I teach math at a special education private school. Before that, I taught 18 years in a college classroom. And before that I was asked, paid, coerced and forced (yes, forced) to tutor friends and relatives. Over the years I’ve put together my top 10 list of ways of tutoring and teaching math.
1. Discourage negative remarks.
Acknowledge their frustration, anger and hate of math. Do this at the beginning of the class or as quickly as you can. Let everyone tell you face-to-face or on paper what their past math history is. Let them explain why they hate math and where their frustrations are.
Validate their anger and fears. If there was a mean instructor in the past, help them understand that that person is no longer with them. And that it’s okay to still be angry with him or her.
Then, encourage them to use this. “You dislike math, I appreciate that. I see where it’s coming from.” Tell them that instead of using negative remarks toward math, from this point forward, they can direct their frustration at the event or person in the past.
Instead of saying, “I hate math. I’m just not good at it.” They will now say, “I am really frustrated that Mrs. Wilson in the fifth grade was so mean to me. I’m going to overcome that. Mrs. Wilson, I’m done with you!”
2. Let the student body coach you through the problems.
After you’ve explained a method, do one example yourself. Do at least two more examples and allow the student body to talk you through them.
Collectively they should be able to get it right. If they make an incorrect decision, write it on the board anyway. Pause to let everyone else observe it. Usually someone else express doubt. Watch the faces of the students carefully. You’ll see the face of the student that doesn’t like that wrong answer. Ask him or her to explain.
3. Use good board etiquette and handwriting.
Know your student body. If they are a different nationality or culture, make a point to learn how they traditionally write numbers and symbols. In the US the division symbol is written with two dots with a horizontal bar between them. In some countries the division symbol lacks the bar. If you traditionally cross your z’s or your 7’s, explain this on the outset, and frequently through the class.
When you write on the board, mentally divided into segments about 2 to 2 1/2 feet wide. Stay within those divisions. If you have to do a sidebar, segment that portion of the board with squiggly lines.
The image above is of a simulated white-board with a good use of space and squiggly lines.
4. Use colors.
This is so much easier with whiteboards than it was with chalkboards. Choose your colors carefully so that they can be seen and differentiated from the back of the room.
Use colors to illustrate the thinking process. Show your own work extensively this way.
Also use colors to differentiate numbers or variables that might get confused:
The image above has two threes, both that end up being positive. With the use of color, the students will be able to see the difference in them.
5. Use magnets, stickie notes, coffee mugs and Ziploc bags.
While you’re teaching, use any props that you can get your hands on. You don’t have to think of them before the class, either. Improvise if the mood hits you!
If you need to show the set containing the empty set, grab your water cup and coffee mug. Are your students having problems remembering the “everything is over 1” rule for changing whole numbers to fractions? Have them put a Post-it with a 1 on it on the bottom of their shoe for the day.
6. Create a safe and interactive environment.
Don’t call on students. This is counter to everything that we are taught in education classes. But math students need to feel safe and comfortable. If you start calling on people they will get nervous that you will pick on them at that exact moment when they don’t understand.
Instead, use silence. When working a problem (the second example after you’ve explained a method) ask the question, “what do I do next?” And wait. It’s your classroom. It can be dead silent for 10 minutes if you want. Eventually someone will volunteer a response.
The person least likely to be intimidated will be the first to respond. You have established the fact that you’re not going to call anyone out and expose them. The comfort level will immediately rise. Your classroom will quickly grow to an interactive environment because it was first established as a safe environment.
7. Validate everything a student says.
If they answer incorrectly, respond with, “That’s curious, can you help me understand where you arrived at that answer?” When you see how they got the answer, say, “Oh, I see now. That’s a good way to think of it. It’s actually not correct ⟨smile⟩ but I’m liking the way you think.”
Validated incorrect responses from the students do three things:
1. Show that you’re not going to laugh at students or chastise them for working through a discovery process.
2. Build the respect that the students have for you.
3. Help you know how your students are thinking, so you can adjust your teaching accordingly.
8. Make mistakes.
In teaching math, this is likely to happen. And it happens to some of us more than others. If you tend to be perfect, stop. Loosen up, make some mistakes so that the students can catch you. It boosts their confidence.
Help the students to understand that no one is perfect in math. The difference between a math teacher and a math student is a math teacher is confident in his or her mistakes.
The students will make many mistakes. If they don’t have your example of messing up to relate to, they will become frustrated. Demonstrate what you do when you find an error, and how calm you are. Make a plan to do this at least once during every class.
Don’t plan your errors ahead of time, they will know. Instead, create examples on the fly. Or pull random problems from the harder section of the problem sets. Mess up honestly.
9. Watch for hidden questions.
Watch their faces during the lecture to see if they understand. When they have the wrinkled forehead of confusion, ask about it. “What’s up with the wrinkled forehead? Did I lose you somewhere along the way?”
Let them tell you what they believe is their confusion. Give a brief explanation to clear it up and look back at their face. Help them drill down into what their actual confusion is.
Be calm in this process for you might discover hidden treasure. The best hidden question I ever got was through a long drill down process like this. The student couldn’t understand why I would sometimes start on one side of an equation and on other times start start on the other side. She was not seeing what was obvious to me.
10. Be crazy excited.
You might as well tell people that you’re an undertaker’s 2nd assistant embalmer’s wife before you tell someone you’re a math teacher at a party. But while you’re in the classroom, it’s the best thing ever. Promise students that quoting the quadratic formula is the easiest way to get phone numbers at a dance. Stand at the board and be excited that your son’s turning pi years old. Claim you’ll bake him a cake at his 3 year and 51 day pi-day celebration.
Be as mathy, geeky and all-round goofy about math as you can. The students will roll their eyes and laugh at you, but the feeling is contagious. After a while, they’ll be thinking it too!
Teaching math isn’t glamourous. It isn’t nice and gentle. But using the tips above will make teaching math rewarding and even pleasurable!