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Math PK-2 > Strategies > Guided Inquiry

Guided Inquiry

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Overview

In guided inquiry, teachers help students use their own language for constructing knowledge by active listening and questioning. While exploring and investigating a problem, teachers guide students to talk through their thinking, which supports development of students' mathematical reasoning and Language Skills.

Teachers can also target specific math skills through guided inquiry activities. Arithmetic Fact Retrieval, Cardinality, Counting, Estimation, Operations, Place Value, and Symbolic Number skills can all be supported through guided inquiry with problems using these skills.

Use It in the Classroom

Watch how this school embraces inquiry-based learning in multiple subjects, including reading and writing. As students and teachers ask questions that drive deeper thinking, students develop their curiosity and excitement for learning.

  • The teacher plays a crucial role in guided inquiry by raising students' awareness of how to use language as a tool for reasoning. Teachers can ask questions that provoke thinking and provide their own ideas for possible answers that stimulate further questions. Additionally, because asking questions elicits deeper thinking and can challenge previous thinking, inquiry in math has the potential to foster growth mindsets.

    • Design It into Your Product

  • Products can embed questions that pop up while learners are exploring content to prompt deeper, reflective thinking at key stages.
    • View References

    Resources

    Below are additional examples, research, and professional development. These resources are possible representations of this strategy, not endorsements.
    Examples

    Ikea Effect

    Tips for implementing guided inquiry in math through an Ikea analogy

    Examples

    Inquiry-Based Learning

    Video on student-led questions through inquiry-based learning

    Examples

    Questions to Guide Investigation

    Sample inquiry-based questions

    Research

    Language, Space & Time

    Subtopic that explores how language can shape our perception and representation of abstract concepts on Digital Promise's Research Map

    Research

    Learning Communities

    Subtopic that includes research on communities of learners on Digital Promise's Research Map

    Research

    Student Confidence in Math

    The importance of embracing errors as learning, emphasizing reasoning, and relating math to student strengths from Digital Promise's Ask a Researcher

    Research

    Teaching for Collaboration & Creativity

    Subtopic that includes research on instructional approaches to encourage collective problem-solving on Digital Promise's Research Map

    Research

    Using Guided Inquiry

    Detailed description of guided inquiry with example math activities

    Factors Supported by this Strategy

    Numeracy and Mathematics
    Arithmetic Fact Retrieval
    Cardinality
    Counting
    Estimation
    Language Skills
    Linearity
    Mathematical Flexibility
    Operations
    Place Value
    Symbolic Number
    Cognition
    Attention
    Cognitive Flexibility
    Inhibition
    Long-term Memory
    Short-term Memory
    Spatial Skills
    Speed of Processing
    Visual Processing
    Working Memory
    Social and Emotional Learning
    Emotion
    Student Background
    Adverse Experiences
    Home Learning Environment
    Physical Fitness
    Safety
    Sleep
    Social Supports
    Socioeconomic Status

    More Instructional Approaches Strategies

    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.

    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.

    Family Engagement

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

    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.

    Mindfulness Activities

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

    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.

    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.

    Real-world Math

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

    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.

    Untimed Tests

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

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