The 8 Mathematical Practices
How does a strong mathematician think?
These 8 mathematical practices are constant mindsets of a strong mathematician. Rather than being a scale of easy to difficult, these practices work in conjunction with one another as a child grows through their K-12 education as a mathematician. Each one is connected to the next, and students will practice all 8 skills continually throughout their school career.
MP.1: Make sense of problems and persevere in solving them
When given a problem, I can make a plan, carry out my plan, and check my answer. I can think: Does my answer make sense?
MP.2: Reason abstractly and quantitatively
I can use numbers and words to help me make sense of problems. I can construct and deconstruct math problems and make sense of quantities while doing so.
MP.3: Construct viable arguments and critique the reasoning of others
I can explain, or justify, my thinking and respond to the mathematical thinking of my peers.
MP.4: Model with mathematics
I can recognize math in every day life, and use the math I know to solve problems. I can justify my thinking by using a drawing or a representation of how I solve the problem.
MP.5: Use appropriate tools strategically
I can use certain tools to help me explore and deepen my math understanding. Some tools may include a ruler, a clock, a scale, measuring cups, a calculator, or other manipulatives.
MP.6: Attend to precision
I can be precise when solving problems, and clear when sharing my ideas. If my answer is incorrect, I try again to make sure I am correct.
MP.7: Look for and make use of structure
I can see and understand how numbers and shapes are organized and put together as parts and wholes.
MP.8: Look for and express regularity in repeated reasoning
I can notice when calculations are repeated, such as in doubles, or in multiplication.
Number Sense
How can children develop a strong foundation of base 10?
Number sense is a group of skills that allow kids to work with numbers. It includes skills like:
Assuring that students have a solid grasp of number sense is key in primary grades. Without it, it is difficult to be a strong mathematician. As students develop their skills using the 8 mathematical practices through their K-12 experience, we seek to ensure that their foundation is solid. Once a child has strong number sense, it makes doing math a more enjoyable, and successful experience.
- Understanding quantities.
- Grasping concepts like more and less, and larger and smaller.
- Recognizing relationships between single items and groups of items (seven means one group of seven items).
- Understanding symbols that represent quantities (7 means the same thing as seven).
- Making number comparisons (12 is greater than 10, and four is half of eight).
- Understanding the order of numbers in a list: 1st, 2nd, 3rd, etc.
Assuring that students have a solid grasp of number sense is key in primary grades. Without it, it is difficult to be a strong mathematician. As students develop their skills using the 8 mathematical practices through their K-12 experience, we seek to ensure that their foundation is solid. Once a child has strong number sense, it makes doing math a more enjoyable, and successful experience.
Mathematical Research
Here are some helpful resources for mathematical research.