If you want to help your child learn new math concepts, then effective teaching and communication methods are your best tools. The first step is understanding your child’s level (learn how to do that here). If you are not working with your student at their level, then it will be difficult for them to understand you and that can actually inhibit your student from learning.
The following three-step process to teach math effectively is what we use at Elephant Learning and it is something you can use in your own work with your child. It includes defining an idea, determining if a child recognizes a definition and then allowing a child to produce the idea in order to demonstrate their comprehension. For example:
This last step is the proverbial checkmark. If your child can do this, then they truly understand the math concept. This three-step process can be used with all math concepts that you would want to teach your child, including counting, subtraction, multiplication and fractions.
Defining a math concept for your child is where the primary “instruction” is going to occur. You’re going to show them an idea, have them exhibit the idea and then label it with the name of the concept. Let’s go back to a previous analogy we’ve given on how to teach a child their colors.
You can’t just verbally tell a child what the color red “is” and expect them to understand it. What you do is you show a child red objects and then label them as red, so they can then recognize the color at a later time. Similarly, you have to show a child a math concept and then label it, therefore defining the idea, before they can truly comprehend the concept. You can’t describe to a child what addition is if you’re not doing it. Defining a math concept with a child isn’t as complex as it sounds. Ask the child to give you five things and then four more things. Now how many do you have? Nine. That’s addition. After the child counts to get the answer let them know, “That is right! Four added to five is nine.”
Can your child accurately give you four building blocks, then five more building blocks and then tell you how many they have total? Then they recognize addition.
At first, your child is likely going to count all nine building blocks in order to give you an answer, and that’s okay. But at some point, you want them to move to a more advanced counting strategy. They should be able to “count on,” or start at five and then count on to nine, without having to count all of the building blocks over again.
The Elephant Learning app accomplishes this by hiding the first amount of items from the app user, so they’re forced to start at their original number (five) and add on the four items that they can see to get to the correct answer of nine.
Once your child is confidently and correctly using the concept to solve problems, they are demonstrating comprehension. For counting, this would be if they are able to produce, for example, seven objects and stop at seven. For addition and subtraction, that is identifying that addition or subtraction would answer a word problem, or a real life problem. For multiplication, that is using it as a tool to solving questions with grouping or arrays.
If you’re working with your child and he or she is not demonstrating that they’re able to recognize the definition, it’s just a matter of going back to the definition and explaining it again. This is where you don’t want to get frustrated. You want to remain calm and patient, but don’t repeat yourself too much. If you and your child are both frustrated because they’re not getting the answers right, it can only lead to math anxiety and later avoidance of math on their part down the road.
Maybe it’s not a matter of your child not understanding, but it’s that you’re not teaching the definition properly, at which point it might be time to consult Elephant Learning or another online resource to see how best to teach these definitions.
Teaching math effectively is so much more involved than giving your child a math sheet filled with problems or asking them to memorize some multiplication tables. It requires passing on the experience of math concepts and ensuring a child truly comprehends a math concept before going on to the next one. However, with a little bit of work and a lot of patience, parents can teach their children math in a way that sets them up for future success.
Math anxiety — a fear of getting math concepts and problems wrong and the resulting avoidance of math because of that — is something I’ve seen many times over my life and not just in children. It’s just as prevalent in adults and, believe it or not, despite my PhD in math, I experienced math anxiety as a child, too. While some children allowed their math anxiety to grow into a lifelong avoidance of math, mine fueled my competitive spirit and led me to push ahead of my peers, learning advanced math concepts even when I wasn’t able to get into the advanced math classes my middle school offered.
It is never too late to understand math. At a young age, many of us had the experience of being told that “we are just not a numbers person.” Books have been written on this social phenomena, and half of all Americans report Math anxiety. As it turns out, mathematics is really about learning jargon, a jargon that is so fundamental to humanity that we consider it vocabulary.
At the end of the day, algebra comes down to these three steps: define, recognize and produce. No matter if your child is in middle school or a PhD math program, it’s all about defining (can you understand it?), recognizing (can you identify it?), and producing (can you use it to produce results or new research?). If you can help your child with these three aspects of algebra at home, they’ll be better set up for success in the classroom and the future.
Most students learn to multiply in school by memorizing their multiplication tables. There’s nothing wrong with memorizing multiplication tables, but a child must know what the multiplication tables mean. If they’re multiplying seven by six, they need to have that picture in the back of their head of six groups of seven or seven groups of six. If not, they don’t have a true understanding of what multiplication actually is and it won’t serve them later on in life.Take, for example, a child who knows that five times four is 20. She can solve the multiplication problem with ease.
In early elementary education, the first concepts that we work with are counting and comparisons — that is, quantity comparisons versus what's bigger and smaller. We might show a child an image of four objects and an image with 12 objects, and ask them to identify which has more or fewer. It's important for children to know the difference because it sets the stage for addition and subtraction.
Making math fun for your child within the confines of your everyday world is easy. Let’s say you’re walking down the sidewalk with your child and they say, “Oh, there’s a train.” That’s an opportunity for you to ask how many train cars they can see. How many engines are on the train? Even if it’s just their toys sitting out on the floor, you could ask them, “Can you give me three toy dogs right now?” Then your child has to identify what’s a dog, what’s not a dog and how many of them equal three.Take whatever your child can identify and formulate a math lesson that’s on their level.