Preface Research Mathematicians and Mathematics Educators: Collaborating for Professional Development Abstract Introduction Recorded Lessons in Professional Development Theoretical Underpinnings The DATUM Process Subsequent Developments Summary and Future Directions References The Educational Research of Mathematical Competence Abstract Introduction International Student Assessment Standardized Test
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Testing T9"; Statistical Analysis of T9; Qualitative Analysis of T9; Assignment Hotel; Conclusion; Acknowledgments; References. An Analysis of Instruments That Measure the Quality of Early Mathematics Instruction in Early Childhood SettingsAbstract; Introduction; The Early Math Experiences Matter; Measuring Early Mathematics Teaching Quality; An Analysis of Observation Instruments That Measure the Quality of Early Mathematics Teaching; Reformed Teaching Observation Protocol (RTOP); Mathematical Quality of Instruction (MQI); Classroom Observation Student-Teacher Interactions-Mathematics (COSTI-M); Classroom Observation of Early Mathematics-Environment and Teaching (COEMET). High-Impact Strategies for Early Mathematics (HIS-EM)Conclusion; References; Laplace Transform in Chemistry Degrees Mathematics Courses; Abstract; 1. Introduction; 2. An experience in first semester Calculus Courses; 3. Experiences in the ODE Module; 4. Laplace Transform in PDE Module; 4.1. Packed Bed Reactor (PBR); 4.2. Pollution in the Uruguay River; 5. Results; 5.1. Results in First Year Calculus Courses; 5.2. Results Obtained in Differential Equations Courses; Conclusion; Acknowledgments; References. Solving Linear Equations: Will This Pose as a Challenge to Elementary Pre-Service Teachers?Abstract; Introduction; Intrinsic Cognitive Load, Element Interactivity and Understanding; Complexity of Equations; Element Interactivity; Special Features; Equal Sign Concept; The Present Study; Method; Participants; Materials; Procedure; Results; One-Step Equations; Two-Step Equations; Multi-Step Equations; Group Performance; Concept Test; Discussion and Implications; Limitations and Future Directions; Appendix A.; Appendix B.; References. Research Trends in the History of Mathematics Education: The Spanish CaseAbstract; Introduction; Mathematics Education in Spain; A) Areas of Knowledge Were Implemented in the Spanish University System; B) Creation of Societies of Teachers and Researchers in Mathematics Education; C) Implantation of PhD Programs in Mathematics Education; D) State Grants for Research; Research on History of Mathematics and Mathematics Education in Spain; Legislation and Curriculum; Textbooks; Scientific-Historical-Social Context; Institutions; Mathematicians and Books Authors; Concepts.