Background.  The ability to compare numbers, as the most basic form of number sense, has been related to arithmetical achievement. Aims.  The current study addressed the predictive value of non‐symbolic and symbolic (number word (NW) and Arabic number (AN)) comparison for arithmetics by means of a longitudinal design. Sample.  Sixteen children with mathematical disabilities (MD), 64 low achievers (LA), and 315 typical achieving (TA) children were followed from kindergarten till grade 2. Method.  The association of comparison skills with arithmetical skills in grades l and 2 was studied. The performances of MD, LA and TA children were compared. Results.  Regression analyses showed that non‐symbolic skills in kindergarten were predictively related to arithmetical achievement 1 year later and fact retrieval 2 years later. AN comparison was predictively related to procedural calculation 2 years later. In grade 2, there was an association between both symbolic tasks and arithmetical achievement. Children with MD already had deficits in non‐symbolic and symbolic AN comparison in kindergarten, whereas in grade 2 the deficits in processing symbolic information remained. Conclusions.  The combination of non‐symbolic and symbolic deficits represents a risk of developing MD.

This article presents an overview of two studies that examined the relationship between metacognition and mathematical problem solving in 165 children with average intelligence in Grade 3 in order to help teachers and therapists gain a better understanding of contributors to successful mathematical performance. Principal components analysis on metacognition revealed that three metacognitive components (global metacognition, off-line metacognition, and attribution to effort) explained 66% to 67% of the common variance. The findings from these studies support the use of the assessment of off-line metacognition (essentially prediction and evaluation) to differentiate between average and above-average mathematical problem solvers and between students with a severe or moderate specific mathematics learning disability.

Third grade elementary school children solved tests on mathematical reasoning and numerical facility. Metacognitive skillfulness was assessed through think aloud protocols, prospective and retrospective child ratings, teacher questionnaires, calibration measures and EPA2000. In our dataset metacognition has a lot in common with intelligence, but planning measured with teacher ratings plays a role above and beyond IQ. Moreover, we found that skills are generally related, but that it is more appropriate to assess them separately. In addition, results show the value of an experienced teacher as actual measure of metacognitive planning skills. Our dataset suggests convergent validity for prospective and retrospective child ratings, but no significant relationship with the other metacognitive measures. Metacognitive skillfulness combined with intelligence accounts for between 52.9% and 76.5% of the mathematics performances. The choice of diagnostic instruments highly determines the predicted percentage. Consequences for the assessment of metacognitive skills are discussed. IntroductionThis study is devoted to the multi-method assessment of metacognition in elementary school children. The relationship between mathematical problem solving and metacognitive skills is described in young children. In the study it is investigated if prospective (e.g., Metacognition Learning (

In a three-year longitudinal study 471 children were classified, based on their performances on arithmetic tests in first and second grade, as having persistent arithmetic disabilities (AD), persistent low achieving (LA), persistent typical achieving, inconsistent arithmetic disabilities (DF1) or inconsistent low achieving in arithmetic. Significant differences in the performances on the magnitude comparison in kindergarten (at age 5 to 6) were found between the AD and LA and between the AD and DF1 groups. Evidence from a three year longitudinal study on the role of preparatory arithmetic abilities