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We conducted a comprehensive, systematic review and meta-analysis on the effects of the BSCS 5E Instructional Model—and its related variants—on science, math, and motivation outcomes. The 5E Instructional Model is a framework for delivering STEM instruction that is based on constructivist learning theory; it has been used throughout the U.S. and other countries, particularly in Turkey. Despite its wide usage, no comprehensive systematic review and meta-analysis on the effects of 5E and related models has yet been conducted. Our search and screening procedures yielded 61 randomized controlled trial studies, estimating 156 effect sizes; 70% of studies met WWC standards with or without reservations. We found that the 5E instructional model resulted in improved science outcomes ( g = 0.82, 95% CI [0.67, 0.97]), but a large amount of heterogeneity requires some caution ( t = 0.56). We explored numerous explanations for the effect heterogeneity and provided practical recommendations. 

For a complexity class $$C$$ and language $$L$$, a constructive separation of $$L\notin C$$ gives an efficient algorithm (also called a refuter) to findcounterexamples (bad inputs) for every $$C$$-algorithm attempting to decide $$L$$.We study the questions: Which lower bounds can be made constructive? What arethe consequences of constructive separations? We build a case thatconstructiveness serves as a dividing line between many weak lower bounds weknow how to prove, and strong lower bounds against $$P$$, $ZPP$, and $BPP$. Putanother way, constructiveness is the opposite of a complexity barrier: it is aproperty we want lower bounds to have. Our results fall into three broadcategories. 1. Our first set of results shows that, for many well-known lower boundsagainst streaming algorithms, one-tape Turing machines, and query complexity,as well as lower bounds for the Minimum Circuit Size Problem, making theselower bounds constructive would imply breakthrough separations ranging from$$EXP \neq BPP$$ to even $$P \neq NP$$. 2. Our second set of results shows that for most major open problems in lowerbounds against $$P$$, $ZPP$, and $BPP$, including $$P \neq NP$$, $$P \neq PSPACE$$,$$P \neq PP$$, $$ZPP \neq EXP$$, and $$BPP \neq NEXP$$, any proof of the separationwould further imply a constructive separation. Our results generalize earlierresults for $$P \neq NP$$ [Gutfreund, Shaltiel, and Ta-Shma, CCC 2005] and $$BPP\neq NEXP$$ [Dolev, Fandina and Gutfreund, CIAC 2013]. 3. Our third set of results shows that certain complexity separations cannotbe made constructive. We observe that for all super-polynomially growingfunctions $$t$$, there are no constructive separations for detecting high$$t$$-time Kolmogorov complexity (a task which is known to be not in $$P$$) fromany complexity class, unconditionally.