NC NAEP Project Module 3 - Activity 1 Research Synopsis: What is Early Algebra? What Algebraic Topics are Appropriate for Teaching in Elementary School? Elementary Module 3, Activity 1

Goals Develop understanding of what algebraic thinking is and how it builds through the elementary grades and beyond. Learn which algebraic topics are appropriate for inclusion in elementary school mathematics and what topics should be delayed. Elementary Module 3, Activity 1

Getting Started: Brainstorming What is Algebra or algebraic reasoning? Work with your group to write a list of your definitions Elementary Module 3, Activity 1

Examining Early Algebra: What Do the Experts Say? Reading 1: Mason, J. (2008). Making use of children’s powers to produce algebraic thinking. In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the Early Grades (pp. 57 – 94) Elementary Module 3, Activity 1

Reflection Questions for Small Groups Questions for Reading 1: Mason, J. (2008) 1) What does Mason refer to when he discusses “natural powers”? 2) How does Mason characterize arithmetical thinking as pre-algebra? Elementary Module 3, Activity 1

Reflection Questions for Small Groups Questions for Reading 1: Mason, J. (2008) 1) How can a teacher help students become aware of, and learn how to express generality? 2) What does Mason mean by “multiple expressions for the same thing”? Elementary Module 3, Activity 1

Examining Early Algebra: What Do the Experts Say? Reading 2: Schifter, D., Monk, S., Russell, S. J., and Bastable, V. (2008). Early algebra: What does understanding the laws of arithmetic mean in the elementary grades? In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the Early Grades (pp ) Elementary Module 3, Activity 1

Reflection Questions for Small Groups Questions for Reading 2: Schifter, D., Monk, S., Russell, S. J., and Bastable, V. (2008) 1) Explain the significance of students’ developing understanding of the commutative property of addition of whole numbers. Elementary Module 3, Activity 1

Reflection Questions for Small Groups Questions for Reading 2: Schifter, D., Monk, S., Russell, S. J., and Bastable, V. (2008) 2) Explain the significance of students’ developing understanding of the associative property of whole numbers. Elementary Module 3, Activity 1

Reflection Questions for Small Groups Questions for Reading 2: Schifter, D., Monk, S., Russell, S. J., and Bastable, V. (2008) 3) Explain the significance of students’ developing understanding of the distributive property. Elementary Module 3, Activity 1

Reflection Questions for Small Groups Questions for Reading 2: Schifter, D., Monk, S., Russell, S. J., and Bastable, V. (2008) 4) Explain why memorization of whole number properties is not a productive instructional strategy for helping students operationalize these notions. Elementary Module 3, Activity 1

Examining Early Algebra: What Do the Experts Say? Reading 3: Schliemann, A. D., Carraher, D. W., Bizuela, B. M., and Jones, W. (2007). Can young students solve equations? In Analucia B. Schliemann, David W. Carraher, Barbara M. Brizuela (Eds.), Bringing Out the Algebraic Character of Arithmetic: From Children’s Ideas to Classroom Practice. (pp ) Elementary Module 3, Activity 1

Reflection Questions for Small Groups Questions for Reading 3: Schliemann, A. D., Carraher, D. W., Bizuela, B. M., and Jones, W. (2007) 1) What types of verbal problems should young students be exposed to in order to help them develop early algebraic thinking? Elementary Module 3, Activity 1

Reflection Questions for Small Groups Questions for Reading 3: Schliemann, A. D., Carraher, D. W., Bizuela, B. M., and Jones, W. (2007) 2) The children referenced in this study were encouraged to use whatever strategies and tools that seemed to make sense to them to solve the problems. Elementary Module 3, Activity 1

Reflection Questions for Small Groups Questions for Reading 3: Schliemann, A. D., Carraher, D. W., Bizuela, B. M., and Jones, W. (2007) Why did the researchers choose this instructional approach rather than directly instructing the students in specific solution procedures? Elementary Module 3, Activity 1

Reflection Questions for Small Groups Questions for Reading 3: Schliemann, A. D., Carraher, D. W., Bizuela, B. M., and Jones, W. (2007) 3) What were some of the structures evidenced in the verbal problems? Why did the researchers choose problems with these structures? Elementary Module 3, Activity 1

Examining Early Algebra: What Do the Experts Say? Reading 4: Edwards, T. G. (2000). Some big ideas of algebra in the middle grades. Mathematics Teaching in the Middle School. Elementary Module 3, Activity 1

Reflection Questions for Small Groups Questions for Reading 4: Edwards, T. G. (2000). 1) Edwards describes a list of big ideas for learning algebra. How does this list compare with the list you and other participants created at the beginning of this activity? Elementary Module 3, Activity 1

Reflection Questions for Small Groups Questions for Reading 4: Edwards, T. G. (2000). 2) How does Edwards recommend helping students develop understanding of what a variable is? Elementary Module 3, Activity 1

Reflection Questions for Small Groups Questions for Reading 4: Edwards, T. G. (2000). 3) Edwards describes how to use an area diagram to verify the commutative property of multiplication, even when variables are involved. (continued…) Elementary Module 3, Activity 1

Reflection Questions for Small Groups Questions for Reading 4: Edwards, T. G. (2000). 3) How does Edwards suggestions about using the commutative, associative, and distributive properties in this context relate to the discussion of number properties in the article by Schifter, Monk, Russell, and Bastable? Elementary Module 3, Activity 1