Here, the discussion considers some common misconceptions that are hard to change. This misconception grows from the interplay of two factors. First, students thoughtlessly translate the words of the problem from left to right. Second, as they give in to that temptation, they confuse the idea of variables and labels. They fail to apply the idea that variables stand for numerical expressions.
Books cost two dollars each and records cost six dollars each.
They often incorrectly calculate the original price from a sale price by applying the discount to the known sale price, instead of to an unknown original price. Students may misconceive the independent nature of chance events. For example, after getting heads on four consecutive tosses of a coin, they may claim that tails are more likely than heads on later tosses. Their misconception shows that they want to save multiplication for computing increases. The few studies that have investigated mathematical misconceptions among Hispanic students show that their error patterns are nearly always the result of differences in language or culture.