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# Misunderstandings

Misunderstandings or misconceptions in number are common. With informed use of these common misconceptions, teachers will be able to understand where students can struggle or misinterpret mathematical concepts and work to address them. Misconceptions in Place Value

## Misconceptions in Counting and Number

### 1.

Failure to recognise that the last number counted means ‘how many’ and that counting is a strategy to determine ‘how many’.

### 2.

Inconsistent movement between oral words and objects counted (e.g., matches objects to syllables or leaves out certain number names).

### 3.

Counting objects that are already counted.

### 4.

Superficial understanding of reading, writing, and recognising numbers from 0-10.

## Misconceptions in Place Value

### 1.

Inadequate part-part-whole knowledge of the numbers 0 to 10.

### 2.

An inability to recognise 2, 5 and 10 as composite or countable units.

### 3.

Inability to recognise the structural basis for recording 2+ digit numbers, i.e., H, T, O.

### 4.

Transposing the digits in a number, e.g., 51 is written 15 and 18 is written 81.

### 5.

Multi-digit numbers are seen as independent of place value, e.g., 45 is 4 + 3 instead of 40 + 3.

### 6.

Incorrectly writing numbers that pass over a decade or century. E.g., writing one hundred and nine as 1009.

### 7.

Not recognizing zero as a place value holder that denotes an empty set.

### 8.

Incorrectly operating with multi-digit numbers by using the digits instead of the value of each digit. E.g., 26 + 15 = 311 or 26 x 15 = 41

counting
place value

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