*Teachers cannot pour knowledge into the heads of students as they might pour lemonade into a glass; rather, students must make their own lemonade* (Ormrod, 2004).

In a behaviorist classroom, a third-grade mathematics class is playing the “times table” game. Going from row to row, students recite the times table of the number they get. In this behaviorist learning scenario, students recite the multiplication tables and are rewarded for their efforts when they do well.

If we look at a third-grade mathematics class where constructivism is the primary learning theory, we see a teacher focusing on cognitive development and deep understanding. rather than behavior or skills as the goal of instruction (Fosnot, 2005). The goal of the constructivist teacher is for students to be actively engaged with a real problem or concept. Students can activate their prior knowledge and apply that knowledge to a new problem. Students can take their newly acquired knowledge and transfer that learning to another concept. The constructivist teacher allows students to develop their higher order thinking and problem-solving skills (Glatthorn, Boschee, & Whitehead, 2016).

What would the “times table” lesson look like through a constructivist lens? A constructivist approach may consider situations in daily living which offer meaningful opportunities for students to construct mathematical relationships. For example, if there are 8 students sitting at the big table at the back of the room, the teacher may ask how many arms are at that table? The teacher may ask to count the number of birds on the big tree outside our classroom window. How many feet are on that tree?

Constructivism is not suggesting that the students memorize the answer; he or she needs to let them figure things out and work through the problem so he or she can understand the necessary steps it takes to solve it. Constructivism supports play, exploring, as well as trial and error.

To examine psychologist Lev Vygotsky’s Zone of Proximal Development (ZPD) and its role in teaching, let’s take a step back. Are your students ready to multiple?

The ZPD is a graphic with three concentric circles. The center circle represents everything your students can do by him or herself with no help needed. The next circle represents the area where your students can do something (such as multiplying) with help or guidance from an adult. This is the ZPD. The outer circle represents things that your students cannot do, even if you are helping. When working on this activity, take a moment to see where your students’ understanding of multiplication falls. Can your student accomplish the task at hand with your assistance? If so, you are working in the ZPD, which is where you want to be for your students to learn something new. With enough practice and guidance your student’s multiplying ability will move from the ZPD into the center circle of things he or she can do independently.

Vygotsky argued that we learn best in a social environment, where we construct meaning through interaction with others. Enter Bruner’s theory of scaffolding. Scaffolding emerged around 1976 as a part of social constructivist theory. Bruner believed that when children start to learn new concepts, they need help from teachers in the form of active support. To begin with, they are dependent on their adult support, but as they become more independent in their thinking and acquire new skills and knowledge, the support can be gradually faded. This form of structured interaction between the child and the teacher is reminiscent of the scaffolding that supports the construction of a building. It is gradually dismantled as the work is completed.

## REFERENCES

Fosnot, C. T. (2005). *Constructivism: theory, perspectives, and practice*. New York: Teachers College Press.

Glatthorn, A. A., Boschee, F.,Whitehead, B. M., & Boschee, B. F. (2016). *Curriculum leadership:Strategies for development and implementation*. Thousand Oaks, CA: SAGEPublications.

Ormond, J. E. (2004). *Human learning*. Upper Saddle River, New Jersey, USA: Pearson Prentice Hall. (Tiene & Ingram, 2001)

Wood, D. J., Bruner, J. S. and
Ross, G. (1976). The role of tutoring in problem solving. *Journal of
Child Psychiatry and Psychology,* 17(2), 89-100.