Spatial Problem Solving Research Articles

Spatial problem-solving in year 7 mathematics: An examination of the effects of use of a computer-mediated software program

Strong claims have been made about the ability of Interactive Multimedia (IMM) programs to positively affect student learning outcomes. This study sought to evaluate the design of a specific IMM program,Working Mathematically: Space, and to see if use of the program would promote student learning in spatial mathematics when compared to non-computer based instruction. An evaluative framework was established to facilitate examination of program design and focussed attention on the technical and cognitive interaction between student and program. Subsequent investigation focused on the impact of the software use on Year 7 students’ problem-solving processes, their spatial mathematics performance, and student-to-student interaction in teacher supported and unsupported learning environments. Use of the IMM program was not associated with any gain in problem-solving performance when compared with the use of small blocks to solve a tower-building task. The IMM program did, however, result in increased frequency of low-level interaction between student pairs, which appeared to be associated with the technical design of the software. Several aspects of the design seemed to negatively impact on the processing events undertaken by students. Although the results of this study are limited to the detailed examination of one task using one IMM program, the outcomes of the evaluation point to areas that should be of concern to program developers and teachers.

Muscarinic Blockade Slows and Degrades the Location-Specific Firing of Hippocampal Pyramidal Cells

The firing of rat hippocampal pyramidal cells is determined both by the animal's location and by the state of the hippocampal EEG. Because cholinergic transmission plays a role in EEG activity, we expected that its modification would alter place cell activity. We therefore investigated the effects on place cell activity of blocking muscarinic transmission with intracerebroventricular injections of scopolamine. Scopolamine reduced both the rate of place cell discharge inside firing fields and the spatial coherence of the fields; discharge outside of the fields also showed small increases. After injections, fields were shifted farther from their previous location than for saline controls, indicating reduced reproducibility after muscarinic blockade. Scopolamine increased the time rats were stationary, but changes in place cell activity persisted even after analysis was restricted to periods of walking, suggesting that the behavioral changes cannot account for the cell discharge changes. The scopolamine effects were dose dependent to an extent that varied between different measures. The firing rates of interneurons showed only a minor trend to decrease after scopolamine. Nevertheless, the spatial coherence of interneuron firing patterns was reduced, consistent with the recent demonstration that their positional firing is mediated by the location-specific firing of pyramids (Marshall et al., 2002). These results demonstrate that acetylcholine enhances positional firing patterns in the hippocampus. Muscarinic blockade weakens the positional firing of most place cells and therefore renders them less useful for precise representation of the environment. This effect may underlie the difficulties in spatial learning and problem solving caused by abnormalities of cholinergic transmission.

Spatial problem solving and functional relations

Three experiments investigated the role of object knowledge on participants' ability to solve a spatial arrangement problem. The task was to rearrange six real-world three-dimensional objects so that their relative locations agreed with a given set of rules. The aim of the experiments was to tease out the relative extent to which object association, orientation, and object-specific functional relations affect performance on arrangement tasks. When the problem was presented vertically (objects arranged in piles), participants solved functional canonical versions of the problem significantly quicker than functional non-canonical versions both between (Experiments 1a and 2), and within subjects (Experiment 3). When the arrangement problem was presented horizontally (objects arranged flat in two rows), no significant differences in solution times were found between conditions (Experiments 1b and 2). Overall the results provide evidence for the importance of object-specific functional relations as a predictor of the solution time of spatial arrangement problems, although some differences were noted between single and multiple presentation of problems when specific rules within problems were rotated. The importance of functional information in memory as a constraint on the building of mental models and problem spaces is discussed.

The Tower of London Spatial Problem-Solving Task: Enhancing Clinical and Research Implementation

Since its development in 1982, The Tower of London (TOL; Shallice, 1982) spatial problem-solving task has been increasingly employed in test batteries of executive functions. This task has served as a rich source of information on preparation, planning and processing, but a number of issues remain unaddressed in the literature: (1) the problem structure, or problem space of the task, (2) the impact of modifications from the original, Shallice TOL, and (3) the variety of performance measures that can be derived from the TOL. We present here an overview of these issues in the hope that it may lead to a more effective and reasoned use of the TOL task by clinical and nonclinical investigators, alike.

Effects of dorsal-striatum lesions and fimbria-fornix lesions on the problem-solving strategies of rats in a shallow water maze.

In solving a spatial problem, animals can use a place, cue, or response strategy. The present research was designed to evaluate the role of dorsal striatum (DS) in spatial problem solving and to compare it with that of fimbria fornix (FF). Rats were trained with a place + cue task in a shallow pool, then were divided into three groups (DS, FF, control), and lesions were made in the corresponding areas. After retraining, four probe tests were given: Test 1 (start position moved), Test 2 (goal and start positions moved), Test 3 (invisible goal), and Test 4 (curtain test). The test results suggest that the DS and Control groups performed the original task by using the place strategy, whereas the FF group used the cue strategy, which strongly implies that the DS group was impaired in the use of the cue strategy. This research also provides evidence supporting the usefulness of a shallow pool in evaluating animal behavior.

Spatial problem solving and hippocampal place cell firing in rats: control by an internal sense of direction carried across environments

Rats learned to find the baited corner of a box surrounded by a curtain, regardless of whether they had a fixed or random point of entry (POE) through the curtain. On probe trials, rats used an internal direction sense carried from outside the curtain to solve the problem, and only used the visual cue inside the curtain if disoriented and denied access to a view of the room en route. Similar disorientation procedures were required to obtain cue control of hippocampal place fields. The results suggest that: (1) POE effects previously found in the water maze may be task-specific; (2) an undisrupted internal sense of direction carried from one environment to another may provide the preferred solution to spatial problems in the second environment, even when this second environment is a familiar one with stable visual cues; and (3) choice behaviour is sometimes, but not always, representative of the hippocampal representation of space.

Educational Innovation and the Market for Geographers in Hungary

This paper examines the status of geography in higher education in Hungary. Stress is placed on reforms begun in the 1990s to launch new curricula for training professional geographers. The authors played an important role in developing this new curriculum by introducing new subjects into geography programmes, working out the scope and sequence of courses, obtaining accreditation and carrying out market research for graduates. The project was motivated by a decline in demand for geography and geography teachers in secondary schools accompanied by an increase in demand for geographers trained to work in public administration, government and business. The graduates of the new professional geographer curriculum receive a practice-oriented education designed to cultivate their spatial problem solving and applied geographical skills. In this paper the authors present the steps in the curriculum reform and suggest that it may serve as a model for reform in a number of nearby countries planning to join the EU.

Multiple points of entry into a circular enclosure prevent place learning despite normal vestibular orientation and cue arrays: evidence for map resetting.

This study identified sources of map orientation critical for successful spatial problem solving by rats of a plus maze embedded in water. Disorientation slowed, but it did not prevent acquisition of goal location. Use of a circular enclosure with multiple points of entry prevented reliable goal location. A single entry point enabled the rats to locate a fixed goal. A cue array within the enclosure was ineffective in providing orientation. These data suggest that stable map orientation can be derived from entry location when enclosure geometry is uniformative, but is not readily taken from cue arrays. They further suggest that map orientation is reset when rats enter an enclosure.

Types of visual–spatial representations and mathematical problem solving.

Although visual-spatial representations are used extensively in mathematics and spatial ability is highly correlated with success in mathematics education, research to date has not demonstrated a clear relationship between use of visual-spatial representations and success in mathematical problem solving. The authors distinguished 2 types of visual-spatial representations: schematic representations that encode the spatial relations described in a problem and pictorial representations that encode the visual appearance of the objects described in the problem. Participants solved mathematical problems and reported on their solution strategies. The authors were able to reliably classify their visual-spatial representations as primarily schematic or primarily pictorial. Use of schematic spatial representations was associated with success in mathematical problem solving, whereas use of pictorial representations was negatively correlated with success. Use of schematic representations was also significantly correlated with one measure of spatial ability. The research therefore helps clarify the relationship between visual imagery, spatial ability, and mathematical problem solving.

Spatial and contextual factors in human performance on the travelling salesperson problem.

The travelling salesperson problem (TSP) provides a realistic and practical example of a visuo-spatial problem-solving task. In previous research, we have found that the quality of solutions produced by human participants for small TSPs compares well with solutions from a range of computer algorithms. We have proposed that the ability of participants to find solutions reflects the natural properties of human perception, solutions being found through global perceptual processing of the problem array to extract a best figure from the TSP points. In this paper, we extend the study of human performance on the task in order to understand further how human abilities are utilised in solving real-world TSPs. The results of experiment 1 show that high levels of solution quality are maintained in solving larger TSPs than had been investigated previously with human participants, and that the presence of an implied real-world context in the problems has no effect upon performance. Experiment 2 demonstrated that the presence of regularity in the point layout of a TSP can facilitate performance. This was confirmed in experiment 3, where effects of the internality of point clusters were also found. All three experiments were consistent with a global, perceptually based approach to the problem by participants. We suggest that the role of perceptual processing in spatial problem-solving is an important area for further research in both theoretical and applied domains.

Cognitive predictors of young children's readiness for powered mobility.

Independent mobility in early childhood has been associated with the development of various cognitive and psychosocial skills. However, children with physical disabilities are not always able to move independently and may be at risk for delays in these areas. Early provision of powered mobility can offer young children an opportunity for independent mobility. Despite this, there is little information to help determine when a young child has the cognitive skills necessary to operate a powered wheelchair safely. This current research aims to identify these skills. A cognitive assessment battery and a wheelchair mobility training and assessment program were developed. Twenty-six children with physical disabilities between the ages of 20 and 36 months were evaluated on the cognitive assessment and participated in the wheelchair training and assessment program. A stepwise regression analysis was used to determine which of the cognitive skills predicted wheelchair mobility performance. The cognitive domains of spatial relations and problem solving were found to be significant and accounted for 57% of the variance in wheelchair skills. Developmental cut-off points on these scales as they relate to wheelchair skills are presented and clinical applications are discussed.

Cognitive predictors of young children's readiness for powered mobility

Independent mobility in early childhood has been associated with the development of various cognitive and psychosocial skills. However, children with physical disabilities are not always able to move independently and may be at risk for delays in these areas. Early provision of powered mobility can offer young children an opportunity for independent mobility. Despite this, there is little information to help determine when a young child has the cognitive skills necessary to operate a powered wheelchair safely. This current research aims to identify these skills. A cognitive assessment battery and a wheelchair mobility training and assessment program were developed. Twenty‐six children with physical disabilities between the ages of 20 and 36 months were evaluated on the cognitive assessment and participated in the wheelchair training and assessment program. A stepwise regression analysis was used to determine which of the cognitive skills predicted wheelchair mobility performance. The cognitive domains of spatial relations and problem solving were found to be significant and accounted for 57% of the variance in wheelchair skills. Developmental cut‐off points on these scales as they relate to wheelchair skills are presented and clinical applications are discussed.

Cerebral computed tomography and electroencephalography compared with neuropsychological findings in systemic lupus erythematosus.

Central nervous system involvement was evaluated in 36 patients with systemic lupus erythematosus (SLE) using cerebral computed tomography (CT), electroencephalography (EEG), and a neuropsychological test battery. The purpose was to investigate whether brain dysfunction as assessed by comprehensive neuropsychological investigation is associated with findings of routine investigation methods such as CT and EEG which are available in most hospitals. Abnormal EEG was found in 19%, and CT revealed cerebral atrophy in 47% of SLE patients. Few neuropsychological functions were affected by the presence of abnormal EEG, cerebral atrophy, or infarcts. Significant associations were found only between cortical atrophy and impairment of tactile spatial problem-solving and motor dexterity, and between cortical infarcts and motor dexterity in the dominant hand. The value of conventional EEG in assessing cerebral SLE is negligible, except for identifying epileptic activity and focal pathology. Cerebral CT has little relevance in predicting brain dysfunction as established by neuropsychological assessment in SLE, except for detecting cortical atrophy and infarcts.

A study on computer-based geometric modelling in engineering graphics

Conventional projection techniques used in engineering graphics are based on planar projection methods. In modern computer graphics applications the projection methods are not explicitly presented, however, the projection is integrated with the software by implementation of the mathematical relationships of projective geometry. Because of this `automatic' projection, the conventional engineering graphics methods when used for spatial construction in projective space of computer graphics fail to provide students with real spatial geometrical concepts. The students exposed to the present day computer-based graphics instruction are not exercising the principles of projection for solving 3D geometrical problems but are mainly trained in mechanics of geometric construction dictated by the software used. This deficiency in applying basic principles of projection needs to be addressed. The author has used computer graphics systems for improving student's visual abilities, and a research project was conducted to analyse the effect of the use of new technology on students engineering graphics learning. The underlining contemporary computer and engineering graphics methods are analysed and the students' apparent visual learning mechanism was monitored. As a result a new, more computer graphics orientated graphical method for spatial problem solving was developed. This problem solving method independent on the used 3D CAD system is particularly suitable for developing the web-based teaching and learning materials. The paper presents the resulting graphics method, counsel improvements in the instruction methods of 3D engineering graphics, and suggests development of the distance-learning network-based teaching and learning materials.

The cerebellum in the spatial problem solving: a co-star or a guest star?

The experimental findings reviewed here indicate that the cerebellum has to be added to the regions known to be involved in the spatial learning. Cerebellar function is specifically linked to `how to find an object' rather than `where the object is in the space'. In the Morris water maze (MWM) hemicerebellectomized (HCbed) rats displayed a severe impairment in coping with spatial information, displaying only peripheral circling. And yet, when the MWM cue phase was prolonged, HCbed rats succeeded in acquiring some abilities to learn platform position, even in a pure place paradigm, such as finding a hidden platform with the starting points sequentially changed. Conversely, whether the searching strategy was acquired preoperatively, no exploration deficit appeared. Thus, cerebellar lesions appear to affect the procedural components of spatial function, sparing the declarative ones. When intact animals were non-spatially pre-trained and then HCbed, they exhibited an expanded scanning strategy, underlining the cerebellar involvement in procedural component acquisition. By testing HCbed rats in an active avoidance task, first without and then with a request for right/left discrimination, lesioned rats displayed severe deficits. Thus, besides a marked impairment in facing procedural components of spatial processing, cerebellar lesion provokes deficits also in right/left discrimination task. In conclusion, it is possible to propose the cerebellum as one part of a large system that includes frontal, posterior parietal, inferior temporal cortices, hippocampus and basal ganglia. These structures form an allocentric spatial system and an egocentric control system, that interlock to process the information involved in representing an object in the space.

Representations in spatial problem solving in the classroom

Observations of primary students solving spatio-mathematical problems provided data for categorising and interpreting their thinking processes. A model was developed relating students' cognitive processing and their responsiveness during problem solving. The roles of responsiveness, visual imagery, and selective attention are described. Concrete imagery, dynamic imagery, pattern imagery, and action imagery were used in the problem-solving processes of the students. Other visual processes such as disembedding of a part of a shape from the rest of a configuration, analysis, and checking were also important. These processes at times seemed to play a role in selective attention. Other aspects influencing attention included intention, expectation, prior experiences, and interactions with other people. Visualising facilitated, and often steered, the problem-solving processes by which students constructed meaning.

Activities: Patterns and Puzzles for Pyramids and Prisms

Teacher's Guide: The construction projects, puzzles, and experiments presented here provide hands-on experiences in spatial visualization and problem solving for an important class of three-dimensional figures: pyramids and prisms. Students will enjoy creating physical models and performing experiments with the models, but the main goals of the activities are to develop students' geometric intuition and build a concrete foundation on which abstract principles can be grounded.

Problem solving and logical reasoning in the macaque monkey

This study focuses on the performances of monkeys in a spatial problem-solving task that involves working memory. Two monkeys had to find, by trial-and-error, the touching order of 2 or 3 targets in a set of 3 or 4 fixed spatial targets. When a solution was found and performed 6 times, the order was changed and the animal had to resume a new search within the same set of targets. Thus, in a training session, many searches (up to 60) could be initialised. The data show that the animals conducted a methodical search for the hidden order and found the solution in a minimal number of trials. We conclude that the monkey is able to construct complex cognitive structures, similar to logical reasoning, to solve spatial problems of this type.

Effects of parietal cortex lesions on spatial problem solving in the rat

The Maier 3-table task was used to examine spatial representations in rats with lesions of the parietal cortex. Some animals had anteriorly placed lesions, some posteriorly placed in cortical areas, sometimes regarded as ‘parietal’ in earlier studies. After 5 days of familiarization, animals were given 18 days of testing on the standard Maier task. Both parietal groups were initially impaired, but reached the same level of performance as controls by the end of the test period. Learning occurred both within and between sessions for the anterior group, but only between sessions for the posterior group. There was no major functional differentiation apparent on this task between the two ‘parietal’ areas. Rate of exploration increased in both parietal groups across test sessions as task performance improved. It is argued that the change in exploratory activity across sessions in parietal groups may reflect the adoption of a compensatory strategy which improved performance, but that improvement could also have been due to neural changes, as structures, such as the frontal cortex or hippocampus, assume some functions normally mediated by the parietal area.

An Investigation of Vetrbal Spatial Functioning in Chronic Alcoholics

The mild generalized brain dysfunction hypothesis of alcoholic impairment predicts that, as a group, alcoholics will be impaired on both right- and left-hemisphere spatial functioning tests. A verbal-spatial problem-solving task (Luria, 1980) composed of explicitly spatial problems and comparative problems was developed and administered along with a well-known visual spatial problem-solving task (Block Design) to 24 sober male alcoholics and 24 peer controls. As expected, alcoholics performed more poorly and made more configurational errors than controls on Block Design. In accord with the mild generalized hypothesis, alcoholics performed more poorly than peer controls on the more explicitly spatial verbal problems, but not on the easier comparative problems.