Findings on children's proportional reasoning abilities strongly vary across studies. This might be due to the different contexts that can be used in proportional problems: fair-sharing, mixtures, and probability. A review of the scientific literature suggests that the context of proportional problems may not only impact the difficulty of the…

In this exploratory descriptive study, changes in one cohort's responses to an authentic statistical investigation at the commencement of years 3 and 4 were analysed. Forty-four students made predictions by interpreting a data table of historical monthly temperatures, represented these data and explained their reasoning. An Awareness of…

This paper describes elementary students' awareness and representation of the aggregate properties and variability of data sets when engaged in predictive reasoning. In a design study, 46 third-graders interpreted a table of historical temperature data to predict and represent future monthly maximum temperatures. The task enabled students to…

The importance of fostering in students the requisite language to understand what is being communicated and how to communicate their understanding requires educators to conceptualize themselves as teachers of language and content. It is possible to engage in activities of the mathematics classroom and through that participation engage in language…

Understanding fraction magnitudes is foundational for later math achievement. To represent a fraction "x/y," children are often taught to use "partitioning": break the whole into "y" parts, and shade in "x" parts. Past research has shown that partitioning on number lines supports children's fraction…

Understanding fraction magnitudes is foundational for later math achievement. To represent a fraction x/y, children are often taught to use "partitioning": Break the whole into y parts and shade in x parts. Past research has shown that partitioning on number lines supports children's fraction magnitude knowledge more than partitioning on…

The purpose of this study is to examine how the reasoning of elementary school students develops and progresses within a learning progression. In order to do this, we analyzed third, fourth, and fifth grade elementary school students' levels of reasoning about phenomena related to changes of state of water. The results show that higher grades…

Hypothesis-based reasoning with conditionals is a skill that is required for engaging in integral activities of modern elementary school science-curricula. The teaching of this skill at this early stage of education, however, is demanding, particularly in whole school classes in which it is difficult to adapt teaching to children's individual…

This paper considers one of the relevant problems of modern pedagogy - the use of logical approaches in teaching to the development of thought and language of primary schoolchildren. The purpose of the study is to determine the main criteria for the developmental education of thought and language to primary school children and to assess the level…

The present study compares two methods for assessing peer influence: the longitudinal actor-partner interdependence model (L-APIM) and the longitudinal social network analysis (L-SNA) Model. The data were drawn from 1,995 (49% girls and 51% boys) third grade students (M[subscript age] = 9.68 years). From this sample, L-APIM (n = 206…

This study aims to assess the impact of integrative technology on the improvement of the logical thinking of students in mathematics, their goals and the appropriate technological process. The study used mixed research methods. Participants included third-grade students attending elementary schools No. 12 and Ataturk in Kentau (Kazakhstan) during…

Mathematics education research has focused on developing teachers' knowledge or other visible aspects of the teaching practice. This paper contributes to conversations around making a teacher's thinking visible and enhancing a teacher's pedagogical reasoning by exploring the use of pedagogical documentation. In this paper, we describe how a…

The relationship between latent trait and test-taking speed is an important area of study in assessment research. In addition to contributions of such studies to psychometrics, the factors that affect both ability and speed have implications for test development and have policy consequences especially if the tests are high stakes. This study…

This paper gives an example of how to address the challenge of designing a learning progression that describes student thinking, with the necessary specificity to align instructional opportunities and assessment tools. We describe the Conceptual Underpinnings of Evolution project and the iterative process of developing a novel learning progression…

Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input, yet also requires cognitive supports. My dissertation sought to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning.…