{"id":"W4297328614","doi":"10.1007/s11858-022-01435-6","title":"The multi-dimensionality of early algebraic thinking: background, overarching dimensions, and new directions","year":2022,"lang":"en","type":"article","venue":"ZDM","topic":"Mathematics Education and Teaching Techniques","field":"Social Sciences","cited_by":58,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Critical thinking; Mathematics education; Algebraic number; Meaning (existential); Field (mathematics); Statistical thinking; Epistemology; Computer science; Mathematics; Psychology; Pure mathematics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003960199,0.0003684532,0.0008388959,0.003439704,0.00148889,0.006463881,0.0007757406,0.000784768,0.002993402],"category_scores_gemma":[0.009204393,0.0003187253,0.0003129862,0.003873217,0.0163631,0.009040036,0.003360382,0.003229761,0.0001872101],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003400054,"about_ca_system_score_gemma":0.004512313,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002599439,"about_ca_topic_score_gemma":0.003459264,"domain_scores_codex":[0.9982608,0.0007807693,0.0001430733,0.0002556137,0.0004229286,0.000136896],"domain_scores_gemma":[0.9845743,0.01075276,0.001208626,0.001112002,0.00163554,0.0007167681],"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":[0.00005092298,0.00007130274,0.00928461,0.0005942221,0.00001761305,0.00007845485,0.008099981,0.0004458716,0.0002842166,0.8924352,0.001279206,0.08735855],"study_design_scores_gemma":[0.0000119884,0.00004894058,0.01343748,0.0005665838,0.00001271872,0.0004518494,0.005805653,0.001876143,0.0004027853,0.9362473,0.04109369,0.00004500833],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.3627777,0.2878355,0.09152122,0.1056956,0.001145397,0.00008701146,0.0004342507,0.0001142246,0.1503892],"genre_scores_gemma":[0.9335161,0.0392981,0.02168739,0.001536784,0.001068814,0.00007025853,0.00008662262,0.00002352051,0.002712557],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006463881,"threshold_uncertainty_score":0.02466923,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07956675283670506,"score_gpt":0.3674616599582022,"score_spread":0.2878949071214971,"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."}}