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Teaching math has evolved from requiring students to memorize steps and procedures to helping students build strong foundational skills, grasp complex concepts, and become confident problem-solvers. Today, we are actively working to make math more meaningful to everyday life.
So, should teaching math use inquiry based learning or direct instruction? After years of training and experience, I truly believe that inquiry-based learning should play a large role in your math instruction but I do think there’s a time and place for both. If you’re short on time and would rather have it done for you, check out our complete inquiry-based math curriculums for the Ontario Curriculum here.
But first…
What exactly is math Inquiry Based Learning?
Inquiry-based learning in math (IBL) is a student-centered approach where students explore mathematical concepts through questioning, investigation, and hands-on activities.
Using the IBL framework, teachers act as facilitators, guiding students as they engage in meaningful, often open-ended math tasks.
What is Direct Instruction in Math?
Direct instruction in math is a teacher-centered approach that emphasizes clear, structured, step-by-step teaching. Often we see and hear the framework “I do, We do, You do” or ‘gradual release of responsibility’. It offers an approach to learning where teachers demonstrate and students follow specific steps, strategies or algorithms.
Why You Should Be Teaching Math Through Inquiry
1. Builds Deep Conceptual Understanding
- Encourages Exploration: IBL allows students to explore math concepts firsthand, which leads to a deeper, more intuitive understanding.
- Promotes Critical Thinking: Rather than simply following steps, students learn to ask questions and think critically while developing their own meaningful solutions.
- Reduces Memorization: Students focus on understanding the “why” behind mathematical concepts, which minimizes the need to memorize rules (which can easily be forgotten).
- Flexible Math Thinking: Students get to solve problems in ways that make sense to them. They also see multiple strategies for the same problem which increases the likelihood of finding something that works for them.
2. Develops Problem-Solving Skills
- Encourages Perseverance: Students learn resilience as they work through complex, sometimes challenging problems.
- Teaches Multiple Strategies: By exploring multiple paths to a solution, students develop flexible problem-solving skills they can apply across situations.
3. Strengthens Collaboration and Communication
- Fosters Group Work: Inquiry tasks often encourage collaboration, allowing students to explain their reasoning and learn from peers.
- Improves Communication Skills: Articulating math ideas helps students clarify their understanding and strengthens their communication abilities.
4. Promotes Independence and Initiative
- Encourages Ownership: Students are often more motivated when they take charge of their own learning journey.
- Inspires Curiosity: Inquiry-based tasks can be more engaging and encourage students to dig deeper out of genuine curiosity.
5. Reduces the teacher’s workload
- Less Planning and Prep Needed: Once you get the hang of math inquiry teaching, lessons will take less work to plan. A good inquiry-based math lesson is centred around 1-3 questions rather than the many questions you’d have to prepare otherwise. The key is to create good questions!
- Less Marking: If you no longer rely on worksheet after worksheet of boring practice questions to teach a concept, you no longer have to mark them! A lot of assessment can come through observation and anecdotal notes during the lesson, not after.
So Why not Always use Inquiry-Based Math Learning?
At the beginning of this post I said that I believe there’s a time and place for both teaching styles. But if inquiry-based learning is so great (and it is) then why not use it all the time?
There are some drawbacks to inquiry-based learning in math and some situations where I don’t believe it’s the most effective way to teach.
1. It is Time-Consuming
- Pacing Challenges: Inquiry-based activities often take longer, which can be challenging in classrooms with tight schedules or pacing guides.
- Hard to Assess Quickly: Gauging understanding may require multiple assessments or observations, which can be time-intensive.
Counter-Argument: While a lesson will take longer, students shouldn’t need as many lessons to master a concept.
2. Can Lead to Gaps in Procedural Knowledge
- Limited Practice for Skills: Without structured practice, students may struggle to master specific skills, especially in areas like computation.
- Risk of Misconceptions: Students might develop incorrect understandings if they don’t receive enough guidance during the exploration process. (Note: this is why the consolidation phase of the 3-part math lesson is the most important part.)
Counter-Argument: If consolidation is done well, students will learn effective procedures (they just may not be the ‘traditional’ ones we learned).
3. Challenging for Students Who Prefer Structure
- Can Be Overwhelming: Some students may feel lost without clear instructions, especially if they are accustomed to step-by-step guidance.
- Inconsistent Results: The effectiveness of IBL can vary widely depending on students’ readiness and prior knowledge.
Counter-Argument: Students who struggle with the lack of structure may benefit the most from inquiry style lessons – but it will take time!
When Should I use Inquiry-Based Learning vs. Direct instruction?
Both methods have strengths, and combining them can create a dynamic, responsive classroom that meets diverse learning needs. Here are some tips for integrating both approaches.
✓ Start with Inquiry, Then Move to Direct Instruction
Use inquiry to introduce new concepts, allowing students to explore and develop intuitive understandings. Once they’ve built this foundation, use direct instruction to clarify misconceptions and teach procedural skills.
Many of our 3-part math lessons begin with an inquiry approach which is solidified with some follow-up direct instruction. We’ve found this to be the most successful for building a solid understanding.
✓ Build Fluency with Direct Teaching then Apply Skills to Inquiry Problems
Incorporate direct instruction for skills that require fluency (like basic math operations), then transition to inquiry for applying those skills in real-world problems or complex tasks.
✓ Student-Generated Algorithms First
Before teaching a specific algorithm, allow students to try solving problems with their own strategies. This promotes confidence, builds flexible thinking and develops a better of understanding of what is really happening behind algorithms.
Looking for an Inquiry-Based Math Curriculum for Ontario?
We couldn’t find the resources our students needed so we created them! Save yourself countless hours and check out our comprehensive math program that covers the entire 2020 Ontario Math Curriculum for grades 4 – 8.
You’ll get lessons, math centres, practice worksheets, review games and assessments for the entire year for less than your daily double-double!
Final Thoughts on Inquiry-Based Learning in Math
Both inquiry-based learning and direct instruction play vital roles in a comprehensive math education. When used strategically, they can complement each other to provide students with a rich, well-rounded math experience.
Inquiry-based learning fosters curiosity, critical thinking, and deep understanding, while direct instruction ensures students gain fluency and accuracy in essential skills. By combining the best of both worlds, you can create a math classroom where students become confident, engaged, and independent learners.
READ NEXT: Delve deeper into the topic with our 7 top tips for inquiry-based math lessons.
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Inquiry-Based Learning in Math
Key Characteristics of Inquiry-Based Math Learning:
Inquiry based learning in math emphasizes exploration and discovery, encouraging students to investigate, ask questions, and uncover math concepts through hands-on activities.
- Encourages students to pose questions and explore solutions independently or in groups.
- Builds skills like critical thinking, problem-solving, and collaboration.
- Promotes deeper conceptual understanding by involving students in active discovery.
- Often follows a cycle of posing questions, exploring, reflecting, and sharing.
Inquiry-based learning does NOT need to be this big, complex project. For a long time, this false belief held me back from getting started!
Teaching Math Through Direct instruction
In contrast, direct instruction, often organized in an “I do, We do, You do” format, offers a more structured approach where teachers demonstrate, guide, and gradually release responsibility to students.
- I do: The teacher models the concept or skill, providing explicit instructions.
- We do: The teacher and students work together on examples, reinforcing the skill.
- You do: Students practice independently to solidify their understanding.
Direct instruction can be especially effective when teaching algorithms, formulas, or specific problem-solving strategies. However, over-relying on it can lead to rote memorization rather than deep understanding.
Pros of Direct Instruction in Math
1. Efficient for Teaching Specific Skills
- Clear and Direct: Direct instruction is ideal for teaching specific procedures, algorithms, or skills that require precision and repetition.
- Minimizes Confusion: By following clear steps, students can feel more confident and avoid misconceptions.
2. Builds Fluency and Procedural Knowledge
- Supports Automaticity: With guided practice, students can achieve fluency in foundational skills like multiplication or division.
- Great for Reinforcement: Direct instruction provides the repetitive practice necessary for reinforcing key math skills.
3. Structured and Predictable
- Ideal for Sequential Learning: The “I do, We do, You do” structure provides a scaffold that gradually increases student responsibility.
- Suitable for Students Who Need Structure: For students who thrive on predictability, direct instruction offers a comfortable learning environment.
When to Use Direct Instruction:
- Teaching Specific Algorithms or Formulas: Direct instruction is most useful for clear-cut procedures like solving equations or calculating area.
- After Building Conceptual Understanding Through Inquiry: After students have explored a concept through IBL, direct instruction can clarify specific methods or procedures.
- When Students Need Extra Practice: For skills that require fluency, direct instruction offers structured repetition and practice.
Cons of Direct Instruction in Math
1. May Hinder Conceptual Understanding
- Focuses on “How” Over “Why”: Direct instruction can sometimes skip over the underlying reasoning, which may lead to shallow understanding.
- Limits Exploration: Without opportunities to explore, students may miss out on developing critical problem-solving skills.
2. Can Lead to Passive Learning
- Encourages Memorization: Direct instruction often relies on rote learning, which may lead students to focus on memorizing steps rather than understanding concepts.
- Reduced Engagement: This structured approach can sometimes feel repetitive or unengaging, especially for students who thrive on creativity and exploration.
3. May Not Build Higher-Order Skills
- Misses Out on Critical Thinking: Direct instruction emphasizes practice over problem-solving, which can limit students’ opportunities to develop higher-order thinking skills.
- Doesn’t Encourage Collaboration: Unlike inquiry tasks, direct instruction is typically individual, which reduces opportunities for peer interaction and collaborative learning.
