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In this series we explore:
- the difference between computation strategies and operation sense;
- the meaning of and the relationships between the four operations;
- the ways in which operation sense and computational fluency develop over time;
- the importance of representations and models in understanding the operations.
Session one and two have a grades 1-3 focus.
Sessions three and four have a grades 3-8 focus.
The Format:
Videos, readings, tasks and discussion prompts guide the learning, inform conversations, and invite you to test these ideas with students to apply and deepen the learning. Move through the four parts at your own pace. It's not a race, so feel free to take your time and linger in areas that you find most rewarding. Perhaps not surprisingly, it's typically more enjoyable to learn with a friend or a team, so consider who you might invite to join you.
Thank you for your interest in this topic and your willingness to work through these ideas. We hope you enjoy the learning and find it useful as we work to strengthen mathematics achievement and well being for all.
If you plan to be a facilitator for this session, you will find our Facilitator page helpful.
Session 1: Making Sense of Addition and Subtraction
What does it mean to add and subtract? And more importantly, how can students learn to translate word problems and everyday situations into number sentences that they can solve? This session explores the various addition and subtraction “problem structures” that students need to encounter, the types of representations students can use to make the operations visible, and the moves educators can make to help students advance in their learning, regardless of whether students are adding whole numbers, fractions or other types of numbers.
Session 2: Developing Flexible Addition and Subtraction Strategies
How do students learn to add and subtract? This session looks at how the development of magnitude in the early years helps foster a robust and flexible fluency with addition and subtraction in later years. It explores the role of practice and the types of practice that builds understanding as the foundation for fluency. And it looks at the strategies educators can use to help students develop more efficient strategies through the years.
Session 3: Making Sense of Multiplication and Division
What does it mean to multiply and divide? What does a “multiplicative situation” look like and how does it connect to proportional reasoning? And how can students learn to recognize these situations and represent them with the appropriate operation? This session explores the types of multiplication and division “problem structures” that students need to encounter, the relationship between multiplication and division and the various models students can use to make the operations visible. Furthermore, it looks at the role of paraphrasing as a strategy to help students advance in their learning, regardless of whether students are multiplying whole numbers, fractions or other types of numbers.
Session 4: Developing Fluency with Multiplication and Division
How do students learn to multiply and divide? Why do some students have trouble with their “multiplication facts”? And what types of instructional moves can help close these gaps and strengthen efficiency? This session looks at the development of multiplicative thinking through the years, the role that models can play in building understanding and fluency and important mathematical ideas (unitizing, the distributive and associative properties, our place value system) and the role they all play in developing fluency with multiplication and division.
DEVELOPER'S NOTE: This learning series was originally released in 2017 in a different format including a live synchronous element. We are now experimenting with altering the format to better serve small groups working together through the content. Please use the Contact page to share feedback on this format. Google Sites
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