▁a ▁" medium ▁to ▁large " ▁evidence ▁base . ▁ ▁A ▁variety ▁of ▁measures ▁of ▁student ▁achiev ement ▁and ▁learning ▁including ▁state - m and ated ▁standard ized ▁tests , ▁research - based ▁interview ▁protocol s , ▁items ▁from ▁research ▁studies ▁published ▁in ▁peer - review ed ▁journ als ▁and ▁spe cially ▁constructed ▁paper - and - pen cil ▁tests ▁have ▁been ▁used ▁to ▁evaluate ▁the ▁effect iveness ▁of ▁Investig ations ▁ ▁Research ▁featured ▁at ▁the ▁T ER C ▁website ▁states ▁that ▁students ▁who ▁use ▁Investig ations , ▁among ▁other ▁things , ▁' do ▁as ▁well ▁or ▁better ▁than ▁students ▁using ▁other ▁curr ic ula .' ▁To ▁support ▁the ▁assertion ▁that ▁children ▁do ▁better ▁when ▁they ▁are ▁not ▁taught ▁traditional ▁arithmetic , ▁Anne ▁Good row , ▁in ▁her ▁Ph D ▁th esis ▁at ▁Tu ft s ▁University , ▁compared ▁sub tra ction ▁strateg ies ▁of ▁students ▁taught ▁traditional ▁methods ▁with ▁those ▁who ▁used ▁construct iv ist ▁methods ▁with ▁Investig ations ▁curr icul um . ▁Although ▁negative ▁numbers ▁are ▁not ▁taught ▁in ▁the ▁ 2 nd ▁grade , ▁" construct iv ist " ▁student ▁subtract ing ▁ 9 ▁from ▁ 2 8 ▁explains ▁that ▁" 8 ▁minus ▁ 9 ▁equals ▁negative ▁ 1 " ▁and ▁then ▁arg ues ▁that ▁"- 1 ▁plus ▁ 2 0 ▁is ▁the ▁same ▁as ▁ 2 0 - 1 ▁and ▁equals ▁ 1 9 ." ▁On ▁the ▁basis ▁of ▁this , ▁and ▁of ▁the ▁average ▁score ▁of ▁this ▁group ▁of ▁ 1 0 ▁students , ▁the ▁author ▁concluded ▁that