In order to participate proficiently in mathematical activity, a student needs to become fluent in both mathematical sign activity and speaking about the activity with signs. From the theoretical viewpoint of the philosophers Wittgenstein and Peirce, on the one hand, mathematics is seen as a sign game, while on the other hand experiments with…

Background: Traditional math instruction that emphasizes procedures and rote memorization is common in math classes, particularly within the United States. Students may be able to perform steps and recite information, but flexible thinking in math is also an important ability. Lay theories assume that extensive experience in math would lead to…

We analyzed the solution pathways and errors found in the written responses of 469 prospective teachers solving an equation containing fractions. The majority (332, or 70%) used an algebraic method; 141 of the 332 (42%) were correct, and 22% of the algebraic methods were abandoned before a solution was obtained. We identified the steps in the…

According to the big-fish-little-pond effect (BFLP) model, high individual academic performance in a particular subject is related to high self-concept in that subject, whereas high average classroom performance has a negative effect on self-concept. In the present study, data from Finnish primary school students in grade 3 (504 students), grade 4…

The purpose of this research is to classify the mathematical modelling problems produced by pre-service mathematics teachers in terms of the number of variables and to determine the mathematical modelling skills and mathematical skills used in solving the problems in each class. The current study is a qualitative research and the data was analyzed…

Representations of the fingers are embodied in our cognition and influence performance in enumeration tasks. Among deaf signers, the fingers also serve as a tool for communication in sign language. Previous studies in normal hearing (NH) participants showed effects of embodiment (i.e., embodied numerosity) on tactile enumeration using the fingers…

Background: Studies in Down syndrome (DS) and Williams syndrome (WS) have suggested that mathematical abilities are impaired. However, it is unclear which domain-general or domain-specific abilities impact on mathematical development in these developmental disorders. Method: The current study examined the foundations of mathematical development…

Developing computational thinking (CT) skills at a young age is critical for preparing preschool children to engage with the technologies that have become central to nearly every occupation and for improving achievements in STEM, literacy, and other disciplines. This paper builds on foundational research in early childhood math and CT by reporting…

This paper characterizes the engagement of two groups of students in a Precalculus course at a four-year public university. A set of "Multiple Solutions Activities" was designed for the course to expose groups of students to alternative solution methods, allowing instructors to explicitly negotiate productive norms to foster students'…

Reasoning about fraction magnitude is an important topic in elementary mathematics because it lays the foundations for meaningful reasoning about fraction operations. Much of the research literature has reported deficits in preservice elementary teachers' (PSTs) knowledge of fractions and has given little attention to the productive resources that…

The purpose of this study was to examine the effects of an online multi-component intervention (video modeling, virtual manipulatives, digital games, self-monitoring and least to most prompting techniques) on the acquisition of several mathematical skills of two autistic elementary school students. We used a multiple probe design of a single-case…

One of the main objectives of international large-scale assessments is to make comparisons between different countries, education policies, education systems, or subgroups. One of the main criteria for making comparisons between different groups is to ensure measurement invariance. The purpose of this study was to test the measurement invariance…

Successful early mathematical development is vital to children's later education, employment, and wellbeing outcomes. However, established measurement tools are infrequently used to (i) assess children's mathematical skills and (ii) identify children with or at-risk of mathematical learning difficulties. In response, this pre-registered systematic…

This study examines longitudinal associations among reading skills, math skills and emotional well-being in a Finnish sample (n = 586) followed from the end of comprehensive school (Grade 9, age 15-16) to age 20. In particular, we determine whether the associations between skills and well-being are mediated by self-concept beliefs. In Grade 9, the…

Previous studies have found positive effects of Game-Based Learning for mathematics. While most studies assume that this effect is explained by the presence of flow/immersion during games, this has not yet been established. The aim of the current study is to verify if immersion indeed is associated with mathematical skills improvement when using a…