Being a mathematics teacher often leads to envisioning amazing lessons that could be crafted and executed if only there were more time available. However, in reality, time is often scarce, making it challenging to create elaborate teaching materials and organize extensive student-centered activities.
Nonetheless, this doesn’t imply that your teaching quality must decline. Even in time-constrained situations, there are numerous approaches you can employ to enhance student engagement and nurture their comprehension of mathematical concepts in your everyday lessons. Here, we present six straightforward yet impactful instructional strategies for mathematics that can be seamlessly integrated into your daily teaching routine.
Prioritize the Emphasis on Conceptual Understanding
For students to develop the capacity to apply mathematics flexibly and tackle intricate problems, it’s essential to move beyond mere memorization of facts and procedures. Instead, they must cultivate a profound comprehension of the underlying mathematical concepts. Here’s a guide on how to prioritize and promote conceptual understanding in your classroom:
Use visual strategies
Utilizing visual representations enables students to grasp how abstract concepts can be applied to real-world situations. Incorporate illustrated problems or hands-on activities, and motivate students to employ visual techniques, such as drawing, while tackling problems.
Additionally, presenting problems from various perspectives helps in strengthening the neural connections in the brain, leading to improved comprehension and retention.
Use the schema approach
The schema represents the fundamental structure underlying a mathematical concept. For instance, in all subtraction problems, there’s a common pattern of taking away a specific quantity from an initial amount. Once students comprehend this schema, they can recognize it in various types of problems.
To facilitate this understanding, place similar word problems, such as addition problems, adjacent to each other and guide students in identifying the shared characteristics. Encourage them to articulate these similarities in a way that can be applied to other problems of the same category.
Explicitly teach the mathematics vocabulary of a concept
Demonstrate the various verbal expressions that can convey a particular mathematical concept. For instance, addition can be described as the combination of two quantities or the formation of a combined total. By expanding their mathematical vocabulary, students can employ these concepts with greater flexibility.
Here are enjoyable methods to enrich mathematical vocabulary:
- Exhibit mathematical terminology on classroom posters.
- Encourage students to save a mathematics dictionary link in their web browsers.
- Have students select a mathematical term and describe it to a partner without explicitly using the word. The partner must then guess the corresponding mathematical concept.
2. Set meaningful homework that builds on class learning
We’ve all experienced that moment when the bell rings, and in a last-minute rush, we hurriedly assign homework like “Complete exercise 15.2, odd-numbered questions, and every second column.” Despite our best intentions, meaningful homework sometimes falls by the wayside.
However, by seamlessly integrating homework into your lesson plans, you can make it much simpler to design activities that foster deep comprehension and enhance student engagement. Consider how your students can reflect on or connect their newly acquired knowledge at home, moving beyond mere procedural practice.
For instance, they could:
- Act as educators by teaching a family member about what they’ve learned.
- Seek real-life applications of the lesson’s concepts within their home environment.
- Apply theoretical knowledge through hands-on activities, such as creating a timetable or cooking.
- Pose qualitative or value-based questions to family members when relevant, encouraging thoughtful discussions.
By taking this approach, homework can become an extension of the learning experience, promoting meaningful connections and enriching students’ understanding.
3. Use cooperative learning strategies
Cooperative learning offers three significant advantages in the context of mathematics instruction:
- It promotes the articulation of students’ mathematical reasoning, leading to improved clarity of thought and greater self-awareness of their problem-solving strategies.
- Collaborative communication exposes students to diverse mathematical approaches, enhancing their ability to think flexibly and consider multiple perspectives.
- It mirrors the real-world practice of mathematics, where individuals with varying strengths collaborate to tackle complex, practical problems.
To effectively implement cooperative learning strategies in your classroom, consider the following approaches:
The “puzzle pieces” approach to group work
Implement the “puzzle pieces” method, assigning each student a distinctive piece of information to contribute to the group’s problem-solving process. This approach ensures active participation from every student, allowing each of them to make a meaningful contribution, regardless of their individual ability levels. (For specific examples of puzzle piece activities, you can refer to our article on math enrichment.)
Take time to reflect
Incorporate a dedicated reflection period after a collaborative activity, providing students with an opportunity to assess what was effective, which strategies proved beneficial, and how exposure to different reasoning methods has influenced their thinking.
Be strategic when allocating groups
Having a diverse mix of students with varying ability levels allows top-performing students to reinforce their comprehension by leading activities, while their peers can benefit from learning alongside more experienced classmates. This approach ensures that all students have the opportunity to learn and grow, even if some are frequently assisting others. Notably, research indicates that teaching others is one of the most effective strategies for retaining knowledge.
4. Use strategic questioning
Employing strategic questioning can transform a conventional “lecture-style” lesson into a profound learning experience or provide valuable support as students delve into more complex subject matter. Consider utilizing open-ended questions like:
“Tell me how you solved that”
Rather than simply congratulating a student for a correct answer and proceeding, prompt them to articulate their problem-solving approach. This accomplishes two significant objectives:
- Encourages the student to engage in detailed reflection on their own thought process. Instead of mechanically “doing the math(s),” they gain insight into the precise steps they took. This insight can help them recognize how these steps can be adapted for future, more intricate problems.
- Provides an opportunity for other students to learn alternative problem-solving methods, even if they initially struggled with the same question.
“Is there any other way of solving this?”
Inviting students to elaborate on various approaches to a given question underscores the idea that mathematics doesn’t have a single, definitive solution method. Furthermore, this practice allows students to uncover fresh mental mathematics insights or strategies from their peers, which they can apply in future problem-solving activities.
“Does this problem remind you of anything else we’ve done before?”
Before students become perplexed by an unfamiliar problem, prompt them to consider whether it evokes any recollections from previous learning experiences. Encouraging them to search for underlying connections to previously encountered concepts helps cultivate a habit that fosters adaptable and agile mathematical thinking.
“Where could you use this…” or “where would you see this used in the real world?”
These inquiries underscore the practicality of the learning process. Beyond mere procedural knowledge, students will gain insight into how to effectively apply their acquired knowledge.
5. Focus on real problem-solving and reasoning
In the world outside the classroom, mathematics often presents itself as intricate problems rather than straightforward questions with single, definitive answers. Consequently, effective instruction should equip students with the problem-solving and reasoning skills essential for real-life challenges.
However, this doesn’t entail arbitrary word problems involving apples and oranges. The most effective problems are authentic, characterized by:
- Open-endedness: Instead of directing students towards a specific solution, they should be open to various approaches.
- Relevance to the Real World: These problems either mirror real-world scenarios closely or, even better, involve hands-on interaction with actual objects.
- Promotion of Collaboration and Diverse Perspectives: Encouraging students to collaborate and explore different viewpoints enhances their problem-solving skills.
- Freedom in Problem-Solving: These problems do not prescribe exact procedures; instead, they allow students to experiment with different strategies until they discover an effective approach.
Utilizing such exemplary problem-solving tasks can significantly enhance the effectiveness of mathematics instruction.
6. Use mixed modes of assessment
Incorporating a range of formative and summative assessment methods serves several valuable purposes:
- Evaluating Conceptual Understanding and Fact Recall: These assessments enable the evaluation of both conceptual comprehension and factual recall.
- Building on Existing Knowledge: Rather than solely focusing on identifying deficiencies, they allow for building upon students’ existing knowledge base.
- Identifying Learning Gaps Early: They assist in identifying areas of learning that require attention well before the final examination.
Here are several assessment approaches that offer alternatives to traditional timed testing:
- Reflections
- Portfolios
- Peer Assessments
- Interviews
- “Teach the Class” Activities
Tip: Assessment need not interrupt the learning process; strive to integrate assessment seamlessly, such as evaluating students’ collaborative skills during group tasks.
Additional Approaches for Teaching Mathematics
- Effective Mathematics Instructional Approaches
- Engaging Mathematics Activities
- Enjoyable Math Learning Exercises
- Math Enrichment Activities for Home
- STEM Activities for Elementary School Students
- Tailored Strategies for Teaching Specific Mathematical Concepts
- Instructional Techniques for Addition
- Effective Methods for Teaching Multiplication
- Mastering Subtraction with Regrouping
- Proven Strategies for Teaching Addition with Regrouping
- Diverse Instructional Approaches in Mathematics Education
- Strategies for Enriching Math Learning
- Supportive Approaches for Students Struggling in Math
- Mental Math Mastery Techniques
- Effective Problem-Solving Strategies in Mathematics Education
