Traditional Views and New Approaches: Math Makes Sense!
- Most people believe that mathematics is associated with certainty; that knowing mathematics means being able to get the right answer
- Math must make sense
Constructivist Theory - Based on the work of Jean Piaget- Learners are creators of their own learning
- Assimilation - new concept fits with prior knowledge
- Accommodation - new concept does not fit with prior knowledge
- Every learner will construct ideas differently.
- Give learners freedom to create their own ideas
Sociocultural Theory - Based on the work of Lev Vygotsky
- Learners move ideas into his or her own psychological realm (Forman, 2003)
- Semiotic Mediation - How information moves from a social plane to an individual plane.
- Learning depends on the learner, the classroom environment the culture in and out of the classroom.
Implications for Teaching Mathematics
- build new knowledge from prior knowledge
- provide opportunities to talk about mathematics
- build in opportunities for reflective thought
- encourage multiple approaches
- treat errors as opportunities for learning
- scaffold new content
- honor diversity
Understanding Mathematics
- Use multiple methods to solve problems
- Pictures
- Written Symbols
- Manipulative models
- Real-world situations
- Oral language
Van
De Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and
middle school mathematics: Teaching developmentally (7th ed.).
Boston, MA: Pearson
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