimental manipulation, in which participants initially received either an easy or a difficult arithmetic task. Following the manipulation, all participants solved two target math problems: one that was solvable but very hard and another that was unsolvable.

Time spent attempting to solve each problem served as a measure of persistence. Results showed the predicted pattern for the solvable target problem, but not for the unsolvable problem. That is, for the solvable problem, the more of a fixed mindset participants had, the less persistent they were after completing a relatively difficult arithmetic task than after completing an easy task. The results suggest that, for certain types of math problems, students’ persistence may vary as a function of academic mindset and previous experiences of math success or failure.

The article discusses an innovative teaching technology that uses development-focused educational texts (DET Technology) to stimulate school pupils’ intellectual development in grades 5 to 9. It describes the psychological and psychodidactic framework of DET Technology. Development-focused educational texts are distinctive in that they use a framework of academic mathematical knowledge to build up the key components of pupils’ mental experience (cognitive, conceptual, metacognitive, and intentional). Such texts also provide the conditions for the development and usage of students’ personal learning styles. The article outlines the psychodidactic types of development-focused educational texts and the requirements that the psychodidactics proposes for educational texts.

Academic achievement, which is inherently an indicator of progress in the curriculum, can also be viewed as an indirect measure of cognitive development, social adaptation, and motivational climate characteristics. In addition to its direct application, academic achievement is used as a mediating factor in the study of various phenomena, from the etiology of learning disabilities to social inequality. Analysis of sex differences in mathematical achievement is considered particularly important for exploring academic achievement, since creating an adequate educational environment with equal opportunities for boys and girls serves as a prerequisite for improving the overall mathematical and technical literacy that is crucial for modern society, creates balanced professional opportunities, and destroys traditional stereotypes about the roles of men and women in society.

The objective of our research was to analyze sex differences in mathematical achievement among high school students and to compare various methods for diagnosing academic performance, such as school grades, test scores, and self-concept.

The results were obtained through two population studies whose samples are representative of the Russian population in the relevant age group. Study 1 looked at sex differences in math grades among twins (n = 1,234 pairs) and singletons (n = 2,227) attending high school. The sample of Study 2 comprised all twins who took the Unified State Examination in 2010–2012. The research analyzed sex differences in USE math scores across the entire sample and within the extreme subgroups. It also explored differences between boys and girls in opposite-sex dizygotic (DZ) twin pairs.

The key results were as follows. No difference in mathematical achievement was observed between twins and singletons. Sex differences were found in all measures of mathematical achievement. Girls had higher school grades in math than boys, while boys outperformed girls in USE math scores. Boys were more variable and there were more boys at the right tail of the distribution. Girls with a positive math self-concept did better than boys on math tests. In groups of opposite-sex DZ twins, differences between the USE math scores of girls and boys were not significant.

The results obtained are presumed to correspond more closely to assumptions about the roles of non-cognitive factors of variation in mathematical ability than the mathematical ability theory.