Making connections: Compartmentalization in pre -calculus students\u27 understanding of functions

Students develop knowledge constructs that they build into concepts through their experiences. Students demonstrate compartmentalization when they understand a construct or concept within one representation, but not another, or when they do not connect mathematically related ideas. For instance, a student may understand f(x) to mean plug x into the function within a symbolic representation, but the same student may understand f(x) to mean f times x within a tabular representation. A student with these understandings has a compartmentalized understanding of function notation. A two-month study was conducted with a class of pre-calculus students enrolled in a parochial high school. The class was observed and a subset of students (n = 7) were given a series of tasks in an interview setting in order to determine their understanding of functions and in particular periodicity within the three representations: equations, graphs, and tables. The researcher studied compartmentalization in the students\u27 understanding. Three of the seven students showed compartmentalization. All three had a compartmentalized understanding of function notation within the tabular representation. In addition, two had compartmentalization within representations in their understanding of periodicity. Students with compartmentalization in their understanding, had the greatest difficulty in solving the interview tasks. Furthermore, those students who could not translate between representations had an automatic compartmentalization in their understanding and lacked flexibility in problem-solving. All seven of the students preferred the symbolic representation. The students used this representation overwhelmingly in their classwork and homework. Six of the seven students attempted to find equations for the functions in the interview tasks before trying any other solution strategy. However, only one student was able to solve the interview tasks in this representation. Some interesting conceptions of periodicity emerged in the students\u27 understandings. The students used symmetry, familiarity, and continuity to determine whether a function was periodic. The students did not work from a conventional definition of period. Instead, they constructed their own definition of periodicity by generalizing sinusoids and other familiar functions. The generalizations that the students made were often inconsistent with the conventional definitions. These unconventional understandings imply that they need experiences with more than just sinusoids

Organics - PDMS interactions : a phase equilibrium study

The vapour-liquid equilibrium of 80 organics in Polydimethylsiloxane (PDMS) were predicted using the UNIFAC Lynby, Larsen et al., 1987 [1]. The organics were selected from 8 family functional groups namely cycloalkanes, aldehydes, alcohols, carboxylic acids, esters, ethers, thiols and amines. PDMS showed great absorption affinity for all organics in particular carboxylic acids and ethers

Increased Optical Damage Resistance In Lithium Niobate

We have confirmed greatly improved resistance to photorefractive damage in compositions of lithium niobate containing 4.5 at. % MgO or more. Holographic diffraction measurements of photorefraction demonstrated that the improved performance is due to a hundredfold increase in the photoconductivity, rather than a decrease in the Glass current. The diffraction efficiency shows an Arrhenius dependence on temperature, with an activation energy of 0.1 eV for the damage-resistant compositions, compared with 0.5 eV for undoped or low-magnesium compositions. The damage-resistant compositions are distinguished by a 2.83-μm absorption line instead of the usual 2.87-μm line due to the OH-stretch vibration

Promoting Exercise Performance in Adults with Intellectual Disabilities Through Visual Schedules and Systematic Prompting

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Unravelling the contributions of motor experience and conceptual knowledge in action perception: A training study

Prior knowledge affects how we perceive the world and the sensorimotor system actively guides our perception. An ongoing dispute regards the extent to which prior motor knowledge versus conceptual knowledge modulates the observation of others’ actions. Research indicates that motor experience increases motor activation during action perception. Other research, however, has shown that conceptual familiarity with actions also modulates motor activation, i.e., increased motor activation during observation of unfamiliar, compared to conceptually familiar, actions. To begin to disentangle motor from conceptual contributions to action perception, we uniquely combined motoric and conceptual interventions into one design. We experimentally manipulated participants’ experience with both motoric skills and conceptual knowledge, via motor training of kinematically challenging actions and contextual information about the action, respectively, in a week-long training session. Measurements of the effects on motor activity measured via electroencephalography (EEG) during pre- and post-training action observation were compared. We found distinct, non-interacting effects of both manipulations: Motor training increased motor activation, whereas additional conceptual knowledge decreased motor activation. The findings indicate that both factors influence action perception in a distinct and parallel manner. This research speaks to previously irreconcilable findings and provides novel insights about the distinct roles of motor and conceptual contributions to action perception