title: Probability from a socio-cultural perspective

authors: Sharma, Sashi

abstract: There exists considerable and rich literature on students’ misconceptions about probability; less attention has been paid to the development of students’ probabilistic thinking in the classroom. Grounded in an analysis of the literature, this article offers a lesson sequence for developing students’ probabilistic understanding. In particular, a context familiar to teachers—exploring compound events that occur in a game of chance—is presented, and it is demonstrated how the context can be used to explore the relationship between experimental and theoretical probabilities in a classroom setting. The approach integrates both the content and the language of probability and is grounded in socio-cultural theory.

text: Probability from a socio-cultural perspective There exists considerable and rich literature on students’ misconceptions about probability; less attention has been paid to the development of students’ probabilistic thinking in the classroom. Grounded in an analysis of the literature, this article offers a lesson sequence for developing students’ probabilistic understanding. In particular, a context familiar to teachers—exploring compound events that occur in a game of chance—is presented, and it is demonstrated how the context can be used to explore the relationship between experimental and theoretical probabilities in a classroom setting. The approach integrates both the content and the language of probability and is grounded in socio-cultural theory.

year: 2016

title: Synthesis and characterisation of novel ferrocenyl compounds

authors: Alley, Steven R.

abstract: The ferrocenyl phosphonate mono-ester FcCH₂P(O)(OPh)OH 1 (Fc = ferrocenyl) was prepared from FcCH₂P(O)(OPh)₂. The related mono-ester FcCH₂P(O)(OEt)OH 2 was prepared by the reaction of FcCH₂NMe₃I with diethyl phosphite. The ferrocenyl phosphonic acids FcP(O)(OH)₂ 3, FcCH₂P(O)(OH)₂ 4, FcCH₂CH₂P(O)(OH)₂ 5, 1,1'-Fc' [P(O)(OH)₂]₂ 6 and 1,1'-Fc'[CH₂P(O)(OH)₂]₂ 7 were synthesised by hydrolysis of the corresponding phosphonate esters. X-ray crystal structure determinations were carried out for compounds 4 and 7. The ferrocenyl phenylphosphonate esters FcP(O)(OPh)₂ 8 and 1,1'-Fc'[P(O)(OPh)₂]₂ 9 were also synthesised and characterised. The ferrocenyl arsonic acid FcCH₂CH₂AѕP(O)(OH)₂ 10 was prepared by the reaction of FcCH₂CH₂Br with Na₃AѕO₃. The behaviour of 10 and the arsenic acids PhAѕ(O)(OH)₂, 2-NH₂-(C₆H₄)Aѕ(O)(OH)₂ and Me₂Aѕ(O)(OH) in negative ion ESMS was investigated in some depth. The carbon-arsenic bond in these compounds was found to cleave at moderate cone voltages.

The bis(triphenylphosphine)platinum complexes (Ph₃P)₂PtO₃PR (R = Fc 11,CH2Fc 12, CH₂CH₂Fc 13) and 1,1'-Fc'[PO₃Pt(PPh₃)₂]₂ 14 were prepared and characterised. Single crystal structural determination of these compounds showed the expected chelation of the ferrocenyl phosphonate ligand to the platinum centre.

The reduction of various ferrocenyl ethylphosphonate esters gave the known primary ferrocenyl phosphines FcCH₂PH₂ 15, FcPH₂ 16, and 1,1'-Fc'[PH₂]₂ 17 in high yield. In addition the novel ferrocenyl phosphines FcCH₂CH₂PH₂ 18, 1,1'-Fc'[CH₂PH₂]₂ 19, 1,2'-Fc'[CH₂PH₂]₂ 20 and the ferrocenyl arsine FcCH₂CH₂AѕH₂ 25 were prepared and characterised. The X-ray crystal structure determination was carried out for 25. This is one of the few structures known for primary arsine compounds. The crystal structure of 18 was found to be isomorphous with that of 25. The stability of phosphines 15-20 toward air oxidation was investigated using ³¹P nmr. The phosphines 18, 19 and 20 were found to be remarkably stable in air. The stability of 25 toward oxidation in air was investigated using elemental analysis. The arsine showed appreciable stability in air despite the sterically unencumbered nature of the arsine group.

Reaction of 19 and 20 with (Pip)Mo(CO)₄ (Pip = Piperidine) and (thf)Mo(CO)₅ resulted in the complexes, 1,2'-Fc'[CH₂PH₂]₂Mo(CO)₄ 21, 1,1'Fc'[CH₂PH₂]₂Mo(CO)₄ 22, 1,1'-Fc'[CH₂PH₂Mo(CO)₅]₂ 23, and 1,2'-Fc'[CH₂PH₂Mo(CO)₅]₂ 24 which were routinely characterised. A by-product of the synthesis of 22 was the larger oligomer [1,1'-Fc'[CH₂PH₂]₂Mo(CO)₄]₂ 22a which was identified by ESMS.

The chemical oxidation of 15 was undertaken using H₂O₂ and monitored by ³¹P nmr. Oxidation of the phosphine to phosphine oxide and phosphinic acid products was observed. Excess oxidant led to the oxidation of the ferrocene group and decomposition of the sample. The compounds FcCH₂P(O)H₂ 26 and FcCH₂P(O)(OH)H 27 were prepared and characterised by nmr and ESMS.

The ferrocenyl hydroxymethyl phosphines FcP(CH₂OH)₂ 28 and 1,1'-Fc'[P(CH₂OH)₂]₂ 29 were prepared by the reaction of 16 and 17 with formaldehyde. The crystal structure of 28 was determined and compared with that of the known compound ferrocenyl hydroxymethyl phosphine FcCH₂P(CH₂OH)₂.

The hydroxymethyl phosphine chalcogenides FcP(O)(CH₂OH)₂ 30, FcP(S)(CH₂OH)₂ 31 and FcP(Se)(CH₂OH)₂ 32 were prepared and fully characterised. The crystal structures of 30 and 31 were determined from single crystal X-ray data. The structure of 32 was found to be isomorphous with that of 31. Hydrogen bonding networks in the structures of 30 and 31 were compared to each other and to other analogous compounds. The hydroxymethyl phosphine chalcogenides 1,1'-Fc'[P(O)(CH₂OH)₂]₂ 33, 1,1'-Fc'[P(S)(CH₂OH)₂]₂ 34 and 1,1'-Fc'[P(Se)(CH₂OH)₂]₂ 35 were also prepared and characterised.

The platinum complex [FcP(CH₂OH)₂]₂PtCl₂ 36 was synthesised by the reaction of 28 and (COD)PtCl₂. Reaction of 29 with (COD)MCl₂ (M = Pt and Pd) gave the analogous metal complexes, 1,1'-Fc'[P(CH₂OH)₂]₂MCl₂ which were unable to be fully characterised. The platinum and palladium complexes of ferrocenyl hydroxymethylphosphines were found to form [M+Cl⁻]⁻ ions under ESMS conditions.

text: Synthesis and characterisation of novel ferrocenyl compounds The ferrocenyl phosphonate mono-ester FcCH₂P(O)(OPh)OH 1 (Fc = ferrocenyl) was prepared from FcCH₂P(O)(OPh)₂. The related mono-ester FcCH₂P(O)(OEt)OH 2 was prepared by the reaction of FcCH₂NMe₃I with diethyl phosphite. The ferrocenyl phosphonic acids FcP(O)(OH)₂ 3, FcCH₂P(O)(OH)₂ 4, FcCH₂CH₂P(O)(OH)₂ 5, 1,1'-Fc' [P(O)(OH)₂]₂ 6 and 1,1'-Fc'[CH₂P(O)(OH)₂]₂ 7 were synthesised by hydrolysis of the corresponding phosphonate esters. X-ray crystal structure determinations were carried out for compounds 4 and 7. The ferrocenyl phenylphosphonate esters FcP(O)(OPh)₂ 8 and 1,1'-Fc'[P(O)(OPh)₂]₂ 9 were also synthesised and characterised. The ferrocenyl arsonic acid FcCH₂CH₂AѕP(O)(OH)₂ 10 was prepared by the reaction of FcCH₂CH₂Br with Na₃AѕO₃. The behaviour of 10 and the arsenic acids PhAѕ(O)(OH)₂, 2-NH₂-(C₆H₄)Aѕ(O)(OH)₂ and Me₂Aѕ(O)(OH) in negative ion ESMS was investigated in some depth. The carbon-arsenic bond in these compounds was found to cleave at moderate cone voltages.

The bis(triphenylphosphine)platinum complexes (Ph₃P)₂PtO₃PR (R = Fc 11,CH2Fc 12, CH₂CH₂Fc 13) and 1,1'-Fc'[PO₃Pt(PPh₃)₂]₂ 14 were prepared and characterised. Single crystal structural determination of these compounds showed the expected chelation of the ferrocenyl phosphonate ligand to the platinum centre.

The reduction of various ferrocenyl ethylphosphonate esters gave the known primary ferrocenyl phosphines FcCH₂PH₂ 15, FcPH₂ 16, and 1,1'-Fc'[PH₂]₂ 17 in high yield. In addition the novel ferrocenyl phosphines FcCH₂CH₂PH₂ 18, 1,1'-Fc'[CH₂PH₂]₂ 19, 1,2'-Fc'[CH₂PH₂]₂ 20 and the ferrocenyl arsine FcCH₂CH₂AѕH₂ 25 were prepared and characterised. The X-ray crystal structure determination was carried out for 25. This is one of the few structures known for primary arsine compounds. The crystal structure of 18 was found to be isomorphous with that of 25. The stability of phosphines 15-20 toward air oxidation was investigated using ³¹P nmr. The phosphines 18, 19 and 20 were found to be remarkably stable in air. The stability of 25 toward oxidation in air was investigated using elemental analysis. The arsine showed appreciable stability in air despite the sterically unencumbered nature of the arsine group.

Reaction of 19 and 20 with (Pip)Mo(CO)₄ (Pip = Piperidine) and (thf)Mo(CO)₅ resulted in the complexes, 1,2'-Fc'[CH₂PH₂]₂Mo(CO)₄ 21, 1,1'Fc'[CH₂PH₂]₂Mo(CO)₄ 22, 1,1'-Fc'[CH₂PH₂Mo(CO)₅]₂ 23, and 1,2'-Fc'[CH₂PH₂Mo(CO)₅]₂ 24 which were routinely characterised. A by-product of the synthesis of 22 was the larger oligomer [1,1'-Fc'[CH₂PH₂]₂Mo(CO)₄]₂ 22a which was identified by ESMS.

The chemical oxidation of 15 was undertaken using H₂O₂ and monitored by ³¹P nmr. Oxidation of the phosphine to phosphine oxide and phosphinic acid products was observed. Excess oxidant led to the oxidation of the ferrocene group and decomposition of the sample. The compounds FcCH₂P(O)H₂ 26 and FcCH₂P(O)(OH)H 27 were prepared and characterised by nmr and ESMS.

The ferrocenyl hydroxymethyl phosphines FcP(CH₂OH)₂ 28 and 1,1'-Fc'[P(CH₂OH)₂]₂ 29 were prepared by the reaction of 16 and 17 with formaldehyde. The crystal structure of 28 was determined and compared with that of the known compound ferrocenyl hydroxymethyl phosphine FcCH₂P(CH₂OH)₂.

The hydroxymethyl phosphine chalcogenides FcP(O)(CH₂OH)₂ 30, FcP(S)(CH₂OH)₂ 31 and FcP(Se)(CH₂OH)₂ 32 were prepared and fully characterised. The crystal structures of 30 and 31 were determined from single crystal X-ray data. The structure of 32 was found to be isomorphous with that of 31. Hydrogen bonding networks in the structures of 30 and 31 were compared to each other and to other analogous compounds. The hydroxymethyl phosphine chalcogenides 1,1'-Fc'[P(O)(CH₂OH)₂]₂ 33, 1,1'-Fc'[P(S)(CH₂OH)₂]₂ 34 and 1,1'-Fc'[P(Se)(CH₂OH)₂]₂ 35 were also prepared and characterised.

The platinum complex [FcP(CH₂OH)₂]₂PtCl₂ 36 was synthesised by the reaction of 28 and (COD)PtCl₂. Reaction of 29 with (COD)MCl₂ (M = Pt and Pd) gave the analogous metal complexes, 1,1'-Fc'[P(CH₂OH)₂]₂MCl₂ which were unable to be fully characterised. The platinum and palladium complexes of ferrocenyl hydroxymethylphosphines were found to form [M+Cl⁻]⁻ ions under ESMS conditions.

year: 2001

title: Testing a suicidal ideation-to-action framework among Queer and Takatāpui people in Aotearoa New Zealand: An examination of the three-step theory

authors: Schimanski, Irie

abstract: The three-step theory (3ST) of suicide is well-established in the general population and shows promise for explaining suicidal ideation among Queer samples. This study examined the applicability of the 3ST using data from 250 Queer (n = 213) and Takatāpui (n = 37) people aged 18-74 living in Aotearoa New Zealand. The analytic approach entailed hierarchical multiple regression, ANOVA, t-tests, and logistic regression. Step-one was partially supported, with discrimination and hopelessness independently associated with suicidal ideation, but not their interaction. Step-two was fully supported, showing social support associated with lower suicidal ideation when social support exceeded discrimination, compared with the inverse. Full support for step-three was observed, finding higher self-harm among participants with histories of attempted suicide than those who had never attempted. An adapted version of the 3ST for Queer and Takatāpui people is presented, offering novel approaches to testing the ideation-to-action framework with these communities.

text: Testing a suicidal ideation-to-action framework among Queer and Takatāpui people in Aotearoa New Zealand: An examination of the three-step theory The three-step theory (3ST) of suicide is well-established in the general population and shows promise for explaining suicidal ideation among Queer samples. This study examined the applicability of the 3ST using data from 250 Queer (n = 213) and Takatāpui (n = 37) people aged 18-74 living in Aotearoa New Zealand. The analytic approach entailed hierarchical multiple regression, ANOVA, t-tests, and logistic regression. Step-one was partially supported, with discrimination and hopelessness independently associated with suicidal ideation, but not their interaction. Step-two was fully supported, showing social support associated with lower suicidal ideation when social support exceeded discrimination, compared with the inverse. Full support for step-three was observed, finding higher self-harm among participants with histories of attempted suicide than those who had never attempted. An adapted version of the 3ST for Queer and Takatāpui people is presented, offering novel approaches to testing the ideation-to-action framework with these communities.

year: 2025-08-01