The Universal Problem Solving (UPS) framework consists of two models: Model L (for the learner) and Model T (for the teacher), which together illustrate how learning and teaching interact to create education. The axiom E = LT (Education = Learning × Teaching) reflects that education is merely the product of learning and teaching.

Model L focuses on attention, classifying information into three categories:

• ID (What it is)

• Function (What it does)

• Process (How it works)

Model T represents processing, with three levels of problem-solving:

  1. PS1 addresses problems with a single answer, such as "How old are you?"

  2. PS2 involves two possible outcomes, like "Do you like pizza?"

  3. PS3 solves problems with three or more solutions, such as "What are some things we need to buy from the store?"

The Notes in the Pocket method and the Math Backwards approach align with this model by fostering flexible, non-linear and divergent thinking in problem solving. They move beyond simple, single-solution learning, promoting creativity and deeper engagement with the material. Notes in the Pocket encourages students to connect questions and answers in a more visual, structured way, while Math Backwards introduces multiple solutions to arithmetic problems, modeling divergent thought patterns in problem solving.

For teachers, the T and L models help to illustrate the cognitive dynamics at play when using tools that promote divergent thinking. By understanding how attention (Model L) and problem-solving processes (Model T) work together, teachers are empowered to create environments that encourage students to think beyond single solutions or right and wrong answers.

For Parents

The Universal Problem Solving (UPS) framework equips your child with essential skills for navigating the complexities of learning and thus life. By incorporating Model L (for the learner) and Model T (for the teacher), this framework emphasizes flexible thinking and problem-solving. Methods like Notes in the Pocket and Math Backwards encourage your child to engage with information creatively and in a problem solving context, moving beyond mental traps of common logical fallacies and rigid simplistic answers to life's questions. This approach fosters critical thinking and prepares them for real-world challenges, ensuring they develop the ability to think divergently and tackle problems from multiple angles.

For Students

The Universal Problem Solving (UPS) framework enhances your learning experience by emphasizing creativity and exploration. With Model L focusing on attention and Model T representing different levels of problem-solving, you’ll learn to categorize information and approach challenges in innovative ways. Using tools like Notes in the Pocket, you can connect your questions and answers visually, while Math Backwards helps you find multiple solutions to arithmetic problems. This empowers you to think beyond singular or black-and-white answers, making learning more engaging and allowing you to develop valuable problem-solving skills that are applicable in everyday life.

For Teachers

The Universal Problem Solving (UPS) framework empowers you to foster a dynamic learning environment that prioritizes divergent thinking. By understanding Model L (learner) and Model T (teacher), you can effectively guide students in categorizing information and tackling problems at different levels of complexity. Incorporating methods like Notes in the Pocket and Math Backwards allows you to encourage students to think creatively and make connections between concepts and perspectives. This approach not only enhances student engagement but also equips them with the critical thinking skills necessary for success in an increasingly complex world, highlighting the importance of using educational tools that promote a deeper understanding of problem-solving.