An examination of grade three mathematics textbooks for problem solving strategies

Three grade three mathematics textbooks were selected arbitrarily (every other) from a total of six currently used in the schools of Ontario. These textbooks were examined through content analysis in order to determine the extent (i. e., the frequency of occurrence) to which problem solving strategies appear in the problems and exercises of grade three mathematics textbooks, and how well they carry through the Ministry's educational goals set out in The Formative Years. Based on Polya's heuristic model, a checklist was developed by the researcher. The checklist had two main categories, textbook problems and process problems and a finer classification according to the difficulty level of a textbook problem; also six commonly used problem solving strategies for the analysis of a process problem. Topics to be analyzed were selected from the subject guideline The Formative Years, and the same topics were selected from each textbook. Frequencies of analyzed problems and exercises were compiled and tabulated textbook by textbook and topic by topic. In making comparisons, simple frequency count and percentage were used in the absence of any known criteria available for judging highor low frequency. Each textbook was coded by three coders trained to use the checklist. The results of analysis showed that while there were large numbers of exercises in each textbook, not very many were framed as problems according to Polya' s model and that process problems form a small fraction of the number of analyzed problems and exercises. There was no pattern observed as to the systematic placement of problems in the textbooks.

Anxiety and learning / response behaviour in the context of intellectual problem solving by young children

Twenty-eight grade four students were ca.tegorized as either high or low anxious subjects as per Gillis' Child Anxiety Scale (a self-report general measure). In determining impulsivity in their response tendencies, via Kagan's Ma.tching Familiar Figures Test, a significant difference between the two groups was not found to exist. Training procedures (verbal labelling plus rehearsal strategies) were introduced in modification of their learning behaviour on a visual sequential memory task. Significantly more reflective memory recall behaviour was noted by both groups as a result. Furthermore, transfer of the reflective quality of this learning strategy produced significantly less impulsive response behaviour for high and low anxious subjects with respect to response latency and for low anxious subjects with respect to response accuracy.

Using genetic algorithms for the single allocation hub location problem

Hub location problem is an NP-hard problem that frequently arises in the design of transportation and distribution systems, postal delivery networks, and airline passenger flow. This work focuses on the Single Allocation Hub Location Problem (SAHLP). Genetic Algorithms (GAs) for the capacitated and uncapacitated variants of the SAHLP based on new chromosome representations and crossover operators are explored. The GAs is tested on two well-known sets of real-world problems with up to 200 nodes. The obtained results are very promising. For most of the test problems the GA obtains improved or best-known solutions and the computational time remains low. The proposed GAs can easily be extended to other variants of location problems arising in network design planning in transportation systems.

A phenomenological approach to understanding the psychological response to chronic low back pain

Chronic low back pain (CLBP) is a complex health problem of psychological manifestations not fully understood. Using interpretive phenomenological analysis, 11 semi-structured interviews were conducted to help understand the meaning of the lived experience of CLBP; focusing on the psychological response to pain and the role of depression, catastrophizing, fear-avoidance behavior, anxiety and somatization. Participants characterized CLBP as persistent tolerable low back pain (TLBP) interrupted by periods of intolerable low back pain (ILBP). ILBP contributed to recurring bouts of helplessness, depression, frustration with the medical system and increased fear based on the perceived consequences of anticipated recurrences, all of which were mediated by the uncertainty of such pain. During times of TLBP all participants pursued a permanent pain consciousness as they felt susceptible to experience a recurrence. As CLBP progressed, participants felt they were living with a weakness, became isolated from those without CLBP and integrated pain into their self-concept.