Hands-on and real-life experiences are interesting and fun but are only powerful if the learning involves higher level questioning and integration of the big ideas. The larger ideas help the students to understand their learning in real-life contexts. It allows for open-ended exploration and higher level questioning within a defined topic.
Students also need to elaborate on the experiences with language (written or spoken) and not just do the activity. This helps them to clarify and provide understanding to the experience.
Some Big Ideas In Math:
Math is a language and is useful for describing events and solving problems.
Math is all around us.
Math is in nature.
Math is the study of quantity and shapes.
Math is a process. (self-discipline)
Math involves patterns and relationships between quantities and shapes.
Math involves community.
There are obstacles in doing math. (courage) (conflict)
Math has purpose.
Math fills an inner drive to discover and create. (exploration)(curiosity)
There is joy and fulfillment in discovery. (invention)
Math has useful real-life applications. (growth) (wisdom)
Some problems have more than one answer.
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For more reading on the subject the book
Integrating Differentiated Instruction and Understanding by Design
by Carol Ann Tomlinson and Jay McTighe is recommended.
Integrating Differentiated Instruction and Understanding by Design
by Carol Ann Tomlinson and Jay McTighe is recommended.