Misconception 1: Skip counting: Ensure students are repeatedly adding the same value i.e. when skip counting by twos, students are not getting confused and start to count by ones or threes etc. Students may think that skip counting patterns must always increase. (Model a decreasing skip count pattern even though the content descriptor states ‘starting from zero’.) Students can skip count - but really they have just rote memorising and will not be able to transfer the skills later. Skip counting is connected to multiplicative thinking and must be taught with meaning.

Misconception 2: Jump strategy: Incomplete understanding of place value; for example, thinking 16 + 10 = 1610, and Using inefficient strategies, such as counting on by ones, and ending up with a wrong answer due to miscounting.

Misconception 3: Be aware of the language of grouping, the number IN each group is different to the number OF groups.

Misconception 4: Repeated addition is not multiplication. Multiplication of natural numbers certainly gives the same result as repeated addition but that does not make it the same. Addition requires identical units. The sum must always have the same units as the addends:

2 apples + 3 apples = 5 apples             2 apples + 3 oranges = ??

What does that second equation give you? Fruit salad? In order to add quantities with unlike units, we need to find a common denominator. Apples and oranges are both pieces of fruit, so…

2 apples + 3 oranges =  2 pieces of fruit + 3 pieces of fruit 

                                   = 5 pieces of fruit

Multiplication requires different units. The product does not have the same units as either the multiplier or the multiplicand,

e.g. 2 baskets × 3 apples per basket = 6 apples                                                                      

How can we make multiplication come out the same as repeated addition? The only way to do it is to change the units.

How should we teach it? Change the focus from how to why. We can teach multiplication in much the same way that we do now, using manipulatives arranged in groups, rows, diagrams and arrays. But instead of drawing our students’ attention to the process of adding up the answer, we want to focus on the fact that the items are arranged in equal sized blocks. In other words, we teach our students to recognise the multiplicand.

Misconception 5: Word problems - I don’t need to draw a diagram - that’s childish. This is often a belief held by older students in Primary and it is one that we must remove, by simply putting value on diagrams. Diagrams are acceptable working and must be presented.

Misconception 6: You have to teach the tables to ten - the whole she-bang! Neuroscience will tell you that this is not the case with the diminishing chunking memory. Students will learn the multiplication facts in the following order:

• 0 and 1 times table;

• 2 times table;

• 3 times table;

• 10 times table;

• 5 times table;

Why? Students learn the easiest facts first that connect to the prior learning. By the time they reach the more ‘difficult’ tables, there will be very few to learn.

Misconception 7: Assuming multiplication always results in a larger value. Because students initially learn that multiplication is repeated addition, it makes sense that students generalise that the product of two values will always be greater than both of the multipliers. This assumption only holds true with positive whole numbers. Decimals, fractions and negative values contradicts this assumption. 

Misconception 8: Multiplying numbers in the order they are listed. Multiplication is like addition in that it is commutative. A deep understanding of the commutative property assists students in mental calculations. Consider the 5 x 13 x 2. Using the commutative property successfully, students could multiply 5 and 2 first, resulting in 10, then multiply by 13.

Misconception 9: Just add zeros when multiplying by a power of 10. Students who accept the shortcut of ‘when you multiply by a power of 10, just add that many zeros onto the number being multiplied’ without a true understanding of the underlying mathematics often apply this rule incorrectly. It works for integers, but not decimals.

Misconception 10: 27 x 3 = 20 x 3 + 7 x 3 ← Where did the "+" come from? Students often don't understand the concept of expanded notation which is to their detriment in multiplying larger numbers.

Misconception 11: Be very careful with just listing terms that ‘mean’ multiplication. Taken out of context can sometimes be confusing for students.