Vygotsky's Scaffolding Theory in Math Education

Introduction: Human Learning and Child Development Theories

All humans have the capacity to learn. More than any other animals, people have evolved to be creative learners and to actively pursue new knowledge and skills. The majority of knowledge is gained through formal education, with structured and organized instruction in reading, mathematics, science, literature, and history. How students best acquire this knowledge has been of interest to psychologists since the early 20th century. Since then, a wide range of child development theories have been proposed, some more applicable in certain areas of learning than others.

One of the most influential child development theorists was Lev Vygotsky, who suggested that learning can be enhanced by building on prior knowledge — a process he called "scaffolding." This form of learning is particularly beneficial when teaching mathematics, since math is a process in which each step of learning builds on the one before it.

Five Key Areas of Contemporary Learning Research

In the last three decades, research has generated new concepts of learning in five areas. Based on these studies, effective learning processes have shifted from an emphasis on drilling and practicing to a focus on students' understanding and application of knowledge (Bransford, Brown, and Cocking). The five areas of study are as follows:

1) Memory and structure of knowledge. Memory is now recognized as much more than simple associations. A better understanding of how learners acquire information has provided insights into comprehension and thinking.

2) Analysis of problem solving and reasoning. It has been found that expert learners acquire skills to search a problem space and then use general strategies to solve problems. There is a clear distinction between how novice learners and those who are proficient in a subject solve problems.

3) Early foundations. Infant and child studies in controlled settings have significantly advanced knowledge of early learning acquisition. This research has revealed connections between children's learning inclinations and their emerging abilities to organize and coordinate information, make inferences, and discover strategies for problem solving. Educators are increasingly recognizing the importance of building on the skills and abilities children bring with them to school.

4) Metacognitive processes and self-regulatory capabilities. People can learn to regulate their own behavior, enabling self-monitoring and control over their performance. This includes strategies such as predicting outcomes, planning in advance, managing time, self-explanation to improve understanding, and recognizing gaps in comprehension.

5) Cultural experience and community participation. Participating in social practice is a fundamental mode of learning. It involves awareness of available resources as well as possible constraints. As Bransford, Brown, and Cocking note, "Learning is promoted by social norms that value the search for understanding." Early learning is furthered by the support of family and the social environment through child-adult activities, which provide young children with established norms, rules, and processes before they enter school.

Vygotsky's Sociocultural Theory and the Zone of Proximal Development

Lev Vygotsky's sociocultural theory aligns closely with these five learning essentials. Vygotsky's central premise is that social interaction is an integral aspect of cognitive development: "Every function in the child's cultural development appears twice: first, on the social level, and later, on the individual level; first, between people (interpsychological) and then inside the child (intrapsychological)" (Chang, Sung, & Chen, 57).

Vygotsky's theory also holds that the potential for cognitive development depends upon the Zone of Proximal Development (ZPD) — a level of development reached when children engage in social participation. The greatest development within the ZPD is driven by full social interaction. The level of skill that can be developed with adult support or peer interaction exceeds what can be attained independently.

According to Vygotsky, scaffolding describes the "role of teachers and others in supporting the learner's development and providing support structures to get to that next stage or level" (Raymond 176). As learners gain more knowledge, the scaffolding is progressively withdrawn until they are able to independently complete tasks or master concepts. The student evolves into an independent, self-regulating learner and decision-maker. Vygotsky observed that with "more sophisticated cognitive systems, related to fields of learning such as mathematics or language, the system of knowledge itself becomes part of the scaffold or social support for the new learning" (ibid). Vygotsky's theory describes a process that moves from social consciousness to the internalized end product. In language learning, for example, a baby's first words are primarily used to communicate, but once this skill is mastered it becomes internalized and enables "inner speech."

Scaffolding as a Teaching Strategy

Scaffolding is based on a teaching strategy that offers personalized support in relation to the learner's ZPD (Chang, Sung, & Chen). When scaffolding is used for educational purposes, someone with greater knowledge scaffolds — or supports — the student in order to build on prior knowledge and facilitate the acquisition of new information. Scaffolding assignments are set just beyond the level the learner can reach independently. The more knowledgeable person provides scaffolds so that learners are able to complete, with additional support, tasks they could not otherwise accomplish, thereby helping them progress through the ZPD (Bransford, Brown, & Cocking).

In a classroom, scaffolding may include using models, cues, prompts, hints, partial solutions, think-aloud modeling, and direct instruction (Hartman). When providing instruction in rounding numbers, for instance, a math teacher might give students a list of steps required to round to the nearest hundred, beginning with step one. The teacher may say, "Look at the number in the tens position" (Olson and Platt 180), which provides a hint and prompts students to complete the next required steps.

Asking questions is another common scaffolding technique. The number of prompts may be increased incrementally until the student arrives at the correct answer. For example, if a teacher does not receive a response — or receives an incorrect one — after asking, "How do we change the singular form of baby to the plural form babies?" it may be necessary to follow up with a verbal prompt: "What is the rule in this case?" — as a reminder that a particular rule applies. If needed, the teacher continues with, "What do you do when a word ends in y to make it plural?" — offering part of the rule (Olson and Platt 186). This process continues in scaffolded steps until the student can complete the task without hints and work independently.

Following the use of teacher-provided scaffolds, the educator may then have students engage in cooperative learning. In this type of environment, students assist one another in small group settings while still having access to some teacher support. This serves as a transitional step in the process of gradually reducing the scaffolds provided by the educator (Hartman, 2002). Scaffolding is also helpful for problem-based learning, an educational approach that encourages students to "learn to learn." In such situations, the teacher identifies tasks that students can complete independently and the requirements needed for successful completion. The teacher then designs activities that provide only enough scaffolding to help students overcome gaps in knowledge and skills.

References

Bransford, John, Brown, Ann, and Cocking, Rodney (Eds). Brain, Mind, Experience and School. Washington, DC: National Academy Press, 1999.

Chang, Kuo-En, Sung, Yao-Ting, and Chen, Ine-Dai. "The Effect of Concept Mapping to Enhance Text Comprehension and Summarization." The Journal of Experimental Education (2002). 71.1, 5–23.

Hartman, H. Scaffolding & Cooperative Learning. Human Learning and Instruction (pp. 23–69). New York: City College of City University of New York, 2002.

McKenzie, Jamie. Scaffolding for Success. Beyond Technology, Questioning, Research and the Information Literate School Community. Bloomington, IN: Indiana University Press, 2000.

Olson, Judy and Platt, Jennifer. "The Instructional Cycle." Teaching Children and Adolescents with Special Needs (pp. 170–197). Upper Saddle River, NJ: Prentice-Hall, Inc., 2000.