Anastasios (Tasos) Barkatsas is a Senior Academic in Mathematics and Statistics Education and a Quantitative Data Analyst at the School of Education, RMIT University, Australia and has published more than 100 refereed papers, chapters and books. Tasos is also the Series Editor of the Brill | Sense series Global Education in the 21st Century.Dianne Siemon is a Professor of Mathematics Education in the School of Education at RMIT University (Bundoora). Di has directed a number of large-scale research projects including the Scaffolding Numeracy in the Middle Years Project (2003-2006), the Researching Numeracy Teaching Approaches in Primary Schools Project (2001-2003), and the Middle Years Numeracy Research Project (1999-2001). Di is a past President of the Australian Association of Mathematics Teachers and a life member of the Mathematical Association of Victoria.Rebecca Seah is a Mathematics Education lecturer in the School of Education, RMIT University, Melbourne, Australia. She is part of the research team in the Reframing Mathematical Futures II project. Her research interests include: spatial and geometric reasoning, assessments and instructional design, numeracy and students with special needs.

• AcknowledgementsFigures and TablesNotes on ContributorsIntroductionDianne Siemon, Tasos Barkatsas and Rebecca Seah1 Knowing and Building on What Students Know: The Case of Multiplicative ThinkingDianne Siemon2 Learning Trajectories in Early Mathematics EducationJulie Sarama and Douglas H. Clements3 HLT: A Lens on Conceptual Transition between Mathematical “Markers”Ron Tzur4 Using Digital Diagnostic Classroom Assessments Based on Learning Trajectories to Drive InstructionJere Confrey, William McGowan, Meetal Shah, Michael Belcher, Margaret Hennessey and Alan Maloney5 Researching Mathematical Reasoning: Building Evidence-Based Resources to Support Targeted Teaching in the Middle YearsDianne Siemon and Rosemary Callingham6 Reframing Mathematical Futures II: Developing Students’ Algebraic Reasoning in the Middle YearsMarj Horne, Max Stephens and Lorraine Day7 A Learning Progression for Geometric ReasoningRebecca Seah and Marj Horne8 Statistics and Probability: From Research to the ClassroomRosemary Callingham, Jane Watson and Greg Oates9 Investigating Mathematics Students’ Motivations and PerceptionsTasos Barkatsas and Claudia Orellana10 Secondary Students’ Mathematics Education Goal OrientationsTasos Barkatsas and Claudia OrellanaEpilogueMike Askew

Anastasios (Tasos) Barkatsas is a Senior Academic in Mathematics and Statistics Education and a Quantitative Data Analyst at the School of Education, RMIT University, Australia and has published more than 100 refereed papers, chapters and books. Tasos is also the Series Editor of the Brill | Sense series Global Education in the 21st Century.Dianne Siemon is a Professor of Mathematics Education in the School of Education at RMIT University (Bundoora). Di has directed a number of large-scale research projects including the Scaffolding Numeracy in the Middle Years Project (2003-2006), the Researching Numeracy Teaching Approaches in Primary Schools Project (2001-2003), and the Middle Years Numeracy Research Project (1999-2001). Di is a past President of the Australian Association of Mathematics Teachers and a life member of the Mathematical Association of Victoria.Rebecca Seah is a Mathematics Education lecturer in the School of Education, RMIT University, Melbourne, Australia. She is part of the research team in the Reframing Mathematical Futures II project. Her research interests include: spatial and geometric reasoning, assessments and instructional design, numeracy and students with special needs.

• AcknowledgementsFigures and TablesNotes on ContributorsIntroductionDianne Siemon, Tasos Barkatsas and Rebecca Seah1 Knowing and Building on What Students Know: The Case of Multiplicative ThinkingDianne Siemon2 Learning Trajectories in Early Mathematics EducationJulie Sarama and Douglas H. Clements3 HLT: A Lens on Conceptual Transition between Mathematical “Markers”Ron Tzur4 Using Digital Diagnostic Classroom Assessments Based on Learning Trajectories to Drive InstructionJere Confrey, William McGowan, Meetal Shah, Michael Belcher, Margaret Hennessey and Alan Maloney5 Researching Mathematical Reasoning: Building Evidence-Based Resources to Support Targeted Teaching in the Middle YearsDianne Siemon and Rosemary Callingham6 Reframing Mathematical Futures II: Developing Students’ Algebraic Reasoning in the Middle YearsMarj Horne, Max Stephens and Lorraine Day7 A Learning Progression for Geometric ReasoningRebecca Seah and Marj Horne8 Statistics and Probability: From Research to the ClassroomRosemary Callingham, Jane Watson and Greg Oates9 Investigating Mathematics Students’ Motivations and PerceptionsTasos Barkatsas and Claudia Orellana10 Secondary Students’ Mathematics Education Goal OrientationsTasos Barkatsas and Claudia OrellanaEpilogueMike Askew