Sequential development of algebra knowledge : a cognitive analysis

Learning to operate algebraically is a complex process that is dependent upon extending arithmetic knowledge to the more complex concepts of algebra. Current research has shown a gap between arithmetic and algebraic knowledge and suggests a pre-algebraic level as a step between the two knowledge types. This paper examines arithmetic and algebraic knowledge from a cognitive perspective in an effort to determine what constitutes a pre-algebraic level of understanding. Results of a longitudinal study designed to investigate students' readiness for algebra are presented. Thirty-three students in Grades 7, 8, and 9 participated. A model for the transition from arithmetic to pre-algebra to algebra is proposed and students' understanding of relevant knowledge is discussed.

Cognitive skills required in contemporary workplaces

This paper discusses some of the changes occurring in contemporary workplace practices, and the implications these have for the types of knowledge and skills required to work in such environments. Increasingly, workers need to be multi-skilled to function effectively in contemporary work environments. The nature of multi-skilling is explained in terms of cross-skilling, up-skilling and higher-order thinking skills, and the relevance of multi-skilling in today's workplaces is examined. Finally, the paper explores some factors affecting the acquisition of these desired skills in light of current work practices.

Primary students’ interpretation of maps : gesture use and mapping knowledge

Maps are used to represent three-dimensional space and are integral to a range of everyday experiences. They are increasingly used in mathematics, being prominent both in school curricula and as a form of assessing students understanding of mathematics ideas. In order to successfully interpret maps, students need to be able to understand that maps: represent space, have their own perspective and scale, and their own set of symbols and texts. Despite the fact that maps have an increased prevalence in society and school, there is evidence to suggest that students have difficulty interpreting maps. This study investigated 43 primary-aged students’ (aged 9-12 years) verbal and gestural behaviours as they engaged with and solved map tasks. Within a multiliteracies framework that focuses on spatial, visual, linguistic, and gestural elements, the study investigated how students interpret map tasks. Specifically, the study sought to understand students’ skills and approaches used to solving map tasks and the gestural behaviours they utilised as they engaged with map tasks. The investigation was undertaken using the Knowledge Discovery in Data (KDD) design. The design of this study capitalised on existing research data to carry out a more detailed analysis of students’ interpretation of map tasks. Video data from an existing data set was reorganised according to two distinct episodes—Task Solution and Task Explanation—and analysed within the multiliteracies framework. Content Analysis was used with these data and through anticipatory data reduction techniques, patterns of behaviour were identified in relation to each specific map task by looking at task solution, task correctness and gesture use. The findings of this study revealed that students had a relatively sound understanding of general mapping knowledge such as identifying landmarks, using keys, compass points and coordinates. However, their understanding of mathematical concepts pertinent to map tasks including location, direction, and movement were less developed. Successful students were able to interpret the map tasks and apply relevant mathematical understanding to navigate the spatial demands of the map tasks while the unsuccessful students were only able to interpret and understand basic map conventions. In terms of their gesture use, the more difficult the task, the more likely students were to exhibit gestural behaviours to solve the task. The most common form of gestural behaviour was deictic, that is a pointing gesture. Deictic gestures not only aided the students capacity to explain how they solved the map tasks but they were also a tool which assisted them to navigate and monitor their spatial movements when solving the tasks. There were a number of implications for theory, learning and teaching, and test and curriculum design arising from the study. From a theoretical perspective, the findings of the study suggest that gesturing is an important element of multimodal engagement in mapping tasks. In terms of teaching and learning, implications include the need for students to utilise gesturing techniques when first faced with new or novel map tasks. As students become more proficient in solving such tasks, they should be encouraged to move beyond a reliance on such gesture use in order to progress to more sophisticated understandings of map tasks. Additionally, teachers need to provide students with opportunities to interpret and attend to multiple modes of information when interpreting map tasks.

User-driven saliency maps for evaluating Region-of-Interest detection

Detection of Region of Interest (ROI) in a video leads to more efficient utilization of bandwidth. This is because any ROIs in a given frame can be encoded in higher quality than the rest of that frame, with little or no degradation of quality from the perception of the viewers. Consequently, it is not necessary to uniformly encode the whole video in high quality. One approach to determine ROIs is to use saliency detectors to locate salient regions. This paper proposes a methodology for obtaining ground truth saliency maps to measure the effectiveness of ROI detection by considering the role of user experience during the labelling process of such maps. User perceptions can be captured and incorporated into the definition of salience in a particular video, taking advantage of human visual recall within a given context. Experiments with two state-of-the-art saliency detectors validate the effectiveness of this approach to validating visual saliency in video. This paper will provide the relevant datasets associated with the experiments.

An investigation of the effect of individual cognitive preferences on learning through computer-based instruction

This paper reports a study investigating the effect of individual cognitive styles on learning through computer-based instruction. The study adopted a quasi-experimental design involving four groups which were presented with instructional material that either matched or mismatched with their preferred cognitive styles. Cognitive styles were measured by cognitive style assessment software (Riding, 1991). The instructional material was designed to cater for the four cognitive styles identified by Riding. Students' learning outcomes were measured by the time taken to perform test tasks and the number of marks scored. The results indicate no significant difference between the matched and mismatched groups on both time taken and scores on test tasks. However, there was significant difference between the four cognitive styles on test score. The Wholist/Verbaliser group performed better then all other groups. There was no significant difference between the other groups. An analysis of the performance on test task by each cognitive style showed significant difference between the groups on recall, labelling and explanation. Difference between the cognitive style groups did not reach significance level for problem-solving tasks. The findings of the study indicate a potential for cognitive style to influence learning outcomes measured by performance on test tasks.

Cognitive load and assembly tasks : effect of instructional formats on learning assembly procedures

The study investigated the effect on learning of four different instructional formats used to teach assembly procedures. Cognitive load and spatial information processing theories were used to generate the instructional material. The first group received a physical model to study, the second an isometric drawing, the third an isometric drawing plus a model and the fourth an orthographic drawing. Forty secondary school students were presented with the four different instructional formats and subsequently tested on an assembly task. The findings indicated that there may be evidence to argue that the model format which only required encoding of an already constructed three dimensional representation, caused less extraneous cognitive load compared to the isometric and the orthographic formats. No significant difference was found between the model and the isometric-plus-model formats on all measures because 80% of the students in the isometric-plus-model format chose to use the model format only. The model format also did not differ significantly from other groups in total time taken to complete the assembly, in number of correctly assembled pieces and in time spent on studying the tasks. However, the model group had significantly more correctly completed models and required fewer extra looks than the other groups.

Cognitive load and mental rotation : structuring orthographic projection for learning and problem solving

Cognitive load theory was used to generate a series of three experiments to investigate the effects of various worked example formats on learning orthographic projection. Experiments 1 and 2 investigated the benefits of presenting problems, conventional worked examples incorporating the final 2-D and 3-D representations only, and modified worked examples with several intermediate stages of rotation between the 2-D and 3-D representations. Modified worked examples proved superior to conventional worked examples without intermediate stages while conventional worked examples were, in turn, superior to problems. Experiment 3 investigated the consequences of varying the number and location of intermediate stages in the rotation trajectory and found three stages to be superior to one. A single intermediate stage was superior when nearer the 2-D than the 3-D end of the trajectory. It was concluded that (a) orthographic projection is learned best using worked examples with several intermediate stages and that (b) a linear relation between angle of rotation and problem difficulty did not hold for orthographic projection material. Cognitive load theory could be used to suggest the ideal location of the intermediate stages.

Computer assisted instruction and individual cognitive style preferences in learning : does it matter?

This paper reports the findings of a pilot study aimed at improving learning outcomes from Computer Assisted Instruction (CAI). The study involved second year nursing students at the Queensland University of Technology. Students were assessed for their preferred cognitive style and presented with either matched or mismatched instructional material. The instructional material was developed in accordance with four cognitive styles (Riding & Cheema, 1991). The findings indicate groups that received instructional material which matched their preferred cognitive style, possibly, performed better than groups that received mismatched instructional material. The matched group was particularly better in the explanation and problem solving tasks.

Motivational Interviewing changes the treatment trajectory of group Cognitive-Behavioural Therapy for anxiety

Anxiety disorders have been viewed as manifestations of broad underlying predisposing personality constructs such as neuroticism combined with more specific individual differences of unhelpful information processing styles. Given the high prevalence of anxiety and the significant impairment that it causes, there is an important need to continue to explore successful treatments for this disorder. Research indicates that there is still room for significantly improving attrition rates and treatment adherence. Traditionally Motivational Interviewing (MI) has been used to facilitate health behaviour change. Recently MI has been applied to psychotherapy and has been shown to improve the outcome of CBT. However, these studies have been limited to only considering pre- and post-treatment measures and neglected to consider when changes occur along the course of therapy. This leaves the unanswered question of what is the impact of pre-treatment MI on the treatment trajectory of therapy. This study provides preliminary research into answering this question by tracking changes on a weekly basis along the course of group CBT. Prior to group CBT, 40 individuals with a principal anxiety disorder diagnosis were randomly assigned to receive either 3 individual sessions of MI or placed on a waitlist control group. All participants then received the same dosage of 10 weekly 2 hour sessions of group CBT. Tracking treatment outcome trajectory over the course of CBT, the pre-treatment MI group, compared to the control group, experienced a greater improvement early on in the course of therapy in their symptom distress, interpersonal relationships and quality of life. This early advantage over the control group was then maintained throughout therapy. These results not only demonstrate the value of adding MI to CBT, but also highlight the immediacy of MI effects. Further research is needed to determine the robustness of these effects to inform clinical implications of how to best apply MI to improve treatment adherence to CBT for anxiety disorders.

The Cannabis Expectancy Questionnaire for Men who have Sex with Men (CEQ-MSM): A measure of substance-related beliefs

Objective Substance-related expectancies are associated with substance use and post-substance use thoughts, feelings and behaviours. The expectancies held by specific cultural or sub-cultural groups have rarely been investigated. This research maps expectancies specific to gay and other men who have sex with men (MSM) and their relationship with substance patterns and behaviours following use, including sexual practices (e.g., unprotected anal intercourse). This study describes the development of a measure of such beliefs for cannabis, the Cannabis Expectancy Questionnaire for Men who have Sex with Men (CEQ-MSM). Method Items selected through a focus group and interviews were piloted on 180 self-identified gay or other MSM via an online questionnaire. Results Factor analysis revealed six distinct substance reinforcement domains (“Enhanced sexual experience”, “Sexual negotiation”, “Cognitive impairment”, “Social and emotional facilitation”, “Enhanced sexual desire”, and “Sexual inhibition”). The scale was associated with consumption patterns of cannabis, and in a crucial test of discriminant validity not with the consumption of alcohol or stimulants. Conclusions The CEQ-MSM represents a reliable and valid measure of outcome expectancies, related to cannabis among MSM. Future applications of the CEQ-MSM in health promotion, clinical settings and research may contribute to reducing harm associated with substance use among MSM, including HIV transmission.