When it comes to teaching Maths, there is no one-size-fits-all approach. Different students have different learning styles, so it's important to cater to these differences in order to ensure that everyone is able to engage with the material and reach their full potential.
One approach that has been shown to be particularly effective is inquiry-based learning. But what exactly is inquiry-based learning? And why is it so important in Maths?
What is the inquiry learning method?
Inquiry-based learning is a student-centred approach to learning that encourages learners to ask questions, investigate problems, and find solutions for themselves. This type of learning has been shown to be highly effective in developing critical thinking and problem-solving skills.
One of the key benefits of inquiry-based learning is that it allows students to learn at their own pace. This is particularly important in maths, as some concepts can be difficult to grasp and require time and practice to master.
By being able to investigate problems and find solutions for themselves, students are more likely to retain what they have learned. Additionally, this type of learning can encourage creativity and independent thinking.
What are the 4 types of inquiry-based learning?
There are four main types of inquiry-based learning. In fact, think of them as four levels that decrease in structure:
Confirmation inquiry: This is the simplest and most structured type of inquiry-based learning. Students are given a problem, the solution and a set of instructions on how to solve it. They then follow these instructions to confirm that the answer is correct.
Structured inquiry: Students are still given a problem to solve, as well as a prescribed method. They must use the method to try and craft a solution.
Guided inquiry: This is an even more open-ended type of discovery learning, where students are only given a research question. They must design their own method and tests to reach a conclusion.
Open inquiry: Students formulate their own questions to investigate. They design their own method and execute it, presenting their findings and results.
According to Banchi and Bell (2008), teachers should start inquiry instruction at lower levels and gradually move towards open inquiry in order to effectively develop students' inquiry skills. Open inquiry exercises can only be successful if students are motivated by intrinsic interests, and if they have the skills to conduct their own research.
Regardless of which type of inquiry-based learning you choose to use, the important thing is that students are actively engaged in the learning process and able to direct their own investigation.
8 Benefits of inquiry-based learning
An Inquiry-based learning approach has a number of benefits for science education, particularly in the study of mathematics. When implemented correctly, it can be a powerful tool for educators. We take a look at the top 8 benefits of inquiry-based teaching below.
1. Boosts problem-solving and critical thinking skills
Inquiry-based learning encourages students to think critically. By being actively involved in the learning process, they'll begin to question their approach and look for alternative solutions to problems.
The cognitive skills that students gain through inquiry learning can also be transferred to other areas of their lives. From maths problem solving techniques to creative thinking, the benefits go far beyond the classroom.
2. Develops a deeper understanding of mathematical concepts
Inquiry teaching and learning can help students develop a deeper understanding of Maths, as compared to information delivery. When you explore a mathematical concept in a more hands-on way, you begin to question why it exists, where it came from, how it works and in what scenarios it can be applied.
This is because the process of asking open questions and then finding the answers yourself helps you feel more in control of your knowledge. This type of experiential learning places the student's role at the centre of the experience, rather than the teacher.
3. Encourages students to think creatively about solutions
The beauty of Maths is that there is never just one way to solve a problem. Inquiry learning can encourage students to explore different methods and to think creatively about how they can arrive at a solution.
By allowing students to develop their own methods, they'll be more likely to find a solution that makes sense to them. This leads to better retention, due to them taking ownership of the entire process.
4. Allows students to learn at their own pace
We know the importance of self-paced learning in boosting academic performance. If students are in control of their investigation, they can move through the content at a speed that's comfortable for them.
This is particularly beneficial for struggling students, or for those who want to challenge themselves and move ahead more quickly. Discovery learning provides the perfect balance and architecture to personalise content at both ends of the spectrum, ensuring that every student is catered for.
5. Improves student motivation and engagement
Inquiry learning can be a great way to foster a love for learning in your students. When children are engaged and excited about new knowledge, they put in the effort required to succeed.
Empowering students with the direction of their own learning can also lead to improved motivation. This is because they have a personal stake in the outcome.
A Harvard educational review found inquiry instruction can also lead to students becoming motivated by the intrinsic reward of learning itself!
6. Fosters a positive attitude towards maths
Problem-based learning can help make Maths more interesting and enjoyable for students, which in turn can lead to improved grades and a better conceptual understanding of the content.
A positive attitude toward Maths is essential for academic success and an inquiry-based approach can cultivate just that. It provides students with a safe space to explore options, take risks, and make mistakes. Skills necessary for a lifetime of learning.
7. Promotes collaboration among students
Inquiry-based learning is often done in groups or even within the whole class, which gives students the opportunity to share ideas and learn from each other.
This type of cooperative learning has been shown to have a positive impact not only on academic performance but also helps students master social skills such as communication, teamwork and empathy.
8. Inspires higher-order thinking
In order for students to effectively engage in inquiry-based learning, students need to be able to think abstractly. This forces them to move away from memorising facts and formulas and instead focus on understanding concepts, which is paramount to success in Maths.
The inquiry approach goes beyond simply acquiring knowledge. Children learn to apply, analyse, evaluate and create new ideas. Higher-order thinking skills are essential for success in school and in life, which is why we must encourage them from an early age.
Strategies for implementation
If you're interested in incorporating inquiry-based learning into your Maths lessons, here are some simple ways you can get started.
Use technology effectively
There are a number of great websites and maths apps for kids that can be used to support discovery learning in the Maths classroom. Some of our favourites include:
Mathigon – an online platform that uses engaging stories and challenges to teach Maths concepts.
Math for Love – Dan Finkel's website is full of Maths games, openers, rich tasks and more inquiry-based learning activities.
Make it extend across multiple topics
Inquiry-based learning doesn't have to be limited to a single Maths topic. You can easily incorporate numerous strands to help build connections.
One way to do this is to set up a project-based learning activity that combines elements from different curriculum areas. For example, you could create a measurement project that requires students to use algebra as well as analyse data.
Follow the guiding principles for effective student learning
Ensure learners are always at the centre of the inquiry process and that they have some degree of control over the direction of their learning.
Keep the Maths task open-ended and allow for different methods and potential solutions.
Encourage collaboration among students and provide opportunities for them to share their ideas.
Make sure the focus is on understanding concepts rather than simply acquiring facts.
Set up a Maths investigation centre
Create a space in your classroom with all the materials students will need for their investigations. This might include books, manipulatives, tablets, worksheets and anything else you think would be useful.
A designated learning environment that nurtures exploration will help students develop critical and creative thinking skills as well as a desire to learn more.
Facilitate the exercise with a clear demonstration
As students might not be familiar with this type of learning, you must provide a clear demonstration at the beginning.
Show them how to use the materials and model the inquiry process for them.
This will help them feel more comfortable as they embark on their own investigations. Using a mock example as a class, show your students how to:
Phrase a big question that has more than one solution
Contribute and develop ideas as a team
Question themselves and others in a constructive format
Use tools to investigate procedures and test solutions
Allow time for reflection
After students have had a chance to explore and discover new Maths concepts, it's important to give them time to reflect on their learning. This can be done through whole-class discussions, individual journaling or even simply by asking them to share their thoughts with a partner.
Reflection helps students make connections as well as solidifies their understanding. It also allows them to see the value in actively engaging and how the learning experience can be used to solve problems beyond the classroom.
Inquiry activities and examples
Retention in Mathematics increases ten-fold when concept mastery replaces memorization. So, if you want your students to remember what they're doing in Maths, focus on exercises that promote hands-on active learning, collaboration and understanding. Listed below are a few of our faves.
Surface area dissection (Grade 4 - 9)
Rather than just giving your class formulas for the surface area of 3d solids, create a hands-on experience for your students by having them dissect them. You can print out the nets or have your students do it themselves. This exploration will help them see how the formulas are created and why they work.
Circle Theorems & Properties (Grade 9 - 10)
To help your class uncover various circle theorems, have them use a protractor, compass and ruler to draw various angles, lines and shapes. They can then label the parts and write out the theorem or property that applies.
Cost and Benefit Analysis (Grade 5 - 8)
Create project-based tasks that investigate the costs and benefits of various real-world scenarios. For example, have students imagine they're trying to start a new environmentally sustainable business.
They'll need to consider the costs of materials, labour, advertising, etc. and then weigh that against the potential benefits before making a decision. Financial applications are a great way to introduce many mathematical concepts:
Unit rates & unit prices
Operations with decimals
Conversions with time & money
Percentage profit and loss
Dream House Planning (Grade 4 - 8)
With the goal of exploring compound shapes, have your students design their dream houses. They can use graph paper to plan it out and then create a model. You can even extend the lesson by having them calculate the costs based on the materials and square footage. This is a great opportunity to introduce or review concepts like:
Measurement (length, width, height)
Perimeter & area
2D & 3D shapes
Challenges you might face in the learning process
The success of inquiry-based learning rests heavily on the teacher's ability to effectively facilitate and manage the class. Here are a few challenges you might face and some tips on how to avoid them:
Too much freedom
If students are given too much freedom, it's easy for them to get off track. Be sure to provide structure by giving clear instructions, timelines and expectations.
Lack of engagement
If students are struggling to stay engaged, it might be because the task is too easy or too difficult. Whether it's maths strategies or scientific concepts, make sure the level of challenge is just right by offering different levels of support.
Not enough time
Inquiry-based learning can take longer than traditional teaching methods, so it's important to plan accordingly. Build in extra time for students to explore, share and reflect on their learning.
These are just a few of the challenges you might face when implementing inquiry-based learning in your classroom. However, with careful planning and execution, you can overcome them and create a truly engaging and enriching learning experience for your students.
When not to use it
While inquiry-based learning is a great way to encourage active and engaged learning, there are some situations where it might not be the best method. Here are a few things to consider:
If students are struggling with the basics of the material, inquiry-based learning might not be the best approach, as they might be ill-equipped to explore on their own. In this case, it's better to focus on mastering the foundation, using direct instruction, before moving on to more open-ended tasks.
Inquiry-based learning is not always appropriate for assessment purposes. If you need to evaluate a student's understanding of specific content, it's better to use more traditional methods, such as tests or quizzes.
Inquiry-based instruction works best with small groups of students. If you have a large class, it might be difficult to manage the different groups and ensure that everyone is on task.
Consider your goals for the lesson and the needs of your students before deciding whether or not to use inquiry-based learning. While this approach has many benefits, it might not be appropriate in all situations.
Sweller's cognitive load theory
Cognitive load theory was proposed by Australian educational psychologist John Sweller in 1988. It's based on the idea that working memory, where new information is processed and stored, has a limited capacity. As a result, when learners are presented with too much information at once, they have difficulty processing it all and struggle to learn.
Sweller's research suggests, that the decline in Australia's academic performance in the international student assessment is in large part due to the emphasis on inquiry-based learning, rather than explicit instruction.
That might be a huge leap given the number of factors that contribute to academic performance, but it's an interesting perspective nonetheless.
The ultimate goal is to activate curiosity
As the facilitator of the investigation, your goal is to pique students' curiosity and get them thinking about the mathematical concepts at hand.
It's not just asking a class what they think the answer is to a question or what it is they want to learn. It's about encouraging students to explore and develop their own understanding of the concepts.
The best way to get students thinking is to start with a question. Here are a few questions that ignite curiosity:
Can you think of another way to solve this problem?
Is there a pattern here?
Could you explain your reasoning to me?
What do you notice about this pattern?
How could we represent this data in a different way?
Why does this process work?
Where could it be improved?
What would happen if we changed this variable?
At Math Minds, this teaching method is what we live and breathe. We firmly believe in the power of inquiry and its ability to engage and excite students about mathematics.
That's why our maths tutoring program is designed around a pedagogy that guides students to question, explore and discover mathematical concepts. We believe this is the best way for you to gain a true understanding of the content. We empower students to ask the right questions, so they can find the answers they're looking for.
If you're in search of a mentor who can inspire your child to fall in love with learning, you're in the right place. Book a free online assessment and awaken the joy of discovery today!