Mathematics, often viewed as a complex subject, is not solely about calculations and memorization. At its core, math is about dynamic problem-solving. From the early stages of cognitive development, children are naturally inclined towards problem-solving. However, the true essence of teaching mathematics lies in cultivating and refining these skills. In this blog post, we discuss the importance of teaching problem-solving techniques in math class, drawing insights from educational theorists, mathematicians, and contemporary teaching standards.
Select Rich, Real-world Problems
Start by curating a collection of rich, real-world problems that resonate with your students. These problems should be rigorous and result in student responses that can help pinpoint where they are in the learning process. They should draw on their experiences, making math relevant and meaningful. Align these problems with students' developmental stages and interests to capture their attention and engagement. Introduce scenarios that require critical thinking and logical reasoning, allowing students to connect mathematical concepts to practical applications.
Implement Cognitive Guided Instruction
Cognitive Guided Instruction (CGI) is a teaching methodology that encourages you to follow a child’s mathematical thinking—as opposed to forcing every child to solve problems the same way. Present problems to your students that can encourage their own mathematical thinking, and probe them with questions like, “how did you arrive at your answer?” or “what did you do to help get your answer?” This encourages students to think outside of the box and develop their own strategies for problem solving. This interactive, non-linear approach mirrors the complexities of real problem-solving and equips students with a diverse set of problem-solving strategies.
Encourage Discourse and Reflection
Plan for and promote mathematical discourse in the classroom. Encourage students to explain and discuss the strategies and processes they use to solve mathematical problems. This discourse-rich environment allows students to connect everyday language with specialized mathematical vocabulary. Provide opportunities for students to justify their solutions, fostering a deeper understanding of mathematical concepts. Actively listen to students during these discussions, using their thinking as a valuable resource for further learning.
Pro Tip: Use the ASSISTments Assignment Report as a reflection tool to encourage students to discuss the methods they used to arrive at their answers. The Assignment Report is a catalyst for discussions on mathematical reasoning and problem-solving, placing the focus on understanding their thinking - how they arrived at the answer. By providing objective insights such as pinpointing common misconceptions and encouraging discourse on shared misunderstandings, teachers establish consistent routines and structures. These elements contribute to creating a supportive and predictable learning environment, fostering a sense of belonging and safety among students.
See how Instructional Coach and Middle School Math Teacher Nikki Scheib shares how she uses the Assignment Report daily.
In this process, the teacher takes on the role of guiding students in explaining their thinking, while the dynamic of student-led discussions further amplifies the learning experience. This collaborative analysis of answers by the entire class allows teachers to pinpoint areas requiring focused instruction. Consequently, this results in a more efficient use of class time and seamless integration of homework and classwork with new material. Such an approach aligns with best practices in math education, cultivating both mathematical reasoning and meaningful discourse among students.
Promote Collaborative Learning
Foster a collaborative learning environment by incorporating group problem-solving activities. Group students with diverse knowledge and skills on the topic into small groups and provide them with challenging yet accessible problems. Encourage them to discuss and share their individual approaches, promoting a diverse exchange of ideas. Successful collaborative learning activities apply clear, practiced norms around student roles in the group. Group work not only enhances students' problem-solving skills but also cultivates effective communication and teamwork. This collaborative approach mirrors real-world situations where problem-solving often requires input from various perspectives.
Balance Independence and Guidance
Strike a balance between independent problem-solving and guided instruction. Allow students the freedom to work independently on certain problems, promoting self-directed learning and decision-making. Simultaneously, provide structured guidance through well-crafted questions that scaffold the problem-solving process. This approach helps students develop both confidence in their independent problem-solving abilities and an understanding of when to seek guidance. It reflects the dynamic nature of problem-solving, where students move between independence and collaboration.
Integrating these five strategies into middle and high school math instruction will not only enhance students' problem-solving skills but also create an engaging and enriching learning experience. ASSISTments, a dynamic math assessment platform designed to support teachers and students, offers a seamless integration of these strategies into everyday instruction. By utilizing the Assignment Report as a reflection tool, teachers can deepen students' understanding of problem-solving processes and create a supportive learning environment. This collaborative and technology-enhanced approach not only aligns with best practices in math education but also empowers students to develop into proficient problem solvers.
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