Using Effective Teaching Strategies and Personality Type to Enhance the Mathematics Classroom: A Handbook for Intermediate Math Teachers

This project addressed the need for more insightful, current, and applicable resources for intermediate math teachers in Canadian classrooms. A need for a handbook in this division seemed warranted by a lack of government resource support. Throughout an extensive review of the literature, themes and topics for the handbook emerged. The handbook was designed to not only provide educators with examples of effective teaching strategies within the mathematics classroom but to also inform them about the ways in which their personal characteristics and personality type could affect their students and their own pedagogical practices. Three teaching professionals who had each taught in an intermediate math class within the past year evaluated the handbook. The feedback received from these educators was directly applied to the first draft of the handbook in order to make it more accessible and applicable to other math teachers. Although the handbook was written with teachers in mind, the language and format used throughout the manual also make it accessible to parents, tutors, preservice education students, and educational administrators. Essentially, any individual who is hoping to inspire and educate intermediate math students could make use of the content within the handbook.

Extending relAPS to first order logic

RelAPS is an interactive system assisting in proving relation-algebraic theorems. The aim of the system is to provide an environment where a user can perform a relation-algebraic proof similar to doing it using pencil and paper. The previous version of RelAPS accepts only Horn-formulas. To extend the system to first order logic, we have defined and implemented a new language based on theory of allegories as well as a new calculus. The language has two different kinds of terms; object terms and relational terms, where object terms are built from object constant symbols and object variables, and relational terms from typed relational constant symbols, typed relational variables, typed operation symbols and the regular operations available in any allegory. The calculus is a mixture of natural deduction and the sequent calculus. It is formulated in a sequent style but with exactly one formula on the right-hand side. We have shown soundness and completeness of this new logic which verifies that the underlying proof system of RelAPS is working correctly.

Early Development of Auditory-Verbal and Visual-Spatial Short-Term Memory: Age and Sex Effects

Memory is a multi-component cognitive ability to retain and retrieve information presented in different modalities. Research on memory development has shown that the memory capacity and the processes improve gradually from early childhood to adolescence. Findings related to the sex-differences in memory abilities in early childhood have been inconsistent. Although previous research has demonstrated the effects of the modality of stimulus presentation (auditory versus verbal) and the type of material to be remembered (visual/spatial versus auditory/verbal) on the memory processes and memory organization, the recent research with children is rather limited. The present study is a secondary analysis of data, originally collected from 530 typically developing Turkish children and adolescents. The purpose of the present study was to examine the age-related developments and sex differences in auditory-verbal and visual-spatial short-term memory (STM) in 177 typically developing male and female children, 5 to 8 years of age. Dot-Locations and Word-Lists from the Children's Memory Scale were used to measure visual-spatial and auditory-verbal STM performances, respectively. The findings of the present study suggest age-related differences in both visual-spatial and auditory-verbal STM. Sex-differences were observed only in one visual-spatial STM subtest performance. Modality comparisons revealed age- and task-related differences between auditory-verbal and visual-spatial STM performances. There were no sex-related effects in terms of modality specific performances. Overall, the results of this study provide evidence of STM development in early childhood, and these effects were mostly independent of sex and the modality of the task.

Optimizing Computational Frameworks to Study the Influence of the Protein Environment on the Individual Site Energies of Chromophores in Photosystem II of Photosynthesis

Photosynthesis is a process in which electromagnetic radiation is converted into chemical energy. Photosystems capture photons with chromophores and transfer their energy to reaction centers using chromophores as a medium. In the reaction center, the excitation energy is used to perform chemical reactions. Knowledge of chromophore site energies is crucial to the understanding of excitation energy transfer pathways in photosystems and the ability to compute the site energies in a fast and accurate manner is mandatory for investigating how protein dynamics ef-fect the site energies and ultimately energy pathways with time. In this work we developed two software frameworks designed to optimize the calculations of chro-mophore site energies within a protein environment. The first is for performing quantum mechanical energy optimizations on molecules and the second is for com-puting site energies of chromophores in a fast and accurate manner using the polar-izability embedding method. The two frameworks allow for the fast and accurate calculation of chromophore site energies within proteins, ultimately allowing for the effect of protein dynamics on energy pathways to be studied. We use these frame-works to compute the site energies of the eight chromophores in the reaction center of photosystem II (PSII) using a 1.9 Å resolution x-ray structure of photosystem II. We compare our results to conflicting experimental data obtained from both isolat-ed intact PSII core preparations and the minimal reaction center preparation of PSII, and find our work more supportive of the former.