Children's math learning (N = 217; M[subscript age] = 4.87 years; 63% European American, 96% college-educated families) from an intelligent character game was examined via social meaningfulness (parasocial relationships [PSRs]) and social contingency (parasocial interactions, e.g., math talk). In three studies (data collected in the DC area:…

Educators often argue that students should engage in activities such as conjecturing, proving, and deductive reasoning. The underlying principle is that learning mathematics means doing as mathematicians do. However, "mathematician" implicitly refers to a pure mathematician at university. "The aim of our paper is to critically…

The value of some university mathematics courses gets characterized within a liberal arts course of study in terms of supporting "critical thinking skills" or some other phrase for generally improved reasoning. This can be seen as an application of the millennia old "Theory of Formal Discipline" that claims that mathematics…

Using the data from the Program for the International Assessment of Adult Competencies (PIAAC), this Data Point summarizes the number of U.S. adults with low levels of numeracy and describes how they differ by nativity status and race/ethnicity. [Standard error tables are available at https://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2020025 in…

Solving problems by different methods, identifying the knowledge put at stake in each case, and stating variants of the problems are fundamental aspects of the competence of analysis of mathematical knowledge for teaching. This paper reports on the design, implementation, and results of a formative intervention with primary education prospective…

The importance of mathematical problem posing has been acknowledged by many researchers. In this theoretical paper, we want to capture different meanings and aspects of problem posing by approaching it from three different levels: (1) by comparing definitions, (2) by relating it to other constructs, and (3) by referring to research and teaching…

This case study explores how 12-13-year-old students encounter proportional reasoning while working with geometric patterning tasks using concrete materials. The focus is on the students' use of spontaneous concepts when first dealing with such patterns in the context of collaborative work. Based on video recordings of a single lesson, a…

This systematic review and meta-analysis considered evidence of guided play compared to direct instruction or free play to support children's learning and development. Interventions from 39 studies were reviewed (published 1977-2020); 17 were included in meta-analysis (N[subscript total] = 3893; M[subscript childage] = 1-8 years; M[subscript…

In this paper, Harel and Sowder's proof schemes of taxonomy were applied for identifying eighth grade students' learning of proof and proofing. This study aimed to examine what kind of proof schemes are used in geometry and measurement learning areas and student's skills in giving proof and their opinions about proof. Qualitative methods were…

We focus on students' mathematical reasoning in a technology-enhanced collaborative learning environment. We adopt a dialogical approach to analyze students' mathematical reasoning. The participants of this study include six middle school students. The data consist of participants' written productions, dynamic materials, and the transcriptions of…

This paper examines the relationship between early geometric skills, behavioral self-regulation skills, teacher-mother reported self-regulation skills, child age and family income in 5-6 year-old children. The participants (N = 202; 104 girls, 98 boys) average age was 71 months (sd = 4.82; Data on race/ethnicity were not asked to participants).…

Today, hundreds of studies on the technique known as Realistic Mathematics Education (RME) have been discovered. Numerous trials yielding contradicting results. The purpose of this meta-analysis is to ascertain the overall effect of RME and to examine the moderator variables in order to explore the consequences. The ERIC database, Sage…

We discuss classroom activity comprised of small groups of students collaboratively tinkering with programs of dynamically manipulable figural models, posing problems regarding their mathematical properties and behaviors. We analyzed data from students' discourse taken from two classroom interventions employing a framework of creative mathematical…

Modelling competencies are currently included in numerous curricula worldwide and are generally accepted as a complex, process-oriented construct. Therefore, effective measurement should include multiple dimensions, like the sub-competencies required throughout the modelling process. Departing from the characteristics of modelling problems as open…

Schooling traditionally affords students more experience in learning and practicing procedures than in identifying what a situation calls for. When asked to choose appropriate numerical data to support their causal claims, college students perform surprisingly poorly. In one case we describe, almost all chose limited, inconclusive data as…