I’m going to be a grandfather, this coming August.
This momentous event is not unexpected, since our daughter has been married to her wonderful husband for 3.5 years. Nevertheless, it has made me think again about small children I have a particular interest in, and what happens to them at school. This post is just a touch indulgent, but I invite you to join me in thinking about the qualifications for teaching children.
What do children need from their math teachers? How important is it? If you really were going to be my grandkids’ teacher, these are the questions I’d be keen for you to answer:
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Math Teacher Job Interview: Questions for Candidates

How did you do at math when you were at school?
It’s not important if you were an “A” or a “F” student; you could become a brilliant teacher of math from either starting point. Now, on balance, I’d rather that you got great marks at math, since you obviously “get it” and will be able to understand math more deeply than most. But either way, I’d like an answer to the second part of this question:

Do you understand why lots of people find math difficult, scary or downright horrible?
To teach students who really don’t understand math, and therefore most likely hate doing math, you need to be able to empathize with them. Did you ever feel that learning math was pointless, illogical, impossible or just plain frustrating? If so, great! Can you put that knowledge to work as you help students who feel that way? If not, are the ways for you to learn what it feels like to students who hate math?

Do you love math? If not, are you at least enthusiastic about math?
Not everyone loves math. Even math geeks get that. But teachers of math have a responsibility to encourage students who do love it, who will go on to do amazing, important math later in their lives. I have decided to never discourage a student who has, or is developing, a passion for something, anything almost. If a student loves dancing, or BMX bike riding, or astronomy, or writing poetry, I will do everything in my power to support, encourage and promote success for that student in that endeavour. How can you do that in math?

Which is most important to you: understanding, or correct answers?
We should never pretend that correct answers aren’t important. But just as giving a poor person a fish is a lousy substitute to teaching that person how to catch fish, focusing on correct answers should come after we are sure the student understands the math, never before. Great math teachers have the attitude that correct answers are the product of correct thinking, and in some cases aren’t even that important, providing the student understood the process.

Do you teach “tricks and shortcuts” to math processes?
This is really the corollary of the previous point. A shortcut (eg, to convert a decimal to a percentage, move the decimal point two places to the right) will lead a nonunderstanding student to the correct answer, providing (and this is the dealbreaker right here) the student can remember the correct trick to use. But the shortcut or trick will let the student down in situations in which the math is not so obvious, and thinking has to be applied to solve a problem. Good mathematicians do use shortcuts, but that happens way, way, way after they understood why the shortcuts worked.

How important is memorization of times tables and number facts to you?
Since calculators first became a consumer item, teachers have had a challenge with this question. Do we really need to spend the time that some of us remember from our own school days on learning times tables, or can we now let calculators handle that process? Answer: unless students have fast, accurate, confident recall of basic number facts and times tables, they will be hampered and slowed down by the need to reach for a calculator every time they need one of those facts. If you have to know “13 x 24”, by all means use a calculator – it will be quicker. But if the question is “6 x 7”, recalling the answer quickly will save huge amounts of time and cognitive load.
By the way, to see a series of classroomtested, systematic workbooks for teaching all the basic facts and times tables in 10 minutes a day, visit our store.

What math teaching blogs, forums, wikis or Facebook pages do you read?
In most places where teaching is a profession, a certain amount of professional development is required every year. Where once that PD came in the form of visiting academics to run workshops and sessions after school, nowadays it should also include use of online communities and other sites, where other teachers and educators meet to exchange ideas and encourage each other. Some examples from hundreds of great sites:
 Chris Sears’ blog at Omega Unlimited
 Malke Rosenfeld’s blog “at the intersection of dance, rhythm & math”: The Map is Not the Territory
 Bon Crowder’s blog for parents and math teachers at MathFour
 Aviva Gunsiger’s Grade 1 class blog at Miss D
 If you use Twitter (and you should ), join us for #mathchat each week
 Facebook pages: Classroom Professor (mine); Teach Science & Math (Dr David Wetzel); Puzzled by Math (Trish CaldwellLandsittel)

Do you use technology to help your students learn math? How?
I already wrote about the necessity of math students knowing their number facts. The way some nonmath people talk, this is an “eitheror” situation: either you learn times tables by rote, or you use technology. My view: the true answer belongs in the middle somewhere. Yes, students need to learn number facts. No, they don’ t need to use unthinking rote methods (see here for more on this). Yes, they should use technology. A great math classroom will have lots of appropriate technology: calculators, iPads, iPods, laptops, data projector and interactive whiteboard, internet connection (duh!), etc., etc. The technology opens up unlimited possibilities for connecting classroom math to real life math, for using microchip tech to make more complicated math possible, for practising skills using online interactive widgets, and so on and so on.

Do you assign math homework? What sorts?
Homework is a huge topic which I don’t have space to address adequately here. But for the purposes of this post, let’s agree that homework is a great way to connect your math lessons with parents and other family members. By sending home suitable activities to apply and practise the math being learned in class, you make space for child and parent/grandparent/carer to have conversations about math. My advice: make the homework something every child can succeed on, so that it becomes an enjoyable part of family life, not one of the biggest frustrations. Build in activities for children to talk about math at home, for the benefit of child and adult.

Do you integrate math into other subjects’ lessons? What about integrating other subjects into math lessons?
Math can seem a pretty lonely subject in some classrooms. It can be the only one which lots of students don’t like, the only one done solely using textbook or worksheets, the subject most likely to lead to the question “When are we ever going to use this?”. You can help to change these perceptions by showing students how useful math really is, by allowing math to serve other subjects and help solve their particular problems. For example: in social studies or geography classes, use math to examine statistics and graph the data on how people behave, how the environment is being affected by pollution, etc. The reverse is also worth doing: include reallife examples from other subjects when preparing problems and investigations for math class.
How did you go? Do you agree with my views? Would you be happy to teach my grandchildren? Leave a comment below and let me know…
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Photo Credits:
 Grandfather and boy: © iStockphoto.com/Pavel Losevsky
 Teacher interview: © iStockphoto.com/Jacob Wackerhausen
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Here goes, Peter:
1. I got solid marks in math, my favorite subject. Then calculus and firsttimeonmyown freedom came at the same year and I got my first C LOVE calculus now though!
2. I get it that people struggle with math, like I struggle with [name just about anything else], but what I can’t stand is the “bragging,” literally bragging that they are bad in math. Parents say this to me often, and I find it so annoying because they would never disclose that they are poor at reading!
3. I love math more than I love my husband. (He’s standing right here
4. Understanding and correct answers are both important, but concept knowledge trumps algorithms any day.
5. Tricks must come AFTER the understanding; I coach kids in competitions, so we have to do it FAST!!
6. I want to post a sign on my door that says, “Fluent in multiplication tables only to enter.” It’s a must.
7. The Classroom Professor blog
8. Whenever possible. My kids are so excited to start their first electronic portfolios. Geometer’s Sketchpad is an integral part of our curriculum, we use TinkerPlots too.
9. My math homework sucks right now. Must rethink. I struggle with this every year. The A and B students are the ones diligently doing the homework, while the others not so much, thus grade sinks even lower.
10. I try whenever possible, still not enough, but I want it to be more natural, not forced like what I see in textbooks. And math itself is so beautiful, I don’t want to dance and sing to make it “better.”
So, do I get the job? I know August can’t come soon enough for you. Congratulations!!
Wow, Fawn, great answers! 10/10, A++!
I love the fact that you and I are in agreement on so much about teaching math – it is encouraging to know that other teachers and I believe the same stuff.
I will have to look at TinkerPlots and Geometer’s Sketchpad; I’ve heard of the latter, but not seen it in action.
Give your husband my best regards! You made me laugh that you love math that much… I have always loved math, I think, but as a teacher the challenge is to reach those who have been “burned” and just hate it.
These are great questions for all math teachers. Thanks for sharing!
Thanks, Denise!
Of course, I mean these questions to apply to every teacher of math. The commentary summarizes what I believe is necessary for good to excellent math teaching. Thanks for stopping to comment!
Ah, may I add that a sense of humor would be required also? Teaching is too hard otherwise.
Well, when I taught callucus, I told my students to use Wolfram Alpha whenever they couldn’t figure out how to do the problem by hand. I told them to try figuring out the steps on the website, then write the solution in their own words, then write with help from WA next to their answer. They seemed happy to do that, and they seemed to instinctively know that if WA did it for them, they weren’t exactly on top of things.Homework was not a big part of the grade, though, and if it were I think there would have been more motivation to use WA as a way to fakeit. Not sure what I would have done in that case. I’m also not sure what to do in the cases where the students view the whole class as an obstacle (like remedial math classes), except to say that I can tell when you’ve done all your homework by computer (the steps are often overly detailed or technically awkward).
Sevak, thanks for the comment. I’m pleased to hear of your experience with students who realised that they needed to understand the mathematics for themselves, and not rely on an automatically computed answer. This is a message that needs to be part of how we all teach our students to use technology in their learning.