About Intuitive Math

Some students naturally enjoy math and are good at it. Others can’t bear to even look at a math problem.

What makes the difference?

Neurologically, math is a highly specialized and abstract mental activity. Learning an abstract mental function requires building bridges from the concrete skills that we already understand and enjoy – touch, vision, sound, play, and social relationships, for example.

In early education, teachers use many hands-on activities to build math skills. By middle school, students are expected to have already developed the ability to do math abstractly. The many students who haven’t are left frustrated, confused, and upset.

The secret of people who are good at math is that they do use concrete, hands-on, visual, graphic tools for solving math problems. But they do it intuitively, without necessarily even realizing what they are doing. When approaching a challenging math problem, they create new bridges between the concrete information and the abstract thinking that they need in order to solve the problem.

Anyone can learn and master these intuitive tools. They simply need high quality instruction and practice.

Our math anxiety program teaches students many intuitive tools for many kinds of math problems. And we teach students how to start drawing on their own intuitions and natural strengths.

We work with typical ACT math and SAT math problems, so a bonus of the program is that students are better prepared for taking the ACT exam and the SAT exam.

In the words of one of our adult math-phobic learners: “I can actually understand what I’m doing! How come no one ever taught me math like this before?”

What are intuitive math tools?

Standard math tools, like algebra, are very abstract. When attempting a difficult algebra problem, high powered math pros start by using intuitive tools to organize the information in the problem before they use algebra. This intuitive work shows them how to apply the algebra.

Students who struggle with math often have memorized the algebra tools but don't have the intuitive tools to know how to apply it. Ironically, many such students have wonderful strengths in intuitive areas, including art, music, movement, and social relationships. They simply haven’t learned how to apply those strengths to mathematical problems.

A simple example:

Here is a relatively simple problem, similar to problems that you find on ACT math and SAT math.

The ratio of 1/5 to 5/24 is most closely equal to the ratio of:

A. 1 to 24

B. 24 to 1

C. 24 to 5

D. 24 to 25

E. 25 to 24

The standard “math” way to solve this involves finding common denominators or simplifying complex fractions. In intuitive math, the simplest, most understandable strategy is the best.

You can be confident that if you multiply both fractions by the same number, it will not change the ratio. (The ratio of 3 to 7 is the same as the ratio of 6 to 14.)

Now you can multiply both fractions by 5. This will change the first fraction, 1/5, to the number 1, which will be a lot easier to work with!

1/5 x 5 = 1, 5/24 x 5 = 25/24

Now I’m concerned only with the ratio of 1 to 25/24.

What do you intuitively see about 25/24? It is just a tiny bit bigger than 1. This means the problem boils down to a smaller number on top and a slighlty larger number on the bottom.

In other words, we're looking at the ratio of 1 to 1 plus a little bit. Am I ready to solve the problem yet? Let’s look at the answer choices. Remember that we are looking for a fraction that is closest in value to 1 over 1+.

In choice A, the two numbers are very far apart. Our two numbers are very close. Choice A is out. Choice B is out for the same reason. Choice C has numbers that are also quite far apart, so that is out.

Choices D and E both have numbers that are very close. What is the difference between choice D and choice E?

In choice D, the top number is slightly smaller than the bottom number. In choice E the top number is a little bit greater than the bottom number. Choice D matches our problem – 1 is a little smaller than 1 plus a tiny bit.

Choice D is the answer.

It's true that the problem still requires working with numbers but it uses an approach that stays with the information that I’m clear on. It uses the simplest possible approach. Doing this decreases the chances of getting lost in abstract math and increases the chances of finding the right answer.

Math is about relationships!

Numbers, figures, distances, parts of triangles, time, space, people. Math problems are always about the relationships between the elements of the problem. What high school student is not interested in relationships!

The first step in becoming comfortable with math is to begin seeing it as relationships that you can understand.

The second step is to draw on skills that you already have for negotiating relationships.

Here’s a famous quote from the movie Romy and Michele’s High School Reunion that summarizes everything we need to know about students who are wrestling with math:

Hey Romy, remember Mrs. Divitz’s class, there was like always a word problem. Like, there’s a guy in a rowboat going X miles, and the current is going like, you know, some other miles, and how long does it take him to get to town? It’s like, ‘Who cares? Who wants to go to town with a guy who drives a rowboat?

Math anxious?

Does math make you feel confused, overwhelmed, and physically uncomfortable? If so, you probably find that your math classes don't help much. Intuitive Math teaches you a very different set of strategies for solving math problems. You learn to use your intuitions, visual and artistic skills, and your understanding of relationships to solve simple and complex math painlessly. You may even find that you enjoy it!

Some people already understand these tools naturally. For the rest of us, the tools can be learned with a little expert guidance.

Math genius?

Are you really good at math. You probably use intuitive tools naturally, without realizing you are doing so. Purposely and systematically studying intuitive math strategies helps you expand your natural skills and become a true math expert.