IT TRUE THAT SOME PEOPLE JUST CAN’T DO MATH?
While it is true that some people are better at math than others just like some are better than others at writing or building cabinets or anything else it is also true that the vast majority of people are fully capable of learning K–12 mathematics. Learning mathematics does not come as naturally as learning to speak, but our brains do have the necessary equipment. So, learning math is somewhat like learning to read: we can do it, but it takes time and effort, and requires mastering increasingly complex skills and con-tent. Just about everyone will get to the point where they can read a serious newspaper, and just about everyone will get to the point where they can do high school–level algebra and geometry even if not everyone wants to reach the point of comprehending James Joyce’s Ulysses or solving partial differential equations.
“I am just no good at math” is said so often and with so little embarrassment that it seems as though our society has accepted the “fact” that math is not for most of us. The problem is that this notion is a myth. Virtually everyone is fully capable of learning the numeracy content and skill required and understanding of arithmetic procedures, algebra, geometry, and probability deep enough to allow application to problems in our daily lives.
Just how “naturally” do children learn mathematics?
Two important findings from the last 20 years are relevant:
- Humans are born with the ability to appreciate the concept of number
First, humans are born with two ways to appreciate number. One is an approximate number sense. This sense cannot support precise enumeration, but it does enable us to compare two sets of objects and immediately know which set is larger. For example, if you saw 50 beans scattered on one table and 100 beans on another table, you would know at a glance, without counting, which table had more beans on it. Carefully conducted laboratory tests confirm that people can use their natural sense of numeruosity to make these judgments, and are not making judgments by the area taken up by the beans, the density, or other cues
- Humans seem to be born with a sense that numbers and space are related.
The other important finding from the last 20 years of research is that humans seem to be born with a sense that numbers and space are related. There is a variety of evidence for this relation-ship; we’ll review just a handful of it. First, many cultures make use of a spatial representation of numbers, for example, via a number line. Second, numbers and space are represented in overlapping areas of the brain. Damage to a particular region of the brain (the intraparietal sulcus, which is on the upper part of the brain, toward the back) leads to difficulties with directing spatial attention and difficulties with processing numbers.
What do students need to be successful in math?
In its recent report, the National Mathematics Advisory Panel argued that learning mathematics requires three types of knowledge:
- Factual: Factual knowledge refers to having ready in memory the answers to a relatively small set of problems of addition, subtraction, multiplication, and division. The answers must be well learned so that when a simple arithmetic problem is encountered (e.g., 2 + 2), the answer is not calculated but simply retrieved from memory.
- Procedural: A procedure is a sequence of steps by which a frequently encountered problem may be solved. For example, many children learn a routine of “borrow and regroup” for multi-digit subtraction problems.
- Conceptual: Conceptual knowledge refers to an understanding of meaning; knowing that multiplying two negative numbers yields a positive result is not the same thing as understanding why it is true.
Increased conceptual knowledge may help student or anyone for that matter to move from bare competence with facts and procedures to the automaticity they need to be to be a good problem solver
Adapted from THE AMERICAN EDUCATOR JOURNAL | WINTER 2009–2010IS