THE EFFECT OF PURPOSEFUL MATHEMATICS DISCOURSE IN THE CLASSROOM ON STUDENTS’ MATHEMATICS LANGUAGE IN THE CONTEXT OF PROBLEM SOLVING

This study examines how one secondary school teacher’s use of purposeful oral mathematics language impacted her students’ language use and overall communication in written solutions while working with word problems in a grade nine academic mathematics class. Mathematics is often described as a distinct language. As with all languages, students must develop a sense for oral language before developing social practices such as listening, respecting others ideas, and writing. Effective writing is often seen by students that have strong oral language skills. Classroom observations, teacher and student interviews, and collected student work served as evidence to demonstrate the nature of both the teacher’s and the students’ use of oral mathematical language in the classroom, as well as the effect the discourse and language use had on students’ individual written solutions while working on word problems. Inductive coding for themes revealed that the teacher’s purposeful use of oral mathematical language had a positive impact on students’ written solutions. The teacher’s development of a mathematical discourse community created a space for the students to explore mathematical language and concepts that facilitated a deeper level of conceptual understanding of the learned material. The teacher’s oral language appeared to transfer into students written work albeit not with the same complexity of use of the teacher’s oral expression of the mathematical register. Students that learn mathematical language and concepts better appear to have a growth mindset, feel they have ownership over their learning, use reorganizational strategies, and help develop a discourse community.

Completion strategy or emphasis manipulation? Task support for teaching information problem solving

While most students seem to solve information problems effortlessly, research shows that the cognitive skills for effective information problem solving are often underdeveloped. Students manage to find information and formulate solutions, but the quality of their process and product is questionable. It is therefore important to develop instruction for fostering these skills. In this research, a 2-h online intervention was presented to first-year university students with the goal to improve their information problem solving skills while investigating effects of different types of built-in task support. A training design containing completion tasks was compared to a design using emphasis manipulation. A third variant of the training combined both approaches. In two experiments, these conditions were compared to a control condition receiving conventional tasks without built-in task support. Results of both experiments show that students' information problem solving skills are underdeveloped, which underlines the necessity for formal training. While the intervention improved students’ skills, no differences were found between conditions. The authors hypothesize that the effective presentation of supportive information in the form of a modeling example at the start of the training caused a strong learning effect, which masked effects of task support. Limitations and directions for future research are presented.

Evaluation of creative problem solving abilities in undergraduate structural engineers through interdisciplinary problem based learning

For a structural engineer, effective communication and interaction with architects cannot be underestimated as a key skill to success throughout their professional career. Structural engineers and architects have to share a common language and understanding of each other in order to achieve the most desirable architectural and structural designs. This interaction and engagement develops during their professional career but needs to be nurtured during their undergraduate studies. The objective of this paper is to present the strategies employed to engage higher order thinking in structural engineering students in order to help them solve complex problem-based learning (PBL) design scenarios presented by architecture students. The strategies employed were applied in the experimental setting of an undergraduate module in structural engineering at Queen’s University Belfast in the UK. The strategies employed were active learning to engage with content knowledge, the use of physical conceptual structural models to reinforce key concepts and finally, reinforcing the need for hand sketching of ideas to promote higher order problem-solving. The strategies employed were evaluated through student survey, student feedback and module facilitator (this author) reflection. The strategies were qualitatively perceived by the tutor and quantitatively evaluated by students in a cross-sectional study to help interaction with the architecture students, aid interdisciplinary learning and help students creatively solve problems (through higher order thinking). The students clearly enjoyed this module and in particular interacting with structural engineering tutors and students from another discipline

Problem solving competency and the mathematical kangaroo

The goal of the study was to investigate differences in how two groups of students activated mathematical competencies in the mathematical kangaroo (MK). The two groups, group 1 and 2, were identified from a sample of 264 students (grade 7, age 13) through high achievement (top 20 %) in only one of the tests: the MK or a curriculum bounded test (CT). Analysis of mathematical competencies showed that the high achievers in the MK, activated the problem solving competency to a greater extent than the high achievers in the CT, when doing the MK. The results indicate the importance of using non-traditional tests in the assessment process of students to be able to find students that might possess good mathematical competencies although they do not show it on curriculum bounded tests.

Dyslexia, problem solving and text processing : a conceptual framework describing reading difficulties in dyslexia as an information-processing problem

Résumé : Une définition opérationnelle de la dyslexie qui est adéquate et pertinente à l'éducation n'a pu être identifiée suite à une recension des écrits. Les études sur la dyslexie se retrouvent principalement dans trois champs: la neurologie, la neurolinguistique et la génétique. Les résultats de ces recherches cependant, se limitent au domaine médical et ont peu d'utilité pour une enseignante ou un enseignant. La classification de la dyslexie de surface et la dyslexie profonde est la plus appropriée lorsque la dyslexie est définie comme trouble de lecture dans le contexte de l'éducation. L'objectif de ce mémoire était de développer un cadre conceptuel théorique dans lequel les troubles de lecture chez les enfants dyslexiques sont dû à une difficulté en résolution de problèmes dans le traitement de l'information. La validation du cadre conceptuel a été exécutée à l'aide d'un expert en psychologie cognitive, un expert en dyslexie et une enseignante. La perspective de la résolution de problèmes provient du traitement de l'information en psychologie cognitive. Le cadre conceptuel s'adresse uniquement aux troubles de lectures qui sont manifestés par les enfants dyslexiques.||Abstract : An extensive literature review failed to uncover an adequate operational definition of dyslexia applicable to education. The predominant fields of research that have produced most of the studies on dyslexia are neurology, neurolinguistics and genetics. Their perspectives were shown to be more pertinent to medical experts than to teachers. The categorization of surface and deep dyslexia was shown to be the best description of dyslexia in an educational context. The purpose of the present thesis was to develop a theoretical conceptual framework which describes a link between dyslexia, a text-processing model and problem solving. This conceptual framework was validated by three experts specializing in a specific field (either cognitive psychology, dyslexia or teaching). The concept of problem solving was based on information-processing theories in cognitive psychology. This framework applies specifically to reading difficulties which are manifested by dyslexic children.

Observed Social Problem Solving and Friendship Quality in Children with a Traumatic Brain Injury

Children who have experienced a traumatic brain injury (TBI) are at risk for a variety of maladaptive cognitive, behavioral and social outcomes (Yeates et al., 2007). Research involving the social problem solving (SPS) abilities of children with TBI indicates a preference for lower level strategies when compared to children who have experienced an orthopedic injury (OI; Hanten et al., 2008, 2011). Research on SPS in non-injured populations has highlighted the significance of the identity of the social partner (Rubin et al., 2006). Within the pediatric TBI literature few studies have utilized friends as the social partner in SPS contexts, and fewer have used in-vivo SPS assessments. The current study aimed to build on existing research of SPS in children with TBI by utilizing an observational coding scheme to capture in-vivo problem solving behaviors between children with TBI and a best friend. The current study included children with TBI (n = 41), children with OI (n = 43), and a non-injured typically developing group (n = 41). All participants were observed completing a task with a friend and completed a measure of friendship quality. SPS was assessed using an observational coding scheme that captured SPS goals, strategies, and outcomes. It was expected children with TBI would produce fewer successes, fewer direct strategies, and more avoidant strategies. ANOVAs tested for group differences in SPS successes, direct strategies and avoidant strategies. Analyses were run to see if positive or negative friendship quality moderated the relation between group type and SPS behaviors. Group differences were found between the TBI and non-injured group in the SPS direct strategy of commands. No group differences were found for other SPS outcome variables of interest. Moderation analyses partially supported study hypotheses regarding the effect of friendship quality as a moderator variable. Additional analyses examined SPS goal-strategy sequencing and grouped SPS goals into high cost and low cost categories. Results showed a trend supporting the hypothesis that children with TBI had fewer SPS successes, especially with high cost goals, compared to the other two groups. Findings were discussed highlighting the moderation results involving children with severe TBI.

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.