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.

SO2 emissions at Volcan de Colima, 2003-2007

Volcán de Colima has been continuously erupting since the onset of dome growth in 1998. This period of unrest has had 4 prominent periods; 1998-1999, 2003, 2004-2005, and the current dome growth that began in February of 2007. Each of these episodes was marked by lava extrusion forming a dome and lava flows, followed by explosions that destroyed the dome. The Correlation Spectrometer (COSPEC) was used to determine SO2 emission rates on 164 days from May 2003 to February 2007, using both stationary ground based scans and some flight traverses. Scans were separated into the categories of explosive degassing and passive, or background degassing. These scans show variation in the SO2 flow rate from below detection limit (~3 t/d depending on environmental conditions) during background, passive emissions to a peak of 2949 t/d (34 kilograms/second) during an explosion on 9 October, 2004. Both passive and explosive degassing increased when there was lava extrusion in 2004 and with the increased explosive activity in 2005. These two different processes of degassing wax with each other when activity increases and wane together as well, indicating a parallel cyclicity in the volcanic eruption and degassing rates, where the conduit partially seals (pressurizes) between explosions. Colima’s gas and eruptive behavior is compared to similar systems such as Santiaguito and Soufrière Hills, Montserrat. About 2/3 of Colima’s SO2 degassing, amounting to 1.3 x 105 tonnes in 3.74 yrs has come in short lived small (VEI=0-1) vertical explosions that occurred at the rate of 100-3000explosions/ month, and the remaining third has occured in continuous passive degassing. Colima emits sulfur at a rate equivalent to about 0.04 to 0.08 wt % S, similar to other andesitic convergent plate boundary volcanoes. There has been an explosive destruction of the dome in every cycle for that past 5 years, and it is assumed that the current dome which began growth in February, 2007 (just at the end of this study) will be destroyed. Higher emission rates seen in the quiescence of 2006 may have eased the pressure at the time, resulting in the slow effusion of the current dome and lack of explosivity.