In this case study with Devin (pseudonym), which was part of a larger, constructivist teaching experiment with students identified as having learning difficulties in mathematics, we examine how a fourth grader constructed a dual anticipation involved in monitoring when to start and when to stop the simultaneous count of composite units (numbers…

The aim of this study is to compare the mathematical thinking experiences of fourth grade students at faculty of education and faculty of arts and sciences in the stages of specializing, generalizing, conjecturing, and proving. The study was conducted with 72 fourth grade students in the spring term of the academic year of 2015-2016. While 36 were…

The present mixed-methods quasi-experimental study (embedding a case study and a mixed factorial within-between ANOVA test), conducted in a private English school in Limassol, Cyprus, investigated how the use of the schematic learning aids (researcher-made color-coded flash-cards and grids) influence year-2 children's ability to read, write and…

This action research project looks at what happened when a small group of adult numeracy teachers with widely different experiences of learning and teaching mathematics explored their own informal numeracy practices and undertook a series of collaborative mathematical tasks. Evidence from qualitative data collected during the enquiry suggests that…

Behavioral research suggests that two cognitive systems are at the foundations of numerical thinking: one for representing 1-3 objects in parallel and one for representing and comparing large, approximate numerical magnitudes. We tested for dissociable neural signatures of these systems in preverbal infants by recording event-related potentials…

This paper explores misconceptions of the number line which are revealed when pre-service primary teachers locate negative decimals on a number line. Written test responses from 94 pre-service primary teachers provide an initial data source which is supplemented by group responses to worksheets completed during a lesson and individual interviews.…

In the present research, we evaluated the effectiveness of a multi-year professional development program in mathematics for elementary teachers. Each year the program focused on a different domain of mathematics. We found the program increased teachers' knowledge of (a) number and operations, (b) measurement and geometry, and (c) probability and…

Fifteen elementary and secondary teacher candidates solved sixteen integer addition and subtraction problems during think-aloud interviews. Investigators further probed participants' solution strategies as well as what they noticed first when starting a new problem. Task analyses of participants' solutions led to the creation of two distinct maps…

This paper presents the results of a pre-test, instruction, post-test study that investigated students' integer mental models and how their models changed based on instruction. Sixty-one first graders' responses to questions about the values and order of negative numbers were categorized according to a series of mental models. The models reveal…

Upper primary school students' difficulties with decimal place value are widely recognised due largely to the availability of assessment tools that accurately identify students' misconceptions in this domain. Yet, many students' decimal difficulties seem to stem from a lack of understanding of whole number place value for which there are few, if…

In this article, Derek Hurrell, points out that while it's easy to fall into the impression that the proficiency strand "Fluency" is all about knowing basic number facts in all its many and splendid ways. He add it is easy to overlook, that within Fluency there are requirements that are based in Algebra; Measurement and Geometry; and…

All numerate humans have access to two systems of number representation: an exact system that is argued to be based on language and that supports formal mathematics, and an Approximate Number System (ANS) that is present at birth and appears independent of language. Here we examine the interaction between these two systems by comparing the…

The international comparison of students' mathematics knowledge and competencies is an effective method of evaluating students' mathematics performance and developing policies to improve their achievements in mathematics. Trends in International Mathematics and Science Study (TIMSS) are among the most well-recognized international comparisons that…

Purpose: The present study examined the relationship between mathematics and language to better understand the nature of the deficit and the academic implications associated with specific language impairment (SLI) and academic implications for English language learners (ELLs). Method: School-age children (N = 61; 20 SLI, 20 ELL, 21 native…

This study investigated contributions of general cognitive abilities and foundational mathematical competencies to numeration understanding (i.e., base-10 structure) versus multidigit calculation skill. Children (n = 394, M = 6.5 years) were assessed on general cognitive abilities and foundational numerical competencies at start of 1st grade; on…