Problem Solving, Experiential Learning, and Critical Thinking

High school courses allow for practice time during class. This is why many students find themselves unprepared for university, because they are now responsible for planning their own practice time. It is important to learn how to manage your time wisely, so you are able to balance all your coursework and studying.
 
Below are some tips to help you make the most of your study time, especially when it comes to problem-solving courses: 

• Before studying:
  • Go to class.
    • Even if you aren't enjoying the teaching style, going to class will help you get familiarized with your professor's expectations.
    • Be sure to attend each class and keep up with the homework, so you are up to date on the content.
  • Get the big picture.
    • Make sure you understand concepts before attempting any problems. 
  • Learn the notation.
    • If you do not understand terms being used, you won't be able to start the problems properly. 
• Getting started:
  • Try practicing problems yourself first.
    • Always attempt problems without assistance and without a guide.
    • Do not look at homework solutions until you have attempted the problems yourself.
    • Analyze how the problem is set up and consider the clues that are in the question that help you see how to solve it.
  • Set time limits.
    • If you find yourself getting caught up on problem-solving questions, be sure to set clear boundaries for studying.
    • Give yourself a realistic amount of time to solve a problem.
      • The complexity of a question will help in determining whether we need 10 minutes or an hour to solve it.
      • Make sure the time you set is reasonable
      • Time yourself so you can recognize and complete problems quickly. 
    • If you find yourself struggling to complete the problem note where you got stuck.
    • Always try to solve the problem yourself first, but there is no shame in reaching out for help if you get stuck! 
    • If you are struggling with a question, you can attempt to work backwards. Look at the answer to see if you can figure out steps you can take to get there.
• Re-mix your studying:
  • Make a list of common equations and types of problems.
  • Mix up the type of problems when practicing.
  • Perfect your skills and focus on perfecting blind spots in your knowledge.
  • Use correct notation.
• Practice, practice, practice:
  • Problem solving requires significant practice.
    • The more you practice, the faster you can recognize and solve a problem.
    • Don’t start practicing at the last minute – integrate practice sessions into your weekly study schedule.
  • Use productive practice strategies.
    • Spreading your practice throughout the day and throughout the week.
    • When you get the basic idea of a concept, don’t answer multiple problems with the same solution; instead, answer multiple, unrelated problems before returning back to this type of problem.
    • Mixing in questions from previous weeks of class to keep the information fresh and to reflect on how new knowledge builds on previous knowledge.

Word problems can seem daunting, you have a big chunk of writing that you need to examine and find an answer for.  

Break It Down

You should break the problem down into simpler bits. Based on the text of the problem, answer the following questions:  

• What are you solving for?
  • Define this with a variable (make a let statement – for example, if you are solving for the number of atoms, say "let the number of atoms = x"). 
• What are your givens and unknowns?
  • Define any unknowns (again, make let statements). 
• Can you draw a picture or a diagram?
  • Drawing a picture is especially helpful if the problem involves lengths, areas, or volumes. 
• What relevant theorems or equations can you use? 

These questions will help break down problems and inform you what information you do and don’t need. Using let statements gives you simple variables to work with, making it easier for equation set up.
 
Key words can help explain what operations are involved in a question. This can help in turning word problems into equations, making them easier to solve. Look for the following key words: 

• Addition: Sum, added to, increased, combined, more, total. 
• Subtraction: difference, taken from, decreased, left-over. 
• Multiplication: multiplied by, times, product, doubled, tripled, increased by a factor of. 
• Division: divided by, per, quotient, ratio, split, out of. 

CUBES Strategy

The following video outlines the CUBES technique for making word problems much easier to solve:

 
These are the steps involved in using the CUBES technique:
 

• C: circle the key numbers
• U: underline the question
• B: box any math action words
• E: evaluate (what steps should I take)
• S: solve and check

Dimensional Analysis

Science and engineering problems will have real-life applications, which means that the quantities in your calculations will often have units.
 
Dimensional analysis is a way to make problems easier by considering the units involved and how they relate to each other.
 
The following video explains how to set up and solve equations based on their units:

Experiential learning involves learning from experience or learning by doing, and problem solving is an important component of this.  

Ontario Tech University offers experiential and work-integrated learning to its students. Experiential learning helps prepare students with the critical thinking, problem-solving, and decision-making skills necessary for careers in the workplace.
There is a wide range of design models that aim to embed learning within real-world contexts, including:

• laboratory, workshop or studio work.
• apprenticeship.
• case-based learning.
• cooperative (work or community based) learning.
• inquiry-based learning.
• problem-based learning.
• project-based learning.

Project and Problem-Based Learning

Let’s expand on some of these design models, focusing on problem-based learning (PrBL) and project-based learning (PBL).

Problem-Based Learning (PrBL): 

Problem-based learning is a teaching method where students are encouraged to learn by solving the complex problems we encounter, often in a real-world setting. In PrBL, problems are raised at the start of a lesson, before students have been taught all of the relevant knowledge.

University graduates need to be able to integrate knowledge and skills from a number of disciplines in order to conceptualize, create, and implement solutions. PrBL activities are designed to help students develop transferable skills while gaining appropriate discipline-specific knowledge.
In PrBL, students generally must:

• Examine and define the problem.
• Explore what they already know about underlying issues.
• Determine what they need to learn and where they can acquire the information and tools necessary to solve the problem.
• Evaluate possible ways to solve the problem.
• Solve the problem.
• Report on their findings.

The following video provides a helpful overview of problem-based learning: 

PrBL provides students with the opportunity to develop various transferable skills, such as:

• Digital literacy and information-seeking/ researching skills.
• Teamwork abilities.
• Leadership and management skills.
• Independent learning skills and self-directed learning.
• Oral and written communication and ability to explain concepts.
• Self-awareness, critical thinking, and analysis.
• Applying course content to real-world examples.
• Problem solving across disciplines.

PrBL requires students to take on responsibility for their education and pushes them to connect what they learn in class to their own lives.
Additional resources to prepare for PrBL:

The following website provides further information and resources on problem-based learning.
 
Project-Based Learning (PBL):

Project-based learning is a form of learning, which requires students to create a comprehensive project to act on their problems and solutions. PBL takes more time and has many steps to see the project through. Good time management and organizational skills are important for project-based learning.

Check out Getting Smart’s “Learning in a Project-Based World: A Quick Start Guide for Students” for an overview of project-based learning

Experiential Learning Skills: 

There are some general strategies that can be useful for students engaged in this type of learning:

• Foster your motivation and cultivate a positive attitude.
  • You are gaining valuable experience to help you grow academically and prepare for a professional career. Try to keep hold of the big picture and stay positive throughout the process.
• Set clear goals and manage time effectively, especially for larger projects.
  • Ensure all work is thorough and that your deliverables are submitted on time.
  • It can be helpful to break down larger deliverables into smaller tasks and milestones to help you stay on track.
  • Check in regularly with mentors and faculty members.
  • Read over all assignment instructions and rubrics carefully to understand expectations and ask questions if anything is unclear.
• Maintain professionalism.
  • Be sure to maintain professional conduct especially if you are working with an external partner.
  • Adhere to any rules established by your supervisor, especially confidentiality.
  • Follow established communication channels and communicate thoughtfully to different partners.
  • Consider booking an appointment with the Career Centre to help you develop professional skills.
• Practice critical thinking.
  • Think outside the box as you work through your projects.
• Reflect carefully.
  • Be sure you can articulate what you are learning in relation to the academic objectives. If you aren’t sure, ask your professor.

Critical thinking is the ability to think clearly and rationally about things. It uses reflective and independent thinking in order to analyze and solve problems systematically. Critical thinking is not having a good memory or thinking a lot about one subject. Critical thinkers are also not argumentative or critical of others.  
Instead, critical thinkers:

• Understand the logical connections between ideas.
• Identify, construct, and evaluate arguments and sources.
• Detect inconsistencies, logical fallacies, and common mistakes in reasoning.
• Solve problems systematically and through careful analysis.
• Ask the right questions.
• Apply inductive and deductive reasoning.
• Identify the relevance and importance of ideas.
• Reflect on the justification of one’s own beliefs and values.
• Minimize the biasing influence of thoughts from culture and upbringing.
• Seek out (and are guided by) evidence that is systematically tested.
• Are willing to change their positions when presented with new evidence.
• Engage in cooperative reasoning.

Watch this video that provides a helpful overview of some of the principles of critical thinking:

As highlighted in the video, critical thinking is a cumulation of many different skills, such as:

• Self-reflection
• Self-reliance
• Curiosity and creativity
• Flexibility
• Argumentation
• Skepticism
• Evaluation
• Reasoning
• Nuanced thinking
• Communication and presentation skills

The following video provides a step-by-step process to thinking critically:

• Formulate your question.
• Gather your information.
• Apply the information.
• Consider the implications.
• Explore other points of view.

Your time at Ontario Tech will help prepare you with the critical thinking skills necessary for your personal and professional development. Critical thinking is not specific to any discipline and it will come in handy wherever you find yourself in life.

Your ability to think critically will be essential to a functioning society. We need to be able to appropriately weigh and evaluate different sources of information, apply logical reasoning, and analyze effectively.