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Recently, left spatial neglect phenomena have been reported for the mental representation of numbers, i.e. the mental number line (Zorzi et al., 2002; Vuilleumier et al., 2004). The present study aimed at replicating the findings of Zorzi et al. (2002) in a number bisection task with small numbers and at extending the investigation to larger numbers up to 100, letters in the alphabet, days of the week and months of the year. Five patients with left spatial neglect and 20 healthy control subjects performed four mental bisection tasks (numbers, letters, days, and months tasks) where participants were asked to estimate the midpoint of a verbally presented interval. Results showed that left spatial neglect may disrupt the mental bisection of numerical intervals when small numbers have to be processed. Size of the numerical interval affected patients' performance in number range 1-9, i.e. longer intervals led to right-sided errors whereas the smallest interval did not (as in Zorzi et al., 2002). Spatial mental representations may thus exist for small numbers, while for larger numbers no consistent pattern was found. In non-numerical bisection tasks a spatial bias was found in letters and days sequences, but not in the months sequence. Patients made more shifts to letters "later" in the alphabet in the letter bisection task and more shifts to days earlier in the week in the day bisection task. It could be argued that shifts to days earlier may correspond to right-sided shifts, when the representation of days in the week is cyclic as hours on a clock.

The present study investigates implicit memory and arithmetic reasoning in a group of severely amnesic patients. Priming effects have been observed in the retrieval of arithmetic facts in amnesic patients (Delazer, Ewen and Benke, 1997), but no studies have so far investigated the effect of previous experience in a pure reasoning task. Findings indicate that answering to a first numerical series (e.g, 1 3 5 7, answer "9") facilitates answering to a second numerical series (2 4 6 8, answer "10") including different numbers but sharing the same underlying algorithm (+ 2). Within the model of Langdon and Warrington (1997) priming effects are attributed to the stage of abstract formula generation.

The study investigates calculation abilities in 12 patients with probable Alzheimer's disease (AD) and compares them to calculation abilities of healthy control subjects (NC) and patients with focal left hemisphere lesions (LHL). AD patients scored significantly lower than NC in all calculation tasks and lower than LHL patients in the execution of complex written calculation, but not in the retrieval of arithmetic facts. In the AD group a subject-by-subject error analysis on the complex written calculation showed a low consistency and a high variability of error types. It is suggested that AD patients' difficulties in complex calculation arise from a monitoring deficit and not from incomplete or distorted calculation algorithms. Overall, deficits in monitoring calculation procedures may be an early and common symptom of AD.

The paper presents a single-case study of patient J.G. showing severe calculation problems (and also agraphia, finger agnosia, right-left disorientation and apraxia) after the surgery of a left parietal tumor. Although the patient completely lost conceptual knowledge of arithmetic, she preserved part of memorised fact knowledge (multiplications and some additions and subtractions). The study indicates that arithmetic facts can be represented at a superficial level without understanding of the operation performed. The study completes a valid double dissociation between two types of knowledge involved in calculation (memorised facts and conceptual knowledge).

We report a patient, MT, who presented a specific, though not isolated, deficit in written calculation. Despite a preserved knowledge of simple arithmetic - single-digit addition and subtraction - he failed systematically in multi-digit subtraction. The nature of errors was consistent across problems and reflected the application of a disturbed underlying algorithm. Moreover, the pattern of error observed mimies a very common finding in developmental studies on arithmetical procedure acquisition (Fuson, 1990, 1992, Young and O'Shea, 1981; VanLehn, 1986, 1990). The data suggest that, within calculation skills, syntax may exist as a system of stable, but inappropriate, rules which are independent of any underlying conceptual knowledge.

We report the improvement following rehabilitation of two patients with a selective deficit on multiplication facts. The remediation experiments were conducted in specific designs to test a series of hypotheses about both the process of reacquisition and organisation of arithmetical facts in memory. The results show a significant and stable recovery and the pattern of reacquisition reflects the different strategy used by the patients to relearn the multiplication facts. Quantitative and qualitative changes in error patterns in the course of remediation reveal the underlying (re)organization of the memory network representing multiplication facts.

We present the case of a young, highly educated patient who showed severe problems in basic arithmetic after a bone marrow transplant followed by extensive irradiation and chemotherapy. Despite his inability to resolve arithmetical fact problems (as 2 + 3), he showed intact processing of algebraic expressions and excellent understanding of complex arithmetic text problems. He perfectly knew arithmetic principles and applied them in various tasks. The performance of the patient suggests that conceptual knowledge (in addition to arithmetical fact knowledge and arithmetic procedures) is a functionally independent component of the calculation system.