Policy and Complex Systems
Research Methodology
Through the mixed-methods design
the researchers studied interactions of eighth-grade charter school mathematics classrooms and impact on student achievement , from a complexity context perspective . The approach was used to capture simple , complicated , complex , and chaotic systems in classrooms . The multiphase approach , which incorporated a complexity conceptual frame , guided data collection strategies and analyses . Also the complexity context allowed for comprehensive integration of approaches , theories , data , methodologies , and analyses , facilitating an emergent synergy from all the phases . Investigating the deeper levels of complexity of the research phenomena ’ s comprehensive whole necessitated interrelated and sequential steps . First , the results from Phase 1 of the CES qualitative survey and classroom CLASS observations of behavioral markers , that impact achievement , set up Phase 2 of data collection for quantitative regression analysis . The results from Phases 1 and 2 set up the data collection for Phase 3 , a network analysis . The results from Phases 1 , 2 , and 3 set up the data collection for a data-driven , predictive ABM . The results from Phases 1 , 2 , 3 , and 4 set up the data collected for the overall analysis . Figure 1 provides an overview of the data sources , outputs , and analyses .
Summary of Results
Phase I results . The results of Phase I are measures of central tendency . For the 16 classrooms from the four schools , the 2014-2015 achievement score mode was 4 and the mean score was 3.25 . This average score represented a 91 % increase since the common core was initiated in 2013-2014 ( n = 271 ). The intervention classrooms scored , 22 %, on average , higher than the other classes on CES Teacher Support and scored , 12 %, on average , higher than nontreatment classes on CES Teacher Control .
Phase II results . The results of Phase II of the statistical regression analyses formed two models . The first model ran first-semester math grades as the primary independent variable against achievement scores for 2014-2015 , the dependent variable of . Neither the firstsemester math grades nor the treatment variable of Teacher Support measured significant . Teacher Control was significant in the model , suggesting that the more control a teacher exercises in the classroom the higher students will perform on achievement tests . The next model was run with second-semester math grades as the primary independent variable . The second model suggested that second-semester math grades were significant at the . 001 level ( p < . 001 ) and Teacher Control was significant at the . 05 level ( p < . 05 ). Teacher Support did not show statistical significance . The second model had an Adjusted R Square of . 33 ( R ² = . 33 ). Thereby , 33 % of the variance in 2014-2015 achievement scores was explained by second-semester math grades , while controlling for gender , race , and CES classroom dimensions ( Johnson , 2016 ).
Phase III results . Phase III provided network analyses . Classroom interaction patterns of classrooms were translated into network graphs to capture dynamism and temporal sequences of classroom interaction networks over half hour observation sessions . Figure 2 illustrates three novel approaches for capturing classroom structures of network of interactions :
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