Problem-solving is a vital skill for students in the 21st century, but how do you integrate it into your curriculum? Foster a culture of inquiry and creativity in your classroom can be beneficial to students in many ways. In this article, learn some strategies to align problem-solving with the curriculum and enhance your students' critical thinking and problem-solving skills.
What is the main challenge or question that you want your students to solve? How does it relate to your learning outcomes and standards? How does it connect to your students' prior knowledge and interests? A well-defined problem should be relevant, engaging, and challenging for your students, but also manageable and solvable within the given time and resources. Use a problem statement, a scenario, a case study, or a question to present the problem to your students.
Mathematical Music Theory - Music for everyone through mathematics fundamentals
My PhD research project focuses on developing student awareness of musical meter and its representation through the ski-hill graph to determine the mathematical aspects of timing and expression. The process of listening to music and Cohn's meter theories enable me to develop my student's knowledge and understanding of the meter fundamentals through Ski-hill Graph Pedagogy which I designed for teaching the meter fundamentals inspired by Cohn’s meter theory.
I want students to be able to understand the challenges that take place around the world because that allows them to be able to be comfortable moving to another place for their education. Problem definition for me is global challenges that do not posses simple or singular solutions. I want to provide background to allow my students to understand the task but not too much that they do not do their own research. Perspective-taking must be a central part of all of these tasks and the definitions must be clear enough to allow that. Students need enough time to use their resources but not too much time so that they do not feel a sense of urgency. A variety of lessons about academic procedures can be taught from the start if in the definition.
What steps or stages will they go through? What skills or strategies will they need to apply? What tools or resources will they use? How will they collaborate and communicate with each other and with you? How will they document and present their solutions? Use a problem-solving model, such as the 4C's (Clarify, Choose, Create, Check), or a framework, like the design thinking cycle (Empathize, Define, Ideate, Prototype, Test), to guide your students through the process. Provide scaffolds, such as prompts, questions, rubrics, or checklists, to support your students' thinking and learning.
Meter fundamentals requires a thorough understanding of the mathematical aspects of timing and expression from listening and accurate representation achieved through the ski-hill graph to determine the cycles of the meter experiences.
How will you measure and evaluate their solutions? How will you provide feedback and celebrate their achievements? How will you help them reflect and improve their problem-solving skills? Use self-assessment, peer assessment, teacher assessment, or external assessment, to assess your students' problem-solving outcomes. Products, performances, portfolios, or presentations can also demonstrate your students' problem-solving outcomes. Criteria to help assess the outcomes can be accuracy, creativity, feasibility, or impact, to judge your students' problem-solving outcomes.
Meter fundamentals benefits students when they visualise the meter through the ski-hill graph because it enables students to see each pulse related as meter. Cohn’s theory is backed by neuroscientific research which acknowledges the meter experiences are psychoacoustic.
How will you modify and improve your problem-solving activities to make them more effective and engaging for your students? How will you respond to your students' questions, challenges, or suggestions? How will you encourage your students to try new approaches or perspectives to solve the problem? Use a cycle of inquiry, such as the Plan-Do-Study-Act cycle, or a process of action research, such as the Observe-Reflect-Plan-Act cycle, to adapt and iterate your problem-solving activities. Data found through surveys, interviews, observations, or tests can also inform your decisions and actions.
Align your problem-solving with the curriculum is to integrate and transfer your problem-solving activities to other contexts and domains. How will you connect your problem-solving activities to other subjects or disciplines? How will you link your problem-solving activities to real-world situations or issues? How will you help your students apply their problem-solving skills to new problems or challenges? Cross-curricular or interdisciplinary approaches, such as project-based learning, inquiry-based learning, or service learning, can integrate and transfer your problem-solving activities. Also use authentic or relevant contexts, such as local or global problems, personal or social issues, or career or life goals, to integrate and transfer your problem-solving activities.
Time signatures provide little helpful information on the meter fundamentals. By representing the meter with the ski-hill graph meter mathematics students solve problems of timing and expression. They can identify the best cycle sizes of the meter fundamentals and apply the meter mathematics to all music. Ski-hill graphs show that inclusive music education is possible in diverse cultures when the applied processes enable equal access to representation.
The sixth step to align your problem-solving with the curriculum is to inspire and motivate your students to become lifelong problem-solvers. How will you spark your students' curiosity and interest in solving problems? How will you foster your students' confidence and resilience in facing problems? How will you cultivate your students' passion and purpose in solving problems? Use storytelling, modeling, mentoring, or gamification, to inspire and motivate your students to solve problems. Also use values, such as curiosity, creativity, collaboration, or citizenship, to inspire and motivate your students to solve problems.
When students apply their knowledge of the meter through listening and representation through the ski-hill graph, the information has currency for their projects.The new knowledge motivates students because they engage critical thinking and metacognition to achieve new learning. Confidence grows and performance skills develop as students learn about the meter fundamentals through Ski-hill Graph Pedagogy.