Does this classroom seem familiar to you? The teacher stands in front of the class. She explains a method for solving a particular type of problem, and does a few examples. Some of the students eagerly answer her questions about the next step. When it comes time to practice more problems, that small group of students forges ahead. The rest of the class struggles with the homework.

My friend Darcy was one of those students who always put her hand up to answer the teachers’ questions, zipped through the homework and got A’s. She was admitted to a prestigious college and majored in physics. Upon graduation, she got a job as a geophysicist for an oil company. After 30 years of consistently earning a very good salary, she will retire with a six figure retirement savings. Sounds like a success story, doesn’t it?

Digging deeper, however, it turns out Darcy really wanted to be an astronomer. She spent two summers working at an observatory as an undergraduate, and absolutely loved it. But she did not feel her math background was sufficient to pursue a doctorate, which was required to be an astronomer. While she appreciates the salary of a geophysicist, which has allowed her to raise her children as a single parent and live a comfortable life, she has never enjoyed the work. It’s a job to her.

How could it happen that a person who did well in math in high school, and was able to earn a degree in physics from a highly regarded college not feel confident in her ability in math?! How could this lack of confidence cause her to give up her dream and settle for a job she can only tolerate?

The reason is that the way math was taught to Darcy did not involve true understanding. It was largely “monkey see, monkey do.” The ability to mimic the steps the teacher demonstrated was considered to be learning. As an example, the ability to add fractions with different denominators and consistently get the correct answer does not equate to an understanding of what the symbols mean; this is a fifth grade example. The situation just compounds as the years roll on. Darcy is an honest learner who recognized that she did not have true understanding. True understanding was not what she was offered in her school experiences.

Of the approximately 25% of students who are able to excel with the “monkey see, monkey do” system that exists in most of our schools, fewer than half are able to make the leap to real understanding.

The way for all students to really understand math is to give them a solid foundation in the very few critical concepts. This solid foundation consists of the three step process described by learning theorists such as Piaget. First the student has experiences with concrete objects, then moves to pictures, and then to the symbols of math. Darcy was taught the way most American students are taught – with the third step of symbols only. The three step method of teaching would have benefited Darcy and allowed her to follow her true professional passion.

I can relate to Darcy because I also “learned” math with Step 3 only, symbols not connected to the real world, and went on to earn a masters degree in physics. I worked with Darcy as a geophysicist myself.