As students get into Geometry, Algebra, and higher math classes, a common question arises: “when will I ever need this?” Students now often encounter challenges that go beyond simple calculations and core math skills; these higher math classes require critical thinking and problem-solving skills that not only lead to success in math but also transfer over to decision-making and analytical tasks in other subjects and even the real-world.
Why do problem-solving skills matter?
Unlike early math where problems have direct, formulaic solutions, Algebra introduces students to abstract concepts like variables, equations, and inequalities, while Geometry requires spatial reasoning and understanding of established rules (properties and theorems). Both subjects teach students to approach problems methodically, break them down into manageable steps, and recognize patterns – all skills that are valuable inside and outside the classroom.
What are some challenges students face in developing math skills?
Succeeding in math can be a challenging prospect, and for some students, a key hurdle is developing these problem-solving skills. It’s important to help students master problem-solving techniques, making math less intimidating and more manageable. Here are some of the more common challenges and key focuses:
– Difficulty Setting Up Equations: Many students struggle with the initial step of translating word problems into algebraic equations. A key focus is showing students strategies for identifying keywords, understanding relationships, and organizing information, building a strong foundation for more complex problem-solving.
– Understanding Geometric Proofs: Geometry places more significance on taking known information and extending it a step further. It also introduces formal proofs, which require logical reasoning and the ability to connect theorems and properties. A key focus is guiding students through the thought process behind proofs, teaching them to analyze each step critically and communicate their reasoning clearly.
– Handling Multi-Step Problems: High school math often includes problems that need to be tackled in stages. A key focus is to develop strategies for managing problems: breaking down bigger problems into parts, ensuring students are organized, don’t feel overwhelmed, and can approach each part systematically and confidently.
– Building Persistence: Sometimes, students feel frustrated by the trial-and-error nature of solving difficult problems. A key focus is building resilience and fostering an adaptive mindset, attacking challenging concepts from different angles.
Math isn’t just about getting the answer, and learning isn’t just about being correct. It’s important to develop the correct strategies to help students become independent critical thinkers, both for doing well in their current class and excelling in the future. To do so, it’s important to encourage critical thinking, demonstrate multiple approaches, use real-world examples, and provide consistent practice and feedback.
What are some things students (and parents) can do outside of a learning environment?
A few of the critical components that influence students both inside and outside of structured learning environments are encouraging a positive attitude toward challenges and asking open-ended questions.
– Positive Attitude: Students sometimes need to be reminded that challenges are normal and that we wouldn’t have solutions without problems. Celebrating even small victories, progress, and improvements are critical to helping students develop a great mindset and attitude towards problem-solving.
– Open-Ended Questions: It’s important to facilitate critical thinking to help students develop their problem-solving skills. Open-ended questions help students to think through the steps and process on their own. For example, it may be a good idea to ask “What information do you already know?”, “What can we do as our first step?”, or “What’s your reasoning for doing that?” It usually leads students to a deeper understanding of concepts, problems, and solutions.
Problem-solving skills are not only important to develop, but it’s also important to start early to lay a strong foundation to build on. There’s a reason why many people will say math (and problem-solving) is so fundamental. It’s not something you can just memorize or easily master; instead, we try to set up a strong foundation and continue to build our skills. Having that strong foundation just makes it easier to learn in the future, and I’ll end with a very appropriate adage: the best time was yesterday, but the second best time is now!
