Throughout my years of teaching, I have come to understand that if children are introduced to abstract concepts before they have a solid basis for understanding those concepts, they tend to resort to memorization and rote learning, which is not a solid foundation for further learning.

Upon entering my classroom, students are encouraged to be active, independent problem solvers. They are encouraged to invent and share their own ways for doing operations and learn to think and use their common sense, as well as skills and knowledge when solving real-world mathematical problems. Giving students the opportunity to invent and share their own operational procedures has the following benefits:

• Children are more motivated to solve problems when they are allowed to come up with their own strategy instead of just following a rote procedure.

• Children with different learning styles are given problem-solving options. They may choose to use manipulatives, drawings, oral and written words, or symbols to represent and solve problems.

• Children become adept at changing problems into easy-to-solve equivalent problems. For example, 30 – 17 is equivalent to 30 – 10 – 7.

• When children explain and discuss their own algorithms with other children, they internalize what the operations mean and learn from each other. Children's discussions also provide valuable information that can help teachers assess the development of their numerical thinking.

• Children develop persistence and confidence in dealing with challenging problems.

After students have had many opportunities to experiment with their own computational strategies, they are introduced to several algorithms for each operation.

Illustrative Mathematics is a problem-based core curriculum rooted in content and practice standards to foster learning and achievement for all. Students learn by doing math, solving problems in mathematical and real-world contexts, and constructing arguments using precise language. Teachers can shift their instruction and facilitate student learning with high-leverage routines that guide them in understanding and making connections between concepts and procedures.

To enrich and extend our learning, we use many resources such as Connected Mathematics, Engage NY, and teacher created resources. Below you will find the links to these resources.