Energy-interaction diagrams: Fostering resources for productive disciplinary engagement with energy

The integrated values of the electron population, electron energy, nucleuselectron potential energy interaction, dipole moment and volume of the oxygen atoms, and the main properties of the OC bond critical points, were determined by employing the theory of atoms in molecules and 6-31++G**//6-31G* wave functions for a series of 25 unbranched alkyl monoethers. These results were used to assess the degree of approximate transferability of the oxygen atom along this series in terms of the particular alkyl radicals bonded to it. It has been found that a set of six different oxygen atoms is necessary to classify all the computed values. It can be established that the oxygen atoms bonded to propyl and larger radicals can be treated, in practice, as a transferable fragment, while those bonded to at least one smaller radical are specific. Though the total HF energy and the available experimental heats of formation are well fitted by a traditional additivity scheme that distinguishes only among O, CH2, and CH3 units, it has been found that the energy properties are influenced by the size of the molecule.Key words: transferability, AIM theory, ethers.

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Bridging powerful knowledge and lived experience: Challenges in teaching mathematics through COVID-19

Pythagoras ◽

10.4102/pythagoras.v42i1.593 ◽

2021 ◽

Vol 42 (1) ◽

Author(s):

Karin Brodie ◽

Deepa Gopal ◽

Julian Moodliar ◽

Takalani Siala

Keyword(s):

Lived Experience ◽

Mathematical Knowledge ◽

Teacher Practices ◽

School Experiences ◽

Task Design ◽

Teaching Mathematics ◽

Disciplinary Knowledge ◽

Productive Disciplinary Engagement ◽

Powerful Knowledge ◽

Out Of School

The coronavirus disease 2019 (COVID-19) pandemic supported an investigation of ongoing challenges as to whether and how to make mathematics relevant to learners’ lifeworlds. Given that COVID-19 created major disruptions in all learners’ lives, we developed and taught tasks that attempted to make links between their experiences of the pandemic and disciplinary mathematical knowledge. We located our investigation in current debates about the extent to which disciplinary knowledge can be linked to learners’ out-of-school experiences. We developed and analysed two tasks about COVID-19 that could support link-making and productive disciplinary engagement, and analysed one Grade 10 teacher teaching these tasks. We found that linking mathematics to learners’ lifeworlds is both possible and extremely difficult in relation to task design and how the teacher mediates the tasks. In relation to task design, we argue that teachers cannot do it alone; they need to be supported by the curriculum and textbooks. In relation to mediation, we saw that teacher practices are difficult to shift, even in the best of circumstances. We articulate the complexities and nuances involved in bridging powerful knowledge and lived experience and thus contribute to debates on how to teach powerful knowledge in relation to learners’ lifeworlds.

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