Gap reasoning is an inappropriate strategy for comparing fractions. In this article, Patrick Sullivan and Joann Barnett look at the persistence of this misconception amongst students and the insights teachers can draw about students' reasoning.

The development of computational thinking is as important as writing, reading and arithmetic, and, it should start as early as kindergarten (Wing, 2008). However, little has been done in terms of investigating the factors influencing the development of computational thinking in preschool education (Bers et al., 2014; Ching et al., 2018; Kazakoff…

This research asks whether analogical processing ability is present in human infants, using the simplest and most basic relation--the "same-different" relation. Experiment 1 (N = 26) tested whether 7- and 9-month-olds spontaneously detect and generalize these relations from a single example, as previous research has suggested. The…

This study aims to implement empirically students' abstraction with socio-cultural background of Indonesia. Abstraction is an activity that involves a vertical reorganization of previously constructed mathematics into a new mathematical structure. The principal components of the model are three dynamic nested epistemic actions: recognizing,…

Working with language-independent logic structures can help students develop both inductive and deductive reasoning skills. The Japanese publisher Nikoli (with resources available both in print and online) produces a treasure trove of language-independent logic puzzles. The Nikoli print resources are mostly in Japanese, creating the extra…

The present study examined the factor structure of the Luria interpretive model for the Kaufman Assessment Battery for Children-Second Edition (KABC-II) with normative sample participants aged 7-18 (N = 2,025) using confirmatory factor analysis with maximum-likelihood estimation. For the eight subtest Luria configuration, an alternative…

Measurement activities were designed in this study on the basis of authentic professional practices in which linear regression is used, to study considerations of variability by students in Grade 12 (aged 17-18). The question addressed in this article is: In what ways do secondary students consider variability within these measurement activities?…

Increasingly, research on cognition, learning, and education seeks to understand the cognitive processes underlying conceptual understanding. This is especially true for efforts to understand how students learn science. The present case summarizes work that examines 6- to 10-year-old students engage in scientific reasoning to learn new scientific…

According to Lev S. Vygotsky (1896-1934), the highest levels of abstract thinking and self-regulation in preschool development are established in "pretend play using object substitutions." An extensive research literature supports Vygotsky's empirical model of the internalization of self-guiding speech (social speech > private speech…

When proportional information is pit against whole number numerical information, children often attend to the whole number information at the expense of proportional information (e.g., indicating 4/9 is greater than 3/5 because 4 > 3). In the current study, we presented younger (3- to 4-year-olds) and older (5- to 6-year-olds) children a task…

We present study findings that depict the natural and fractional number knowledge of one third grade student with learning disabilities (LDs) in seven experimental sessions. We utilize qualitative analysis methods to illustrate how this student evidenced her knowledge of natural number and fractions through her interactions with varied learning…

This research tests whether analogical learning is present before language comprehension. Three-month-old infants were habituated to a series of analogous pairs, instantiating either the "same" relation (e.g., AA, BB, etc.) or the "different" relation (e.g., AB, CD, etc.), and then tested with further exemplars of the…

The purpose of this study is to determine the mathematics teacher performance category in building high order thinking skills (HOTS) of students. The study was conducted on 560 students taken randomly from ten junior high schools and eight high schools from eight districts in North Sumatra Province. Data collection techniques and instruments are…

Growing human populations place increasing demands on our planet, resulting in an array of challenges with both scientific and non-scientific dimensions. These challenges are collectively known as socio-scientific issues (SSIs). It is essential to understand how students learn to use values to reason about SSIs, particularly when dealing with…

Two key research issues in the field of causal learning are how people acquire causal knowledge when observing data that are presented sequentially, and the level of abstraction at which learning takes place. Does sequential causal learning solely involve the acquisition of specific cause-effect links, or do learners also acquire knowledge about…