Students are significantly worse at translating two-step algebra story problems than matched one-step problems, implicating a hidden integrative knowledge component¶

Claim · All claims
Evidence · 1 study · theoretical r2 · q2
Currency · newest study 2010 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q2 i? Students were significantly worse at translating two-step algebra story problems (like 800-40x) than closely matched one-step problems, and instruction targeting the hypothesized integrative KC improved performance. → Kenneth R. Koedinger 2010

Evidence¶

Kenneth R. Koedinger 2010¶

Kenneth R. Koedinger, Albert T. Corbett, Charles Perfetti. (2010). The Knowledge-Learning-Instruction (KLI) Framework: Toward Bridging the Science-Practice Chasm to Enhance Robust Student Learning. Carnegie Mellon University Technical Report. http://learnlab.org/research/wiki

q2 · i? · theoretical · r2

The article reports, citing Heffernan and Koedinger (1997), a performance difference between two-step and matched one-step algebra translation tasks, attributed to a missing integrative KC (an algebra grammar rule for composing expressions). It adds that instruction targeting this hidden KC 'significantly improved student performance' (Koedinger & McLaughlin, in press).

"Heffernan and Koedinger (1997) found students were significantly worse at translating two-step algebra story problems into expressions (like 800-40x) than they were at translating two closely matched one-step problems"

Discussion¶

Related Claims¶

• Simpler knowledge components are executed faster: correct application times rise from about 3-6 seconds for constant-constant KCs to 10-14 seconds for variable-variable KCs
• KLI complexity-matching hypothesis: instructional principles of a given complexity are effective for knowledge components of equal or greater complexity but not less complex ones
• Personalizing algebra story problems to student interests improved accuracy on easy knowledge components within the tutoring unit — related
• Personalization to student interests improved accuracy on hard knowledge components involving algebraic expression-writing within the tutoring unit — related
• In a small subgroup of struggling students (n = 25), interest personalization greatly improved expression-writing accuracy within the tutoring unit — related
• Personalization reduced time spent on hard expression-writing steps, and students who had received it were still faster at writing expressions in a later non-personalized unit — related
• An IES practice-guide presentation recommends personalized problem contexts, asserting without cited studies that students engage more actively and perform better in them — related