Author: Bon Crowder

  • What is a Ruler and Compass Construction?

    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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  • Math Teacher Interview Questions

    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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  • Yummymath for Kids & Cheap Help for Grownups

    Yummymath for Kids & Cheap Help for Grownups

    Daughter is into Goldfish. So much so that my brother has dubbed my car The Goldfish Burial Ground. If my Harry Potter wand worked, I could “poof” my car clean. Alas, Daughter loves Goldfish, and my magic wand is defunct.

    So when Yummymath shared these activities with me, one on Goldfish and one on HP movies, I was pretty excited. They’re long, so they put them in PDF form:

    Notice that, although there are some right and wrong answers, it’s a lot of investigation. Furthermore, in the Harry Potter worksheet, kids get to decide on their own what determines success for a movie. Both great things to do in the world of teaching math.

    Yummymath provides about three or four of these worksheets for free on their website every week. Yes, for free!

    They also provide a parent/teacher help guide…

    …if you’re a member. “Oh yeah, there’s the catch,” I hear you thinking. Indeed, at the whopping fee of $9 dollars per year (yes, per year) you have access to the solutions/help guide for all the exercises.

    Here’s what they look like:

    I’m trying to convince them to up their price. I think it should be a monthly fee. It’s extremely hard to make exercises like these, not to mention all the effort they put into the parent/teacher guide.

    They’ve informed me that they’re likely to go up to $12 per year. ARG

    In the meantime, you probably should get in quick, before I convince them of the amazing value they are offering.

    Oh – and tell me in the comments how you like the exercises and guides – I’d love to hear your feedback!

    UN-Disclaimer: They didn’t give me squat for this article except these exercises to give to you for free. I don’t even get commission on sales. (Not that they could afford it at that ludicrously cheap price!) What they’re doing is great. Yummymath is an awesome resources for homeschool and classroom teachers everywhere!

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  • HELP – Logic Puzzle Announcing The Homeschool Blog Awards

    HELP – Logic Puzzle Announcing The Homeschool Blog Awards

    Okay, y’all, I’m in over my head. I’m trying to create a logic puzzle as a nifty way to announce The Homeschool Blog Awards. Having never created a logic puzzle before, I thought, “How hard can it be?”

    Well, pretty darn hard.

    So I thought I’d put my start out there, as well as the solution, and see if I can get some help from y’all.

    Read the puzzle, try to figure out the solution, then suggest in the comments one or more clues that I should add (or get rid of).

    The Puzzle

    The Homeschool Post is the sponsor of The Homeschool Blog Awards every year. Writers of The Homeschool Post aren’t allowed to win, nor be nominated. So some of the writers of thought it might be fun to do a “within the family” blog award for themselves.

    After all was said and done, they decided to pass all information over to me, the math mom in the team, and let me figure out the winner. Alas, the information wasn’t well organized. So I had to figure out which blog went with which person, who voted for whom and who was the winner.

    The Clues

    Six of the writers decided to participate. They were

    • Lana (like Banana)
    • The writer of OK Homeschool Mom
    • Heather
    • The writer of Knit 1 Kids 4
    • Gidget
    • Rachel
    1. Heather said, “I love everyone. I’m just voting for them all!”
    2. Someone suggested that nobody should vote for themselves. So they agreed on that.
    3. The writer of Finding Joy voted for three people, including Heather and Kristal.
    4. Everyone who voted for Rachel also voted for the blog I Love My 5 Kids.
    5. Everyone but Gidget voted for the author of the blog SprittiBee.
    6. The author of  Homeschooling Unscripted only got two votes.
    7. Donnetta and Gidget got the same number of votes. As did the authors of SprittiBee and Knit 1 Kids 4. Also, Rachel and the author of I Love My 5 Kids had the same number.
    8. The author of Finding Joy is very popular – everyone voted for her.

    The Solution

    Here is the solution of who voted for whom. The initial of the person is on the left and the initial of the people for whom they voted is in the curly brackets. Click on the picture to enlarge.

    Owners/writers of the blogs are here:

    • Donetta publishes OK Homeschool Mom
    • Gidget publishes Homeschooling Unscripted
    • Heather publishes SprittiBee
    • Kristal publishes Knit 1 Kids 4
    • Lana publishes I Love My 5 Kids
    • Rachel publishes Finding Joy

    Don’t forget…

    Suggest a clue in the comments!

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  • Wordless Wednesday: Fibonacci Baskets

    Wordless Wednesday: Fibonacci Baskets

    I rarely do Wordless Wednesday, but some photos just lend themselves to it!

    These are from IKEA.

    In case you’ve not yet taught the Fibonacci Sequence, it starts with 1, 1 and then each next number is the sum of the previous two numbers:

    • Next is 1 + 1 = 2
    • Then 1 + 2 = 3
    • Then 2 +3 = 5, etc.

    How about some questions…

    • How many sets do I need for the next number? (A set from Ikea has 1, 2, and 3 in it.)
    • How many sets do I need for each number after that?
    • Is there a pattern? Like for the 12th number I need 12-2=10 sets and for the 17th number I need 17-2=15 sets?

    Do you have more questions? Or answers? Share in the comments.

    (150 words later my headline is pretty much wrong, huh?)

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  • Present Value vs Future Value – How Can You Tell the Difference?

    Present Value vs Future Value – How Can You Tell the Difference?

    No formulas here, only how to figure out which formula you might need to use if you’re working with present value annuities or future value annuities. (These are part of finance and often found in a Finite Math class.)

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  • Mathematician Parent: Libby Often

    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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  • What is “Living Math”?

    What is “Living Math”?

    Look – there’s a 30 degree angle!

    Some folks over at the Living Math Forum were wondering if they were doing living math right.

    There’s probably a fancy definition of living math, but I don’t know it.

    The fact is that we all live math! The trick for parents and teachers is to point it out to our kids.

    Ever sat waiting in a doctor’s office with a child? You find yourself “edutaining” them with, “Look, the chair is BLUE!”

    Remember to also say things like, “Look, there are five chairs and six people…”.

    Encourage them to notice that one lady is sitting on the floor because there aren’t enough chairs. Voila! Subtraction!

    So counting people is living math. As is going grocery shopping, cooking, drinking 1/2 cup water, and breathing 87% O2.

    You’re doing it right because you just can’t do it wrong!

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  • [50 Word Friday] Quit Counting Up to Punishment!

    [50 Word Friday] Quit Counting Up to Punishment!

    “You have until 5 to stop! 1, 2…” says the mom to her child.

    Isn’t it interesting how even punishment involves math? And it involves it negatively so!

    Why don’t we say, “Stop that. Now.”

    Or, “I’m going to give you until E to stop! … A, B, C, D, E.”

    Learn more about 50 Word Friday here.

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  • Motivation or Inspiration – How do you teach?

    Motivation or Inspiration – How do you teach?

    In order to see what the difference is between motivation and inspiration when teaching math, I’m going to start with a quick story…

    You have a dog named Herman. Herman is cute, fuzzy, has a pink nose and loves you unconditionally. You think he’s great. So you want to share him.

    You put a bow around his neck, and hand him to your children, Abby and Dirk.

    “Here is Herman. He’s cute, lovable, and a perfect pet. Isn’t he fabulous?” you tell them.

    Abby looks at Herman and is so excited. She thinks he’s fabulous, wonderful and sees in him everything that you do. Inspiration hits her – she loves him like you do!

    Dirk, on the other hand, wants a cat. He’s not sure how to voice this. But since you’re so excited about Herman the dog, he rolls with it.

    He wants to please you, so he feigns interest in Herman.

    Herman’s not a dog.

    Herman is your curiosity. Herman is what you find interesting and inspirational.

    And just because Herman is wonderful for you, doesn’t mean Herman is perfect for everyone else.

    Abby loves Herman. And Dirk loves Herman, but only because loving Herman pleases you.

    We offer Herman, and they take him. Because they want to please us.

    Lots of educators these days are talking about helping children connect with math through real life experiences. They want to give children curiosity about math in the real world.

    But the real world means different things to different people. And it means different things to different kids.

    • Some children like to build things. Give them a stack of Legos and they’ll work for hours.
    • There are kids who are outdoor people, always running around and wanting to see what next thing they can find in nature.
    • Some kids want to be in the kitchen, helping their parents cook dinner.
    • Some kids are quite happy connecting math just to math.
    • Some children are gamers, enjoying puzzles, riddles and games just for the fun of it.
    • And the list goes on…

    Grownups take their connection to the real world, their own curiosity, and pass it on to children. We take everything that we find fascinating, our own personal Herman, and hand it to the child.

    And they take it. Some because they are excited about it, and some because they want to please us.

    Motivation is not inspiration.

    The growing thought among educators is that children need to be curious in order to learn math. So we’re creating ways to get children curious.

    But are we doing it right?

    The child will happily take Herman, your form of curiosity. This could mean they are truly inspired by what you give. And it could mean that they are merely motivated.

    Motivation isn’t a bad thing, for sure! But if we mistake motivation for inspiration we are doing the children a disservice.

    If they’re motivated, they’ll only do what’s next to get praise. It’s about you, the grown-up, and how much they can please you.

    If they’re inspired, they’ll want to take their learning to the next level – even when you’re not around. They’ll want to see and do things to enhance their understanding without needing your praise and attention. It’s about them.

    And when things are about them, they own it. They succeed because they can, not just because we want them to.

    What’s your Herman?

    And have you passed him along? Was he inspirational or motivational? Share your thoughts in the comments!

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