Have you ever been in the situation where you can easily do your child's math homework, but you cannot figure out how to explain it to him or her? Even in elementary school, you see questions that you know how you would go about answering the question, but you aren't sure how the teacher has presented it and you don't want to confuse your already stumped student. Does it feel like you are guessing what the teacher has said in class?
Here is a simple way to help. Our brains are always trying to make meaningful connections to our new learning. How can we create meaning for our student when it comes to math? One great way is to create a context for the problem. For example, if they are multiplying 731 x 8, you might ask them to think of a real-life situation where they would have to combine 8 groups which each contained 731 items in each group. This is where your student can have no wrong answers! Let their groups be silly. Create a context for meaning. For example, they may say 731 fleas on each of eight dogs. This helps the student visualize the quantity and understand the operation that will be performed.
Next, ask the student for multiple ways to show how to combine 8 groups of 731. Suggest that they draw a picture to illustrate their thinking. The goal is to help them see more than just one way to complete the problem. Students can feel a great deal of pressure to remember the exact algorithm, or formula, which has been taught in class. Remember that one of the common core objectives for math is flexible thinking, or using multiple strategies to approach a problem. Ask the student to explain to you how to do the problem. You will quickly see any erroneous thinking in their conceptual understanding.
The student may list 731 eight times in a column. This is one correct way! The student may add eight 700s, then eight 30s, then eight 1s. This is correct also. They may use the distributive property and write 8(700 + 30 + 1) or (8x700) + (8 x 30) + (8 x 1). Using the traditional algorithm, with regrouping and carrying is the most abstract approach, and requires an underlying understanding of the other strategies if it is to have meaning.
Flexible thinking and meaningful contexts will build your student's confidence and competence in approaching their math lessons.