Errors that learners make
There are different types of errors that learners make. This article review looks at how errors mislead. Hard as they may be for students to recognize, catching, and correcting them is paramount. With conceptual misleading, the math computation is correct. They may use the wrong formula to solve a problem or misunderstand a concept. A case in point is students’ tendency to do multiplications first when told to multiply and divide in the order of appearance. They commit this error by literally following the PEMDAS rule. An example is 18/3×3. When multiplied first, the answer is 2. Contrarily, multiplying and dividing from left to right gives 18. These different results prove how the PEMDAS version poorly states the rules (Peterson, 2019). Likewise, several students taught with BODMAS mnemonic are at a loss to imagine that division comes first. It is not the case.
18 ÷ 3(3+3) =?
The question above involves operation orders that prove controversial because the operation order changed slightly in the early ’90s. The present algebraic notation grants lesser precedence to addition than quotient. Such conventions made annotations brief and simultaneously eliminated ambiguity. However, minus as a unary operator has differing conventions. For example, -32 = 0 – (32) = -9 in printed and written mathematics. Contrarily, programming languages often give less priority to binary operators than the urinary one. Consequently, the precedence is lesser for the exponentiation than the urinary minus (Peterson, 2019). Hence, the interpretation -32 = (-32) =9. Below is the answer when using PEMDAS to solve the math equation.
18 ÷ 3(3+3) = 18÷3 (6) = 6(6) = 36.
Out of 340,000 people who did an almost similar question, 195 individuals of every 500 went about this question as worked above. However, about 200,000 of the poll takers, that is around three-fifths of the sample population found that the answer equaled one (Kerpen, 2019). Such an occurrence makes one wonder who or what went wrong. The majority were taught BODMAS to be math’s operations order while they were children. Below is how to tackle the question using BODMAS.
18 ÷ 3(3+3) = 18 ÷ 3(6) = 18 ÷ 18 = 1.
Both answers are correct, depending on what operations one got introduced to in school. It is also right to argue that the question is not well written. Besides employing the ‘/’ sign, more parentheses would serve as a better indicator of what order an examiner wants to test (Kerpen, 2019). Besides emphasizing or overriding convention, the ‘/’indicates the default order or an alternative one. Below is the question expressed more explicitly. The former adheres to PEMDAS while the latter follows the BODMAS rule. In improving clarity, nested parentheses can get utilized on the second re-arrangement, thus replacing brackets, as shown below too.
(18/3)(3+3) =? Or 18/ (3(3+3)) =?
18/3 [3(3+3)] =?
This operation is also a challenge because kids are often taught to work from the left towards the right. Operations order is a new way of looking into the problem. Students’ abilities vary. Therefore, giving them the rules does not guarantee understanding by all of them. Numbering the acronyms go a long way in making them realize the function of such operations. Another notable practice introduces learners to several easy problems and progressively builds up to more complex issues (Peterson, 2019). Below is an example of a simple to the full version of this question.
(18/3) =?
(18/3)3 =?
(18/3)(3+3) =?
Math misleads the moment mathematicians commit careless errors as well. They fall into this trap when they work to fast or pay less attention. For example, they could write a wrong number or copy the question wrong, like 18 – 3 (3 × 8) =?. At times they proceed to key it wrongly in their calculators. One way of avoiding such carelessness is slowing down. Then there are computational errors that come from incorrect subtraction, addition, division, and multiplication. The moment it occurs, the final solution is wrong, and so is the working used to arrive at it (Peterson, 2019). Showing a step-by-step operation confirms the comprehension of the concept. Reducing computational errors requires one to check the answer as soon as solving the problem ends. Accuracy determines the correctness of the work. A calculator comes in handy too, especially when the computation is long and tedious.
Three issues are evident here. First, the definition of a problem should always be clear. Next, the solution to a math problem might be more complicated than the examinee thinks. Then, a math question can have more than one right answer. On the other hand, math is a skill that needs practice, and one is bound to make mistakes in the process. To minimize such misunderstandings in the future, tutors should take a hands-on approach while introducing concepts (Peterson, 2019). This way, students understand the reasons for mathematical formulas and properties. Teaching the theory using several ways proves useful too. For this case of orders of operation, learners develop deep comprehension. Another remedy is having math talks that serve to reveal learners’ misconceptions. As a teacher, one can go over a concept that multiple students misunderstand to demystify it.