Transcript NC NAEP Project

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. 413 447)
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. 37 - 61)
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