Thinking Mathematically
"Children do not always think about mathematics in the same ways that adults do. If we want to give children the opportunity to build their understanding from within we need to understand how children think about mathematics." (Carpenter, 1999). This approach is a result of research led by Elizabeth Fennema and Thomas P. Carpenter at the UW-Madison.
What is Thinking Mathematically?
* Thinking mathematically is an approach to teaching mathematics where teachers utilize what they know about children's understanding of the mathematics to select problems, pose problems, question students, and facilitate discussion and sharing. (Carpenter 1999).
What We Know:
* Children enter school with a great deal of informal or intuitive knowledge of mathematics that can serve as the basis for developing understanding of mathematics.
* Children CAN construct viable solutions to a variety of story problems without formal or direct instruction.
* As students are solving problems, they are using a variety of strategies that make sense to them. They are discovering the fundamental principals of mathematics! Typically, students will go through these stages:
Direct Modeling: child draws 10 tallies to represent 10 items
Counting Strategies: counting on -- 5 + 3; starts at 5, - 6, 7, 8.
counting down -- 11 - 5 = 6; start at 11,- 10, 9, 8, 7, 6.
Recall Number Facts: since I know my doubles, 5 + 5 = 10, then 5 + 6 must equal 11, since 6 is just one more than 5.
"Children do not always think about mathematics in the same ways that adults do. If we want to give children the opportunity to build their understanding from within we need to understand how children think about mathematics." (Carpenter, 1999). This approach is a result of research led by Elizabeth Fennema and Thomas P. Carpenter at the UW-Madison.
What is Thinking Mathematically?
* Thinking mathematically is an approach to teaching mathematics where teachers utilize what they know about children's understanding of the mathematics to select problems, pose problems, question students, and facilitate discussion and sharing. (Carpenter 1999).
What We Know:
* Children enter school with a great deal of informal or intuitive knowledge of mathematics that can serve as the basis for developing understanding of mathematics.
* Children CAN construct viable solutions to a variety of story problems without formal or direct instruction.
* As students are solving problems, they are using a variety of strategies that make sense to them. They are discovering the fundamental principals of mathematics! Typically, students will go through these stages:
Direct Modeling: child draws 10 tallies to represent 10 items
Counting Strategies: counting on -- 5 + 3; starts at 5, - 6, 7, 8.
counting down -- 11 - 5 = 6; start at 11,- 10, 9, 8, 7, 6.
Recall Number Facts: since I know my doubles, 5 + 5 = 10, then 5 + 6 must equal 11, since 6 is just one more than 5.