Why kids start to flail in upper elementary math
The Pitfall
Many, many kids (and adults) still count on their fingers long after 1st or 2nd grade. So what? Is that a problem? Actually it can be a huge problem. It can hold kids back from a deeper understanding for numbers that will create major hurdles as they delve into complicated subjects like multiplication, division, fractions, decimals, pre-algebra, and beyond.
It's Ok Though!
Before you go worrying that it's too late for your kid (or you!), that you won't have time or energy to deal with this, or that you can't afford a tutor, please know that you absolutely can fix this fairly easily with the right strategies. As a math tutor I did this with countless kids in 4th, 5th, 6th grade, and even older, and have been amazed by how much they could excel once this barrier had been removed.
Step 1: Understand Why Finger Counting Can Be a Problem
In order to fix or prevent this, it's important to understand why things like counting on your fingers may be holding your kid back. And I should start by clarifying that it isn't always bad. When kids are learning to add in preschool, kindergarten, and 1st grade, their fingers are a great way to begin to concretely understand what adding and subtracting really mean. It also helps them to see patterns like that adding makes a number larger and subtracting makes it smaller.
But once a kid understands the basic concept of adding and subtracting and they start doing more complicated things, like adding two-digit numbers, there starts to be a problem. Imagine doing the problem 14+9 by counting on your fingers. The numbers you say out loud or in your head are "15, 16, 17, 18, 19, 20, 21, 22, 23." So you have said or thought a whole string of numbers that have almost nothing to do with 14, 9, or what the problem means. It will get you to the correct answer for this one problem, but you did it by clouding your brain with unrelated information rather than making a connection or practicing creativity or problem solving.
Step 2: Stop Getting An Answer!
The natural desire for a kid doing math, or a parent watching their kid do math, is to get the right answer. Fill in the blank! But the answer is like the last page of a book. You don't read only the last page of a book and then say, "That was a great book." Of course the last page matters to the story, but so do the other pages. It's time to start focusing way more on the process of solving a problem and way less on getting to an answer.
This is where you have to start convincing your kid, and yourself, that rethinking your process is worth a little extra time and practice. Eventually, they will be able to do 14+9 in their head without fingers, not to mention far more complicated arithmetic, pre-algebra, multi-step word problems, etc. But they have to get past this first hurdle. For many kids and parents this feels like slowing down or going back to kindergarten. Explain that this is about learning a more advanced way to work with numbers and it will help them with much harder math.
Step 3: Learn Your Ten Pals
If your kid can take any number 0-10 and tell you how many more it takes to get to 10, then you get to skip this step. The "ten pals" are the numbers that go together to make 10: 0+10, 1+9, 2+8, 3+7, 4+6, 5+5. They will need to have these memorized in order to easily manipulate numbers in higher order math. There are a bunch of ways to work on this and your kid may respond best to a combination of them:
- Have them use their fingers for good! If they have ten fingers, they can hold up some of them and then see how many are down. Hold up 6 fingers, then 4 are down. You might think, "I thought we were supposed to stop counting on our fingers." But the difference is that this helps them to visualize the relationship between the two numbers, and they aren't saying/thinking a bunch of unrelated numbers in between.
- You can also give them 10 - x problems to do with their fingers. For example, give them 10-3 and have them practice holding all 10 fingers up, putting down 3, and seeing how many are left. It's best to use this method for subtracting 5 or less from 10 because it makes the visualization simpler.
- Use ten frames. You can easily find free blank ten frames sheets online, or just draw them with a pen. Then have your kid practice filling them in (top to bottom, left to right) partway with one color marker and the rest of the way in another color. Have them write the two numbers next to the ten frame. Or you can make flash cards that show the same thing and then have them say the two numbers represented (eg "six and four").
- There are also games you can buy like Ten On The Spot or Clumsy Thief. These work especially well for kids who are hard to motivate, but they aren't free like 10 frames or fingers.
- Have a chart of Ten Pals and let them use it to find and circle ten pals in addition problems. For example, give them 2+4+8 and then they have to circle the two numbers that make ten together. Pro tip: this is a great time to tell them NOT to find the "answer" (the total) but just to focus on that one task of finding the ten pals.
Step 4: Show Some Strategies
With ten pals memorized and some experience focusing more on the process than the answer, there are now a bunch of new strategies available to them. Showing them a few strategies can start to give them ideas for how to create their own strategies.
You can start by adding single-digit numbers that add to more than 10, such as 6+8, 4+9, and 5+7. Plus 9s are the easiest to begin with. Use legos or other physical objects to show how 4+9 can become 3+10 by moving one lego from the first group to the second group. Have them practice changing __ + 9 to __ + 10 by moving one over (and don't ask them to find the answer - just focus on the strategy of simplifying). Then they can try problems like 24+9 by using the same strategy: 24+9 --> 23 + 10. Once they have practiced this strategy a lot, try doing the same thing with Plus 8s and moving 2 over (ex: 37 + 8 --> 35 +10).
Another good strategy is using two people's hands to find doubles. For example, for 8+8, you and your kid each hold up 8 fingers (all five fingers on one hand and three on the other). Then put your hand with 5 together with their hand with 5 and say, "That's 10. What's left?" Put your hand with 3 fingers together with their hand with 3 fingers and let them say, "that's 6." And then say, "Ten plus six is sixteen." Once you have practiced this with them a bunch, they will be able to do it just by looking at their own fingers and imagining another set of hands. And eventually they will just have their doubles memorized.
Step 5: Praise Creativity
Anytime they come up with a creative way to manipulate numbers, praise their creativity. If they say, "I have to do 6+5, and I know 5+5 is 10, so this is just 11," throw them a tiny party with your words. "Ooooh, that's great idea! I love your thinking!" Or if they give you a quick answer, ask them how they figured it out. Their strategy might be different from yours, and that's awesome. Point out that there are lots of different ways to come to the same answer in any problem. You can even challenge them to find two different ways to do the same problem.
Another note: learn what growth and fixed mindset are. Saying things like, "I wasn't good at math either" or "You're so smart" are detrimental to their ability to persevere, practice, and improve. Humans can get better at anything with practice. Praise practice too:
- "Wow, this is really hard and you are working hard on it."
- "I can tell you have practiced this because it's getting easier for you."
- "I know you'll get this with practice."
- "I can see that this is super hard for you. Your brain must be growing so much right now!"
Step 6: Eventually Expand Beyond Addition
You might be wondering why I've spent this whole post talking about addition. The truth is that addition is the building block for almost all basic math. Addition going backwards becomes subtraction. Repeated addition becomes multiplication. Multiplication backwards becomes division. Division and multiplication become fractions and decimals. Once they have good strategies, understanding of numbers, and practice being creative in addition, they can apply similar techniques in everything else.
Backup Plan: Have Them Start Over
There was a 5th grade teacher who had their entire class go on Khan Academy math and start from Kindergarten and work their way back up to grade level. By the time they completed all this, their math test scores were significantly improved, and the kids' attitudes towards math was significantly more positive. The reason this works is that it a) builds confidence, and b) fills in any gaps they have. Our school uses a site called IXL, so I have my kids use that instead of Khan, but the concept is the same.
How do I get them to do this? Each skill they complete is one point, and once they get to five points, I let them have 15 minutes of junk tv (ie, not educational). If they want any junk tv time they have to earn it with math points! Sometimes they save up enough points to watch multiple episodes or a movie. They have spent HOURS on math during evenings and weekends to earn junk tv time, and it has majorly improved their math skills. One of my kids increased her math skills by a grade and a half in a few months by doing this.
Note: I always encourage the kids to use tools when they are unsure or struggling. Hundreds chart, counting cubes, whatever helps. These tools may seem like a crutch, but they are actually scaffolding. When constructing a new building, workers stand on the scaffolding in order to build and make the building strong. Once it's strong, they can take down the scaffolding. The same is true in education. The tools help them to visualize or strategize and then they will internalize it over time.
Hope this is helpful! Best of luck in your math journey. You got this.
