Young Mathematicians at Work Constructing Algebra

And the most recent addition to the series ...

Young Mathematicians at Work Constructing Algebra

Constructing math algebra book image

Chapter 1 Algebra:Structures or Structuring?

Chapter 2 The Landscape of Learning

Chapter 3 Early Structuring of the number system

Chapter 4 Continuing the Journey: The role of contexts and models

Chapter 5 Equivalence on the Horizon

Chapter 6 Variation Versus Variables

Chapter 7 Further Horizons: Integers and equivalence

Chapter 8 Comparing Quantities and Relations

Chapter 9 Developing Algebraic Strategioes with Minilessons

Chapter 10 Proof

Required Readings - Constructing Algebra
Prereading	This is what I think about arithmetic and algebra.
Chapter - 1 Support materials: factors to 50 factors 50-100 # factor for #'s 1-50 # factors for #'s 1-100 Planning notes	Concepts - structure(s), part-part-whole, algebrafying, symbolizing, generlization, structuring, bridge, conjecture, additive, multiplicative, What does the research say about children understanding the use of symbols and how does it fit with facilitating mathematical literacy? How early is early? How can we expect students to work with conjectures at different grade levels?
Chapter - 2 Support materials: Simultaneous equation p. 31 Pythagorean Theorem image More proofs than I bet you think there are	What is a landscape approach of learning or teaching mathematics? What is a linear approach like “Saxon Math” of learning or teaching mathematics? What are the advantages and disadvantages of a landscape approach and linear approach? How has or will thinking similar to the kind of thinking described in the Landscape of Learning help you facilitate students' learning of mathematics? What disadvantages could there be? What implications for connectedness, density, and ... How are models different than representations? or are they? Is there anytime that they are not of value for mathematics use?
Chapter - 3 I would like to work with a group to turn ideas in this chapter into lesson plans. Beaded Necklace worksheets Beaded necklace worksheet 1	algebra, structuring, number value, and ... Additive, multiplicative... and place value? Math congress, gallery walk... What does or will "mathematizing" mean for your classroom? How is mathematizing different than developing mathematical thinking in the Thinking Mathematically book?
Chapter - 4	Systematic thinking and algebra? Additive, multiplicative, spatial visual... Models and representations... What are the big ideas for multiple dimensions?
Chapter - 5	How is equality thought of and used differently during child development? What is equality and how can it be facilitated? Bridges, instruction, internal, external representations What is a proof, what are different ways of proving?
Chapter - 6	What does the research say about children understanding variables and how does it fit with facilitating mathematical literacy? How early is early? Expressions as objects not procedures. Conceptual vs. procedural... Internal - external representations... Bridges
Chapter - 7	Integers, equivalence Random search, systematical thinking... Object thinking Variables...
Chapter - 8	Quantities, relationships, equivalence, substitution, combinatorial thinking, Algebra, arithmetic
Chapter - 9	Putting it all together, strings, minilessons, problem solving, landscape, models, context, Planning and facilitating...
Chapter - 10	What is proof and justification for different levels of students? What does the research say about children's use of if, then thinking and how does it fit with facilitating mathematical literacy? How early is early? What is or has been your thoughts about the development of relational thinking?