{"id":"W2064934178","doi":"10.1007/s10649-006-9024-6","title":"Syntax and Meaning as Sensuous, Visual, Historical forms of Algebraic Thinking","year":2006,"lang":"en","type":"article","venue":"Educational Studies in Mathematics","topic":"Mathematics Education and Teaching Techniques","field":"Social Sciences","cited_by":58,"is_retracted":false,"has_abstract":false,"ca_institutions":"Laurentian University","funders":"","keywords":"Semiotics; Syntax; Linguistics; Constitution; Meaning (existential); Abstract algebra; Metalanguage; Natural language; The Symbolic; Natural (archaeology); Algebraic expression; Computer science; Algebra over a field; Algebraic number; Mathematics; Epistemology; Psychology; Pure mathematics; Philosophy; History","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001275206,0.0001075447,0.0002526299,0.0001423078,0.0003554907,0.00002864175,0.0001501091,0.00005847274,0.00006207894],"category_scores_gemma":[0.00173966,0.0000977067,0.00003821253,0.0002185884,0.0002292033,0.00009294492,0.00006475728,0.0001156209,0.00000603833],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004882171,"about_ca_system_score_gemma":0.0001632724,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006758161,"about_ca_topic_score_gemma":0.0004325503,"domain_scores_codex":[0.9987757,0.00006912424,0.0004316359,0.0001407942,0.0004100672,0.0001726785],"domain_scores_gemma":[0.9983779,0.001096777,0.0002405076,0.0001112619,0.0001377151,0.00003580551],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[6.920891e-7,0.0003071469,0.001703088,0.0001512156,0.00001486866,3.238869e-7,0.06177865,8.306504e-7,0.00001835932,0.9318745,0.004010219,0.0001401026],"study_design_scores_gemma":[0.00005105209,0.00001400007,0.0002549354,0.0001854979,0.00001299643,0.000004545916,0.01591774,0.00002370774,0.00006499433,0.9812182,0.002147324,0.0001050191],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7215835,0.00277852,0.002463517,0.01042529,0.0008901823,0.0007507043,0.000002302497,0.0001907396,0.2609152],"genre_scores_gemma":[0.9396663,0.0002272785,0.057471,0.00005709619,0.0002077277,0.00004626955,0.000002733152,0.0000135097,0.002308063],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2586072,"threshold_uncertainty_score":0.3984363,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05352657000093444,"score_gpt":0.406993921037717,"score_spread":0.3534673510367826,"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."}}