Deconstructing Overall and Specific Expecations

Module Two - Unit Three - Deconstructing Overall and Specific Expectations

Understanding Big Ideas: The term big ideas has been used to refer to key learnings or essential understandings in mathematics. Dr Marian Small indicates: Big ideas are ideas that underpin a great number of problems, concepts, or ideas that we want students to learn. A big idea is not a concept or topic such as fractions. It might be an idea like “A fraction only makes sense if you know the whole”. Big ideas help educators clarify what aspects of an expectation or cluster of expectations to focus on. Big ideas help educators design appropriate assessments.Big ideas help students build essential connections.

This unit has three sections: Choose two of the three sections

A. Big Ideas Fractions

B. Big Ideas Number Sense and Numeration

C. Big Ideas Pedagogy

A. Big Ideas Fractions

Read,View,Reflect

Engage in the following readings to develop understanding of big ideas:

1. p 5-7 of Big Ideas Questioning: Proportional Reasoning
2. p 11-23 of volume 5 Fractions, A Guide to Effective Instruction in Mathematics grades 4-6 Number Sense and Numeration to develop content knowledge related to fractions

Additional Suggested Resources:

1. View the Fractions learning pathway.
2. Choose any resources of personal interest from the Leadership Symbaloo.

Respond

Begin with a response in one or two paragraphs in your group.What ideas in these readings are important for your work context next year ? Are there any resources from the collection in the Leadership Symbaloo that could support these ideas in your work? Respond to others.

B. Big Ideas Number Sense and Numeration

Read, View, Reflect

Choose from the following Resources:

Read the following mathematics content sections from A Guide to Effective Instruction in Mathematics K-3 Number Sense and Numeration

• Counting p 5-9
• Operational Sense p 17-23
• Quantity p 32-36
• Relationship p 46-50
• Representations p 55-57

Additional Suggested Resources:

1. Marian Small Chapter 2-Math Makes Sense-Focusing Instruction On Big Ideas and Mathematical Processes
2. Marian Small Powerpoint
3. Marian Small Big Ideas
4. Cathy Fosnot- Big Ideas, Strategies and Modelling

Respond

In a couple of paragraphs, articulate your understanding of one or two big ideas in mathematics that are important for your context and identify some of the foundational understandings we want students to develop in Number Sense and Numeration. What does this mean for supporting other educators as Leaders? Respond to others.

C. Big Ideas-Pedagogy

Read/View/Respond

Jo Boaler’s youcubed.org:

1. *Memorizers are the Lowest Achievers
2. Fluency Without Fear
3. Speed and Time Pressure Blocks Working Memory
4. Select one of the following sections to read from A Guide to Effective Instruction in Mathematics K - 6 Volume Teaching Basic Facts and Multi-Digit Computations
   • Basic Facts: Addition and Subtraction, Multiplication and Division p 12- 34, or
   • Multi Digit Whole Number Calculations p 35-56

Respond

Comment on the key differences in the messages in the readings above from more traditional instruction which focused on memorization and standard algorithms. How does this affect your role as a Leader?