**Mathematical Mindsets – What They Are:**

- Present naturally in children who like to inquire, build things, solve puzzles, notice/make patterns, etc
- Seeing math as a conceptual subject that they can grow to make sense out of
- Stepping forward deliberately and deeply in math while making sure each step makes intuitive sense before moving more forward

**How to Stunt Development of Mathematical Mindsets:**

- Presenting math as a dry set of methods can stop development of mathematical mindsets
- this is especially true if methods do not make intuitive sense to students

- Presenting math as seires of short questions obscures growth opportunities – math is something you get or you don’t, instead of something to make sense of
- Assigning large homework sets with simple isolated problems
- Valuing rote memorization and speed over deep thinking and conceptual understanding

**How to Develop Mathematical Mindsets:**

- Encourage students to play with numbers, shapes and puzzles
- Present math as a broad landscape of unexplored puzzles that create opportunities for wandering around, asking questions, thinking of relationships, …
- Present math as a flexible conceptual subject that is about thinking and sense making
- Be mindful when designing practice set because mindless practice does not lead to brain growth, thoughtful practice does – mindful practice involves applying same strategy to many different situations
- Assign less homework that requires more reflection – example 5 carefully selected problems and one student chosen reflection question such as:
- What are the main mathematical ideas we discussed in class today?
- What questions do you have about ________?
- Describe a mistake or misconception you or a student had in class today. What did you learn from this mistake or misconception?
- How did you approach your practice set? Was your approach successful? What did you learn from your approach?

**Cultivating Number Sense:**- Approach arithmetic operations flexibly and conceptually:
- concept of sum -> counting on
- concept of product -> repeated addition

- Try to help students make sense of concepts and patterns so that their brain can more readily go from
*compression*more efficient storage of concepts (not rules)**–** - Math facts are stored in working area of brain – this area can be blocked when students are stressed
- Avoid techniques that value speed of knowing math facts (example – timed tests)
- Do NOT emphasize rote knowledge and speed – gets in the way of thinking about numbers and their relationships to each other
- Teach strategies instead of memorization of facts
- example: 17 x 8
- strategy – 17 x 10 – 17 x 2 = 170 – 34 = 136
- memorize 17 x 8 = 136

- example: 17 x 8
- play math games that activate both sides of brain by using visual and intuitive math thinking:
- example: grid multiplication game
- object of game – fill as many grid squares as possible in a 10 x10 grid
- roll 2 number dice – color in area that corresponds to product of 2 numbers rolled and write number sentence
- partners take turns rolling dice, coloring in areas and writing related number sentences until no more arrays can be added to the grid

- example: multi rep matching game
- players take turns picking pairs of equivalent cards and explaining why they are equivalent
- find cards and more cool strategies here

- example: grid multiplication game
- Do “Number Talks” as warmups
- pose a tough problem that can be solved multiple ways
- ask students to solve it using mental math
- have students present their mental math solutions
- Books / Videos with Number Talks:

- Recommend math games that emphasize concepts over drill & kill:

- Approach arithmetic operations flexibly and conceptually:

Developing mathematical mindsets will help student approach mathematics with a growth mindset. Mathematical mindsets help students understand math concepts more deeply and apply them more flexibly. Valuing conceptual understanding over speedy rote memorization is one way to cultivate mathematical mindsets.

**Preparation Steps**

- Research more strategies for developing mathematical mindsets. See Mathematics articles for ideas.
- Develop lesson plan components (Warmups, practice sets, discussions, activities, etc) that promote mathematical mindsets

**Early Implementation Steps**

- Regularly use scaffolding and assessments that promote mathematical mindsets
- Have students reflect often on what they are learning
- about concepts
- about how concepts are applied to problem solving
- from mistakes
- from different problem solving approaches

**Advanced Implementation Steps**

- Have students interact with mathematicians and professionals who apply mathematical reasoning often and learn about their problem solving approaches
- Develop bank of Number Talk problems and games that promote mathematical mindsets and incorporate these into classroom routines

- Mathematics articles
- Understanding articles