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Get Them Off Their Fingers And Into Math
Moving towards mastery
Mastering 45 additions is an important step on the way to making calculations easier. Addition is simple, if the concepts are understood. 5 + 7 is the same as 7 + 5 and when 7 and 5 are combined they will always end up 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 tens “just for driving.” You’d be amazed at the number of students who don’t understand that simple concept. They will get to 21 or 23 instead of 22 when they add 15 + 7. They can also use a simple “I want to be ten” algorithm to make it easier: 7 takes 3 from 5 making one ten and two OR 5 takes 5 from 7 making one ten and two . It’s 12 anyway, and the best way to do it is the way the student likes best.
This method allows the student to get off the finger by making a “ten and something” when adding two numbers. As it turns out, there are only 45 combinations… once students understand this simple “I want to be ten” algorithm, addition becomes much easier and they can solve bigger problems on their own. Then it just comes down to practice and repetition. Use a wide variety of tasks to practice this skill and teach other concepts at the same time to prevent the practice from becoming a mental exercise that will also distract students from math.
Using fingers is a step on the way to mastering addition facts, unfortunately many students remain stuck at this step well into adulthood. For kinesthetic students who use fingers and hands, IT IS IMPORTANT: that’s how they learn and you have to help them through this: manipulatives are a great way to encourage them to “work for themselves”. For young learners, using their fingers and hands is quite natural…you can also spot kinesthetic learners as they will rely more on their fingers and move away from them more slowly. This does not mean they are “slow” or less capable than visual or auditory learners, they grasp concepts just as quickly or faster than those who use other learning styles. Also, when it comes to sports and other activities that require hand-eye coordination (such as arts and crafts) they often excel. Using your fingers is great! And you have to get past that stage if you want to be fast at adding and achieve mastery. Fast addition leads to easy mastery of multiplication as an added bonus. Maybe they even like math, why not if it’s fun and easy?
Many speed reading courses involve using a finger to guide the eye along the page, some use this to start and then drop it for other courses, this is the mainstay 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. DO NOT discourage or skip a step all together. Some students will naturally NOT use their fingers when doing mental calculations…for those who use their fingers later it will become a handy cap. Counting fast makes math easier, because all math is counting; however, do not confuse calculus with mathematics. Mathematics is the use of calculation and critical thinking skills to solve problems and express reality numerically.
Addition and subtraction as well as multiplication are just fast counting. They are among the first steps to understanding mathematics and must be mastered to ensure success. Using fingers can also lead to a loss of accuracy, often children (and adults) are off by one, sometimes even two.
Oral practice with accessories, building walls and towers, playing games like what’s under the glass, simple story problems and picture worksheets give the student the experience they need to make the transition from fingers to symbols so they can do it “into their heads.” Drawing rectangles and other math concepts, as well as drawing the manipulatives they use, helps the student understand 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 grade algebra to teach addition and multiplication facts.
Indeed, if you take the concept far enough, they can also take off the symbols, so to speak, and do EVERYTHING in their heads if necessary, without paper or pencil. This is perfectly illustrated by a five year old who is able to factor trinomials in his head because he can see pictures when he hears expressions like x^2 + 3x +2 he can see it and tell you the sides. Or if you tell him the sides (x+3)(x+2) he can tell you the whole rectangle not because he sees symbols but because he sees PICTURES. Further he “cements” his additions and multiplication facts in his memory. How much easier is it to see that 6 takes 4 from 7 to get 13 when a problem like x = 6 + 7 is set than to do algebra? It’s also pretty easy to see 6 + x = 13 or x + 7 = 13, especially if you give them a simple algorithm to solve this “I want to be a ten” based concept. He also gets a ton of positive reinforcement because people think he’s a little genius which motivates kids to work harder. Never underestimate the power of a simple compliment.
Once they learn some basic concepts 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 as the mind works on images not symbols so memorizing 45 addition and multiplication tables is easier as the mind can store images much more easily than symbols. Then, when it’s time to recall, the image or symbols or just words can be easily retrieved from that place we call long-term memory.
Have you ever known someone who remembers phone numbers by picturing the keypad in their head? They can even point to numbers and move the pointer on an imaginary keyboard in the air as they recall 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 say seven to ten digits? Especially if you have a method to visualize them if you somehow forget?
A simple exercise: ask the student to draw a picture of a cow. Then ask if they saw a COW or a picture of a cow? Ask what color was it? This lets you know they haven’t seen the symbols. The problem is with math, most students have no idea if 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 pretty well proven that symbols ie. 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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