What does "learning" mean?

Learn about the difference between doing math and learning math!

For true learning to happen in any subject, it must be understood intuitively. Cooking is a great example of this concept. Cooking might begin as following the steps of the process to the letter but discovering the purpose of each part of the recipe is when the magic of learning starts to happen. Then, the cook can alter the recipe, making substitutions or additions, customizing the outcome of the dish. Cooking also requires a variety of tools – pans, forks, spatulas, etc. A person can follow a recipe that says, “use an 8” nonstick skillet”, but once a person can answer questions such as: “Can you use a different cooking instrument to achieve the same goal? Why?”, then the person is truly learning how to cook. But learning these things doesn’t happen all at once. You wouldn’t expect someone who has never cooked before to be able to pick up Gordon Ramsay’s cookbooks and be able to make one of his famous dishes on the fly. That person would need to make that dish dozens of times before they had truly mastered how to make that specific dish and the reason for each ingredient. They could then use those ingredients and techniques in other dishes and, as they began to grow the repertoire of ingredients and skills they had mastered, could start to combine them in other ways to make new dishes.

Math is the same way. Students need to spend time with each topic, digesting it, learning its details, and they need to do this regularly and often to truly learn a concept’s ins and outs. Much like cooking, learning math requires building a web of skills that support each other and very little of it has to do with the ability to memorize a recipe. For example, students can memorize “7 times 6 equals 42”, but this is just a string of words and numbers that when put together make what looks like the understanding of a math fact.

Students who rely on memorization often confuse operations because they are not comprehending what the operation is, they simply remember the words that make up the fact. To go back to our cooking example, confusing multiplication with addition is like confusing a knife with a spoon – they are tools with different purposes and understanding what they are used for allows for more versatile use of both. In math, skills and concepts that have been learned become tools, while facts and rote processes that have been memorized can often be misconstrued, like trying to eat spaghetti with a spoon.

What is the difference between doing math and learning math?

Many students can “get an answer” in math by memorizing a series of steps and following those steps to get to an answer. Most of the time, this mechanical process would go unnoticed as the correct answer was reached and no one is the wiser. However, many students eventually reach a point where this memorization no longer works, and they cannot rely on their ability to simply memorize a series of steps and then execute those steps correctly. Then, when a new set of steps comes in, the previously memorized steps often get thrown out to make room for the new information. All too often, this goes on for a long time until someone notices that the student is no longer able to parse what is happening in the classroom. When this is happening, students are doing math, but they are not learning math and haven’t been for some time.

When students need to be reminded about or shown tools again, the tools have not been learned and are not always available as tools when needed. Students go through stages of learning where they may be aware of a tool’s existence but not really know its function, much the same way as a child might be aware of the existence of a cheese grater but might not know when it is appropriate to use or even what it is used for. Even after learning what a tool’s function is, students still need to use the tool to perform that function regularly to be proficient in its use.

When a student is truly learning math, they can effortlessly recall which tools to use to approach problems they have done in the past as well as use those tools in new scenarios or applications. Being able to solve a variety of word problems without examples months after the core skill has been learned is a strong indicator of true learning and retention. Similarly, being able to describe a strategy using simple terms is also a strong indicator of a student’s comprehension of a strategy.

How do I know if my child is doing math or learning math?

Some important indicators at various levels are included below. Often when we encounter students who are struggling, they have not been learning math for some time. Math is one of the few subjects where every new skill builds on previous skills and identifying opportunities to help students truly understand the strategies and reasons behind them is crucial to long-term retention and success.

Contact us to learn more about the difference between learning math and doing math and how Mathnasium can help your child!