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Get Them Off Their Fingers And Into Math
Advance to mastery
Mastering the 45 complements is an important step on the way to making calculus easier. Addition is simple, if the concepts are understood. 5 + 7 is the same as 7 + 5 and when 7 and 5 are added together it will always end in 2… so 17 + 5 and 15 + 7 are easy and students can also see that 37 + 5 is basically the same problem like single digit problems with dozens “just along the ride”. You’d be surprised how many students don’t understand this simple concept. They will find 21 or 23 instead of 22 when they add 15 + 7. They can also use the simple “want to be a ten” algorithm to make it easier: 7 takes 3 from 5 making a ten and two, OR 5 takes 5 from 7 making a ten and two Either way, it’s 12, and the best way to do it is the way the student likes it the most.
This method allows the student to remove their fingers by doing “a ten and a bit more” when adding two numbers. As it turns out, there are only 45 combinations… once students understand this simple “want to be ten” summation of algorithms it becomes much easier and they can tackle bigger problems on their own. Then it just comes down to practice and repetition. Use a wide variety of problems to practice this skill and teach other concepts at the same time to prevent the practice from becoming a mind-numbing simulation exercise that will also turn students off to math.
Fingering is one step on the way to mastering addition facts, unfortunately, many students remain stuck at this step well into adulthood. For kinesthetic learners who use their fingers and hands IT IS IMPORTANT: this is how they learn and you need to help them overcome this – manipulators are a great way to get them to “get their head around”. For young learners, using their fingers and hands comes naturally…you can also spot kinesthetic learners because they will rely more on their fingers and be slower to advance them. This does not mean that they are “slow” or less capable than visual or auditory learners, but that they grasp concepts as quickly or faster than those with other learning styles. We also find that they often excel when it comes to sports and other activities that require hand-eye coordination (like arts and crafts). Using your fingers is great! And you need to get past this stage if you want to be fast at adding and achieve mastery. Being quick at addition leads to easy mastery of multiplication as an added bonus. They might 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 abandon 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 that you want to encourage students to go through this step when it comes to math NOT discourage or skip the step all together. Naturally, some students will NOT use their fingers when doing mental math…for those who do use them later, it will become a handy cap. Counting quickly makes math easier, because all math is counting; however, do not confuse computing with mathematics. Mathematics is the use of computation and critical thinking skills to solve problems and express reality numerically.
Addition and subtraction, as well as multiplication, only count quickly. They are among the first steps in understanding mathematics and must be mastered to ensure success. Using fingers can also cause a loss of accuracy, often children (and adults) are off by one, sometimes even two.
Practicing verbally with addends, building walls and towers, playing games like what’s under the cup, simple story problems, and picture worksheets give the student the experience they need to make the transition from fingers to symbols to be able to do it “in their heads”. Drawing rectangles and other math concepts, as well as drawing the manipulatives they use, help the student make sense of the symbols and see what they are doing. It also adds variety and helps students (and teachers) see that you’re 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.
In fact, if you take the concept far enough, they can also pull out the symbols and do it ALL in their head if necessary, 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 PHOTOS. In addition, he is “cementing” his additions and multiplication facts in his memory. How much easier is it to see how 6 subtracts a 4 from a 7 to make 13 when presented with a problem like x = 6 + 7 than to do algebra? It’s also pretty easy to see 6 + x = 13 x + 7 = 13, especially if you give them a simple algorithm to solve these concepts based on “wanting to be a ten”. He also gets a lot of positive reinforcement because people think he’s a little genius who motivates kids to do more. Never underestimate the power of simple compliments.
Once they learn some basics and understand what the symbols mean, 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 commit to memory because the mind works on images not symbols, so memorizing the 45 adders and multiplication tables is easier because the mind can store much more images. easily than the symbols. Then, when it’s time to be remembered, an image or symbols or just words can be easily retrieved from this place we call long-term memory.
Have you ever met someone who remembers phone numbers with the image of the keypad in their head? They can even point to the numbers and move their index finger on an imaginary keyboard in the air as they remember the number. This is a visual kinesthetic way of storing long numbers. The brain works with images and this makes it easier to extract information. How much easier is it to add two numbers than to recite seven to ten digits? Especially if you have a method to view them if you somehow forget?
A simple exercise: ask a student to draw a cow. Then ask if they saw COW or a picture of a cow? Question what color was it? This lets you know they didn’t see symbols. The problem is with math, most students have nothing to imagine, be it 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 pretty well proven that symbols ie letters and numbersthey are a difficult way to get information there.
Manipulators are the perfect bridge to get information there. After all, storage is never the problem of recovery.
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