This paper is part of broader research being conducted in the area of algebraic thinking in primary education. Our general research objective was to identify and describe generalization of a 2nd grade student (aged 7-8). Specifically, we focused on the transition from arithmetic to algebraic generalization. The notion of structure and its…

Many recently added studies concerning reforms on teaching Early Mathematics were taken into consideration by different countries all over the world. The rhetoric that has accompanied such reforms has often justified them in terms of the need to produce citizens who are better able to cope with the demands of the twenty-first century. As an area…

The study set out to explore different mathematical difficulties among 877 second-grade children and to test the effect of memorization versus conceptual practices with number combinations. It used a latent profile analysis of baseline measurements of digit writing speed, number combination fluency, multidigit calculation, and number sense skills…

Background: Early numeracy interventions including basic arithmetic are crucial for young students at risk for early mathematics difficulties (MDs), yet few studies have evaluated numeracy interventions in second grade with a randomized controlled design. Aim: This pre- and post-test randomized controlled study evaluated the effects of an…

In this paper, we detail the outcomes of a small-scale intervention study that aimed to support the mathematising processes of Grade 2 South African learners when working with additive relations problems. We report on the mathematising shifts that were evident in pre- and post-test responses prior to and after a sequence of 13 intervention…

The use of artifacts to introduce the distributive law of multiplication over addition in primary school is a diffused approach: it is possible to find pre-constructed learning trajectories in instructional materials. However, it is still unclear how the teacher might support his/her students in transitioning from concrete to symbolic…

Overall mathematics proficiency of fourth graders in the U.S. continues to be poor and students falling at or below the 25th percentile display declining performance (NCES, 2017), which suggests the need for schools to provide supplemental intervention supports as soon as skill gaps are observed. Unfortunately, there is a paucity of small group…

In this study we investigate the effects of long-term technology enhanced learning (TEL) in mathematics learning performance and fluency, and how technology enhanced learning can be integrated into regular curriculum. The study was conducted in five second grade classes. Two of the classes formed a treatment group and the remaining three formed a…

Ensuring students correctly understand the notion of equality is a fundamental problem in teaching mathematics. Is it possible to teach arithmetic in such a way that students do not misinterpret the equal sign "=" as indicating the result of an arithmetic operation and, consequently, viewing the arithmetic operation symbols (+, -, or x)…

In Norway, children are encouraged to pose a problem that they can solve using an arithmetical calculation. This is known as 'regnefortelling'. During a larger project, we became interested in a small group of "regnefortelling" which used unusual contexts, contexts that made us uneasy and invoked a feeling of uncertainty about how we…

The aim of this study was to propose a new conceptualization of early number sense. Six-year-old students' (n = 204) number sense was tracked from the beginning of Grade 1 through the beginning of Grade 2. Data analysis suggested that elementary arithmetic, conventional arithmetic, and algebraic arithmetic contributed to the latent construct early…

This paper describes some elements of a specific kind of design-based research, cooperative engineering. In the first part of the paper, we argue that cooperative engineering can be analyzed through a joint action framework. We first present some conceptual tools that the Joint Action Theory in Didactics proposes in order to understand didactic…

In this study 2nd grade primary school students' skills and success of subtraction especially with borrowing three digit numbers is investigated. Two different models of the subtraction are analyzed. One of them is used in Turkey (1) and the proposed method which is used in Austria (2). The present paper describes the success, both of the…

Digit comparison is strongly related to individual differences in children's arithmetic ability. Why this is the case, however, remains unclear to date. Therefore, we investigated the relative contribution of three possible cognitive mechanisms in first and second graders' digit comparison performance: digit identification, digit--number word…

When a second-grade class struggled to make sense of the algorithms for multidigit addition and subtraction, attitude and morale were down, and student discourse was at an all-time low. When daily mathematics class started, the teacher was hearing an overall class moan. The instructed needed to turn it around, to find a way to help excite and…