How to Teach Math
Introduce a new concept and explain its usefulness., Break it down into steps., Explain why., Give a simple example and go through it step-by-step., Give a more difficult example., Introduce any exceptions to the rules., Practice., Assess the...
Step-by-Step Guide
-
Step 1: Introduce a new concept and explain its usefulness.
When teaching math, you will be teaching one new concept at a time.
For example, you might be teaching students how to do multiplication.
Therefore, begin by introducing the topic of multiplication.
Give them examples of how they will use multiplication in their daily lives, even when they are out of school.It may be useful, when you are trying to explain the importance of a math concept, to include a demonstration.
For example, if you are teaching division, and you want to demonstrate how they will use it in their daily lives, you could bring a batch of cookies (make sure you have a number that is divisible by the number of students.
If you have 12 students, bring at least 24 or 36 cookies, so that it will be easy for them to understand).
Tell the students you have brought cookies, but you don’t know how many each student should get.
Ask them to help you think of ways to figure it out, and then introduce the concept of division. -
Step 2: Break it down into steps.
You can begin by explaining a broad mathematical principle to the student, but then break it down into the smallest steps possible.
This will help the student understand why you are doing it the way you are doing it, and therefore, will help them learn and remember how to do it on their own.For example, you might begin by showing a student that 2x3=6 but then show them exactly how you came to that conclusion.
You can explain that this problem is actually asking you to add up 2+2+2.
Ask them to add those numbers up so that they can see that multiplication is just a shorter way of asking you to add one number a certain number of times. , Often in math, teachers explain how to do something, but not why it is done that way.
This may be fine for some students, but for most, it is difficult to grasp concepts if they do not understand why it is being done that way.
Many students who can find the right answer to a mathematical problem have simply memorized the steps, but have not actually understood the reasons why a particular concept works the way it does.
Unless they understand the theory behind the problem, they are likely to forget it very quickly.You could, for example, explain who came up with this method, and the logic that was used to create the method.
With younger children, though, it is unlikely that this will be useful.
If you want to explain the theory, try to make it visual and interesting.
Try to tell a story about how the math concept came to be.
Be patient when doing this.
Inquisitive students may ask many questions about your “why” explanation.
Take the time to answer each question as best you can, and if you don’t know, find out together.
If it is in a classroom situation where you can’t find the answer immediately, ask them to come see you after class so you can have a look. , Once you have introduced the concept, and explained the different steps involved in doing the calculation, provide a simple example.
Show them how you figure it out step-by-step.
If you are teaching to a classroom of students, use the blackboard to write out the problem, then use a different color piece of chalk (or marker) to show them each step involved in the calculation.
Be sure when you are doing this that students have opportunities to ask questions about each step you are performing.
If you normally require students to raise their hands to ask questions, now may be a good time to let that rule slide.
This will allow them to stop you as soon as you have a question. , If the students don’t have any more questions once you have shown them the simple example, move on to a more difficult example problem.
Instead of just showing them how to do it, ask them to guide you.
If they make a mistake when guiding you say something like, “I can see why you think that’s the next step, but don’t forget about…” and then explain what they’ve forgotten or gotten mixed up. , In some mathematical concepts, you will come across concepts that typically work in a certain way, but have specific exceptions.
These types of concepts, especially, require that the student truly understand how the concept works.
They are unlikely to remember or be able to figure out when the exception applies if all they’ve done is memorized the steps.
For example, in division, you can divide any number by another number to get some kind of answer.
However, you cannot divide any number by
0.
This is because you can’t, for example, split 5 pieces of chocolate among 0 friends., The students will get better at understanding the concepts if they are given several opportunities to practice the material.
You can even space the practice material out over weeks or months so that the student returns to the same material at various intervals, which will reinforce what they’ve learned.If possible, mix up the practice exercises with straightforward worksheets (e.g. a page with 25 long-division worksheets where you ask the student to show their work on each problem) as well as real world problem solving exercises.
For example, the following problem will ask the student to do long division, but in a real world setting: "Each week you will need to work 26 hours.
The work week is 5 days.
How many hours will you need to work each day in order to meet the 26 hour requirement? Assume that you need to work the same number of hours each day." Ask the student to tell you the answer.
If they get it wrong, ask them to do the work on paper so you can see where they went wrong. , Once you have explained, worked through problems together, and practiced a specific concept, you should test the student’s understanding of the concept.
Depending on the setting of your teaching, you may simply provide them with a few problems to complete so you can see which questions they get wrong and which they get right, or you might have to conduct testing that will determine a grade point average for the course.
Regardless of the type of assessment you use, it is important to go through the student’s test and discuss with them the problem areas they have.
It can be valuable for the student because it may simply be one small thing that they have misunderstood. -
Step 3: Explain why.
-
Step 4: Give a simple example and go through it step-by-step.
-
Step 5: Give a more difficult example.
-
Step 6: Introduce any exceptions to the rules.
-
Step 7: Practice.
-
Step 8: Assess the student’s progress.
Detailed Guide
When teaching math, you will be teaching one new concept at a time.
For example, you might be teaching students how to do multiplication.
Therefore, begin by introducing the topic of multiplication.
Give them examples of how they will use multiplication in their daily lives, even when they are out of school.It may be useful, when you are trying to explain the importance of a math concept, to include a demonstration.
For example, if you are teaching division, and you want to demonstrate how they will use it in their daily lives, you could bring a batch of cookies (make sure you have a number that is divisible by the number of students.
If you have 12 students, bring at least 24 or 36 cookies, so that it will be easy for them to understand).
Tell the students you have brought cookies, but you don’t know how many each student should get.
Ask them to help you think of ways to figure it out, and then introduce the concept of division.
You can begin by explaining a broad mathematical principle to the student, but then break it down into the smallest steps possible.
This will help the student understand why you are doing it the way you are doing it, and therefore, will help them learn and remember how to do it on their own.For example, you might begin by showing a student that 2x3=6 but then show them exactly how you came to that conclusion.
You can explain that this problem is actually asking you to add up 2+2+2.
Ask them to add those numbers up so that they can see that multiplication is just a shorter way of asking you to add one number a certain number of times. , Often in math, teachers explain how to do something, but not why it is done that way.
This may be fine for some students, but for most, it is difficult to grasp concepts if they do not understand why it is being done that way.
Many students who can find the right answer to a mathematical problem have simply memorized the steps, but have not actually understood the reasons why a particular concept works the way it does.
Unless they understand the theory behind the problem, they are likely to forget it very quickly.You could, for example, explain who came up with this method, and the logic that was used to create the method.
With younger children, though, it is unlikely that this will be useful.
If you want to explain the theory, try to make it visual and interesting.
Try to tell a story about how the math concept came to be.
Be patient when doing this.
Inquisitive students may ask many questions about your “why” explanation.
Take the time to answer each question as best you can, and if you don’t know, find out together.
If it is in a classroom situation where you can’t find the answer immediately, ask them to come see you after class so you can have a look. , Once you have introduced the concept, and explained the different steps involved in doing the calculation, provide a simple example.
Show them how you figure it out step-by-step.
If you are teaching to a classroom of students, use the blackboard to write out the problem, then use a different color piece of chalk (or marker) to show them each step involved in the calculation.
Be sure when you are doing this that students have opportunities to ask questions about each step you are performing.
If you normally require students to raise their hands to ask questions, now may be a good time to let that rule slide.
This will allow them to stop you as soon as you have a question. , If the students don’t have any more questions once you have shown them the simple example, move on to a more difficult example problem.
Instead of just showing them how to do it, ask them to guide you.
If they make a mistake when guiding you say something like, “I can see why you think that’s the next step, but don’t forget about…” and then explain what they’ve forgotten or gotten mixed up. , In some mathematical concepts, you will come across concepts that typically work in a certain way, but have specific exceptions.
These types of concepts, especially, require that the student truly understand how the concept works.
They are unlikely to remember or be able to figure out when the exception applies if all they’ve done is memorized the steps.
For example, in division, you can divide any number by another number to get some kind of answer.
However, you cannot divide any number by
0.
This is because you can’t, for example, split 5 pieces of chocolate among 0 friends., The students will get better at understanding the concepts if they are given several opportunities to practice the material.
You can even space the practice material out over weeks or months so that the student returns to the same material at various intervals, which will reinforce what they’ve learned.If possible, mix up the practice exercises with straightforward worksheets (e.g. a page with 25 long-division worksheets where you ask the student to show their work on each problem) as well as real world problem solving exercises.
For example, the following problem will ask the student to do long division, but in a real world setting: "Each week you will need to work 26 hours.
The work week is 5 days.
How many hours will you need to work each day in order to meet the 26 hour requirement? Assume that you need to work the same number of hours each day." Ask the student to tell you the answer.
If they get it wrong, ask them to do the work on paper so you can see where they went wrong. , Once you have explained, worked through problems together, and practiced a specific concept, you should test the student’s understanding of the concept.
Depending on the setting of your teaching, you may simply provide them with a few problems to complete so you can see which questions they get wrong and which they get right, or you might have to conduct testing that will determine a grade point average for the course.
Regardless of the type of assessment you use, it is important to go through the student’s test and discuss with them the problem areas they have.
It can be valuable for the student because it may simply be one small thing that they have misunderstood.
About the Author
Mary Clark
Dedicated to helping readers learn new skills in pet care and beyond.
Rate This Guide
How helpful was this guide? Click to rate: