Explain how you applied these mathematics concepts or principles

1. Education
Most of education focuses on skills. Skills are easier to observe and grade because a person can demonstrate skills. Proving that you understand a concept is difficult. Teachers try to measure a student’s understanding by asking them to write about, discuss or draw concepts. Even then, students are still limited in showing their understanding by their language, writing or artistic skills. For example, most adults in the U.S. understand the concept of basic nutrition. How many adults in the U.S. could explain basic nutrition in a foreign language? Our limited skill set in the foreign language would limit how well we could prove our understanding.

Retaining concepts is easier than retaining skills. What happens when we don’t practice a skill? We lose the skill. Most adults can think of a skill that they frequently practiced as child, but don’t practice now (piano for example). Chances are that their younger selves were much better at that skill than their current self.

If you understand a concept, you have that understanding forever. You may need to think about it before you remember all the details, but the underlying concept will always be there. You will always be able to build upon the concepts you understand and your previous understanding makes learning easier and faster.

2. Progression
Skills build on top of each other. When learning to swim, most children learn to float around the same time as learning to flutter kick. They are both beginning level skills. They must master all the beginning level skills before attempting an advanced skill, like swimming in open water or attempting the butterfly stroke.

Concepts are also best taught progressively. Our brains use neural pathways to make connections. Our understanding of underlying concepts pave the way for understanding new concepts. The deeper and broader our knowledge base is, the easier it is for us to connect it to new concepts.

3. Math Success
Skills are the “how-to” parts of math. Children should master adding and subtracting before starting multiplication. They must know how to multiply and divide before attempting percentages.

Concepts are the underlying ideas of math. Concepts are ideas like equality and symbolic representation. Many math concepts build upon each other. A child who has a solid understanding of the relationship of quantity and numbers, or “number sense”, will find the concept of “wholes and parts”, naturally makes sense.

How Skills and Concepts Work Together
Understanding concepts makes learning skills easier. Mastering skills, especially thinking skills, makes learning concepts easier. Each prepares the brain differently.

People might be able to do a skill without understanding “why” it works. Understanding why a skill works in sports is helpful, but not critical. Can you imagine swim lessons at the neighborhood pool to 5 year-olds including a study of fluid dynamics and propulsion?

People might also have a concept about something, without the skill to execute it. Many adults understand the concept of bacteria and wound maintenance, but they still go to a skilled professional to get stitches. Some people call this “book smarts” versus “street smarts.” Understanding the why helps you build your knowledge base and your retention of skills.

Most people in life don’t care about what others understand. They care about what others do. A conceptual understanding helps build skill sets faster.

How Skills and Concepts Work Together in Math
Math skills and concepts should be taught simultaneously. Children who learn math skills without learning the underlying concepts, will find math can get very confusing. Their lack of understanding will limit their ability to apply math in a variety of problem solving situations. Without understanding a concept, we are forced to rely on remembering and practicing a skill. For example, let’s say a 5th grader learned how to divide fractions using the "copy, dot, flip" method but never understood the concept behind why that process worked. Then the 5th grader progresses to 6th grade and stops practicing dividing fractions because they are learning new skills. When that child stops practicing, he will then likely forget how to divide fractions. This will be a problem when dividing fractions comes up again in algebra and advanced math. The child who has both the skills and the concepts will be much better prepared.

Children who learn math concepts without learning the skills, will struggle to apply what they know. Knowing the difference between concepts and skills helps to identify the problems that arise in math.

How we Approach Skills and Concepts at Mathnasium
At Mathnasium of Littleton we focus on teaching foundational math skills like Counting, Numerical Fluency (adding and subtracting and multiplication facts), time and money and the order of operations while also teaching concepts such as Number Sense, Wholes and Parts, and Proportional Thinking. These latter are concepts that also involve skills. Additionally, thinking is a skill that must be practiced. Thinking skills enable a child to learn the concepts and we never neglect to teach concepts. We encourage our students to ask us questions and we ask them questions to promote deep thinking and conceptual understanding.

The progression of skills and concepts and how they work together is exactly why at Mathnasium of Littleton, we work hard to close math gaps.

For more information about our methods, click here. The result is stronger math skills with a deeper understanding of mathematical concepts. Our motto is: “We Make Math Make Sense!”

Give us a call today! 303-979-9077

Articles referenced in this post:

Practice Makes Perfect so Perfect Practice is Essential

Multiple Practice Sessions Provide Better Learning than Cramming

Where Does your Child Go To Practice Math?

Is Mathematical Understanding Really Necessary?

Worried Your Child has Not Memorized the Multiplication Tables?

4 Tips for Figuring Out Percentages the Easy Way

Learning Math Symbols in Elementary School Takes Time

Prepare Your Child for Calculus Starting in Second Grade

Is Your Child Dependent on Algorithms and is that a Bad Thing?

Why Does Mathnasium of Littleton Focus on Foundational Math Skills?

Counting … Its More Complex Than You Imagine

Teaching Number Sense

Focus on Math: Wholes and Parts

Focus on Math: Proportional Thinking

What is Numerical Fluency?

Multiplication Fluency is Coming to Mathnasium of Littleton

Focus on Math: Learning About Money

Does Your Child Ask Questions in Math Class?

Focus on Math: Order of Operations

Understanding Mathematical Reasoning

Understanding Math Learning Gaps

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