# What are the most common errors or misconceptions that students may exhibit when they are attempting to compare and order decimal fractions?

Table of Contents

- 1 What are the most common errors or misconceptions that students may exhibit when they are attempting to compare and order decimal fractions?
- 2 What is a common misconception about the operation of multiplication?
- 3 How misconceptions and errors occur in mathematical problem solving?
- 4 What are the common misconceptions in adding and subtracting fractions?
- 5 What are the main causes of errors and misconceptions in the learning of mathematics?
- 6 What is the most conceptual method for comparing weights of two objects?
- 7 How common are mathematical misconceptions?
- 8 Are there completeness properties of the real numbers system?

## What are the most common errors or misconceptions that students may exhibit when they are attempting to compare and order decimal fractions?

Longer-is-Larger Misconceptions

- Whole Number Thinking. Learners with this way of thinking assume that digits after the decimal point make another whole number.
- Column Overflow Thinking.
- Zero Makes Small Thinking.
- Reverse Thinking.
- Denominator Focussed Thinking.
- Reciprocal Thinking.
- Confusion in High Places.
- Negative Thinking.

**What are some misconceptions about place value?**

Common Misunderstandings – Level 2 Place-Value

- inadequate part-part-whole knowledge for the numbers 0 to 10 and/or an inability to trust the count (see Level 1);
- an inability to recognise 2, 5 and 10 as composite or countable units (often indicated by an inability to count large collections efficiently);

### What is a common misconception about the operation of multiplication?

It is a very common misconception that multiplication makes things bigger. The word ‘multiple’ itself carries a sense of many or a great number. Children first encounter multiplication in the context of whole numbers, a situation where you mostly end up with a larger number.

**What is a common error and or misconception for addition and subtraction?**

One key misconception that pupils may have when solving column addition and subtraction is considering each digit as a separate number rather than as a representation of the number of tens or ones.

## How misconceptions and errors occur in mathematical problem solving?

Mistakes are usually one-off, while misconceptions, the gods forbid, could be for keeps. Mistakes are made by a few, misconceptions are made by many and, repeatedly. Students can figure out their mistakes by themselves because mistakes are usually due to carelessness. They cannot do the same for misconceptions.

**Which of the following is shown through research to be a common error or misconception when students are comparing or ordering decimals?**

Which of the following is shown through research to be a common error or misconception when students are comparing or ordering decimals? The decimal that is the shortest is the largest. Students may think that shorter is larger, as they believe any number of tenths is larger than any number of hundredths.

### What are the common misconceptions in adding and subtracting fractions?

Basic Fractions A common misconception in adding or subtracting fractions is pupils treating the numerators and denominators as whole numbers so end up adding or subtracting the denominators as well (see above illustration 1 – misconception).

**What are errors and misconceptions in mathematics?**

## What are the main causes of errors and misconceptions in the learning of mathematics?

The main cause of errors and misconceptions is superficial understanding, which was most probably due to teachers rushing to complete the extensive syllabus, and consequently, students resorted to memorizing rules because of surface understanding.

**Which of the following reasons best describes why arithmetic and algebra should be closely connected?**

Which of the following reasons best describes why arithmetic and algebra should be closely connected? Place value and operations are generalized rules; a focus on algebraic thinking can help students make connections across problems and strengthen understanding. You just studied 6 terms!

### What is the most conceptual method for comparing weights of two objects?

Converting between metric and customary units. What is the most conceptual method for comparing weights of two objects? – Place objects in two pans of a balance.

**What is a common misunderstanding when comparing unit fractions?**

A common misconception is that learners believe the numerator and denominator are the same. Let’s start with the fractions basics to help address this misconception. ‘Denominator’ means ‘that which names’ in Latin. The denominator can also tell you the size of the parts.

## How common are mathematical misconceptions?

Mathematical Misconceptions 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. Needless to say that misunderstood concepts could have disastrous effects on all stakeholders.

**What is the real number system and is it important?**

The Real Number System is a tricky concept for students. It is very abstract especially irrational numbers and often doesn’t really seem important. To be quite honest, I didn’t fully grasp it until my college level course where our professor demonstrated how to teach it.

### Are there completeness properties of the real numbers system?

This person is not on ResearchGate, or hasn’t claimed this research yet. The real numbers system is one of the topics that pre-service mathematics teachers have to master. There is no exception to supremum and infimum, the basic concept of completeness properties of the real numbers system.

**What are common misconceptions about money and value of coins?**

children often hold a core misconception about money and the value of coins. Some students believe that nickels are more valuable than dimes because nickels are larger. Some elementary and even middle school students believe that 1/4 is larger than 1/2 because 4 is greater than 2.