A Math misconception is essentially an incomplete understanding that we have developed from our Math experience. A misconception is different from an error. A misconception is therefore a student’s understanding of the concept or relationship that is incomplete or incorrect.
In math, every digit in a number has a place value. Place value can be defined as the value represented by a digit in a number on the basis of its position in the number. For example, the place value of 7 in 3,743 is 7 hundred or 700. However, the place value of 7 in 7,432 is 7 thousand or 7,000. Here, we can see that even though the digits are the same in both the numbers, their place value changes with the change in their position.
Understanding the place value of digits in numbers helps compare numbers. It also helps in writing numbers in their expanded forms.
Through this article, let us have an insight into the misconceptions that can occur while learning about place value.
Place value: A concept inescapable
Why is place value so important? Learning place value is essential because it provides the foundation for regrouping, multiple-digit multiplication, and more in the decimal system, as well as a starting point for the understanding of other base systems. Almost all mathematical concepts build on the understanding of Place Value making it one of the key concepts in mathematics.
Math is all about patterns, and our number system is based on patterns of ten. Once a child truly understands this, they can work with any number, including negative numbers and including decimals.
Place value finds significance in almost every aspect of daily life. All these factors make learning place value important.
Place value misconceptions
There is an interplay of various factors in understanding place values. If a child is struggling with place value it means that there exists a misconception in either of these.
1. Base 10 structure
Hindu-Arabic system uses symbols for the numbers 1 to 9 and then a place value system with a place holder of 0. Using these ten symbols we are able to represent large numbers just by their value in different positions. It is very difficult for the child to initially understand how the numbers change from 9 to 10. The child may not be able to put zero and one in the right places.
Learners need to recognize 0 as a label for an empty set, or nothing, as well as a placeholder for numbers in our base-10 structure. This might seem very confusing for a child. Children tend to get confused and are in a fix about what to denote the empty ‘place value’ with.
Partitioning involves separating out numbers so that the value of each digit can be seen, for example, 385 = 300 + 80 + 5. The child may denote this as 3+8+5. Here, Multi digits are seen as digits independent of place value by the child, which is a misconception. –
The child misapplies the rule for reading numbers from left to right (this difficulty is often caused by teen numbers) as in 71 could be read as 17; 41 as 14.
This is related to the value and position of each digit. Ten in any ‘place’ in a number can be exchanged for one in the next place to the left, so, for example, 10 hundred can be exchanged for 1 thousand. Conversely, one in any ‘place’ can be exchanged for ten in the next place to the right. Kids generally get confused about this concept and end up writing the wrong place value of a digit.
Can misconceptions make the concept harder for young learners?
The biggest misconception about Math is that the concepts are not applicable in real life. But this is a myth. Preconceived fears and misconceptions make learning less enjoyable and induce stress.
Other misconceptions like Math is difficult and one needs an inborn talent for it has always ruled the minds of children and made the subject intimidating.
Debunking these myths could play a large role in furthering math education. Any one of these misconceptions could stop a student from embracing the subject and possibly end their attempt at pursuing a career in it. When studying math it can be easy to get frustrated. Math concepts can be hard to understand at first and often it just takes a little bit of time and effort to get a student to the point of understanding.
Concepts like place value need a thorough understanding of numbers and counting. Although it might seem tricky at first, the misconceptions that surround it can make it seem more difficult to master. Activities in counting or games help foster an enjoyable learning atmosphere.
To wrap up, a misconception is the result of a lack of understanding or in many cases the misapplication of a rule‟ or mathematical generalization (Spooner, 2002);
Any misconception in learning has to be tackled as it causes a gap in knowledge. It becomes imperative to overcome this in order to proceed with the learning.
Misconceptions in mathematics are inevitable and often predictable. But they can be used to support deep learning by helping students recognize their misconceptions and revise their thought processes. These Misconceptions are as common as any other phenomena in real-life situations. Just about any concept, regardless of how well it is taught, could be misunderstood.
Misconceptions are therefore a problem with understanding, not with fluency or memory.