Do your students have the incorrect idea that addition "makes numbers bigger" and subtraction "makes numbers smaller"? Do they believe that subtraction is always "taking away"? What tasks can you offer--what questions can you ask--to determine what your students know or don't know--and move them forward in their…

Of the "big four", division is likely to regarded by many learners as "the odd one out", "the difficult one", "the one that is complicated", or "the scary one". It seems to have been that way "for ever", in the perception of many who have trodden the learning pathways through the world of…

One of the common tasks of inferential statistics is to compare two data sets. Long before formal statistical procedures, however, students can be encouraged to make comparisons between data sets and therefore build up intuitive statistical reasoning. Such tasks also give meaning to the data collection students may do. This study describes the…

The notion of periodicity stands for regular recurrence of phenomena in a particular order in nature or in the actions of man, machine, etc. Many examples can be given from daily life featuring periodicity. Mathematically the meaning of periodicity is that some value recurs with a constant frequency. Students learn about the periodicity of the…

The internal representation of numbers generated during calculation has received little attention. Much of the mathematics learning literature focuses on symbolic retrieval of math facts; in contrast, we critically test the hypothesis that internally generated numbers are represented analogically, using an approximate number system. In an fMRI…

This paper presents a study that investigated the process of change in 5-6-year-old children's successful problem-solving approaches when tackling a multiple-step task in elementary arithmetic. Micro-developmental changes in children's successful problem-solving behavior were analyzed using Karmiloff-Smith's model of representational redescription…

Multichannel EEG traces from healthy subjects are used to investigate the brain's self-organisation tendencies during two different mental arithmetic tasks. By making a comparison with a control-state in the form of a classification problem, we can detect and quantify the changes in coordinated brain activity in terms of functional connectivity.…

While infants' ability to discriminate quantities has been extensively studied, showing that this competence is present even in neonates, the ability to compute ordinal relations between magnitudes has received much less attention. Here we show that the ability to represent ordinal information embedded in size-based sequences is apparent at 4…

Subtractions of the type M - S = ? can be solved by various strategies, including subtraction by addition. In this study, we investigated children's use of subtraction by addition by means of reaction time analyses. We presented 106 third to sixth graders with 32 large non-tie single-digit problems in both subtraction (12 - 9 = .) and addition…

Mathematical skills are becoming increasingly critical for achieving academic and professional success. Developmental dyscalculia (DD) is a childhood-onset disorder characterized by the presence of abnormalities in the acquisition of arithmetic skills affecting approximately 5% of school age children. Diagnosing students with possible dyscalculia…

Theories of psychology and mathematics education recommend two instructional approaches to develop students' mental representations of number: The "exact" approach focuses on the development of exact representations of organized dot patterns; the "approximate" approach focuses on the approximate representation of analogue magnitudes. This study…

Designers of interactive learning environments with a focus on word problem solving usually have to compromise between the amount of resolution paths that a user is allowed to follow and the quality of the feedback provided. We have built an intelligent tutoring system (ITS) that is able to both track the user's actions and provide adequate…

Weiss, Keith, Zhu, and Chen (2013a) and Weiss, Keith, Zhu, and Chen (2013b), this issue, report examinations of the factor structure of the Wechsler Adult Intelligence Scale-Fourth Edition (WAIS-IV) and Wechsler Intelligence Scale for Children-Fourth Edition (WISC-IV), respectively; comparing Wechsler Hierarchical Model (W-HM) and…

Children struggle with mathematics for different reasons. Developmental dyscalculia and low numeracy--two kinds of mathematical difficulties--may have their roots, respectively, in poor understanding of exact non-symbolic numerosities and of symbolic numerals. This study was the first to explore whether Chinese children, despite cultural and…

This study sought to review literature pertinent to difficulties encountered by students in the learning and usage of mathematical terminology. The need to carry out this study arose from the concern by the Kenya National Examinations Council, and the general public, over the poor annual results in mathematics. Therefore, the objective of this…