Number Sense
This is the foundation for all higher-level mathematics.
What is number sense?
Memorization of math facts did not lead to this.
What are students with higher math ability or higher IQ scores?
This is the core of mathematics.
What is reasoning?
This is the primary goal of Number Talks.
What is computational fluency?
This is one of the best methods for teaching number sense and math facts at the same time.
What are number talks?
This is what high achieving students did to combine numbers 19 + 7.
What is to change the problem to 20 + 6?
These are a very small part of mathematics.
What are math facts?
This happens when students develop number sense.
What is fluency?
Number talks are NOT intended to replace this.
What is the curriculum?
Number talks lead to three things.
What is conceptual understandings, mental math, and an opportunity to memorize math facts?
Changing numbers to friendlier numbers shows this kind of mathematical thinking.
What is flexibility?
According to Parish, this is the definition of fluency.
What is knowing how a number can be composed and decomposed and using that information to be flexible and efficient with solving problems?
This shouldn't be emphasized while teaching students number sense and number facts.
What is speed?
Daily Double!
1. By allowing students to solve problems in their own ways.
2. By presenting problems at varying levels of difficulty.
3. By providing models for support.
What are three ways teachers can promote access for all students into a number talk?
5-15 minutes, everyday
What is the amount of time/frequency for a number talk?
According to research, this created students who became less willing to think about numbers and their relationships.
What is memorization of facts?
These brought on math anxiety for students.
What are timed tests?
Daily Double!
An incorrect interpretation of fluency is this.
What is speed and memorization?
1. Asking questions
2. Describing what the child did
3. Writing down the process
What is how teachers help students clarify their thinking during a Number Talk?
1. Teacher presents the problem.
2. Students figure out the answer.
3. Students share their answers.
4. Students share their thinking.
5. The class agrees on the "real" answer for the problem.
6. The steps are repeated for additional problems.
What are the 6 basic steps/format of a number talk?
According to Boaler, this is the best way for students to gain mathematical fluency.
What are rich mathematical problems, where students use, work with, and explore numbers?
Students who are most successful with number problems are those who focus on these.
What are numerical, symbolic, and spatial relationships to lead to visual understanding?
Students develop more complex functions through this.
What is number sense and the development of deep understandings of numerical principles (aka conceptual understandings)?
1. A safe environment
2. Problems at various levels that can be solved in a variety of ways
3. Concrete models
4. Opportunities to think first and then check
5. Interaction
6. Self-correction
What are elements that must be in place to ensure students get the most from their Number Talk experiences?
Provides a safe environment where each child's thinking it valued.
Selects groups or strings that allow access to all children.
Selects problems that intentionally highlight mathematical concepts.
What are some of the teacher's role during a Number Talk?