Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
|Mathematics: What's the Big Idea?|
Algebra: It Begins in Kindergarten.Content Guide: Monica Neagoy
Supplies Needed for Workshop #7
About the Workshop
What is the theme of the workshop?
Whom do we see? What happens in the videoclips?We will see students from kindergarten through eigth grade using variables, studying relationships, exploring multiple representations, and making generalizations, all of which are at the heart of algebra.
What issues does this workshop address?Algebra is not the meaningless abstraction nor the symbolic manipulation that math leaders are pushing to incorporate into the early curricula. Nor is it what we studied it in high school. What, then, constitues algebra in the primary and middle grades? The answer to this question is the main issue of this workshop.
What teaching strategy does this workshop offer?A variety of teaching strategies will be modeled and discussed. Of note is the integration of graphing calculators in the teaching and learning of algebra. We will also see students working alone, in pairs, and in small groups and using a variety of manipulatives.
To which NCTM Standards does this workshop relate?This workshop will stress number sense and spatial sense (Standards 6 and 9 in the K-4 content standards). The activities we will explore involve finding patterns and exploring relationships (Standard 13 in the K-4 standards, Standard 8 in the 5-8 standards), and measurement (Standard 10 in the K-4 standards, Standard 13 in the 5-8 standards). The four process standards (Mathematics as Problem Solving, Communication, Reasoning, and Making Connections) will also figure into this workshop.
Suggested Classroom Activities and Strategies
Developing Algebraic Reasoning Through Literature (K-2)
Suggested Strategies This activity can be done with the entire class. Invite a volunteer to come up in front of the class and model the solution. This first solution may be in the form of a sentence or picture. Thereafter, invite others to give alternative representations for the same relationship (assuming it is correct). Explore multiple representations with the class (concrete, numerical, tabular, graphical, symbolic), pointing out the similarities and differences among them.
(a) Do they see the "change" from one term to the next? Can they articulate it?
Suggested Strategies This activity could begin as a whole-class activity for one or two sequences. After stressing what is important (i.e., looking at the "change" from term to term, devising generalization techniques, etc.), have students make up their own sequences and quiz their peers. It is important, every now and then, for students to be problem writers, not simply problem solvers. They invest more energy if the problem is their own creation. Also, creating a good problem can be more involved and challenging than solving one.
Ask students to verbalize their findings. Encourage them to express the relationship between C and D symbolically.
Suggested Strategies This activity (as well as the previous one) could be assigned to small groups of students. Divide the tasks beforehand. When the groups are done, have group reporters take turns sharing their work with the rest of the class. Encourage the "listening" groups to be attentive to the presentations by requiring an "intelligent question" of them. Finally, conclude by articulating the "big ideas."
Suggested ResourcesEdwards, Ronald. Algecadabra! Algebra Magic Tricks. Pacific Grove, CA: Critical Thinking Press and Software, 1992.
Lappan, Glenda, et. al. Variables and Patterns. Palo Alto, CA: Dale Seymour Publications, 1997.
Laycock, Mary. Algebra in the Concrete. Hayward, CA: Activities Resources Co., Inc., 1997.
Mathematics Teaching in the Middle School. NCTM. February, 1997.
National Council of Teachers of Mathematics. Algebra for Everyone. Reston, VA: NCTM, 1990. (Book and Videotape).
National Council of Teachers and Mathematics. The Ideas of Algebra, K12. Reston, VA: NCTM, 1988. (Yearbook).
National Council of Teachers of Mathematics. Patterns: K-4 Addenda Series. Reston, VA: NCTM, 1993.
National Council of Teachers of Mathematics. Patterns and Relationships: 5-8 Addenda Series. Reston, VA: NCTM, 1991.
Teaching Children Mathematics. NCTM. February, 1997.
Pre-Workshop Assignment for Workshop #8The main purpose of this assignment is to become familiar with Pascal's Triangle. If you are already familiar with it, see if you can discover patterns within the triangle which you have never found before.
Let n denote the row number, beginning with:
n = 0 for row "1", and then
n = 1 for row "1 1",
n = 2 for row "1 2 1",
n = 3 for row "1 3 3 1", and so on.
Mathematics: What's the Big Idea?