A spotlight on mathematics education in the Netherlands and the central role of Realistic Mathematics Education

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Seen through other eyes – Opening up new vistas in Realistic Mathematics Education through visions and experiences from other countries

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Mapping kindergartners’ quantitative competence

In this study we investigated the structure of quantitative competence of kindergartners by testing a hypothesized four-factor model of quantitative competence consisting of the components counting, subitizing, additive reasoning and multiplicative reasoning. Data were collected from kindergartners in the Netherlands (n = 334) and in Cyprus (n = 304). A confirmatory factor analysis showed that the four-factor structure fitted the empirical data from the Netherlands. For the Cyprus data a one-factor structure was found to have a more adequate fit. Regarding the effect of country on performance, a comparison at item level showed that the kindergartners in the Netherlands outperformed those in Cyprus in the majority of quantitative competence items. Analyses of variance revealed for each country a significant effect of kindergarten year on performance, with children in K2 (second kindergarten year) outperforming those in K1 (first kindergarten year). A statistical implicative analysis at item level revealed that in both countries the relevant implicative chain, showing what successful solving of an item implies for correct solving of another item, reflects by and large the sequential steps mostly followed in teaching kindergartners early number. This sequence starts with counting and subitizing, then continues with additive reasoning and finally multiplicative reasoning. These implicative chains also clearly show that the development of early quantitative competence is not linear. There are many parallel processes and cross-connections between the components of quantitative competence.publishedVersionPaid Open Acces

Образование как Квазирыночный процесс

В работе обосновывается, что обмен знаний на часть дохода, обусловленного получением этого знания, который в течении тысячелетий обеспечивал передачу знаний от старшего поколения к младшему не отвечает современной ситуации непрерывных изменений и неопределенности, и порождает коррупцию и протекционизм.This paper is grounded, that exchange knowledge for a part of extra income, which is conditioned by this knowledge, was effective from the primitive society to industry society. But now, when we have situation of changes and uncertainty such exchange has become uneffective and raises corruption and patronage

METACOGNITIVE PROMPT AS A MEANS TO IMPROVE STUDENTS’ TASK COMPREHENSION

One of the most dominant errors made by (Indonesian) students when solving context-based PISA mathematics tasks is error in comprehending the task. This paper reports a study on improving students’ comprehension of context-based tasks. A total of 299 eight graders from six junior high schools in the Province of Yogyakarta participated in this study. The study employed a field experiment with a pretest-posttest control-group design for which we used an intervention program comprising a set of context-based tasks which were supplemented with metacognitive prompts. The result of the study shows a significant difference between the experimental group and the control group on the decrease in the total number of errors (² (1, n = 4127) = 4.149, p = .042). In comparison to their counterparts in the control group, the students in the experimental group had a better improvement regarding two aspects of task comprehension: understanding the instruction of the task and selecting relevant information. Key words: context-based tasks; metacognitive prompts; task comprehensio

Picture books stimulate the learning of mathematics

In this article we describe our experiences using picture books to provide young children (five- to six-year-olds) with a learning environment where they can explore and extend preliminary notions of mathematics-related concepts, without being taught these concepts explicitly. We gained these experiences in the PICO-ma project, which aimed to generate more knowledge about the effect of picture books on young children\u27s learning of mathematics. The project\u27s goal is to investigate how picture books can contribute to the development of mathematical concepts in young children, and how the actions of the teacher can strengthen the characteristics of picture books that support learning. The reading sessions described in this article were not intended to be mathematics \u27lessons\u27. Instead, the reading sessions were intended to tell the children a pleasant story and, at the same time, give them something to think about. Based on our research we provide reasons for using picture books to develop mathematical thinking, and include recommendations for practitioners interested in using picture books for mathematics learning.<br /

Чи бувають сприйнятні ціни?

This paper describes a classroom experiment on the use of digital technology in initial algebra. Indonesian grade seven students of 12-13 year-old took part in a four session teaching sequence on beginning algebra enriched with digital technology, and in particular applets embedded in the Digital Mathematics Environment. The intervention aimed to improve students’ conceptual understanding and procedural skills in the domain of equations in one variable. The qualitative analysis of written and digital student work, backed up with video observations during the experiment, reveal that the use of digital technology affects student thinking and strategies dealing with equations and with related word problems. Practical and theoretical consequences of the results are discussed

Процедура внесення змін до конституції: порівняльно-правовий аспект

Розглядається процедура внесення змін до Конституції, проводиться її порівняльно правовий аналіз, досліджуються особливості цієї процедури в різних країнах. Ключові слова: Конституція, зміни до Конституції, суб’єкт законодавчої ініціативиРассматривается процедура внесения изменений в Конституцию, проводится е сравнительно правовой анализ, исследуются особенности этой процедуры в различных странах. Ключевые слова: Конституция, изменения в Конституции, субъект законодательной инициативы.In article procedure of modification of the Constitution is considered, its ratherlegal analysis is carried out, features of this procedure in the various countries are investigated. Key words: Constitution, modification of the Constitution

Research on early childhood mathematics teaching and learning

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Assessment in the hands of primary school mathematics teachers : Four studies in China

In this paper, we describe four studies that have been done in the project Improving Classroom Assessment in China (ICA-C). The project was a sequel to the ICA project in the Netherlands. To shed light on the current situation of Chinese primary school mathematics teachers’ perception and practice of classroom assessment, we first did a review study based on teacher-written papers addressing classroom assessment. Then a large-scale questionnaire survey was conducted by means of which we could identify different assessment profiles of teachers. With the gained knowledge, two other studies were set up to explore the possibility for improving Chinese primary school mathematics teachers’ assessment activities, with a particular focus on using classroom assessment techniques in the domain of division and multiplication.publishedVersio