NONSTANDARD MATH WORD PROBLEMS AND ANALYSIS OF THE PARTIAL STAGES OF ITS SOLUTION

Choosing the right strategy is an important condition to successfully solve math problems. Research studies often present individual types of strategies more or less separately. This study aims to determine student solutions of selected word problems in the whole context of the solution process. In this context, such nonstandard word problems combine verbal formulation and the character of nonstandard problems (impossible to be solved using an algorithm). In order to get an overall picture of the stages of word problem solution, an analysis of solving a given word problem was conducted among 171 respondents aged 10-11. The analysis was conducted in compliance with partial steps of word problem processing, as the solving of the problem was viewed from a wider perspective. The student’s reaction to the problem, working with the given information, individual forms of solution, and answer formation were recorded. In order to have a more complex idea and possibility to compare, the chosen way of solving the problem was also presented to a selected sample of 26 teachers. Available solutions were analyzed, and there were sought ways how the solution was assessed by the teachers based on selected parameters. Especially their meta-cognitive estimation of the correctness of their own solution was subject to scrutiny. Despite the fact that the respondents chose different strategies of solution (graphic, arithmetical, using judgment, etc.), it appears that the success rate of solving the given nonstandard word problem was very low. Thus, it is necessary to implement such word problems into standard math lessons, also within pre-graduate teacher preparation. Keywords: mathematics teaching, primary school mathematics, problem-solving, prospective teachers, word problem

What determines cognitive estimation ability? Changing contributions of semantic and executive domains as a function of age

The Cognitive Estimation Test (CET) is commonly used in neuropsychological assessment. It is typically assumed to load on executive functions, although research has shown that CET performance also depends on semantic knowledge. Yet, it is unknown whether these contributions vary with age. It is important to examine this question as these abilities have divergent life course trajectories: executive functions tend to decline as people age but semantic knowledge continues to accrue. We investigated cognitive predictors of CET performance in healthy young and older adults. We found that better executive function was associated with more accurate estimation in both age groups. However, the effect of semantic knowledge on CET performance was significantly larger in older people, having no predictive power in the younger group. The ability to detect weak semantic associations, a measure of controlled semantic retrieval, also had divergent effects on CET performance in the two age groups. Our results provide empirical support for the idea that older people are more reliant on semantic knowledge when estimating quantities, which may explain why age-related decline in CET scores is not typically found. We conclude that deficits on the CET may be indicative either of semantic or executive impairments, particularly in older age groups.

On the (lack of) association between theory of mind and executive functions: a study in a non-clinical adult sample

We investigated in a sample of non-clinical adults the association between Theory of Mind (ToM) and Executive Functions (EFs), that is the set of skills that allow people to control and modulate lower-level cognitive processes in order to produce appropriate behaviour. To this aim, we assessed both affective (i.e., understanding other people’s emotions and feelings) and cognitive (i.e., understanding others’ beliefs and intentions) ToM, as well four subcomponents of EFs, that is Updating, Shifting, Inhibition, and Access. The association between ToM and non-verbal fluid intelligence, verbal reasoning, and cognitive estimation abilities was also investigated. Eighty-one healthy participants were recruited, and a set of psychometrically validated tests was administered. Multiple regression analyses were run to assess significant predictors of ToM performance when potentially confounding predictors (sociodemographic variables) were controlled for. Results showed a lack of association between affective/cognitive ToM and EFs, whereas non-verbal fluid intelligence for cognitive ToM and verbal reasoning for affective ToM were found to be significant predictors of ToM performance. These results represent a contribution toward a deeper understanding of the ToM-EFs relationships and highlight the importance of broadening the analysis of these relationships to the role played by other domain-general functions in both affective and cognitive ToM.

The right anterior temporal lobe critically contributes to magnitude knowledge

Cognitive estimation is a mental ability applied to solve numerical problems when precise facts are unknown, unavailable or impractical to calculate. It has been associated with several underlying cognitive components, most often with executive functions and semantic memory. Little is known about the neural correlates of cognitive estimation. To address this issue, the present cross-sectional study applied lesion-symptom mapping in a group of 55 patients with left hemineglect due to right-hemisphere stroke. Previous evidence suggests a high prevalence of cognitive estimation impairment in these patients, as they might show a general bias towards large magnitudes. Compared to 55 age- and gender-matched healthy controls, the patient group demonstrated impaired cognitive estimation. However, the expected large magnitude bias was not found. Lesion-symptom mapping related their general estimation impairment predominantly to brain damage in the right anterior temporal lobe. Also critically involved were the right uncinate fasciculus, the anterior commissure and the right inferior frontal gyrus. The main findings of this study emphasize the role of semantic memory in cognitive estimation, with reference to a growing body of neuroscientific literature postulating a transmodal hub for semantic cognition situated in the bilateral anterior temporal lobe. That such semantic hub function may also apply to numerical knowledge is not undisputed. We here propose a critical contribution of the right anterior temporal lobe to at least one aspect of number processing, i.e. the knowledge about real-world numerical magnitudes.

Executive Functioning in Healthy Aged Population in comparison to Young Adults Using Cognitive Estimation Test

Background and objective: Cognitive estimation is an important task in which people engage themselves in estimating the environment in different aspects of their life, such as; distance, quantity, size, weight etc The study was taken up to evaluate the cognitive estimation skills in Healthy Aged Population in comparison to Young Adults. Methodology: A total of 40 healthy young and old adults participated in the study. The participants were divided into two groups. Cognitive Estimation Test (CET) was administered for both the groups. The CET, was modified to suit Indian population consisted of 18 questions under the domains of distance, quantity, size, weight, temperature and time. Responses were scored for Under-estimation (UE), Over-estimation (OE), Approximate answer (AA), and No answer (NA). Number of UE, OE, AA, and NA were calculated. Independent t-test was employed to find out the significant differences between the means of both the groups. Results: Results revealed that young adults were better in estimating the environment when compared to healthy aged population, which was significant .Distance and size dimensions were remarkably affected in comparison to all other dimensions. Instances of No answers (NA) were higher in healthy aged population in comparison to young adults. Conclusion: The results indicate that, the decline in cognitive estimation abilities is a part of healthy aging rather than a pathological condition. Thus CET can be used as a tool in the assessment and management of cognitive disorders.

Functional Dissociation between Cognitive Estimation and Object Naming in Focal Temporal and Frontal Lobe Epilepsies

Purpose This study addresses specific impairments of cognitive estimation and object naming in patients with focal temporal lobe epilepsy (TLE) and frontal lobe epilepsy (FLE). It was investigated whether selective impairments can be explained by differences in lesion localization and functional hemispheric specialization. Materials and Methods Seventy-eight patients (39 females, 39 males) with FLE and TLE were investigated using the German “Test zum Kognitiven Schätzen” and the “Boston Naming Test” to assess cognitive estimation abilities and visual object naming. Questions According to theoretical models that support a distinct hemispheric dominance for estimation and naming, it was expected that epilepsy localization in the right hemisphere would result in impairments of cognitive estimation, whereas patients with left epileptogenic foci would show deficits in object naming. Results In comparison to a healthy control group, a significant impairment in estimation performance was present in patients with right temporal mesial and right frontal epilepsy. A significant impairment of naming performance was found in patients with left temporal mesial, right temporal mesial, left temporal neocortical, and left frontal epilepsy. Overall, localization-dependent deficits were detected in patients with hippocampal sclerosis (cognitive estimation and object naming), right frontal epilepsy (cognitive estimation), and left temporal neocortical/left frontal epilepsy (object naming). In patients with right temporal neocortical epilepsy, no functional deficits were found. Conclusion It is hypothesized that there is a functional dissociation between cognitive estimation processes and object naming due to different functional specialization of the left and right hemispheres, respectively.