Students with mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient problem-solving strategies (McIntosh et al., 1997; Yang, 2005). Despite being highlighted in national standards and policy documents (CCSS, 2010; NCTM, 2000), the association between…

Roundoff error is an error. It can be dramatically reduced by the use of additional low-order digits, i.e. "guard digits." Although the significant-figures idea in its standard form is incompatible with guard digits, this problem can be neatly solved by underlining the last "significant" digit, and then appending guard digits…

The teaching of mathematics does not only require the teacher to have knowledge about the subject, but the teacher also needs mathematical knowledge that is useful for the teaching and explaining thereof, as the teacher's knowledge effects the students' knowledge. A teacher should use appropriate mathematical explanation to be understood well by…

This study investigates how the approximate number system (ANS) and young children's symbolic skills jointly develop and interact. Specifically, the study aims at disentangling the directionality of the association between ANS acuity and a wide range of symbolic skills that reflect 4- to 5-year-olds' symbolic quantitative knowledge (enumeration…

Understanding negative numbers can be challenging for many students, as these concepts may seem less tangible than counting objects, which are commonly represented by positive numbers. In addition, the multiplication of two negative numbers resulting in a positive might appear inconsistent and puzzling to young learners who are used to seeing the…

In this paper we studied the personal mathematical work of 14 students in initial teacher training, in their first year of studies at a public university in Chile, based on two tasks on complex numbers. These tasks were set in a Computer Aided Assessment System (CAA) based on Moodle and Wiris and it was proposed to solve them using different…

Online learning affects students' curiosity, so it is important to develop students' curiosity during the pandemic. The purpose of this study is to describe and analyze students' curiosity about online learning. This study was conducted in the Department of Mathematics Education during the odd semester 2021/2022 with 106 students in three…

The power and value of mathematics cannot be underestimated. Mathematics is essential in the workplace, for economic growth, for technological advancements and as part of our cultural heritage. Despite this, research reports that second-level students do not appreciate the value of mathematics and fail to see its relevance. One potential reason…

The usage of digital media, especially tablet apps, is currently a major concern in educational settings. A controversial discussion is also taking place in relation to mathematics education at primary schools. While on the one hand there are empirical findings on helpful isolated examples and related subject-didactic potentials of digital media,…

The proliferation of standardized testing and administrative statistics in compulsory education is embedded in the rise to prominence of quantified accountability as a mechanism of education governance. Numbers work by stripping away the contexts of their production and the granular and ambiguous detail of the phenomena they claim to represent.…

Perceptual judgments result from a dynamic process, but little is known about the dynamics of number-line estimation. A recent study proposed a computational model that combined a model of trial-to-trial changes with a model for the internal scaling of discrete numbers. Here, we tested a surprising prediction of the model--a situation in which…

People tend to underestimate subtraction and overestimate addition outcomes and to associate subtraction with the left side and addition with the right side. These two phenomena are collectively labeled 'operational momentum' (OM) and thought to have their origins in the same mechanism of 'moving attention along the mental number line'. OM in…

The duo of artefacts is a simplified model of the complex systems of various manipulatives (either tangible or virtual) that mathematics teachers and their students use in classrooms. It offers a means to study the complexity of the interweaving of the tangible and of the digital worlds in the teaching and learning processes. A duo of artefacts is…

Perceptual judgments result from a dynamic process, but little is known about the dynamics of number-line estimation. A recent study proposed a computational model that combined a model of trial-to-trial changes with a model for the internal scaling of discrete numbers. Here, we tested a surprising prediction of the model--a situation in which…

This dissertation conducted two studies that examined two methods of instructional planning to effectively match students to a whole number computation intervention that would best meet their needs. Study 1 was a systematic synthesis of all studies that used brief experimental analysis (BEA) to determine an effective mathematics intervention for…