The Problem of Solving Problems in Maths Classes

While there is a notion that Math classes are basically for solving “problems”, the reality is that there are several factors involved in tackling every problem. For every question asked in the math class, few things that I try to probe;

• • What is the question meant to achieve?
  • How is the question presented?
  • How much time is available for the students to understand the questions before answering?

Mathematics is a fundamental subject that underpins many areas of study and practical applications. However, solving math problems can often be stressful and less interesting.

One major thing that needs to be addressed is the perception of the subject “Mathematics” and by extension what happens in mathematics classes. Call it a “mindset” problem and you won’t be far from the “causative organism”.

It is important to note that a lot of activities will be done in math classes to teach and solidify concepts – questions, observations, assessments etc. are part of the processes.

I’ve often wondered if there’s any subject that is “easy” (Yes… I’m making a case for mathematics… lols).

So… I ask you, “is there any subject that is easy/simple to teach or learn?”

There is more to what goes into teaching and learning, some factors are not paid any attention – choice of words, examples, mode of explanation etc.

Problems… Questions… Drills… Tasks… Quizzes… Puzzles…

Each of those words comes with different interpretations/perceptions and each has a way of affecting the mood and reaction of the students.

Mathematics is a fundamental subject that underpins many areas of study and practical applications. However, solving math problems can often be stressful and less interesting.

This article is to share some insights into how to handle math questions/problems with the aim of helping students having a grasp of the concept and going beyond getting the answers. For the sake of emphasis, procedural fluency is not enough without conceptual understanding.

In this series, I’ll be sharing 8 procedures – OCTOSPICE;

1. Make sense of the problem:

• • Encourage students to carefully read and understand the problem statement
  • Have them identify the key information, constraints, and goals
  • Prompt them to rephrase the problem in their own words

 

2. Reason abstractly and quantitatively:

• • Teach students to think about the problem conceptually, not just numerically
  • Encourage them to represent the problem using diagrams, models, or other visual aids
  • Have them analyze the relationships between quantities and variables

 

3. Construct arguments, critique reasoning:

• • Provide opportunities for students to explain and justify their problem-solving approaches
  • Teach them to identify flaws or weaknesses in their own and others’ reasoning
  • Foster a classroom culture of respectful discourse and constructive feedback

 

4. Model with Mathematics:

• • Guide students in translating real-world problems into mathematical representations
  • Encourage them to use appropriate mathematical models, equations, or simulations
  • Discuss the strengths and limitations of the mathematical models

 

5. Use appropriate tools strategically:

• • Introduce students to a variety of problem-solving tools (e.g., calculators, software, manipulatives)
  • Help them select the most suitable tools based on the problem and their needs
  • Teach them to use the tools effectively and efficiently

 

6. Attend to precision:

• • Emphasize the importance of accuracy, clarity, and attention to detail
  • Encourage students to use precise language, units, and mathematical notation
  • Provide feedback on their work to help them improve their precision

 

7. Look for and make use of structure:

• • Guide students in identifying patterns, relationships, and underlying structures in problems
  • Teach them to recognize and apply familiar problem-solving strategies or techniques
  • Help them make connections between different problem types or mathematical concepts

 

8. Express regularity with repeated reasoning:

• • Provide opportunities for students to practice similar problems or problem-solving approaches.
  • Encourage them to look for shortcuts, generalizations, or broader principles.
  • Discuss how repeated practice and reflection can lead to more efficient problem-solving.

 

Details of each OCTOSPICE will be shared in subsequent articles. Follow through!