Inquiry and problem solving refer to an array of learner-centered processes that facilitate deep engagement with a question or problem and strategies to develop subsequent solutions and explanations.
With any approach to inquiry and problem-solving, students follow a series of phases or specific discipline-based practices to take them through an intentional process. These phases or practices are not necessarily completed in a linear or lock-step manner, but provide some structure for students to address a question, issue, problem, or need.
Common elements of inquiry and problem-solving include:
The elements are most effective when applied in an iterative cycle, so that students have the opportunity to revise their solutions and explanations based on utility, analysis, and feedback. Here's how different sets of discipline-based practices and inquiry models can align to the four common elements of inquiry.
Inquiry Elements
Scientific and Engineering Practices
Standards for Mathematical Practice
Inquiry Arc
Design Thinking
Asking questions or defining problems
Asking questions and defining problems
Make sense of problems and persevere in solving them
Developing questions and planning inquiries
Empathize with users
Define the problem
Exploring solutions or explanations
Planning and carrying out investigations
Make sense of problems and persevere in solving them
Developing questions and planning inquiries
Ideate potential solutions
Prototype solutions
Analyzing or testing solutions or explanations
Developing and using models
Analyzing and interpreting data
Using mathematics and computational thinking
Constructing explanations and designing solutions
Model with mathematics
Reason abstractly and quantitatively
Use appropriate tools strategically
Attend to precision
Look for and make sense of structure
Look for and express regularity in repeated reasoning
Applying disciplinary concepts and tools
Evaluating sources and using evidence
Test solutions
Communicating or taking action on solutions or explanations
Engaging in argument from evidence
Obtaining, evaluating and communicating information
Construct viable arguments and critique the reasoning of others
Communicating conclusions and taking informed action
Implementation of solution
Inquiry and problem-solving opportunities encourage students to engage with relevant concepts and skills within authentic, real-world contexts. Research suggests that combining real-world application with sustained participation in inquiry and problem solving experiences can lead to increased student engagement and support deeper learning of concepts and skills. Additionally, opportunities for inquiry and problem solving can help students develop:
Developing these skills prepares students for college, career, and community success, and help students meet the HIDOE general learner outcomes. To further examine the benefits of inquiry-based learning, see the following resources:
Students can engage in deep learning of concepts and skills through a variety of inquiry-based models, including: instructional approaches, instructional sequences, and/or design processes.
Examples of inquiry-based models, their essential features and ideas for getting started with them are presented below:
Whatever process or model is chosen to engage students in inquiry and problem-solving, it is important to consider different approaches to structured vs open inquiry. For many students and at earlier grade levels, a scaffolded approach is ideal when students first encounter an inquiry investigation. Considering a variety of scaffolding and differentiation approaches will ensure that students’ different learning needs are addressed. Over time, with more practice, the teacher can gradually release decision-making and control to the students. It is also helpful for the teacher to consider the types of questions they will ask students to support their inquiry process.
The following sites showcase examples of learning experiences that are inquiry- and problem-based.
Visible Thinking: A site with a variety of thinking routines that can be used to scaffold students’ inquiry and problem solving skills.
Design Thinking: Resources for facilitating design thinking with students curated by Hawai‘i educators.
Making Sense of Problems: A site with examples of classroom practice of the standards for mathematical practice, including, “Making sense of problems and persevere in solving them.”
Hawai‘i educators developed inquiry-based STEM Units that align to the FAIR features of STEM learning experiences.
C3 Hawai‘i Hub: Provides inquiry lessons for social studies developed by Hawai‘i educators using the inquiry design model.
Provides inquiry lessons for science developed by Hawai‘i and other U.S. educators using the Gather - Reason - Communicate Approach and 5E instructional sequence.