The present-day knowledge society expects school education to ensure the development of higher-order thinking skills, such as novel problem solving. Experimental evidence shows that such skills can be developed in students by using classroom activities enhancing higher-order cognitive processes more often. However, the impact of such activities on knowledge acquisition in specific disciplines, mathematics in particular, remains unclear. Data obtained in the longitudinal study Trajectories in Education and Careers conducted on a TIMSS-PISA sample is used to evaluate the presence of teaching practices that promote higher- and lower-order thinking in the classroom and the correlations between those strategies, on the one hand, and teacher characteristics and mathematics achievement at the end of 9th grade, on the other hand. Teaching practices of both types were found to be related positively to student achievement in mathematics. Yet, higher-order thinking teaching practices have a stronger positive effect on mathematics achievement gains between 8th and 9th grades, whereas the effects of practices implying lower-order thinking lose their significance or become negative a year later. It is also shown that the use of a specific type of teaching practices is not related to teacher credentialsor qualifications.

Numerical information can be represented in three formats: two symbolic (visual (digits) and verbal (number words)) and one nonsymbolic (analog) format. Studies have shown that the precision of symbolic numerical representation is associated with math performance. The precision of symbolic representation is mostly discussed as the precision of representation in a visual format, whereas the precision of representation in verbal format and its relation with math performance is less studied. The current study examines the precision of symbolic numerical representation in visual and verbal formats and the relationship between such precision and math performance when controlling for prior math performance, nonsymbolic numerical representation, phonological processing, reading skills and working memory. We used data from 367 Russian first graders (mean age, 7.6 years; 53% girls). To assess the precision of symbolic numerical representation, magnitude comparison tasks with digits and number words were used. It was found that the precision of symbolic representation in verbal format did not have a direct effect on math performance, but has an indirect effect via visual format of symbolic representation, even when controlling for prior math performance and other cognitive abilities.

The present-day knowledge society expects school education to ensure the development of higher-order thinking skills, such as novel problem solving. Experimental evidence shows that such skills can be developed in students by using classroom activities enhancing higher-order cognitive processes more often. However, the impact of such activities on knowledge acquisition in specific disciplines, mathematics in particular, remains unclear. Data obtained in the longitudinal study Trajectories in Education and Careers conducted on a TIMSS-PISA sample is used to evaluate the presence of teaching practices that promote higher- and lower-order thinking in the classroom and the correlations between those strategies, on the one hand, and teacher characteristics and mathematics achievement at the end of 9th grade, on the other hand. Teaching practices of both types were found to be related positively to student achievement in mathematics. Yet, higher-order thinking teaching practices have a stronger positive effect on mathematics achievement gains between 8th and 9th grades, whereas the effects of practices implying lower-order thinking lose their significance or become negative a year later. It is also shown that the use of a specific type of teaching practices is not related to teacher credentials or qualifications.

This article provides an empirically grounded analysis for two fundamentally different models of mathematics teachers’ beliefs about student diversity in Russian secondary schools: exclusive and inclusive models. Although teachers’ beliefs are considered a central factor for the differentiated approach, teachers’ beliefs could be stereotyped and, consequently, the evaluation of a student’s ability would be systematically shifted and decisions about the possibility of teaching a student would be incorrect. Semi-structured interviews with 30 mathematics teachers allowed us to investigate what criteria teachers claim to employ while classifying students in the classroom and what expectations they have for each group of students. It was found that within the exclusive model, teachers have an image of a “normal” student and use discrete categories for labelling students with reference to the “normality”. Within the inclusive model, teachers tend not to match students with discrete categories; rather they prefer to compare a student only with herself or himself. Research findings are discussed in the context of a possible “fixed effect” on a student’s development. However, there is a need for further investigation of a connection between teachers’ belief systems, teaching practices and student achievement.

Осетия г.Севастополь Карачаево-Черкесская Респ.Респ.Дагестан

Традиционно считается, что образование в российских школах отличается высоким качеством, однако в силу достаточно больших социальных и территориальных различий доступ к нему может быть неоднородным.

Solutions to word problems are moderated by the semantic alignment of real-world relations with mathematical operations. Categorical relations between entities (tulips, roses) are aligned with addition, whereas certain functional relations between entities (tulips, vases) are aligned with division. Similarly, discreteness vs. continuity of quantities (marbles, water) is aligned with different formats for rational numbers (fractions and decimals, respectively). These alignments have been found both in textbooks and in the performance of college students in the USA and in South Korea. The current study examined evidence for alignments in Russia. Textbook analyses revealed semantic alignments for arithmetic word problems, but not for rational numbers. Nonetheless, Russian college students showed semantic alignments both for arithmetic operations and for rational numbers. Since Russian students exhibit semantic alignments for rational numbers in the absence of exposure to examples in school, such alignments likely reflect intuitive understanding of mathematical representations of real-world situations.

This article provides an empirically grounded analysis for two fundamentally different models of math teachers’ beliefs about student diversity in Russian secondary schools: exclusive and inclusive models. Although teachers’ beliefs are considered a central factor for the differentiated approach, teachers’ attitudes could be stereotyped and, consequently, the evaluation of a student’s ability would be systematically shifted and decisions about the possibility of teaching a student would be incorrect. In-depth interview research allowed us to investigate what criteria teachers employ while classifying students in the classroom and what expectations they have for each group of students. It was revealed that within the exclusive model, teachers have an image of a “normal” student and use discrete categories for labeling students with reference to the “normality”. Within the inclusive model teachers tend not to juxtapose students with discrete categories; rather they prefer to compare a student only with herself or himself. Research findings are discussed in the context of a possible “fixed effect” on a student’s development. However, there is a need for further investigation of a connection between teachers’ belief systems, teaching practices, and students’ achievements.

The Russian education standards stress the importance of real-life applications of mathematics. However, the educational outcome standards do not provide a clear idea of how a math teacher should organize their syllabus to develop relevant skills in students. As long as there is no universal definition of a real-world math problem, it is rather difficult to qualify the problems that teachers use in the classroom. We analyzed algebra problems that teachers give to secondary school students. Using three parameters, 83 word problems were coded: situational relevance, mathematical modeling, and non-triviality. We carried out a cluster analysis to identify typical categories of mathematical problems. As a result, we determined three types of problems differing in the above mentioned characteristics. Only one cluster appeared to feature all three characteristics typical of real-world problems. Therefore, a portion of the tasks that teachers give students as real-world fail to qualify as such according to the proposed theoretical model.

Попов Дмитрий Сергеевич - кандидат социологических наук, старший научный сотрудник Центра мониторинга качества образования Института образования НИУ ВШЭ. E-mail:dmitry_popov@sociolog.netТюменева Юлия Алексеевна - кандидат психологических наук, старший научный сотрудник Международной лаборатории анализа образовательной политики Института образования НИУ ВШЭ. E-mail: jutu@yandex.ruЛарина Галина Сергеевна - аналитик Центра мониторинга качества образования Института образования НИУ ВШЭ. E-mail: larina.gala@gmail.comСоциальный бэкграунд молодого человека в существенной степени предопределяет его образовательную траекторию и достижения. В исследовании, основанном на данных второй волны лонгитюдного обследования, предпринимается попытка проверить, насколько успешное обучение в школе, результаты внешкольной деятельности учащегося, его упорство и намерения относительно будущего образования могут быть независимыми от социального окружения школьника и изменить предзаданную социальным окружением образовательную траекторию. Обнаружено, что значимыми медиаторами эффекта семейных ресурсов являются личные образовательные достижения выпускника основной школы и его намерения относительно будущего образования.