Author: Bon Crowder

  • Mathematician Parent: Marilyn Curtain-Phillips

    Mathematician Parent: Marilyn Curtain-Phillips

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

    I am honored to be able to interview one of math education’s leading minds, Marilyn Curtain-Phillips, author of Math Attack – How to Reduce Math Anxiety in the Classroom, at Work and in Everyday Personal Use. She also created the amazing playing card deck (also named Math Attack) where the numbers on the numbered cards are tiny expressions –  the 4 of diamonds has 22 on it!

    MathFour: Thanks so much, Marilyn for sharing some of you time with us. First, I’d like to ask about your background. What is your degree and career? How long have you been in math?

    Marilyn: My bachelor of science degree is in mathematics. My master degree is in education with a concentration in mathematics and then an additional 30 hours of mathematics. I have been teaching mathematics for 21 years. I have taught grades 6 through 12. In addition I am now teaching on the college level at a local university for the past three years in the evenings while teaching high school during the day. Prior to teaching, I worked in government and banking for 10 years in the area of accounting.

    MathFour: Wow, your life has been so full of math stuff! Tell me about your children. Are any of them more or less interested in math than the other children?

    Marilyn: I have two children ages 23 and 18. My son, the oldest, has a degree in graphic design. His interest since elementary school has always been in art. Therefore he never showed an interest in mathematics and it was a bit of a struggle. My daughter has just graduated from high school and is going to college with a major in early childhood education. She has been much stronger in mathematics than her brother. But she doesn’t want to teach mathematics, of which I think she is really capable of.

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

    I encourage them to do what they enjoy. I feel they have adequate mathematics skills and a good foundation due to my additional help provided at home. As a high school mathematics teacher, I have grown more concerned at the foundation that students are coming to high school with.

    MathFour: How did you play with your kids? Did you incorporate math into your play?

    Marilyn: We enjoyed playing board games such as checkers, chess, uno, sorry, playing cards. I wanted to use games that help thinking and reasoning skills. This made great family discussion times while having fun.

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

    Marilyn: I have always spoken positively about mathematics. Many parents will say in front of children that they dislike mathematics or is not good at it. To me this almost like telling children that mathematics is something that is tolerated and should be dreaded and avoided whenever possible. As a mathematician I know how much mathematics is a gateway to many
    opportunities. This is one of the reasons that I list careers in my book, Math Attack.

    MathFour: Have you ever had any of your children express negative thoughts about math and how did you handle it?

    Marilyn: Yes, my children have spoken negatively from time to time, mostly during test times. I offer advice and encouragement. It is important to stay positive and listen to their concerns and make suggestions.

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

    Marilyn: Yes, I have had a different method of solving math problems. I talked with my children and let them know that many math problems can be done in different ways. Actually I prefer for my children elementary and middle school teachers not know that I am a mathematics teacher. I didn’t want my children to be graded on a tougher standard than other students.

    I experienced this growing up in a small town. My mother was a high school mathematics teacher, I felt looking back that I was graded on a tougher level and was expected to be extremely strong in mathematics. My sister experienced this also. She is an artist and doesn’t like mathematics.

    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?

    Marilyn: I feel that many students do not have a strong foundation and understanding of mathematics. I have far too many high school students who do not have their times table and or addition facts memorized. Many mathematics textbooks cover too many topics. Studies have shown that the United States textbooks are thicker than other countries that are stronger in mathematics. It almost feels like a cram session.

    By the time students get comfortable with a concept it is time to move onto something else. I feel this makes students feel less confident about their mathematics abilities. I think these feelings continue throughout the rest of their adult lives. Which leads to many adults going into careers that require as little mathematics as possible.

    MathFour: What do you see great happening in the world of math education?

    Marilyn: I think that it is good that a more hands on approach to teaching mathematics is now being used. Teachers are teaching to the different learning styles. I think that it is good that more high schools are requiring students to have more mathematics credit before graduating from high school. Many states require students to have three or four credits of high school mathematics. Also many of the mathematics curriculum are teaching with everyday life application.

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

    Marilyn: I would suggest to non-mathematician parents to speak positively about mathematics. Let their children understand that mathematics is like anything else – it takes practice and patience. Just as parents tell their children to practice at playing sports, they should feel that mathematics takes the same time and effort. Also parents should show their children positive ways they use mathematics in everyday activities such as sewing, cooking, planning a family trip, budgeting and grocery shopping.

    MathFour: I noticed that you also have a new math workbook Who is This Mathematician/Scientist? Can you share with us a little about it?

    Marilyn: It is a workbook for grades 6 through 12, after reading the biography paragraph, students must solve the math problems to see who the bio is about. The activities can also be used as a way to promote multicultural awareness and appreciation.

    MathFour: I can’t wait to check it out! Thanks again for your time and sharing with us.

    How about You? Got any questions for this week’s mathematician parent? Ask them in the comments and we’ll drag her in here to answer them.

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  • Cuisenaire Rod Art Inspires Thought and Decision

    Cuisenaire Rod Art Inspires Thought and Decision

    As with all good mathematics, I just spent hours pondering how to set up my super cool Cuisenaire Rod quadtuple.

    It was a great experience. Made me wonder why I was being so selfish in keeping it to myself.

    This is a perfect thing for kids to do!

    The Setup

    Seems simple enough. Make a picture on 1cm square graph paper with Cuisenaire Rods. Then write down the coordinates of the rods. Voila! You have the coordinate representation of your picture. Furthermore, you’ve practiced coordinates!

    Cool, right?

    The rub is that you have to correctly identify the orientation of the rods – are they up-and-down or side-to-side? Or worse – at an angle!

    So now we have four things to identify: size/color, angle of rotation, x coordinate, and y coordinate.

    Since the rods have width, we can’t just say “put it at (3,2).” What part of the rod goes at (3,2)? One of the four corners? The midpoint of one of the sides?

    I just picked one.

    My official Cuisenaire Rod Ordered Quadtuple (CROQ) looks like this:

    (size of rod, angle of rod, x-value of anchor, y-value of anchor)

    The size of the rod is easy.

    The angle of the rod is clear, but we have to define what is zero (up-and-down or side-to-side) and how we rotate (always clockwise, counter-clockwise, either way, etc.).

    I picked up-and-down to be zero degrees. It is the way I naturally look at the rods. Like this:

    See the bright green dot? That’s the anchor point. It stays there (in your mind) and is the bit that you’ll put on the (x, y) point.

    Which means that as you change the orientation (or rotate your rod), it sticks around. Like this:

    This rod is (5, 90, 0, 0) because it is 5cm long, rotated 90 degrees (clockwise) and the anchor is at (0, 0).

    You can do interesting angles too!

    Check out the 45 degree one:

    This one has the 4-tuple (6, 45, 0, 0). Notice that the rotation is always clockwise.

    This works, but isn’t the best way.

    When we graph (typically), zero degrees is horizontal. And sticking out to the right of the origin.

    Perhaps the best way to represent the rods on the plane is to use this type of set up. But it wasn’t the natural choice for me.

    Which is right?

    It doesn’t really matter. Unless you’re running a contest (which I think ETA Cuisenaire is putting together).

    Try this at home. It simulates what researching mathematicians do everyday:

    1. Let your child make a piece of artwork with the rods on graph paper. Go ahead and spring for another home set of rods and let him glue it. You can frame it and put it on the wall later.
    2. Ask him to do this: “Using only numbers, letters and punctuation, write the instructions to recreate your picture.”
    3. Take a piece of graph paper and recreate their picture yourself, based on what he’s written.
    4. Compare yours and his. Are they the same? If not, what happened? If so, were there any challenges for you while redoing it?
    5. Discuss it and let him think about this as long as he wants (minutes, days, weeks, years). Then ask him if he can think of a different way to describe it so it is easier to recreate.
    6. Repeat as many times as is enjoyable. After a while – sometimes years – he’ll create something similar (probably better) than what I have above.

    But, really, which is right?

    This is exactly what mathematics is all about. Not which is right, but which feels best. And which one will we agree on.

    When ETA Cuisenaire puts together their contest, they’ll have the rules clearly defined. “Right” will only be according to how they set it up. When you enter, they’ll recreate your art based on their rules.

    I like my rules. So much so, I’m going to use them next week to give the coordinates for the image at the top of this article. Wanna compare? Do it and post your CROQs in the comments.

    (Notice there’s a whole-lotta math goin’ on in that image – not just coordinates!)

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  • [50 Word Friday] A Conversation Between Parents After a Homeschool Convention

    [50 Word Friday] A Conversation Between Parents After a Homeschool Convention

    “That homeschool convention was wonderful!” she says to him.

    “Yes, and it wasn’t anything like I expected! Daughter is only two, but I’m already thinking about homeschooling.”

    “What changed your mind?” she says.

    “Everything it has to offer – not only great teachers, but all the right content. It’s awesome!”

    Learn more about 50 Word Friday here.

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  • Long Division with Playing Cards

    Long Division with Playing Cards

    I have since shot another video showing this with number tiles instead of playing cards.

    In response to a post on the Living Math Forum, here’s a way to teach long division with playing cards.

    Whatcha think? Will it work? Let me know if it does!

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  • What makes grownups learn?

    What makes grownups learn?

    Originally published as a guest post on MathForGrownups.com, a math blog by Laura Laing.

    Guest Post: Grownups can learn new tricks!

    Bon Crowder, another math evangelist

    A couple of weeks ago, a fellow freelance writer wrote me about her foray into graduate school. She needed to brush up on some math skills, and she wasn’t sure how. I have a feeling that her questions weren’t unique. Whether you need to learn a little extra to help your kid with his homework or you need to take a math class to further your education, learning math again (or for the first time) can be daunting.

    Luckily, my friend and fellow math blogger, Bon Crowder offered to write a guest post on this very topic. I swear, Bon and I were separated at graduation or something, because we approach math education in very similar ways. Plus she’s fun. (See? Math folks aren’t always boring and difficult to understand!)

    I wanted to title this “Being a Great Adult Learner.”

    But that’s dumb. All adults are great learners. If we weren’t, we’d be stumbling around, bumping into doors, starving and naked. We know how to learn, and the proof is that we’re still alive.

    And dressed.

    The question is “What makes you learn?”

    1) You need confidence.

    Confidence involves two things: feeling worthy and knowing you have the ability.

    When people feel they’re entitled to something, they’re more likely to feel confident in getting it. Hang around any Best Buy service desk and you’ll see this in action. People say all kinds of strange things when trying to return a broken product, and these things are said with a sense of entitlement. BY GOLLY they’re going to get their way!

    So how do you gain worthiness and ability? You’re worthy of it because you already have it. And you’re able to do it because you already do.

    You have it all. It’s just hidden behind a wall of words you or someone else (or both) has told you for years. Now’s the time to ignore everybody, even yourself.

    Because here’s the gosh-honest truth: There is not a single thing within a mathematician that is not within you.

    You’ve done math since you were a kid. Even before you were in school. You knew at a deep level that if there was one toy and there was another kid around, you’d better run like the dickens to get it. There’s no dividing that toy evenly between kids.

    You balance your checkbook (or you would be in jail right now), you probably have some rough idea of your gas mileage, and you know that if you have 12 people coming over, you’re going to have to double or triple that recipe for shepherds pie. You know math. Now’s the time to admit it.

    So say this every night before your prayers. If you don’t pray at night, say it twice:

    I do math. Today I woke up on time because I calculated how long it would take to get dressed. I knew how much money to spend because balanced my checkbook. I figured out how much weight I needed to lose – and I used math to do it.

    Modify this statement to fit your lifestyle and run with it. Every night.

    2) You need the right environment.

    Once you’ve tapped in to the realization that you’re inherently good at math, you need the right learning environment.

    This includes location, timing and the other people involved. If you have to drive too far away after working all day and all you get is a lousy quarter-pounder-with-cheese, you’re going to be tired, grumpy and irritable. If your class is full of teenagers fresh out of high school and the professor is 400 years old and believes in death by PowerPoint, things are not going to go well.

    How do you know the right environment?

    Look at all the learning experiences you’ve had through the years. List out the good ones and the bad ones. And then dig deep – what made the good ones good? Why were the bad ones so detrimental?

    Include timing, location, student body, temperature in the room and details of the instructor. List out the attitude of the instructor, his/her teaching style, voice intonations – even how he wrote on the board.

    Pick out the deal-breakers and the nice-to-haves and write them on a special piece of paper. This is your official “Environment Requirement” page. Laminate it, put it in Evernote, tatoo it to your bottom – whatever you do to keep it close so you can refer to it often.

    How do you make sure your Environment Requirements are honored?

    Here’s where that sense of entitlement comes back into play. If your class has a deal-breaker environment element, do something about it. Think, “If this were a faulty remote control that I bought at Best Buy, how would I handle it?”

    Ask the instructor to manage the loud students better. Ask building maintenance to change the temp of the room (or bring a sweater). Don’t sign up for a class during a time when you’ll be tired, hungry and irritable.

    And if you can’t change the environment – leave. Drop the class. Get your money back.

    If it were a crappy remote control, that’s what you’d do, right?

    You’re dressed…

    And fed. You learn all the time. And you do math.

    Now go find a class that fits and have fun!

    Bon Crowder publishes www.MathFour.com, a math education site for parents. But that’s not all! Bon has launched a really, really, really cool initiative called Count 10, Read 10. While parents are encouraged to read to their infants, toddlers and preschoolers, we’re rarely encouraged to inject a little bit of math into the day. Bon will show you how. Take a look at her blog for more information on developing math literacy (or numeracy). I’ll be writing about this more in the coming months.

    Questions or comments? Leave them in the comments section below!

  • Embracing the Not-Knowing at a Homeschool Convention and in Math

    Embracing the Not-Knowing at a Homeschool Convention and in Math

    I’m heading to the Texas Home School Coalition’s Convention this weekend in The Woodlands, close to Houston, Texas. The excitement I have for it makes me think of the excitement due to math…

    (and I have on Husband’s Roger Creager shirt that is faded brown – I’m NOT naked.)

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  • Help! I’m Going to the Texas Home School Coalition Conference!

    Help! I’m Going to the Texas Home School Coalition Conference!

    On Friday and Saturday I’ll be attending my first ever homeschool conference.

    And boy am I pumped!

    I’m so fresh and new at this – but really, I’ve been doing it forever. My ma sent us to public school (a really good one, Tarkington ISD) but as a single parent, she didn’t have much choice. At least back then.

    But she started her own business cleaning houses so she could be an afterschooling mom. She really REALLY wanted us to have the learning and interaction she could provide from 4pm to bedtime.

    Almost everything I know about math, I learned from her. She (and you) might be surprised at that because her degree is in English! But she taught me puns, patterns and a way to look at the world in a totally different light. Which is exactly what math is.

    I’m an afterschooling graduate and parent.

    Husband and I haven’t decided on how we’ll educate Daughter. Right now she’s going to a day school, which is really good for her and us.

    And we afterschool like crazy. It takes me forever to get anywhere with her because I let her observe everything. For as long as she wants.

    Everything I publish on this site is either used on her or I can’t wait to use it on her.

    I need your help!

    My mission is to help the first and most important teachers – parents – to be comfortable enough with math to teach it to their children through experiences. Which means I need to know what parents need from me. How can I help?

    I’ve got experience with infants and toddlers at this point. I know grownups, too (taught college for 15 years). But school-aged kids? I’m depending on y’all.

    So what should I ask when I go to the conference? What should I learn and discover that will help me help you?

    Please, please, let me know in the comments!

    (Oh, and if you want to meet up, let me know that too – I’d love to connect!)

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  • Perimeter and Area of Mommy’s Necklace

    Perimeter and Area of Mommy’s Necklace

    Written as part of the Count 10, Read 10 series.

    I noticed Daughter attempting to bejewel Husband with a strand of my faux pearls the other day. I watched, enthralled with the math learning taking place.

    She held the necklace in her hands – one on each side. Just about equal. So the space available for Husband’s head was almost non-existent. Like this:

    If she were to hold the necklace at two points that were closer together, she would create a “dip” in the necklace where his head could fit. Like this:

    There’s an extended learning opportunity here!

    This made me think of all the nifty things you can show about the relationship of perimeter to area and how you can have the same perimeter but change the area to all sorts of sizes.

    If you aren’t wearing a necklace, find some mardi-gras beads. Daughter has many strands, so I’m guessing your house might be littered with them as well. If not, join the club. Go buy some.

    Play with them in the bathtub or right before bed. (Make sure they give them up before going to sleep, though – it’s a strangulation hazard!)

    Move the necklace around on a flat surface (or on the bed) and let your child experiment with the ways the area changes. Ask questions like:

    • How much “stuff” can you fit inside the shape? (If there are blocks or other toys to act as “stuff,” use them.)
    • How much “stuff” can you fit inside the shape after you move it around?
    • Is that more or less “stuff” than you could fit inside it before?
    • Did the distance around the necklace change? (You can introduce the words perimeter and circumference.)
    • Can you make it into a square? A triangle?

    Be careful how much you do.

    Don’t forget, activities like this should be fun. For your child as well as you. So don’t get too in depth talking the math talk if it feels weird. Go with the flow.

    And let me know how that flow goes, would you? Share your thoughts in the comments.

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  • Mathematician Parent: John Golden

    Mathematician Parent: John Golden

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

    I had the privilege of interviewing John Golden, a university math professor and publisher of Math Hombre, a website with clever and fun math content that’s new every week!

    Just a sample: “As a bad beginning teacher, emulating David Letterman of all people, I realized that I loved teaching math.”

    MathFour: Thanks for taking the time to answer some questions, John. First, what’s your degree and career? And how long have you been in math?

    John: I have a PhD math in 1996, and am working as math ed faculty at GVSU a 25000 student public university in Michigan.

    MathFour: Tell us about your children and how they feel about math.

    John: Xavier – 11, a bit more positive about math than his sister, Ysabela – 12. Neither loves it.

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

    John: They’re both decent problem solvers, but that doesn’t necessarily equip them to do school mathematics. Ysabela, for example, found out this year she wasn’t allowed to use her method to divide and had to use the standard algorithm.

    We encourage them to follow their passions. Both are quite artistic, and Ysabela is an amazing reader. I do worry that I’ve emphasized understanding over grades to the point where they have no interest in academic success.

    MathFour: How do you play with your kids? Do you play math things?

    John: Lots of games: card, board, table. No video games other than some flash games on the computer. I love games for their math like nature, or math for its game-like nature, so I see it as connected.

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

    John: Definitely. Distinguish between what they’re asked to do and what math is, talk about cool and interesting math connections, do think alouds when doing homework, etc.

    MathFour: Have you ever had any of your children express negative thoughts about math and how did you handle it?

    John: More than occasionally. I take it with a grain of salt because I hated math at this age, too – for being boring and repetitive. I talk about the importance or confirm the irrelevance of what they’re doing, and try to emphasize making sense, and help them make sense.

    MathFour: Have you ever disagreed with one of your children’s math teachers?

    John: I always volunteer in their classrooms and bring games and such into it. This year, my daughter’s middle school classroom didn’t have me until the end of the year to do algebra tiles, but that was a positive experience. I strongly respect teachers, whether I agree or disagree, and never feel like they’re doing anything other than what they think is best.

    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?

    John: Irrelevance of school mathematics, anti-math culture, misunderstanding of what math is, professional/governmental insistence on teaching junk, high stakes tests that preserve bad pedagogy…

    MathFour: Wow, that’s a lot. So what do you see great happening in the world of math education?

    John: Internet networking, slow but growing awareness among new math teachers about better ways, leveraging of new technologies and opportunities for change because of bad test results.

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

    John: Give it a go themselves. If it didn’t the first time, try to make sense of it along with your kids if they learn it. Value thinking and communication over the right answer. Play games!

    MathFour: Thanks so much, John! Great tips and insight.

    How about you? What are some questions you have for a mathematician parent? Share them in the comments – I’ll try to get John in here to answer them.

    If you want to connect with John directly, get with him on twitter, find his contact information here and make sure to check out his site, Math Hombre!

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  • Cuisenaire Rods

    Cuisenaire Rods

    Cuisenaire Rods are brightly colored wooden sticks. Technically, they’re “proportionally sized rectangular parallelepipeds.” (But only say that if you want to hear your 3 year old repeat something really cute!)

    The “proportional” thing is important. The white ones are 1cm square, the red ones are twice as long and each color is 1cm more than the next color.

    I’m anticipating many articles and videos on how to teach with these (since  the possibilities with these things are virtually unlimited), so I thought I would start a running series. Here are the ideas and the links to the articles/videos that are ready:

    Creating Coordinate Pairs with Pictures

    Share your own ideas on how to use Cuisenaire Rods in the comments!

    P.S. I spent my hard earned money on these at Teacher Heaven. This small set was $15 in the store, but I see you can get it for less than $13 online. 

    This is also shared on Works for Me Wednesday.

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