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Five unconventional ideas to transform your maths lessons

What can you do to inspire your students to learn maths? Here are five ideas to transform your maths lessons.

Engaging students in learning mathematics goes beyond mere instruction; it involves igniting a spark of curiosity and cultivating a passion for problem-solving. We will explore five innovative ideas that can transform your maths lessons into a dynamic hub of active learning, collaboration, and creativity. From the strategic integration of thinking tasks to the power of random groups and vertical surfaces, each concept is designed to foster a holistic understanding of mathematics while nurturing essential life skills. By incorporating these strategies, educators can guide students towards becoming well-rounded learners, equipped not only with mathematical prowess but also with perseverance, critical thinking, and effective collaboration.


Idea One

Engage students with thinking tasks, progressing from non-curricular to curriculum-related, cultivating deep and sustained learning.

Instead of beginning a lesson with direct instruction, it's recommended to initiate the class with thinking tasks that students can engage in, preferably in groups. These tasks are designed to involve problem-solving activities and mental puzzles. Particularly at the start of the school year, these tasks should be captivating and not necessarily tied to the curriculum. The aim is to motivate students and encourage them to embrace challenges. For instance, you might present a group of students with a hands-on puzzle that requires them to collaborate and strategize. This sets the tone for a mindset of active involvement and problem-solving.


As the academic year progresses and students become more comfortable with this approach to learning, you can gradually transition from these engaging, non-curricular tasks to ones that are directly related to the curriculum. It's crucial to thoughtfully sequence these tasks, ensuring that they become progressively more demanding. For example, if you're teaching algebra, you might begin with a simple real-world problem involving linear equations for students to solve as a team. As they grow accustomed to grappling with mathematical challenges, you can introduce tasks that align more closely with the established curriculum, such as applying algebraic concepts to solve multi-step equations or word problems.


The primary objective of fostering a thinking classroom is not solely to have students engage in non-curricular tasks consistently, as that's relatively straightforward. Rather, the ultimate goal is to cultivate deeper and more sustained thinking within the context of the curriculum. This entails encouraging more students to think critically and analytically, not only about standalone puzzles but also within the framework of the subjects being taught. To illustrate, consider a scenario where students are asked to explore the applications of calculus in real-world scenarios, encouraging them to think about how mathematical principles can be applied in various contexts. By integrating such thinking into the curriculum, students engage in longer and more profound learning experiences, which enhances their overall understanding and retention of the subject matter.


Idea Two

Random groups, role assignments, and standing engagement enhance maths learning by fostering collaboration and inclusivity.

In the classroom, the conventional practice of grouping students by ability or letting them choose their own groups has been found to be less effective compared to using randomised groups. When students are placed in randomised groups, it has been observed that they work more efficiently and are more likely to actively participate. For instance, let's consider a classroom scenario where students are working on a challenging maths problem. If they are grouped based on their abilities, some students might feel intimidated or unconfident, while others might dominate the discussion. However, in a randomised group, every student has an equal chance to contribute and share their thoughts. This breakdown of social barriers leads to improved interaction and knowledge-sharing among students.


Additionally, interviews with students have highlighted some key benefits of randomised groups. These groups foster greater knowledge mobility, meaning that ideas and insights can flow more freely among students. Consider a situation where students are solving a complex mathematical puzzle. In a randomly assigned group, a student who understands a certain concept well can explain it to others who may be struggling, enhancing the overall understanding of the topic. Moreover, the use of randomised groups reduces stress among students. For instance, a student who might be hesitant to speak up in front of a group of high-achievers will likely feel more at ease sharing their thoughts in a randomly formed group where everyone's abilities are mixed.


To ensure the success of randomised groups and make sure every student feels included, it's important to assign specific roles within each group. For instance, roles like the scribe, speaker, inquirer, and manager can be assigned. The scribe takes notes of the group's possible solutions, the speaker communicates the group's thought process to the larger class, the inquirer asks any questions to clarify doubts, and the manager keeps the group on track. This division of responsibilities ensures that every student has a designated role and actively contributes to the group's work. This approach promotes a sense of ownership and accountability, leading to a more collaborative and productive learning environment.


Furthermore, it's interesting to note that having students stand while engaging in collaborative activities can enhance their engagement. According to research, when students are sitting, they might feel anonymous, which can lead to disengagement. By having them stand, they become more physically and mentally involved in the activity. Imagine a scenario where students are discussing various approaches to solving a maths problem. If they are standing, they are more likely to actively participate, share ideas, and take responsibility for the group's progress. This small change in physical posture can have a positive impact on students' level of engagement and participation.


Idea Three

Group maths activities on vertical surfaces boost engagement, risk-taking, collaboration, and quicker problem-solving while fostering creativity.

When you ask your students to engage in group activities, try having them stand around vertical surfaces like whiteboards, blackboards, or windows instead of using traditional notebooks. These surfaces encourage students to take more risks. For instance, when comparing a group using a whiteboard with another using flip chart paper, researchers found that the whiteboard group started working within just 20 seconds. They began jotting down notes and attempting different approaches because they felt comfortable knowing they could erase any mistakes. On the other hand, the group working on chart paper took around three minutes to even make one note. This delay was due to their tendency to wait until their writing was perfect, which actually hinders their thinking process.


Working on vertical surfaces offers several benefits. When students are given challenging tasks and they work on these surfaces, they not only start their tasks faster but also spend more time on them. The large vertical surfaces spread throughout the room enable students to see what their peers in other groups are doing. This setup encourages collaboration and allows them to build upon each other's ideas. By being able to view the work of the entire class, students get inspired by different approaches and solutions. This kind of interaction promotes a deeper level of understanding and creativity.


Incorporating vertical non-permanent surfaces into group activities enhances the learning environment. When students write and discuss ideas on these surfaces, they engage in a more dynamic thought process. The act of physically interacting with the surface seems to eliminate the fear of making mistakes and encourages experimentation. As a mathematics teacher, you can leverage this method to prompt quicker problem-solving and more active participation. Furthermore, the visual accessibility of everyone's work fosters a sense of community and shared learning. Students not only gain confidence in their own abilities but also learn from each other's strategies, making mathematics a collaborative and inspiring subject.


Idea Four

Guide maths students by prioritising thoughtful questions, fostering independence, and using struggles as collaborative learning opportunities.

When students are engaged in group work on vertical surfaces, it's easier for you to monitor their progress and move around the classroom. While questions from students are expected, it's important to discern between questions aimed at quick answers and those that promote deeper understanding. For instance, if a student asks, "Is this right?" you should avoid directly confirming correctness. Instead, the focus should be on encouraging questions that lead to independent thinking.


Rather than readily providing answers or hints to challenging parts of a lesson, you should prompt students to evaluate the difficulties themselves. Encouraging them to grapple with the problem independently before seeking help is crucial. For instance, if a problem is proving tough, ask students to identify what specifically is challenging about it. This approach empowers students to think critically about their thought processes and helps them develop the skills to tackle complex problems on their own.


When a significant portion of the class is facing challenges, you can use the situation as an opportunity for productive discussions. Asking questions like "What's making this difficult?" or "What strategies have we tried?" encourages metacognitive thinking, where students reflect on their own thinking processes. These questions guide them to push through obstacles by critically evaluating their efforts and approaches. This approach not only supports individual growth but also turns struggles into shared learning experiences.


Idea Five

Assess maths skills holistically, focusing on perseverance, collaboration, and learning processes to cultivate well-rounded students.

Students need to cultivate skills like perseverance, academic courage, collaboration, and curiosity. To foster these abilities, it's important to evaluate and assess them in meaningful ways. What you choose to assess sends a strong message about what you prioritise, and students will come to appreciate those values as well. A balanced approach involving both formative and summative assessments is recommended, with a shift away from simply ranking students and focusing more on the process leading to outcomes and the cooperative efforts among groups.


Assessment in mathematics classrooms should encompass a multifaceted approach. While evaluating the work students produce is essential, it's equally important to assess their perseverance in the face of challenges. For instance, observe how well students persist and put effort into overcoming obstacles. Additionally, assessing their ability to set individual goals, track progress toward achieving those goals, and collaborate with group members in problem-solving and decision-making scenarios is crucial. Informing students about their current status and their trajectory in the learning journey is vital for their growth, and this can be done through various means such as observations, questions to gauge understanding, and even ungraded quizzes.


When it comes to summative assessments, the focus should shift from solely evaluating end products to encompassing the processes of learning. This includes evaluating both individual and group efforts. The assessment should shed light on how well students engaged in the learning process, how effectively they collaborated, and the strategies they employed to tackle challenges. By placing emphasis on learning processes, you encourage a holistic understanding of mathematics that goes beyond rote memorization and end results.

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