In order to increase your child’s math skills, you have to identify the starting point of your child’s comprehension. There are strategic ways to do this to ensure you’re not confusing your child even more.
Rather than evaluate your child’s math skills by giving them a problem like “What is 5+4?” or “What is 7x9?”, where they could have memorized the answer, try to evaluate your child’s math skills based on language. If your student does not understand what is happening with the symbols behind what is on a piece of paper, they are not going to be able to apply the math to solve real life problems. Because success and ease at teaching comes from comprehension rather than proficiency, this will also ensure that your student is able to understand what you are saying when you are introducing new ideas.
Ask your child some word questions to determine if they understand what you mean when talking about math. Here are some examples of how you can test understanding math concepts.
To test counting, there are several things you can do. If you want to see if your student has comprehension, you may try a producing exercise with them.
Ask them to give you eight things. If the student is able to pass over eight items, stopping at eight without help, then they are proficient at counting. If they continue, it is okay; let them continue to see how high they may get, but you may then see if they are proficient at “How many?” This is what many parents play with their children already. You hold out eight fingers and you ask the child “How many fingers am I holding up?” If they are able to count and get the answer, that is good. If they say something like “Five and three,” then you will need to continue easing the problems until you can find which numbers they understand and which they do not.
If they are showing that they can produce, you may move ahead a step further. Ask them if you had one more, how many would you have. Remember, it is okay if they count to get the answer or use their fingers; they will develop proficiency at mental math in time. Until then, let them use the strategies they understand to solve the problems. The slowness of the solution should cause them to come up with better strategies.
When it comes to subtraction and addition, some questions you could ask would be something like, “If I had eight peaches, and someone came and took four away, how many would I have left?” You can do this with or without fingers.
Because addition and subtraction are two sides of the same idea, you can alternate between addition and subtraction such as asking, “If I had 14 ships and someone brought me two more, how many would have?”
Remember — it’s okay for your child to count to get the answer or to use their fingers. It means that they understand how to solve the problem and because of that they understand the language. That’s good.
If they are not proficient, that is okay, too. Go to easier subjects and find out what they understand and do not. Catching them up will be fast and easy if you know you are starting in the right place.
When it comes to evaluating multiplication, and knowing whether or not your child understands the language and concept versus having just memorized their multiplication tables, we use groupings by rows or collections.
You may arrange six rows of seven items and ask “How many are there?” If your child is counting to get the answer and they’ve memorized their times tables, then this may be an indication of a problem. You may quickly be able to catch them up if you say something like “What is 6 times 7?” after they count to answer.
A lot of times, when students who have memorized their multiplication tables make this real-life connection of what multiplication actually means, they’re able to get the concept. They glide through multiplication moving forward.
These three math topics are all representations of proportionality. Students that are having issues understanding the idea of proportionality will have issues with all three.
They are best evaluated visually. The easiest way to understand proportionality is through fractions and the best way to do this in real life is through measurements — anything that breaks out a measuring cup, ruler, or measuring tape. By working with your student on a project like this, you will quickly see what they understand and do not. Where they do not understand, take note and back off; where they do understand, you may give them more challenging questions.
When it comes to fractions, it’s important for children to understand that fractions, decimals and percentages are all representations of the same idea: proportionality. It’s just a quirk of human language that we’ve agreed upon these three different ways to represent the same idea. No one way is more correct than another. Telling a student this is important. It is often overlooked in the classroom and ends up contributing to anxiety around these topics.
What can you do if you’re working with a student, but you’re seeing that they don’t understand something? It’s pretty simple, actually.
Let them answer the question incorrectly. Ask them why they think it is the correct answer. Based on their reasoning, you should be able to see exactly what the child does not understand and then give them a hint that allows them to have that “aha” moment or clarify the idea that is misunderstood.
This is the process we encourage our parents to use when working with their child in the Elephant Learning app. Every parent we have spoken to that has used the above advice has been able to coach their child into understanding. For example, one parent discovered that her daughter thought “older” meant “taller” and that was causing the issue!
It’s very important not to get frustrated if your child does not understand a concept. This is where Elephant Learning really excels. We help you find your student’s level without the exhaustion. The computer has infinite patience.
Please don’t keep pounding away at the same concepts in the same manner if your child isn’t getting it. Sometimes it is best to take a break. Go online and see how other people are teaching these concepts; you can even look at how the Elephant Learning app is teaching a concept and replicate our methods.
Evaluating your child’s math skills is so much more than just giving them a math sheet filled with problems, or looking at how well they’re doing in class. It’s all about ensuring they have a strong math foundation that holds up over time as they move into harder and harder concepts. Evaluating their comprehension based on the language surrounding math makes building this foundation that much easier.
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.