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Get Them Off Their Fingers And Into Math
Moving towards mastery
Mastering 45 addends is an important step in making calculations easier. More is simple, if the concepts are understood. 5 + 7 is the same as 7 + 5 and when 7 and 5 are together it will always end in 2… so 17 + 5 and 15 + 7 are easy and even students can see that 37 + 5 is basically the same. The problem as a single digit problem of ten is “just for the ride.” You’d be surprised at the number of students who don’t get that simple concept. By adding 15 + 7 they will come up with 21 or 23 instead of 22. They can also use a simple “let’s be ten” algorithm to make it easier: 7 takes 3 from 5 to make a ten and two, or 5 takes 5 from 7 to make a ten and two. Either way it’s 12, and the best way to do it is the way the student likes it.
This method allows the student to remove their fingers by making “a ten and a few more” when adding two numbers. It turns out that there are only 45 combinations… Once students learn this simple “want to be ten” algorithm it’s very easy to add and they can solve bigger problems on their own. Then it just comes down to practice and repetition. Use a variety of problems to practice this skill and teach other concepts at the same time so that the practice doesn’t become a mind-numbing drill that will keep students grounded in math.
Using their fingers is a step on the way to mastering more facts, unfortunately many students remain stuck at this stage into adulthood. Using fingers and hands is important for kinesthetic learners: This is how they learn, And you need to help them move past it: manipulation is the best way to get them to “get it over their heads”. It’s natural for young learners to use their fingers and hands…you may even find kinesthetic learners because they rely more on their fingers and will be slow to move on from them. This does not mean that they are “slower” or less capable than visual or auditory learners, just that they grasp concepts faster or faster than those with other learning styles. We find they often excel in sports and other activities that require hand-eye coordination (such as arts and crafts). Using your fingers is great! And you need to get through that stage if you’re going to get faster and master the addition. Being fast at addition leads to easy mastery of multiplication as an added bonus. They might even like math, if it’s fun and easy why wouldn’t they?
Many speed reading courses include the use of the finger to guide the eye along the page, some use it to start, and then leave it for other courses. Adding more sensory input increases learning, and the hand and eye are inextricably linked in the reading situation. The point is that you want to encourage students to get past this stage when it comes to math and not get discouraged or skip the step all together. Some students don’t naturally use their fingers when doing mental calculations… this will be a useful hat for those who use their fingers later. Calculating quickly makes math easier, because all math is counting; However, don’t confuse counting with math. Mathematics is the application of calculation and critical thinking skills to solve problems and express reality numerically.
Addition and subtraction as well as multiplication are just calculating quickly. They are the first steps to understanding mathematics, and they must be mastered to ensure success. Using fingers can also cause a loss of accuracy, often with children (and adults) sometimes even two off from one.
Verbally practicing with joints, building walls and towers, playing games like what’s under the cup, simple story problems and worksheets with pictures give the student the experience needed to make the transition from fingers to symbols to be able to do this. their head.” Drawing rectangles and other math concepts, as well as drawing diagrams of the manipulations they use, helps the student understand the meaning of the symbols and see what they’re doing. This also adds variety, and helps students (and teachers) use the same skill sets you use through math. It helps to see that you do, so you see me using third and fourth power algebra to teach addition and multiplication facts.
In fact if you carry the concept far enough they can be symbols like this and do it all in their head if need be, no 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 the sides. Or if you tell him the sides are (x+3)(x+2) he can tell you the whole rectangle because he is seeing symbols but he is looking at pictures. Additionally he is “cementing” his addition and multiplication facts in his memory. How much easier is 6 times 7 to make 4 to 13 when presented with a problem like x = 6 + 7 than doing algebra? It is also very easy to see 6 + x = 13 or x + 7 = 13, especially if you give them a simple algorithm to solve these based on the concept of “wanting to be ten”. He also gets a ton of positive reinforcement because people think he’s a little genius which motivates kids to do more. Never underestimate the power of a simple compliment.
Once they learn some basic concepts and understand what the symbols mean, math becomes easy and fun. Being able to visualize what you are doing makes all the difference, it makes it much easier to commit to memory because the mind works in pictures not symbols, so remembering 45 addition and multiplication tables is easier because the mind can store a lot of pictures. Easier than symbols. So when it’s time to remember, pictures or symbols or just words can be easily retrieved from that place in what we call long-term memory.
Have you ever known someone who remembers phone numbers by picturing a keypad in their head? They can point to numbers and move their index finger in the air over an imaginary keypad as they memorize the number. This is a visuo-kinesthetic way of storing long numbers. The brain works with images and this makes it easier to receive information. How much easier is it to add two digits than to write seven to ten digits? Especially if you have a way to visualize them if you somehow forget?
A simple exercise: Ask students 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 didn’t see the symbols. The problem with math is that most students have it be it algebra or simple addition. The “trick” is to get information into long-term memory, if there is one, so it can be easily recalled and it is well proven that symbols, that is. Letters and numbersThere is a hard way to get information.
Manipulation is the best bridge to get information out there. After all, the problem is that it is never stored or retrieved.
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