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-Statements of conceptual understanding that allow students to make connections between two or more concepts

-Principles are theorems

-An investment of time is necessary to craft quality generalizations

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-A topic is a broad concept

-A concept is a specific idea within that topic

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-Factual knowledge includes rote memorization

-Does not guarantee the conceptual depth of understanding

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-An equation that uses mathematical symbols or variables to show a relationship

-Represented by facts

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-Statements that have been proven

-Connect explanations of conceptual understandings

-Represented by principles

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The symbiotic relationship between the two structures

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The symbiotic relationship between the two structures

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Refers to the knowledge and the strategies and skills needed for mathematical understanding

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-Small operations or actions that are embedded in strategies

-Ex: Being able to create a table of values

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-Broad techniques that students draw upon when learning mathematics

-Ex: Problem-solving

-Composed of strategies, algorithms, and skills

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-Many skills that learners use methodically and systematically to support learning

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-Consist of skills, which allow learners to follow a set of rules leading to a specified outcome

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-A defined series of skills and strategies that form mathematical techniques

-Should be engaging, challenging, and motivating

-Ex: look for a pattern, guess and check, act it out, preserve

Steps:

1. Understand the problem

2. Devise a plan

3. Carry out the plan

4. Review and extend

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-The ability to make generalizations and provide explanations and justifications for arguments is key to the reasoning skill

-Builds mathematical memory to understand concepts

It gives learners opportunities to make mistakes

-Ex: make generalizations, ask "why", use data to make a conjecture

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-Talking and writing about mathematics

-presenting different methodologies allows learners to see different perspectives

-Ex: Listen, discuss, and use correct mathematical terminology, explain ideas

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-The learner's ability to see connections between facts and how they relate to each other, make real-world connections to mathematics, make connections between symbols and procedures, and connect new problems to old problems

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-Are ways to express mathematical ideas

-Helps learners organize, record, and communicate mathematical ideas

-Ex: graphs, tables, symbols, drawings

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A communication tool to help students develop computational fluency by comparing number relationships and looking at different ways to perform operations

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Number Talks are a valuable classroom routine for building flexibility, efficiency and accuracy in mathematical thinking through the articulation and sharing of mental math strategies. When used regularly Number Talks provide a powerful way to help students understand the numerical relationships that are critical to understanding mathematics and result in classrooms where students feel encouraged to explain, justify, and make sense of math.

The anchor charts on this page provide examples of five addition strategies that can be explored during Number Talks, namely Use Doubles, Make a Ten, Place Value, Add Up in Chunks and Compensation. These five strategies can all be extended from one-digit to multi-digit numbers, fractions and decimals.

Free Downloads: Copies of the addition strategy charts shown below (with some additional charts) can be downloaded here. For copies of subtraction strategy charts .
An important aspect of a Number Talk is that students articulate and share their strategies in order to justify their thinking and make sense of the math. To scaffold this work a set of 30 Math Talk Stems for classroom display and a student Math Talk bookmark can be downloaded here in full page size or here in half-page size.

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Number Talks are a valuable classroom routine for building flexibility, efficiency and accuracy in mathematical thinking through the articulation and sharing of mental math strategies. When used regularly Number Talks provide a powerful way to help students understand the numerical relationships that are critical to understanding mathematics and result in classrooms where students feel encouraged to explain, justify, and make sense of math.

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Macro, Meso, and Micro Concepts in Mathematics

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Macro, Meso, and Micro Concepts in Mathematics

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Mathematics is structured by its concepts and the conceptual relationships

Mathematics is a concept-driven discipline