Place-value can be difficult to teach and learn as it is often masked by successful performance on superficial tasks such as counting by ones on a 0-99 or 1-100 Number Chart. The structure of the base ten number system is essentially multiplicative, as it involves counts of different sized groups that are powers of 10. Unfortunately, place-value is often introduced before students have demonstrated an understanding that the numbers 2 to 10 can be used as countable units and/or before any informal work with equal groups. As a consequence, many students develop misconceptions in this area which serve to undermine their capacity to use place-value based strategies to support efficient mental and written computation and their later understanding of larger whole numbers and decimal fractions.

When counting thousands, hundreds, tens, and ones) the student misapplies the procedure for counting on and treats thousands, hundreds, tens, and ones as separate numbers.

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Misconception 1: Can they count or can they recite? Be careful that students can only rote count as the aim of this program is to have rational counting. Rote counting is simply the recitation of whole numbers in the correct order. Rational counting happens when a student is able to:

1. do rote counting;

2. make a one to one correspondence between the objects being counted and the numbers stated, (Perceptual) and 

3. know that the last number stated represents the number of objects in the set. (Gelman & Gallistel, 1978)

The ability to classify is a prerequisite to counting. Why? Because we count things that belong to the same set, e.g. Three tables and two persons are not counted as five. In the same sense, the sum of 3x and 2y is not 5x or 5y. This must be clarified. While the items given for students to learn to count are not necessarily and must not always be identical, they must be easily perceived to belong to the same set.

Misconception 2: Reading numbers incorrectly. Students will literally read a number e.g., a student looks at the number 2008 and reads it as “two hundred and eight”. This student has noticed the ‘200’ and then the ‘8’ and so reads it in that format.

Misconception 3: The student can identify the ordinal numbers that sound similar to the cardinal number (sixth, fourth, etc.) but does not identify the ones that sound different (first, second, etc). ‘First’ can be written as ‘1st’ but is not necessarily 1. In using ordinal numbers in relation to space, we need to always define the reference point.

Misconception 4: Watch for students who reverse the digits - they will need to be retaught the process. Also be aware of students who do not understand regrouping of two digit numbers, or who have difficulty with tens and ones concepts.

Misconception 5: A repeating pattern can be described completely by indicating the unit of repeat and stating the number of repetitions. Young students sometimes have difficulty identifying the unit of repeat, even in one-dimensional patterns.

Misconception 6: Often students confuse “rounding” with the word “around”. The other misconception occurs when money is used to represent rounding - if you round down then you won’t have enough to pay.

Misconception 7: The zero isn't really important. The student recognises simple multi-digit numbers such as 30 or 400 but does not understand the position of a digit determines its value, e.g. Student mistakes the numeral 306 for thirty-six.

Misconception 8: The student orders numbers based on the value of the digits, instead of place value, e.g. 69 > 102 because 6 and 9 are bigger than 1 and 2.

Misconception 9: I must consider all digits. If rounding to a power of 10 larger than tens, the mistake is often made than all digits after the specific rounding place need to be considered. This is incorrect - it is only the place value immediately to the right of the rounding position. So if rounding to the nearest hundred, not interested in the units, only the tens. 

• they can round to some other multiple of 10 or 100 when they don’t understand the concept of “nearest” multiple of 10 or “nearest” multiple of 100;

• rounding is guessing;

• rounding a 2-digit number to the nearest ten simply means replacing the last digit with a zero, e.g. 57 rounded to the nearest ten is 50.

Misconception 10: Students may continuously round. e.g.What is 14 489 to the nearest 1000?

 To obtain the answer, students may apply the following: round to the nearest 10, 100 and then 1000; thus: 14 489 to the nearest 10 is 14 490, 14 490 to the nearest 100 is 14 500, 14 500 to the nearest 1000 is 15 000. Hence, the misconception leads to an incorrect answer - 15 000.

Misconception 11: The spaces mean nothing. Students often do not use the spaces to indicate the groups of thousands, millions, etc.