Teaching and aligning upper level mathematics classes to Michigan high school content expectations in an alternative education setting : approaches and issues

After teaching regular education secondary mathematics for seven years, I accepted a position in an alternative education high school. Over the next four years, the State of Michigan adopted new graduation requirements phasing in a mandate for all students to complete Geometry and Algebra 2 courses. Since many of my students were already struggling in Algebra 1, getting them through Geometry and Algebra 2 seemed like a daunting task. To better instruct my students, I wanted to know how other teachers in similar situations were addressing the new High School Content Expectations (HSCEs) in upper level mathematics. This study examines how thoroughly alternative education teachers in Michigan are addressing the HSCEs in their courses, what approaches they have found most effective, and what issues are preventing teachers and schools from successfully implementing the HSCEs. Twenty-six alternative high school educators completed an online survey that included a variety of questions regarding school characteristics, curriculum alignment, implementation approaches and issues. Follow-up phone interviews were conducted with four of these participants. The survey responses were used to categorize schools as successful, unsuccessful, and neutral schools in terms of meeting the HSCEs. Responses from schools in each category were compared to identify common approaches and issues among them and to identify significant differences between school groups. Data analysis showed that successful schools taught more of the HSCEs through a variety of instructional approaches, with an emphasis on varying the ways students learned the material. Individualized instruction was frequently mentioned by successful schools and was strikingly absent from unsuccessful school responses. The main obstacle to successful implementation of the HSCEs identified in the study was gaps in student knowledge. This caused pace of instruction to also be a significant issue. School representatives were fairly united against the belief that the Algebra 2 graduation requirement was appropriate for all alternative education students. Possible implications of these findings are discussed.

PARTITIONING THE BLOCKS OF A STEINER TRIPLE SYSTEM INTO PARTIAL PARALLEL CLASSES

Does there exist a Steiner Triple System on v points, whose blocks can be partitioned into partial parallel classes of size m, where m ≤ [v⁄3], m | b and b is the number of blocks of the STS(v)? We give the answer for 9 ≤ v ≤ 43. We also show that whenever 2|b, v ≡ 3 (mod 6) we can find an STS(v) whose blocks can be partitioned into partial parallel classes of size 2, and whenever 4|b , v ≡ 3 (mod 6), there exists an STS(v) whose blocks can be partitioned into partial parallel classes of size 4.

Depressive symptoms from kindergarten to early school age: longitudinal associations with social skills deficits and peer victimization

BACKGROUND: Depressive symptoms in children are associated with social skills deficits and problems with peers. We propose a model which suggests different mechanisms for the impact of deficits in self-oriented social skills (assertiveness and social participation) and other-oriented social skills (pro-social, cooperative and non-aggressive behaviors) on children's depressive symptoms. We hypothesized that deficits in self-oriented social skills have a direct impact on children's depressive symptoms because these children have non-rewarding interactions with peers, whereas the impact of deficits in other-oriented social skills on depressive symptoms is mediated through negative reactions from peers such as peer victimization. METHOD: 378 kindergarten children (163 girls) participated at two assessments (Age at T1: M = 5.8, T2: M = 7.4). Teachers completed questionnaires on children's social skills at T1. Teacher reports on peer victimization and depressive symptoms were assessed at both assessment points. RESULTS: Our study partially confirmed the suggested conceptual model. Deficits in self-oriented social skills significantly predicted depressive symptoms, whereas deficits in other-oriented social skills were more strongly associated with peer victimization. Longitudinal associations between other-oriented social skills and depressive symptoms were mediated through peer victimization. CONCLUSION: The study emphasizes the role of deficits in self-oriented social skills and peer victimization for the development of internalizing disorders.

Peer victimisation and depressive symptoms: can specific coping strategies buffer the negative impact of cybervictimisation?

This longitudinal study investigated whether cybervictimisation is an additional risk factor for depressive symptoms over and beyond traditional victimisation in adolescents. Furthermore, it explored whether certain coping strategies moderate the impact of cybervictimisation on depressive symptoms. A total of 765 Swiss seventh graders (mean age at time-point 1 (t1) = 13.18 years) reported on the frequency of traditional and cybervictimisation, and of depressive symptoms twice in six months. At time-point 2 (t2) students also completed a questionnaire on coping strategies in response to a hypothetical cyberbullying scenario. Analyses showed that both traditional and cybervictimisation were associated with higher levels of depressive symptoms. Cybervictimisation also predicted increases in depressive symptoms over time. Regarding coping strategies, it was found that helpless reactions were positively associated with depressive symptoms. Moreover, support seeking from peers and family showed a significant buffering effect: cybervictims who recommended seeking close support showed lower levels of depressive symptoms at t2. In contrast, cybervictims recommending assertive coping strategies showed higher levels of depressive symptoms at t2.

MountainNotes Becomes MountainAgenda: MRD's Third Peer-reviewed Section

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