• Journal of the Korean School Mathematics Society
• /
• v.8 no.3
• /
• pp.367-382
• /
• 2005

In this paper, we deal with various contents relating to the group concept in school mathematics and teaching of algebraic structures indirectly by combining these contents. First, we consider structure of knowledge based on Bruner, and apply these discussions to the teaching of algebraic structure in school algebra. As a result of these analysis, we can verify that the essence of algebraic structure is group concept. So we investigate the previous researches about group concept: Piaget, Freudenthal, Dubinsky. In our school, the contents relating to the group concept have been taught from elementary level indirectly. Tn elementary school, the commutative law and associative law is implicitly taught in the number contexts. And in middle school, various linear equations are taught by the properties of equality which include group concept. But these algebraic contents is not related to the high school. Though we deal with identity and inverse in the binary operations in high school mathematics, we don't relate this algebraic topics with the previous learned contents. In this paper, we discussed algebraic structure focusing to the group concept to obtain a connectivity among school algebra. In conclusion, the group concept can take role in relating these algebraic contents and teaching the algebraic structures in school algebra.

• Journal of the Korean Chemical Society
• /
• v.32 no.5
• /
• pp.436-442
• /
• 1988

The $^1H-nmr$ lineshapes of $H_2O$ in the solution containing $Al^{3+}$ ion have been measured as a function of temperature and $H^+$-ion concentration. Above [$H^+$] = 0.06, the lineshape were analyzed by the uncoupled two-site exchange model. From the proton exchange rate between hexaaquaaluminium ion and bulk water as a function of H-ion concentration. These kinetic data could be fitted to a following linear rate law; that is; 1/${\tau}$ = k$_1$/12 + $k_2$[$H^+$]/6. The following proton exchange parameters were obtained; $k_1^{298}$ = 38.5s$^{-1}$ ${\{Delta}H_1^{\neq}$ = $42.9kJ mole^{-1}$ ${\{Delta}S_1^{\neq}$ = -48.6J $mole^{-1}K^{-1}$ $k_2^{298}$ = $172s^{-1}mole^{-1}$ ${\{Delta}H_2^{\neq}$ = 27.8kJ $mole^{-1}$ ${\{Delta}S_2^{\neq}$ = -90.3J $mole^{-1}K^{-1}$ These activation parameters are indicating an associative interchange, Ia, mechanism for the acid-hydrolysis of hexaaquaaluminium ion and the proton exchange between the hydration spheres of $Al^{3+}$ and $H^+$.