For Teachers: This unit includes a brief introduction to the developmental theories of Piaget and Vygotsky. Below is a list of possible learning objectives that you might want to consider as you prepare your teaching materials:

- The student will know and be able to apply the developmental theories of Piaget, with an emphasis on the Concrete Operational phase.
- The student with know and be able to apply the developmental theories of Vygotsky, with an emphasis on Sociocultural Development and the Zone of Proximal Development.
- The student will become familiar with and will know how to access the NAEYC guidelines for Developmentally Appropriate Practice.

Take your students outside on the lawn and scatter a box of colored toothpicks (with even numbers of red, blue, green and yellow toothpicks) across about a thirty-foot square patch of grass. Ask the students to pick up as many toothpicks as they can find in twenty seconds, then head back to the classroom. Ask the students to count how many toothpicks they found of each color. Keep a running tally of the counts. They will almost certainly have found more red and yellow than green and blue. Explain that this is a good, concrete way to introduce the idea of natural selection to elementary-aged children. Discussion: What are the advantages to presenting concepts concretely before you deal with the abstract ideas? How does this relate to the "Zone of Proximal Development"? How does it relate to Piaget's concepts of assimilation and accomodation? |

Place a double-digit addition or subtraction problem on the board and cover it up. Tell the students that you are going to show them a math problem and you would like them to solve it in their heads in 20 seconds—absolutely no pencils or pens allowed. After the 20 seconds has expired, invite the students to first, share with the class how they felt about the exercise, then to share the strategies they used to solve the problem. You will find that the students used several different approaches, such as adding tens and then ones, carrying as though they were writing the problem on paper, adding ones to the first number, then adding the tens, etc. Use this as a jumping off point for discussing how people approach math problems in many different ways. Explain that some mathmeticians actually solve multi-digit addition or subtraction problems from left to right, rather than the other way around. Discuss the implications for teaching math to children. Discussion: What are the benefits of using a socio-cultural approach (letting children discuss their various strategies) as we teach mathematics? What are the drawbacks? |