# The Five Fundamentals for Teaching Math

Teaching math to students can be a forbidding task simply because math is different in so many ways to all other subjects. Grasping these fundamentals will greatly aid in ensuring students’ mastery of this subject.

To cite a basic example of how this is not the case in math: You cannot do long division without knowing multiplication and subtraction (unless you cheat and use a calculator).

A friend of mine (a computer scientist now no less!) once recounted to me how poorly he performed in Geometry when he was going through grade school. He failed to properly grasp concepts learned in the earlier grades which led to failure in Algebra, and you can’t do certain types of Geometry without a good understanding of Algebra. It’s a vicious circle. When you teach math to kids, make absolutely sure they grasp a foundational concept before they move on to something more complicated.

Teaching Math Fundamentals #2: Be organized-This principle applies in many ways. For the earlier levels, make sure that columns are organized neatly so that you aren’t accidentally multiplying the hundreds place by the thousands place when you intended to multiply the tens place by the thousands place. This concept is especially important when it comes to long-division. Once we get to Algebra, make sure that Z’s are crossed as well as 7’s. Otherwise a Z can easily turn into a 2 and a 7 into a 1.

Teaching Math Fundamentals #3: Break things down and make a list- Regarding word problems or multi-step equations; it is very helpful to simply list all the known information. If we are calculating the area of a trapezoid 1/2(a+b) * h, we can list that Side A = 8 cm, Side B = 4 cm, and the Height = 12 cm. If we want to know if a discount of 25% on a $24 product or a discount of 50% on a $38 product is preferable, we can solve the different equations individually, noting the individual results and finally comparing the two.

Teaching Math Fundamentals #4: Make sure it’s accurate- Unlike in the Liberal Arts and even some of the Sciences, Math is a very right-or-wrong based subject. There is very little room for argumentation or rationalizing. 4+4=8 and never 10. In this day and age, much of our learning is based on justifying responses and encouraging multiple points of view. This is beneficial since it enhances creativity and allows for exploration of new ideas, but this type of thinking needs to be heavily redirected when it comes to math. For instance, one can argue that receiving no credit when one submits 180 as a final answer to a problem whose correct solution is 200 might seem a bit unjust, seeing as how 180 is off by just 10%. But in math, being off by just 10% can have calamitous consequences. Getting the angle off by 10% of a support beam on a bridge can mean the deaths of thousands. It’s important for a teacher to train his/her students to check their work at every step along the way.

Teaching Math Fundamentals #5: Use manipulatives and drawings- Manipulatives are just tools that allow you to transform abstract concepts into concrete objects that your student can touch and hold. This can involve stacking Lego pieces in tens to illustrate the 10’s column of a long-addition problem to placing square tiles next to each other to illustrate area. For visual and tactile learners, these manipulatives are very helpful. In a similar vein, drawings can be used to bring life to word problems. They are particularly useful in fractions. Drawing fractions of a pizza will allow your student to avoid saying that 1/2 + 1/2 = 2/4.

In sum, although math may be considered a difficult subject to tutor, it need not induce fear. Following the Five Teaching Math Fundamentals above will bring about positive results in your students' education. Teaching Math Fundamentals #1: Math is cumulative- One of the greatest differences is that math builds on itself. It is a subject that requires knowledge from previous sessions, much like the dreaded all-encompassing final exams that many of us have faced in our university career. In history, one can get by not knowing what happened in Ancient Greece if the class is on Modern Day Japan. Perhaps it will diminish one’s overall appreciation of the given time period, but it is not usually critical.

To cite a basic example of how this is not the case in math: You cannot do long division without knowing multiplication and subtraction (unless you cheat and use a calculator).

A friend of mine (a computer scientist now no less!) once recounted to me how poorly he performed in Geometry when he was going through grade school. He failed to properly grasp concepts learned in the earlier grades which led to failure in Algebra, and you can’t do certain types of Geometry without a good understanding of Algebra. It’s a vicious circle. When you teach math to kids, make absolutely sure they grasp a foundational concept before they move on to something more complicated.

Teaching Math Fundamentals #2: Be organized-This principle applies in many ways. For the earlier levels, make sure that columns are organized neatly so that you aren’t accidentally multiplying the hundreds place by the thousands place when you intended to multiply the tens place by the thousands place. This concept is especially important when it comes to long-division. Once we get to Algebra, make sure that Z’s are crossed as well as 7’s. Otherwise a Z can easily turn into a 2 and a 7 into a 1.

Teaching Math Fundamentals #3: Break things down and make a list- Regarding word problems or multi-step equations; it is very helpful to simply list all the known information. If we are calculating the area of a trapezoid 1/2(a+b) * h, we can list that Side A = 8 cm, Side B = 4 cm, and the Height = 12 cm. If we want to know if a discount of 25% on a $24 product or a discount of 50% on a $38 product is preferable, we can solve the different equations individually, noting the individual results and finally comparing the two.

Teaching Math Fundamentals #4: Make sure it’s accurate- Unlike in the Liberal Arts and even some of the Sciences, Math is a very right-or-wrong based subject. There is very little room for argumentation or rationalizing. 4+4=8 and never 10. In this day and age, much of our learning is based on justifying responses and encouraging multiple points of view. This is beneficial since it enhances creativity and allows for exploration of new ideas, but this type of thinking needs to be heavily redirected when it comes to math. For instance, one can argue that receiving no credit when one submits 180 as a final answer to a problem whose correct solution is 200 might seem a bit unjust, seeing as how 180 is off by just 10%. But in math, being off by just 10% can have calamitous consequences. Getting the angle off by 10% of a support beam on a bridge can mean the deaths of thousands. It’s important for a teacher to train his/her students to check their work at every step along the way.

Teaching Math Fundamentals #5: Use manipulatives and drawings- Manipulatives are just tools that allow you to transform abstract concepts into concrete objects that your student can touch and hold. This can involve stacking Lego pieces in tens to illustrate the 10’s column of a long-addition problem to placing square tiles next to each other to illustrate area. For visual and tactile learners, these manipulatives are very helpful. In a similar vein, drawings can be used to bring life to word problems. They are particularly useful in fractions. Drawing fractions of a pizza will allow your student to avoid saying that 1/2 + 1/2 = 2/4.

In sum, although math may be considered a difficult subject to tutor, it need not induce fear. Following the Five Teaching Math Fundamentals above will bring about positive results in your students' education. Teaching Math Fundamentals #1: Math is cumulative- One of the greatest differences is that math builds on itself. It is a subject that requires knowledge from previous sessions, much like the dreaded all-encompassing final exams that many of us have faced in our university career. In history, one can get by not knowing what happened in Ancient Greece if the class is on Modern Day Japan. Perhaps it will diminish one’s overall appreciation of the given time period, but it is not usually critical.