Piaget vs. Vygotsky: Math Learning and Common Core Standards

Introduction

Numerous educators, parents, and students are dissatisfied with the Common Core curriculum in mathematics. One of the key objections to Common Core is that the standards are not developmentally appropriate for younger students. Two of the most recognized cognitive psychologists — Lev Vygotsky and Jean Piaget — developed theories that speak to cognitive development and learning among children and teenagers in relation to common core standards. Although there are similarities between the two theories, important differences exist, and those differences are significant to the application and understanding of the theories in educational settings. This paper highlights the major differences as they apply to mathematics, comparing and contrasting Piaget's and Vygotsky's ideas about math in the Common Core.

Common Core Standards in Math

The Common Core concentrates on a clear set of math skills and concepts. The skills and knowledge students need to be prepared for mathematics in college, career, and life are interwoven throughout the mathematics standards. Many Common Core questions, particularly in math, require higher-level and abstract thinking. Jean Piaget brought clarity and understanding to the study of children's cognitive developmental stages. Research has shown that Piaget was one of the most influential early childhood psychologists of all time, carefully mapping the cognitive development of children. Before his work, many people assumed that children's thought processes were essentially the same as adults', just less skilled. Piaget would argue that the Common Core standards are not developmentally appropriate when it comes to math. He would point out that not all students in a class are necessarily working at the same level, and that teachers would benefit from understanding each student's cognitive level and adjusting their instruction accordingly, rather than relying on a uniform set of standards.

Throughout the standards there are elements that connect to numerous learning theories — most notably the social theories of Lev Vygotsky. As a foundation of contemporary constructivism, Vygotsky's ideas are closely aligned with those articulated in the Common Core State Standards (CCSS), particularly in terms of how students need to be learning. According to Vygotsky (1978), the social interaction component of learning tasks is the basis for cognitive growth and knowledge acquisition in mathematics, not the Common Core itself. Vygotsky's theory of social learning, combined with a constructivist context, is vital to the effective application of Common Core State Standards in mathematics. Teachers, through professional development grounded primarily in collegial discussions, peer coaching, and demonstration classrooms, can learn to integrate social and cognitive constructivist philosophies into their mathematics teaching. Math instruction should be regarded as a vital component of both learning and thinking (Tyminiski, 2010). Vygotsky would agree that making sense of math in this way has the power to change and sustain the culture of a school through high-quality models of instruction (Gelman, 2010). The Common Core standards represent an opportunity to promote both excellence and equity in education through high expectations linked to the hard and soft skills students need for postsecondary success (Tyminiski, 2010).

Conclusion

It is clear that Vygotsky and Piaget each have a different perspective on the Common Core Standards in mathematics. Piaget would argue that the Common Core standards are not developmentally appropriate when it comes to math, pointing out that not all students in a class are necessarily working at the same level and that a uniform standard is therefore insufficient. Vygotsky's ideas, however, are more closely aligned with those embedded in the Common Core State Standards. When it comes to instruction, Piaget places the focus on student thinking and self-directed discovery, whereas Vygotsky places greater emphasis on the teacher constructing effective lesson plans and providing structured support through scaffolding. Together, both theories offer valuable and complementary insights for mathematics educators.

References

Gelman, R. M. (2010). Young children's numerical competence. Cognitive Development, 21(9), 1–29.

Tyminiski, A. (2010). Teacher lust: Reconstructing the construct for mathematics. Journal of Math Teacher Education, 13, 295–311.

Ylvisaker, M. H. (2010, March 31). What are concrete and abstract thinking? Retrieved from http://www.projectlearnet.org/tutorials/concrete_vs_abstract_thinking.html