Why 3 + 7 is equal to 10 and not 37? Have you ever wondered about it?

Well, this question reminds me of the “Child’s Why”. At the development stage which typically starts around ages 2 or 3 and continues into ages 4 and 5, children ask “Why” which is a sign of curiosity to understand the world around them and explore it further by talking about it with you. Children’s innate curiosity plays a big part in their “WHY” questions. Their curiosity about the world around them helps to build concepts, skills, vocabulary, and understanding of the unknown. And you can help channel their curiosity and need to know why so that you help foster learning in a positive way. (Dr. Rebecca A. Palacios, Ph.D., NBCT )

I believe that the “Why questions” are the key to raising lifelong learners. And if we, as Math teachers, aim to cultivate students’ curiosity towards Math and develop their thinking and reasoning skills, we have to think outside the box and train our brains to ask Why questions. We need to be a child who is curious to understand and not only know the Math concepts, refuse to take for granted what we already have been taught, and be risk-takers by asking questions we might don’t know the answers to.

Through my weekly newsletter, I will encourage you to THINK about Math. In this way, you can expect the misconceptions students may do and plan for understanding not only for knowledge.

Look at the following picture and take a few minutes to think about it before continue reading the article.

Let’s go back to the Pedagogical Content Knowledge PCK to interpret this question.

The place value is the essential concept needed to understand the number system. Toddles start counting at a very early level. Parents encourage their kids to retell the number sequence even before they realize what a number means or represents. This is necessary but not sufficient to understand the number sense.

In kindergarten, teaching number sense in preschool is critical and requires careful planning. When constructing the meaning of numbers, students will

• understand the one-to-one correspondence
• understand that, for a set of objects, the number name of the last object counted describes the quantity of the whole set
• understand that numbers can be constructed in multiple ways; for example, by combining and partitioning
• understand the conservation of the number
• understand the relative magnitude of whole numbers
• recognize groups of zero to five objects without counting (subitizing)
• understand whole-part relationships

To acquire these outcomes, children need to be provided with a variety of authentic learning experiences practicing these skills, in addition to recognizing written number symbols. Teachers have to be aware at this stage when introducing the writing of 2-digit numerals where the significance of using a digit beside one other has to be connected with the grouping of ten.

Starting at elementary levels, teachers proceed with modeling 2-digit numbers by reinforcing the meaning of tens as a group of ten. Later on, this will be the foundation of the concept of regrouping when adding numbers. Moreover, teachers are encouraged to ask students to make groups of 2 or 5 and compare and contrast different number systems, so they learn that 1 + 1 is equal to 2 in the base 10 system and 10 in a binary system.

Last but not least, be careful when tackling or asking unusual questions; the prerequisite concepts have to be fully understood by students to avoid ambiguity, frustration, or misconception.

Well, don’t get mad if a student tells you 3 + 7 = 10, because you taught them that 3 apples + 7 apples = 10 apples, however, later on you will tell them that 3cm + 7mm = 37 mm and 3 tens + 7 ones = 37. So make the numbers alive and authentic by adding them to a unit (apple, meter, gram, …) and take the mistakes as opportunities for learning and understanding.