{"id":"W1976279193","doi":"10.1007/s10649-011-9330-5","title":"The inverse relation between multiplication and division: Concepts, procedures, and a cognitive framework","year":2011,"lang":"en","type":"article","venue":"Educational Studies in Mathematics","topic":"Cognitive and developmental aspects of mathematical skills","field":"Mathematics","cited_by":41,"is_retracted":false,"has_abstract":false,"ca_institutions":"Carleton University; University of Regina","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Multiplication (music); Division (mathematics); Subtraction; Relation (database); Inverse; Arithmetic; Associative property; Cognition; Mathematics; Computer science; Algebra over a field; Theoretical computer science; Mathematics education; Psychology; Pure mathematics; Data mining","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00241509,0.0003493308,0.0002456705,0.001744446,0.0007944847,0.004188339,0.000995497,0.0008260167,0.003578192],"category_scores_gemma":[0.008570197,0.0002592989,0.0004146235,0.001638051,0.01458383,0.008231476,0.001471311,0.002025255,0.0003377549],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001099713,"about_ca_system_score_gemma":0.001860822,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002890796,"about_ca_topic_score_gemma":0.002051521,"domain_scores_codex":[0.9988262,0.0006536037,0.00006936219,0.0001794904,0.0002184268,0.00005289762],"domain_scores_gemma":[0.9942982,0.004425333,0.0003938896,0.0003652211,0.0003843817,0.0001330567],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"qualitative","study_design_scores_codex":[0.00001680756,0.0000153108,0.0005288243,0.00004542253,0.000004579942,0.00002248081,0.001386161,0.000513117,0.000238867,0.9826992,0.0002530256,0.01427628],"study_design_scores_gemma":[0.000005739449,0.000007957628,0.001025031,0.00002929094,0.000004641936,0.00006122651,0.0003424287,0.0007315037,0.0001824304,0.9930305,0.004572492,0.000006851516],"study_design_candidate":"qualitative","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2754309,0.02938713,0.3625194,0.01644706,0.0005539313,0.00007557107,0.0002269035,0.0002056757,0.3151534],"genre_scores_gemma":[0.9389126,0.003632658,0.0529872,0.0003728019,0.0001696181,0.00007919732,0.00007755544,0.00003373518,0.003734763],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004188339,"threshold_uncertainty_score":0.01277238,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1106191069231166,"score_gpt":0.3941360993612052,"score_spread":0.2835169924380886,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}