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.

Family business: Multiple members of major phytohormone classes orchestrate plant stress responses

Low-molecular-weight compounds such as jasmonic, abscisic and salicylic acids are commonly thought to be regulators of plant stress responses. However, it is becoming clear that these molecules, often referred to as phytohormones, are only a part of bigger groups of compounds with biological activity. We propose that the concept of "hormone families" may help to better understand plant physiological responses by taking into account not only the alleged main regulators, but also their precursors, conjugates and catabolites. Novel approaches to profile potentially active compounds in plants are discussed.

Classes of multichannel EEG microstates in light and deep hypnotic conditions

The study assessed the brain electric mechanisms of light and deep hypnotic conditions in the framework of EEG temporal microstates. Multichannel EEG of healthy volunteers during initial resting, light hypnosis, deep hypnosis, and eventual recovery was analyzed into temporal EEG microstates of four classes. Microstates are defined by the spatial configuration of their potential distribution maps ([Symbol: see text]potential landscapes') on the head surface. Because different potential landscapes must have been generated by different active neural assemblies, it is reasonable to assume that they also incorporate different brain functions. The observed four microstate classes were very similar to the four standard microstate classes A, B, C, D [Koenig, T. et al. Neuroimage, 2002;16: 41-8] and were labeled correspondingly. We expected a progression of microstate characteristics from initial resting to light to deep hypnosis. But, all three microstate parameters (duration, occurrence/second and %time coverage) yielded values for initial resting and final recovery that were between those of the two hypnotic conditions of light and deep hypnosis. Microstates of the classes B and D showed decreased duration, occurrence/second and %time coverage in deep hypnosis compared to light hypnosis; this was contrary to microstates of classes A and C which showed increased values of all three parameters. Reviewing the available information about microstates in other conditions, the changes from resting to light hypnosis in certain respects are reminiscent of changes to meditation states, and changes to deep hypnosis of those in schizophrenic states.

Adjectives in Thai: Implications for a functionalist typology of word classes

Tai languages are often described as “lacking” a major lexical class “adjectives”; accordingly, they and other area languages are frequently cited as evidence against adjectival universality. This article brings the putative lack under examination, arguing that a more complete distributional analysis reveals a pattern: overlap is highest among semantically peripheral adjectives and verbs and in constructions prototypically associated to both classes crosslinguistically, and lowest among semantically core adjectives and verbs and in constructions prototypically associated to only one or the other class. Rather than “lacking” adjectives, data from Thai thus in fact support functional-typological characterizations of adjectival universality such as those of Givón (1984), Croft (2001), and Dixon (2004). Finally, while data from Thai would fail to falsify an adaptation of Enfield's (2004) Lao lexical class-taxonomy (in which adjectives are treated as a verbal subclass) on its own terms, this article argues that in absence of both universally-applicable criteria for the evaluation of categorial taxonomies crosslinguistically and evidence for the cognitive reality of categorial taxonomies so stipulated, even this more limited sense of a “lack” of adjectives in Thai is less radical a challenge to adjectival universality than has sometimes been supposed.

Applicative theories for logarithmic complexity classes

We present applicative theories of words corresponding to weak, and especially logarithmic, complexity classes. The theories for the logarithmic hierarchy and alternating logarithmic time formalise function algebras with concatenation recursion as main principle. We present two theories for logarithmic space where the first formalises a new two-sorted algebra which is very similar to Cook and Bellantoni's famous two-sorted algebra B for polynomial time [4]. The second theory describes logarithmic space by formalising concatenation- and sharply bounded recursion. All theories contain the predicates WW representing words, and VV representing temporary inaccessible words. They are inspired by Cantini's theories [6] formalising B.

Brief Report: HIV Testing Among Pregnant Women Who Attend Antenatal Care in Malawi.

Malawi adopted the Option B+ strategy in 2011. Its success in reducing mother-to-child transmission depends on coverage and timing of HIV testing. We assessed HIV status ascertainment and its predictors during pregnancy. HIV status ascertainment was 82.3% (95% confidence interval: 80.2 to 85.9) in the pre-Option B+ period and 85.7% (95% confidence interval: 83.4 to 88.0) in the Option B+ period. Higher HIV ascertainment was independently associated with higher age, attending antenatal care more than once, and registration in 2010. The observed high variability of HIV ascertainment between sites (50.6%-97.7%) and over time suggests that HIV test kit shortages and insufficient numbers of staff posed major barriers to reducing mother-to-child transmission.