Session 1 What is Multiplicative Reasoning What questions

Session 1: What is Multiplicative Reasoning?

What questions about multiplicative reasoning might you ask your students? The Freudenthal Institute grants permission to use this illustration from Interactieve video on de nascholing rekenenwiskunde by F. van Galen, M. Dolk, E. Feijs, V. Jonker, N. Ruesink, and W. Uittenbogaard (1991) for professional development materials designed by the Ongoing Assessment Project (OGAP). © OGAPMath. LLC 2017 for non-commercial use only 2

A Focus on Multiplication and Division: Bringing Research to the Classroom (Hulbert, Petit, Ebby, Cunningham, Laird) • Most chapters have a focus on the important mathematics content related to multiplication and division • Review of the mathematics education research throughout with over one hundred samples of student work that illustrate the evidence linked to the research. • Short descriptions in most chapters of how the CCSSM relates to the multiplication or division topic and math education research under discussion. • A dedicated chapter on the OGAP Multiplicative Framework (which includes the Multiplication and Division Progressions) © OGAPMath. LLC 2017 for non-commercial use only 3

“Multiplicative reasoning is more than just doing multiplication or division. It is about understanding situations in which multiplication or division is an appropriate operation. It involves a way of viewing situations and thinking about them. ” from NCTM Principles and Standards for School Mathematics (PSSM, 2000) Examine Figures 1. 6 – 1. 9 in Chapter 1: What is Multiplicative Reasoning? © OGAPMath. LLC 2017 for non-commercial use only 4

Based on your own experience, the previous quote, and the student work you examined, complete the sentence: The student who has multiplicative reasoning demonstrates … © OGAPMath. LLC 2017 for non-commercial use only 5

Multiplicative Reasoning: The Mathematics Read pages 1 -6 STOP and JOT - Say Something Protocol: 1. Partners look over a piece of text and read to the designated point. 2. Once partners have reached the stopping point, both partners say something. (The something might be a question, a brief summary, a key point, an interesting idea or a new connection. ) 3. Partners continue this process until the selection is completed. © OGAPMath. LLC 2017 for non-commercial use only Stopping Point 1 Page 1 to Number Relationships and Actions in Addition 2 Number Relationships and Actions in Addition to top of page 4 3 Page 4 to Table 1. 1 (Page 5) 4 Absolute and Relative Difference (page 5) to Multiplicative Reasoning: From a Teaching and Learning Perspective (page 6) 6

What aspects of the question below make it a good choice as a follow-up to the lesson? What concepts were considered when the item was designed? © OGAPMath. LLC 2017 for non-commercial use only 7

With a partner sort the student work into piles based on the different strategies that students used. © OGAPMath. LLC 2017 for non-commercial use only 8

• Identify the location of the different strategies on the OGAP Multiplication Progression. • Select one piece of work and indicate possible instructional implications based on the evidence and location of the framework. © OGAPMath. LLC 2017 for non-commercial use only 9

Examine the Multiplication and Division Progressions • What do you notice? • What is unfamiliar? • What questions do you have? © OGAPMath. LLC 2017 for non-commercial use only 10

Important Ideas About the Multiplication and Division Progressions (Ch. 2 pages 27 -29) 1) 2) 3) 4) 5) Movement along the Progressions is not linear Students’ strategies will be at different levels The Progressions provide instructional guidance The Progressions are not evaluative Collection of underlying issues and errors is important Groups of 3: A - read #1, 4, and 5 B - read # 2 C - read #3 Be prepared to share the important information, referring to the Progressions for clarity. © OGAPMath. LLC 2017 for non-commercial use only 11