Search results for: “interview”

  • Math Teacher Interview Questions

    At 8:30 PM CST tonight, October 20, 2011, Natural Math is hosting a presentation about a new book called Modern Math for Elementary Schoolers by Oleg Gleizer. It’s a Creative Commons book on advanced math for elementary school children! (So it’s free! Get it here.)

    Gleizer’s inspiration is from a similar situation in which I currently find myself: To what school should I send my child? Of course my answer is The Bon Crowder School at Home. Alas, Husband believes there’s no reason to fully homeschool if there great schools out there.

    So are there great schools out there?

    I started reading the book and stopped on page 4. Gleizer is explaining his method of finding math teachers. He asked math teachers of potential schools these two questions in the interviews:

    1. Given a straight line and a point away from it, how would you draw another straight line passing through the point and parallel to the original line, using a compass and straightedge as tools?
    2. How would you draw a four-dimensional (4D) cube?

    Of course, I immediately began to wonder if I was good enough to answer these questions myself!

    I got the answer to #1 after some thought, and am pondering #2. I’m refraining from reading on, as I want to come up with my own answer before I read anything else. But I’ll be attending the presentation this evening.

    What about you? Can you join us?

    P.S. I’ll  have to wait to post the answer to #1 tomorrow, as I have discovered that I don’t have a compass. How on earth can you teach math without that?! How embarrassing! So I’m off to Walmart right now to get one.

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  • Interview with Math Game Sokikom’s Founder

    Sokikom (so-kee-kom) is an award-winning education technology company that develops math social learning games. Their recent offering, launching this week at the ISTE Conference, is an online social math game by the same name. It’s designed to motivate elementary school students in grades 1-6. I did a review of the game here.

    Snehal Patel, founder of Sokikom

    MathFour.com was privileged to interview the creator and founder of Sokikom, Snehal Patel.

    MathFour: Thanks for agreeing to share with our readers, Snehal! Let’s start at the beginning. What is your background?

    Snehal: I moved to the U.S. when I was very young. Through elementary school, my family moved to five different schools in various states across the country, which gave me first-hand experience of the challenges faced in elementary math. I was a math tutor in high school and college, and then went on to earn a degree in computer science from Arizona State University. From there, I became a senior software engineer at Motorola, where I also coached/tutored other engineers. I left that job to start a math tutoring learning center. I became a certified math tutor and also received certification to teach as a substitute. Through that experience, I provided one-on-one tutoring to over 500 students ranging in age from 5 to 72. I’m very passionate about improving learning – specifically in math.

    MathFour: What prompted you to create an online social game using math?

    Snehal: The idea for Sokikom came to me when I was a math tutor and become aware of how many students weren’t excited about and engaged in learning math. As a result, these kids were missing out on building the foundation in math skills that they were going to need to succeed in high school, college and beyond. I saw, however, that math games – especially those that were social – got these same kids excited about and engaged in learning math. This made me think: how many other students in the U.S. face this same problem, and how can we use online technology to address it? That was the genesis of Sokikom – a highly engaging online math game with community and team-play elements.

    MathFour: Have you created other math based games?

    Snehal: Yes, when I was a math tutor, I created various paper-based and card games that I used with my students.

    MathFour: Have you created other online social games?

    Snehal: No. Sokikom is my first online math social learning game.

    MathFour: Do you have children? Did they play a part in the conceptualization or development of Sokikom?

    Snehal: My wife and I don’t have children, but I have a younger sister I helped raise and tutored in math throughout her K-12 schooling. This experience absolutely helped me as I considered how to make Sokikom fun and educational. Another big part in the conceptualization of Sokikom came with my experience tutoring students in math.

    MathFour: The American Academy of Pediatrics recommends limiting exposure to screen media. How much time do you recommend children play on Sokikom?

    Snehal: Sokikom is designed to provide efficient learning within short periods of time. We recommend that children spend between 20 to 40 minutes playing Sokikom each day – a small block of time with a tremendous learning opportunity.

    MathFour: In the multiplayer mode in Sokikom, you can’t actually “see” your opponent – only his scores. Do you plan on adding this feature at some point?

    Snehal: Great question. Two of our multiplayer games don’t allow children to see their opponent teams – just their scores. However, Opirate multiplayer does allow children to see their teammates, but not opponents. In terms of future development, we are planning on adding “power ups,” which will allow interesting interactions between teammates and opponents.

    MathFour: What’s next for Sokikom? What are your goals for the company and the game?

    Snehal: We plan to continue improving Sokikom’s math social learning games! We are continuing with efficacy and usability research and love to hear feedback from parents, teachers and students on ways to improve Sokikom. We will be launching new games and cool virtual features such as “power ups” soon.

    MathFour: Do you have any advice for parents and teachers?

    Snehal: I believe that tools such as Sokikom can greatly increase the motivation for children to learn math, which leads to higher math achievement. In the case of Sokikom, I would advise parents and teachers to make use of the free reporting features available in the control panel. Parents and educators can keep track of children’s progress and usage, and receive alerts when students require extra help.

    Thanks so much, Snehal! Find him and the Sokikom crew on Twitter @Sokikom and check out the game at Sokikom.com.

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  • Links for Learning October 26, 2011

    I’ve been collecting some great articles and finally realized how selfish it was that I wasn’t sharing them. So here’re a few:

    Who doesn’t love Legos? A client of mine gave me a box of Legos from 1973. I can’t wait to use some of Colin’s suggestions in his article 101 Manipulative Lessons with Lego!

    Educating grace has some interesting comments on designing teacher preparation programs. It’s a little deep, so grab a cup of coffee before digging in.

    Paul Salomon over at Lost in Recursion pretty much has exactly my same opinion of the new “Any Questions” model of teaching in his article Real World Math (Dan Meyer and stuff). The best quote: “Real world math is simply mathematical thinking. It’s personal, it’s real, and it can happen to all of us.”

    Richard V. DeMerchant explains some of what happened during a mathematical literacy/numeracy discussion he was involved in. It’s an interesting read to understand some thinking and direction of public schools in the area of numeracy.

    And then I found this article about Danica McKellar, including an interview with her, about the image her math books for girls are portraying. Curious. And the jury’s still out for me.

    What about you? Found any great links for learning lately?

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  • What is a Ruler and Compass Construction?

    I’d never heard of this thing until grad school. And even then, I never asked what it was. Over the course of time I eventually figured it out, but never really got an opportunity to do much with it. Nor have I had a chance to teach it.

    A teacher interview question from Oleg Gleizer’s book inspired me to think about, and learn, this nifty skill.

    So what is it?

    Here’s the definition (mostly from Wikipedia):

    A ruler-and-compass construction is the construction of lengths, angles, and geometric figures using only a ruler and compass.

    This means that you can take one of those “pointer and pencil circle making things” and anything really straight (the side of your new iPhone, the edge of a file folder, etc.) and make pretty much create anything in geometry.

    Pretty cool, huh?

    I gave it a shot!

    I used Oleg’s teacher interview question:

    Given a straight line and a point away from it, how would you draw another straight line passing through the point and perpendicular to the original line, using a compass and straightedge as tools?

    Can I do it? Of course!

    Well… I thought about it and it seemed like I could. So I went out and got a compass, and used a fingernail file as a straight edge. Here’s how I did it:

    Here’s the line and the point. Easy peasy.

    I made an arc from the point through the line, so I would have two spots on the line (where the circle piece went through):

    From those two places, I made two more arcs through the point above and long enough to run into each other below:

    I connected the point with the intersection of the arcs at the bottom and VOILA: perpendicular line to the other line!

    Join me in the journey!

    This is the first in my ruler and compass journey. They’re kind of fun, and I want to do more. So I will house them here, for future reference.

    Here are the first 10 on my list.

    1. Line perpendicular to given line through given point not on given line. (this one)
    2. Perpendicular bisector of given segment.
    3. Right angle at given point on given line.
    4. Square with given segment as side.
    5. Equilateral triangle with given segment as side.
    6. Hexagon with given segment as side.
    7. Copy a given angle to a given segment.
    8. Line parallel to given line through point not on given line.
    9. Dividing given segment into N equal parts.
    10. Bisecting a given angle.

    Grab a straightedge and compass for each member of your family and join me – let me know you’re on board in the comments or via email.

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  • Mathematician Parent: Libby Often

    Most parents aren’t professional mathematicians. But there are a few. This is the seventh in a series of interviews with mathematician parents with the goal of helping parents integrate math teaching into parenting.

    This week we visit with Libby Often, a math teacher at Greater Lowell Regional Technical High School. She’s also an EdD student studying Math and Science Education at the University of Massachusetts Lowell.

    MathFour: Hey there, Libby! Thanks for sharing your time. First, can you tell us a little about your degree and career?

    Libby: Hello Bon, it’s nice to hear from you.

    My undergraduate degree is in history and classical studies. I have the equivalent of an undergraduate major in math as well (but not the degree to show for it!). Additionally, I have an MEd in Secondary Math Education and am currently in the EdD program for Math and Science Education at UMass Lowell. I am a teacher in a technical high school in northeastern Massachusetts, where I have taught math for the past ten years. I am speaking “off the record” here – not as an official school employee 🙂

    In high school, I was on the math team and the calculus team, and I cannot recall not enjoying math. Well, actually, I didn’t really enjoy the first semester of linear algebra, and I have struggled with writing proofs, but there was always something interesting!

    MathFour: Tell me about your family – how many kids do you have and how old are they? Are any of them more or less interested in math than the others in the family?

    Libby: I have two sons, a 10 year old and a 12 year old. Both are in middle school (grades 5 and 7). They both enjoy math, and are successful in it at school. I should add that this is their interest, not mine. Although I did tell my 12 year old that he would need to go into Pre-Algebra in grade 7, and to make sure his grades supported it.

    MathFour: Do you have any worries about your sons, academically? In particular, do you think they will do better in math than in other subjects because of your influence?

    Libby: I don’t really have any worries about my children now – my younger son has poor handwriting, and both my children hate writing projects. My likes seem to not influence them tremendously, especially at this point.

    MathFour: How do you play with your sons? Do you view your playtime as different in any way than other “non-mathematician” parents?

    Libby: I don’t really play with my kids now, other than card and board games. When they were younger, I didn’t play with them in a way that was different from what I saw other parents doing.

    We do talk about strategy, about piece placement in board games, about probabilities in games like Yahtzee, but I don’t see that as very different from other parents – especially those who play board games. My sons really like video games, and I have utilized their interests in some of my lesson planning, so maybe that is different?

    MathFour: Do you think you speak with your sons or behave differently than other parents because you have a math background?

    Libby: I really don’t think I speak or behave differently with my children because of my background in math. The main difference might be in the way that I talk to their friends – I invite friends over to work on homework, summer math, projects, and other school work, and that is definitely influenced by being an educator.

    What I do like about being involved in math education is seeing the different ways that students are taught to approach problems, and having an opportunity to talk to them, and talk about why these approaches work, and when else they may use them.

    MathFour: Have you ever had either of your children express negative thoughts about math? If not, how do you think you will handle it if that happens?

    Libby: In general, my kids don’t express negative thoughts about math, unless they have gotten a low quiz or test score and I insist that they go over the answers and correct them. I think my response would be on par with what their goals are, and what type of negative response they were exhibiting.

    I would be much more upset if, for example, my son told me I was an idiot because no one would ever need to know how to use fractions, than if he decided he wanted to major in English because he didn’t like math, or that he didn’t want to take AP Calculus.

    I try hard to look at the end goal – a happy, well-functioning adult, who can support himself and others. And math is involved in that!

    MathFour: Indeed it is, Libby!

    Have you ever disagreed with one of your children’s math teachers? What happened and how did you handle it?

    Libby: I have disagreed with other teachers, not necessarily the ones teaching my children. Our district is fortunate to have math coaches, and my sons have overall had good teachers, who were interested in the accuracy of what they were teaching. My colleagues at school and I have disagreed on a number of occasions, and the thing is that we all want students to succeed. So we have to come to an agreement about what will lead to student success in understanding and in preparation for what will come next for them mathematically speaking. I would expect to be able to have a similar conversation with my children’s teachers.

    MathFour: Now to change direction a little to a more worldview of math. What do you see as the biggest challenge in math education today?

    Libby: I think the biggest challenge, and the biggest hope, right now in US Math Education is the new Common Core curriculum. I really like these standards and the clarity with which they are written. There is no longer the room for teachers to say, “I taught them that!” because the standards specify what the child should be able to do.

    But at the same time, students are expected to master all the content for, say, grade four, during grade four. In the US, our public education programs take almost everyone – we are not excluding people because of socio-economic status, language, gender, or other protected categories.

    But this can be at odds with the idea that a certain concept is mastered in grade four, and then we move on to utilize and deepen that concept in grade five, six, seven, etc. Some students may need more time, for whatever reason, and the curricula that we devise is going to have to address this need for review.

    In addition, the math standards for high school are really college preparation standards, and do a great job of developing the quantitative reasoning needed for success in college but at the expense of a lot of skills we used to teach in consumer mathematics. For students to be successful in those areas we need to be sure they are picking up the knowledge somewhere, perhaps in a “transitions to work” course, or in extracurricular programs.

    One other thing that I think is very challenging in terms of mathematics education and education in general is that our society tends to be very product focused in a way that works well for business, but not for education. The successful countries don’t see changes in a few months, but over a number of years. So people need to be willing to wait.

    MathFour: What can you say to non-mathematician parents that might help them raise their kids to like and appreciate math?

    Libby: What advice would I offer to parents who aren’t lovers of math? Admit that to your children, and talk to them about some other things that you don’t love.

    Personally, I dislike laundry and ironing, but I am still competent, and the family wears clean and pressed clothes. Also, I am not any good at plumbing work. But I do try to determine what may be causing a problem before I call the plumber, so I can be as helpful as possible. And I treat my plumber like a valuable professional.

    Even if kids and parents struggle with “school math,” they should treat it like any other problem – what do I understand, what do I not understand (and believe me, the answer is never “I don’t understand anything!”), what can I do with what I do know?

    Ian Stewart says something great in his book Letters to a Young Mathematician about mathematicians and what we can use mathematics for. The essence of it is that if someone trains to be a doctor, or a lawyer, or an electrician, you can SEE that, because there will be a sign “Joe Smith, electrician.”

    But mathematics can be more hidden. It is the person who designs the survey to determine who people will vote for, the circuit design in your cell phone, the accountant who does your taxes, the person who wrote your email software. All of these people may have studied math, but their job description doesn’t say it.

    The advice I take from that is look for the “hidden math,” and look too at the beauty of it.

    Bon: That’s awesome, Libby! Thank you so much for sharing not just yourself, but all this great information!

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  • Times Tables Bootcamp

    This is a guest article by Caroline Mukisa who publishes Maths Insider.

    Does your middle- or high-schooler know their times tables? If the answer is a resounding “Yes” then, great, have a great day, and read the other great tips here at MathFour.

    I also have some great tips and advice on how to guide your child to maths success on my Maths Insider site.

    If not, then it’s time to help your teen develop their own times tables boot camp.

    Why are times tables important at all?

    Well it’s used loads in algebra, and those geometry questions usually need a fair bit of multiplication or division. It’s also great for those grown-up things that they’re going to be doing in the years to come, working out payment plans, home remodelling, calculating sale prices and just plain making sure that they’re not ripped off in life.

    Of course we’ve got computers and calculators, but who wants to be fiddling about to open a smartphone app, just to work out the price of a pair of jeans. And if they press the wrong buttons, how will they know the answer is wrong?

    Yep, they’re important!

    Why are times tables a problem for older learners?

    It’s like spending years trying to pass a driving test. Or still not being able to conjugate Spanish verbs after studying them for ages. Or trying to lose those last few pounds of weight. It sucks, and it gets to the point where it’s easier to develop a work-around: catch the train everywhere, just get by with a few Spanish phrases, or buy bigger clothes.

    Of course, your teen can “get by” and may even do rather well at maths without knowing their times tables. But before you give up, try some of the following strategies to help your teen make their own times tables bootcamp to fix those essential times tables facts in their heads. It’s never too late!

    Times tables boot camp strategies

    1) Figure out what they know, and what they don’t know. Are they fine with their 2’s, 3’s and 4’s and 5’s but shaky after that? Then focus on quickly reviewing the easy tables before some concentrated repetition of the harder tables.

    2) Use incremental steps. Make sure the 5’s are solid before moving on to the 6’s and the 6’s are fast before moving onto the 7’s.

    3) Give your teen a fixed target. It’s completely possible to learn the times tables from 2-9 in a month with just 5-10 minutes of daily study.

    4) Let them choose their own activities. Worksheets won’t be a popular option – iphone apps, You Tube videos, online games are all things that teens are more likely to tolerate.

    5) Be encouraging – don’t say, “That’s easy, you should know it” instead say, “I can see you’re working hard on this, keep it up.”

    Use these strategies to help your child plan their own successful times tables boot camp, so they won’t have to just “get by” in maths any longer.

    Caroline Mukisa is a homeschooling mom of 4, who publishes at Maths Insider.

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  • The Math in Credit Card Security

    We had a fun little discussion via email at the day-job. Someone changed the code on the combination lock and the discussion around combinations, permutations, cryptography and all things sneaky-math cranked up.

    It reminded me of this neat fact I learned about credit card security.

    Not all digits on a credit card are created equally!

    A credit card is made up of 16 numbers. But only the first 15 are “random,” according to NRich Math. The last number – the 16th number – is the “check digit.” It’s calculated using a fancy formula using the first 15 digits.

    This check digit helps a computer system quickly determine if a credit card number is fake. Now, it can’t confirm that it’s real – it just can help determine if it is fake.

    The digit is created using a method called Codabar.

    First, let’s define some things.

    An odd digit is a digit in the credit card number that is in an odd position. For the photo of the card here, the number is: 5184 8204 5526 6423:

    The odd digits are 5, 8, 8, 0, 5, 2, 6, 2

    An even digit is a digit in the credit card number that is in an even position. For the photo of the card here, even digits are 1, 4, 2, 4, 5, 6, 4, 3

    The check digit is the last digit – it gets calculated and isn’t considered in either odd or even position. It’s a super special digit.

    The method is weird – and kinda fun!

    Here’s what you do:

    1. Add up all the odd digits, or the digits in the odd positions: 5 + 8 + 8 + 0 + 5 + 2 + 6 + 2 = 36
    2. Double that number: 36 × 2 = 72. Save this number, 72, for later…
    3. Add the even digits together, or the digits in the even positions: 1 + 4 + 2 + 4 + 5 + 6 + 4 + 3 = 29. Save this number, 29, for later…
    4. (This is a freaky step.) Count the number of odd digits that are greater than 4. The odd digits are 5, 8, 8, 0, 5, 2, 6, 2. Of these, 5, 8, 8, 5 and 6 are bigger than 4. There are 5 of those total. Save this number, 5,  for this next step…
    5. Add up the results you saved from steps #2, #3 and #4. 72 + 29 + 5 = 106
    6. Take the answer from step #5 and figure out how many you need to add to get it to the next multiple of 10 (or the next number that ends in zero). The number after 106 that ends in zero is 110. So we need to add 4. 106 + 4 = 110. 4 is the super important number.
    7. That final super important number – well, that’s the check digit! That’s the last number that should be on the credit card – if it were a real card!

    For the picture, the check digit should be a 4. And it’s a 3. So I can tell instantly that this is a fake credit card number.

    You can use this to teach your children!

    Stuck in a waiting room with a 10-year-old? All you need is a pen, piece of paper and any credit card in your wallet.

    Teach them the method and have them check all of your credit cards. Or tell them you can guess the last digit of any credit card number.

    Either way, you’ve got an instant source of entertainment wrapped in a ball of education!

    What do you think? Are you racing to your purse right now to check your cards? Share your thoughts in the comments.

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  • A Mathematical Proof of Creationism

    Over the past ten years or so I’ve been hearing this word “creationism.” It seems that it’s the opposite of “evolutionism.”

    No problem – until I read about people trying to “prove” creationism. And articles trying to refute it.

    I’m not sure what the big hubbub is about. 20 years ago I heard a guy make a simple statement about it all. He proved creationism in 30 seconds.

    And it was a mathematical argument.

    Before I give you that 30 second super-statement, let’s chat a little about what a real mathematical proof looks like.

    Math starts with definitions.

    We say, “Okay, here’s the deal. Let’s define a nebino as a number that’s greater than all prime numbers,” or something of that nature. (And yes, you get to make up your own words if you want.)

    No math – none – ever starts out with confusing terms. If it does, someone jumps in and says, “You’ve got stuff that isn’t defined clearly.”

    Everything shuts down until that gets resolved.

    Math assumes… well… assumptions.

    Once you have your definitions clear, you get to set up what you assume. This actually might come before the defining part. And often it isn’t said out loud at all.

    Which is one reason that scientists sometimes think that they can do math. They’re always assuming the world (i.e. reality). Mathematicians don’t cotton to such vast and willy-nilly assumptions.

    Then you get your hands dirty.

    You’ve got definitions and you know what you’re assuming. You’re foundation is down. Now you build.

    In other words, you create some math.

    But things don’t always work out like you planned. So…

    If it doesn’t work, you change the definitions or assumptions.

    Yep – sometimes we really want something to work, so we just go back and tweak some of the starter points. Which means we change a definition or add (or delete) an assumption.

    (Which means if you’re using someone’s math, you have to make sure you’re working with the same definitions and set of assumptions.)

    And that’s the best argument for Creationism.

    The statement I heard from this Creationist was, in essence, this:

    We don’t have to use any evidence of science to prove God created the world in 7 days, 6,000 years ago. God planted the fossils and created all sorts of nifty things like DNA that would contradict the Bible. It was all meant to test our faith.

    Voila! Creationism proven.

    Brilliant! Change the assumptions, and you’re there.

    Beliefs are just that: beliefs.

    Which means there’s just no proving them. Kinda like my thoughts on the real line. I don’t believe in it – to the chagrin of my Twitter friend Colin.

    So if you want to prove something, change the rules. Or ignore them. Mathematicians do it all the time.

    *If you’re really really interested in my beliefs, I’ve shared them here.

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  • Unrecognized Math Conversations

    I had the pleasure of assisting Sarah Shah in her appearance on Great Day Houston yesterday.

    While preparing for the show, I observed Sarah and the host, Deborah Duncan, in the makeup room having a conversation about math.

    When I said to Sarah later, “that was an interesting math conversation,” she looked at me with anticipation, encouraging me to share what I heard. She had no idea I was referring to her conversation!

    The math conversation was fully on-topic.

    It was national thrift store day, and Sarah was going to share with GDH viewers some tips on shopping at resale shops. The topic of the show inspired their kibitzing behind-the-scenes about buying gold jewelry.

    Deborah was talking about how there’s a difference (sometimes big) between the cost of the gold in a piece of jewelry, and the sale price.

    The cost of craftsmanship should be close to its value.

    Deborah was making the point that there’s value on the design of an object based on the workmanship that went into it. And this goes only so far.

    Right now gold prices are around $1700 per ounce. Since an ounce is around 28 grams, gold is valued at about $60 per gram.

    The QVC bracelet in the picture is 9 grams. It’s selling for $530 – pretty much exactly the value of the gold contained within.

    If the value of gold for a 9 gram bracelet is around $530, charging $3000 for it means you’re paying about $2500 for the craftsmanship!

    Unconscious math is all around.

    Aqua And Gold Fractal by Sharon Apted

    It was a wonderful experience to see two intelligent, educated women having a lively and entertaining conversation about math. It was quite disheartening, though, that Sarah didn’t even recognize it. In a previous life she was a physicist.

    How many other conversations about math are ignored? How many people who claim they aren’t good at math have these conversations every day?

    Look around at your conversations this week. How many of them are about math? Share your conversations in the comments. And with your kids!

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