## 1. Use examples and visuals

## 2. Relational vs. Instrumental understanding

## 3. Strands of Math

### 3.1. Conceptual understanding - comprehension of mathematical concepts, operations, and relations

### 3.2. Procedural fluency - skill in carrying out procedures flexibly, accurately, efficiently, and appropriately

### 3.3. Strategic competence - ability to formulate, represent, and solve mathematical problems

### 3.4. Adaptive reasoning - capacity for logical thought, reflection, explanation, and justification

### 3.5. Productive disposition - habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy

## 4. Relational Understand and Instrumental Understanding

### 4.1. Instrumental - knowing and applying the rule

4.1.1. 3 Main Advantages:

4.1.1.1. Easier to understand

4.1.1.2. Positive results are instantaneous

4.1.1.3. Correct answers can be obtained very quickly and consistently

### 4.2. Rational - knowing and applying the rule while also being able to know why a rule works and connect one rule with another

4.2.1. Relational is much more extensive

## 5. Dan Meyer: Math Class Needs a Makeover

### 5.1. Education system is failing our kids when it comes to mathematics

5.1.1. Explains and demonstrates how confusing and manipulative textbook questions are today; they aren’t engaging students at all

### 5.2. 5 key aspects that needed to be included in the math curriculum:

### 5.3. 1. Use multimedia

### 5.4. 2. Encourage student intuition

### 5.5. 3. Ask the shortest question you can

### 5.6. 4. Let students build the problem

### 5.7. 5. Be less helpful

## 6. Arbitrary vs. Necessary math

### 6.1. “With doubt deviation from the norm progress is not possible”

6.1.1. Success comes from understanding

6.1.2. Have students explain their reasoning

6.1.3. Math class is also a time for talk

6.1.4. Make writing a part of math learning

6.1.5. Support learning with manipulatives

6.1.6. Confusion is part of the process

6.1.7. Encourage different ways of thinking