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Get Them Off Their Fingers And Into Math
The mastery of the 45 addends is an important step to facilitate the calculation. Addition is simple, if the concepts are understood. 5 + 7 is the same as 7 + 5 and when 7 and 5 join it always ends in 2… so 17 + 5 and 15 + 7 are easy and students can also see that 37 + 5 is basically the same problem than single-digit problems with tens “just along for the ride.” You’d be surprised how many students don’t understand this simple concept. They will get 21 or 23 instead of 22 when they add 15 + 7. They can also use the simple “wanting to be a ten” algorithm to make it easier: 7 takes 3 out of 5, which is a ten and two, OR 5 takes 5 of 7 making a ten and two. Either way, it’s 12, and the best way to do it is whatever the student prefers.
This method allows the student to free himself from the fingers by doing “a ten and a little more” when adding two numbers. Turns out there are only 45 combinations…once students understand this simple “I want to be a ten” algorithm addition, it becomes much easier and they can tackle on their own to bigger problems. Then it’s just a matter of practicing and rehearsing. Use a wide variety of problems to practice this skill and teach other concepts at the same time to prevent the practice from becoming mind-numbing boring work that will also distract students from math.
Using their fingers is one step on the way to mastering addition facts, unfortunately many students remain stuck at this step until adulthood. For Kinesthetic Learners Using Fingers and Hands IMPORTANT IS: it’s HOW they learn, and you have to help them overcome this: manipulations are a great way to encourage them to “do it with their head”. For young learners, the use of fingers and hands is just natural…you can also spot kinesthetic learners as they will lean more on their fingers and be slower to move away from them. This doesn’t mean they are “slow” or less capable than visual or auditory learners, they grasp concepts just as quickly or faster than those with other learning styles. We also find that when it comes to sports and other activities that require hand-eye coordination (like arts and crafts), they often excel. Using your fingers is good! AND you need to get past this stage if you want to be faster and achieve mastery. Being quick at addition leads to easy mastery of multiplication as a bonus. They may even like math, why wouldn’t they if it’s fun and easy?
Many speed reading courses incorporate the use of the finger to guide the eye along the page, some use it to begin with then drop it for other courses, this is the main stay of the course. Adding more sensory input increases learning, and in the case of reading, the hand and eye are integrally connected. The point is, you want to encourage students to take this step as far as math goes, NOT discourage or skip the step all together. Some students will naturally NOT use their fingers when performing mental calculations…for those who do use their fingers later, this will become a handy cap. Counting quickly makes math easier, because all math counts; however, do not confuse calculus with mathematics. Mathematics is the use of calculation and critical thinking to solve problems and express reality numerically.
Addition and subtraction as well as multiplication count just quickly. They are among the first steps to understanding mathematics and must be mastered to ensure success. The use of fingers can also lead to a loss of precision, often children (and adults) are off by one sometimes even by two.
Verbal practice with add-ons, build walls and towers, play games like what’s under the cup, simple story problems and worksheets with pictures give the student inspiration experience he needs to transition from fingers to symbols to be able to do it “in their heads.” Drawing rectangles and other math concepts as well as making pictures of the manipulatives they use helps the student make sense of the symbols and see what they do. It also adds variety and helps students (and teachers) see that you are using the same skill sets throughout math, which is why you often see me using third and fourth power algebra to teach addition and multiplication facts.
Indeed, if you push the concept far enough, they can also pull out symbols so to speak and do everything in their heads if need be, without paper or pencil. This was perfectly illustrated by a five year old who is able to factor trinomials in his head because he can see the pictures when he hears expressions like x^2 + 3x +2 he can see it and tell you the sides. Or if you tell it the sides (x+3)(x+2), it can tell you the whole rectangle not because it sees symbols but because it sees IMAGES. In addition, he “cements” his additions and multiplication facts in his memory. Is it easier to see 6 taking a 4 out of 7 to make 13 when faced with a problem like x = 6 + 7 than doing algebra? It’s also quite easy to see 6 + x = 13 or x + 7 = 13, especially if you give them a simple algorithm to solve these “want to be a ten” based concepts. He also gets a ton of positive reinforcement because people think he’s a genius kid who motivates kids to do more. Never underestimate the power of simple praise.
Once they learn some basic concepts and understand the meaning of symbols, math becomes easy and even fun. Being able to visualize what you are doing makes all the difference, it also makes it MUCH easier to memorize because the mind works in pictures not symbols so memorizing the 45 additions and times tables is easier because the mind can store many more images easily than symbols. Then when it is time to remember, an image or symbols or just words can easily be retrieved from that place which we call long term memory.
Have you ever known someone who remembers phone numbers by imagining the keypad in their head? They can even point to the numbers and move their pointer finger on an imaginary keyboard in the air while they dial the number back. This is a visual kinesthetic way of storing long numbers. The brain works with images, which facilitates the dissemination of information. Is it easier to add two numbers than to recite seven to ten digits? Especially if you have a method to visualize them if you somehow forget them?
A simple exercise: Ask a pupil to imagine a cow. Then ask them if they have seen a COW or a picture of a cow? Ask what color was it? This lets you know they weren’t seeing any symbols. The problem is that most students have nothing to do with math, whether it’s algebra or simple addition. The “trick” if there is one is to get the information into long term memory so that it is easily recalled and it is fairly well proven that symbols i.e. letters and numbersare a difficult way to get information there.
Manipulators are the perfect bridge to get information there. After all, it’s never the storage that’s the problem, it’s the retrieval.
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