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Math PK-2

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Math PK-2 > Strategies

Math PK-2

Select one or more factors to see the strategies that support your chosen factor(s). For each strategy, we provide ideas for classroom and product application, videos, and further resources.

Strategies

Accessible Vocabulary & Syntax

Teachers support language development by using and providing vocabulary and syntax that is appropriately leveled (e.g.

Brief Instruction Steps

Content that is provided in clear, short chunks can support students' Working Memory.

Building Blocks

Building with blocks is ideal for promoting early geometric and Spatial Skills.

Building Trusting Relationships

Building positive and trusting relationships with learners allows them to feel safe; a sense of belonging; and that their academic, cognitive, and social and emotional needs are supported.

Collaborative Problem Solving

As students solve problems in a group, they learn new strategies and practice communicating their mathematical thinking.

Concrete-Representational-Abstract (CRA)

CRA is a sequential instructional approach during which students move from working with concrete materials to creating representational drawings to using abstract symbols.

Creating Visual Representations

Students activate more cognitive processes by exploring and representing their understandings in visual form.

Cumulative Review

Continual use of foundational skills with different problems reinforces a conceptual understanding of math skills.

Daily Arithmetic Fact Practice

10 minutes in each math session devoted to building fluent retrieval of basic arithmetic facts sets the foundation for learning new concepts.

Daily Review

Daily review strengthens previous learning and can lead to fluent recall.

Dim or Natural Lighting

Dim or natural lighting provides a calming environment.

Direct Instruction: Explicit Number Naming Approach

In explicit number naming, the structure of the number name labels the number in Place Value order and clearly states the quantity.

Direct Instruction: Math Language

Knowing the language of math is critical because students must use this language to understand math concepts and determine calculations needed.

Direct Instruction: Patterning

Thinking of and about patterns encourages learners to look for and understand the rules and relationships that are critical components of mathematical reasoning.

Direct Instruction: Problem Structures

Teaching students to recognize common problem structures helps them transfer solution methods from familiar to unfamiliar problems.

Direct Instruction: Problem-solving Strategies

Discussing strategies for solving mathematics problems after initially letting students attempt to problem solve on their own helps them understand how to organize their mathematical thinking and intentionally tackle problems.

Discussing Emotions

Teaching students how to label, identify, and manage Emotion helps them learn Self-regulation skills.

Dot Cards

Dot cards build number sense and promote early math skills, particularly Spatial Skills and Non-symbolic Number knowledge.

Encourage Student Self-advocacy

Overtly encouraging all students to seek support and ask questions creates a safe space for risk-taking and skill development.

Family Engagement

Students are more likely to come to school when families feel like a valued part of the community.

Foster Growth Mindset

Teachers can help students understand that learning involves effort, mistakes, and reflection by teaching them about their malleable brain and modeling their own learning process.

Free Collaborative Play

Free collaborative play supports learner interests and promotes the development of more complex social interactions.

Gallery Walk

As students walk through stations working in small groups, the social and physical nature of the learning supports deeper understanding.

Gestures

Adding motions to complement learning activates more cognitive processes for recall and understanding.

Goal Setting & Monitoring

Setting overall goals, as well as smaller goals as steps to reaching them, encourages consistent, achievable progress and helps students feel confident in their skills and abilities.

Growth Mindset Feedback

Providing feedback that focuses on the process of developing skills conveys the importance of effort and motivates students to persist when learning.

Guided Inquiry

In guided inquiry, teachers help students use their own language for constructing knowledge by active listening and questioning.

Guided Play

Teaching students through guided play encourages them to take an active role in their learning and supports the development of a broad array of cognitive skills.

Guided Practice

Spending time with new content helps move concepts and ideas into Long-term Memory.

Incorporate Students' Cultural Practices

Learning about students' cultures and connecting them to instructional practices helps all students feel like valued members of the community.

Individual Deliberate Practice

Practicing until achieving several error-free attempts is critical for retention.

Individual Spaces

Having space where students can go supports Self-regulation and individual deliberate practice.

Learning Strategy & Tool "Fair"

To promote acceptance of learning diversity, students explore learning tools and strategies to see how they work and why they and others might use them.

Math Centers

Math centers with math games, manipulatives, and activities support learner interests and promote the development of more complex math skills and social interactions.

Math Games: Numerical & Spatial

Math games use numbers and Spatial Skills, allowing students to practice many math skills in a fun, applied context.

Math Songs

Rhyming, alliteration, and other sound devices reinforce math skills development by activating the mental processes that promote memory.

Math Talks

When students have meaningful conversations about math and use math vocabulary, they develop the thinking, questioning, and explanation skills needed to master mathematical concepts.

Mindfulness Activities

Through short but regular mindfulness activities, students develop their awareness and ability to focus.

Mnemonic Device

Creating patterns for remembering classroom processes, narrative structures, etc.

Mobility & Flexibility

Multiple tables and chairs on wheels allow for setting up the classroom to support the desired learning outcomes of each activity.

Model Assignment or Skill

By talking through their thinking at each step of a process, teachers can model what learning looks like.

Model Positive Connections to Math

Teachers sharing math-to-self, math-to-math, and math-to-world connections models this schema building.

Movement Breaks

Brain breaks that include movement allow learners to refresh their thinking and focus on learning new information.

Multimodal Instruction

Instruction in multiple formats allows students to activate different cognitive skills to understand and remember the steps they are to take in their math work.

Multiple Display Boards/Screens

Multiple display spaces help develop oral language skills as well as Social Awareness & Relationship Skills by allowing groups to share information easily as they work.

Multiple Representations: Graphic Organizer

Visualizing how ideas fit together helps students construct meaning and strengthen recall.

Multiple Representations: Manipulatives

Providing physical representations of numbers and math concepts helps activate mental processes.

Multiple Representations: Number Line

Easy access to seeing the relationships between numbers promotes number sense as students see these connections repeatedly.

Multiple Representations: Visual Representations

Visual representations help students understand what a number represents as well as recognize relationships between numbers.

Multiple Writing Surfaces

Multiple writing surfaces promote collaboration by allowing groups to share information easily as they work.

Music & Dance

Connecting information to music and dance moves enhances Short-term and Long-term Memory by drawing on auditory processes and the cognitive benefits of physical activity.

Non-intensive HNE Intervention Program

A parent evening meeting about how to support numeracy at home with one follow-up meeting with each family has shown strong results for students' math development.

Physical Activity & Recess

Research shows physical activity improves focus and creativity.

Predictability: Environment & Structure

Maintaining consistent classroom routines and schedules ensures that students are able to trust and predict what will happen next.

Pretending

Pretending allows students to step back from a problem or task and think about it from multiple angles.

Prompt Cards

Cards with strategies for managing emotions help students remember how to act when faced with strong feelings.

Quiet Classroom/Pockets of Quiet

Decreasing extra audio input provides a focused learning environment.

Real-world Math

When teachers connect math to the students' world, students see how math is relevant and applicable to their daily lives.

Reciprocal Teaching: PALS

Students deepen their understanding and gain confidence in their learning when they explain to and receive feedback from others.

Reflect on Learning

Providing space and time for students to reflect is critical for moving what they have learned into Long-term Memory.

Response Devices

Response devices boost engagement by encouraging all students to answer every question.

Rich Resources: Audio & Braille

Math games and manipulatives for vision differences support math development for learners with visual needs.

Rich Resources: Children's Literature

Children's literature can be a welcoming way to help students learn math vocabulary and concepts.

Rich Resources: Diversity

Multicultural resources, such as posters with different types of people and word problems based in different settings, allow all students to see themselves in their math work.

Sensory Stimulation

Incorporating multiple senses with strategies like chewing gum, using a vibrating pen, and sitting on a ball chair supports focus and Attention.

Sound Level

Providing ways for students to adjust sound level supports individual auditory needs.

Sound-blocking Devices

Using earplugs or headphones can increase focus and comfort.

Student Choice

Providing students a voice in their learning is critical for making learning meaningful.

Temperature

Providing ways for students to meet their individual temperature needs supports focus and Self-regulation.

Text-to-speech Software

Transforming written text into audio activates different parts of the brain to support learning.

Think-Pair-Share

Students develop their skills by listening to and speaking with others in informal ways.

Think-alouds

When students explain their thinking process aloud with guidance in response to questions or prompts, they recognize the strategies they use and solidify their understanding.

Three-phase Lesson Format

Three-phase lesson format is a problem-solving structure to promote meaningful math learning by activating prior knowledge, letting students explore mathematical thinking, and promoting a math community of learners.

Timers

Timers help students learn to self-pace and transition.

Tossing Activity

Tossing a ball, beanbag, or other small object activates physical focus in support of mental focus.

Uncluttered Environment

Spaces that are structured, organized, and clean provide increased room for collaboration and active learning.

Untimed Tests

Untimed tests provide students the opportunity to flexibly and productively work with numbers, further developing their problem-solving abilities.

Verbal Repetition

Having students verbally repeat information such as instructions ensures they have heard and supports remembering.

Videos

Providing visuals to introduce, support, or review instruction activates more cognitive processes to support learning.

Visual Reading Aids

Visual supports, like text magnification, colored overlays, and guided reading strip, help students focus and properly track as they read.

Wait Time

Wait time, or think time, of three or more seconds after posing a question increases how many students volunteer and the length and accuracy of their responses.

Word Walls

A word wall helps build the mathematical vocabulary and Language Skills that are necessary for problem solving.

Math PK-2

Students are beginning to understand the concept of number.

Early number knowledge and math skills are fostered by children’s Home Learning Environment.

  • Language Skills, supported through access to books and reading to children, are an important component of early math learning and predict numeracy outcomes.

Children move from reciting the count sequence (1,2,3,4...) without conceptual understanding, to understanding what this order means, and eventually developing Cardinality—an understanding of how many items are in a set.

  • Both formal math teaching and talk, such as practice Counting, as well as informal, math-related games and activities, such as measuring for baking, can support early math skills.

Students learn to flexibly represent and manipulate numbers.

Children’s ability to perform simple arithmetic Operations, including addition and subtraction of multiple numbers, is a foundational math skill and is predictive of later math success.

  • Manipulating real objects can help make these abstract concepts more concrete.

Flexibly representing numbers in different ways allows students to better understand them, how they relate to each other, and how to best work with them to solve problems.

  • These skills are supported by an understanding of the Place Value system for multi-digit numbers, including how numbers can be readily decomposed and re-combined.

Students make connections and persist through challenges.

Students must be persistent and work through the challenge of gaining a deep conceptual understanding of mathematics.

  • Students who find math relevant or fun are motivated to learn—an important mindset to develop early on that can support productive struggle.

Students rely on support from teachers and caregivers to model positive attitudes towards math, as they may pick up on math anxiety and internalize it themselves.

  • Providing feedback on the process of learning and students’ effort can also support a growth mindset, which allows students to view their progress positively.

Next:

Students learn to flexibly represent and manipulate numbers.

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Next:

Students make connections and persist through challenges.

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Next:

Students are beginning to understand the concept of number.

View Theme 1