Author: Bon Crowder

  • Mathematician Parent: Jennifer Wilson

    Mathematician Parent: Jennifer Wilson

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

    Jennifer here shown receiving recognition for being a Mississippi finalist for the Presidential Awards for Excellence in Mathematics and Science Teaching!

    This week we visit with a high school math teacher in Mississippi. Jennifer Wilson, NBCT, teaches at Northwest Rankin High School, and is a Teachers Teaching with Technology (T3) instructor with Texas Instruments.

    MathFour: Thanks so much, Jennifer for giving us your time. First, can you share a little about your degree and career?

    Jennifer: I have a B.S. and an M.S. in mathematics. I have been teaching high school mathematics for 18 years.

    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?

    Jennifer: I have two daughters who are 6 and 9. They are okay with math – but the 9 year old will tell everyone very quickly that her first love is reading.

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

    Jennifer: I feel very lucky to not be worried about my children academically. They love to learn. My husband and I both encourage their curiosity and try not to stifle their desire to ask why or come up with a different idea of how to do something, especially when the only good reason we can think of is “because I told you so”.

    I think they will do well in math – but not necessarily better than other subjects. My husband and I both love to learn, and so the girls definitely recognize that desire and enjoy learning as well.

    MathFour: That’s great! How do you play with your daughters? Do you view your playtime as different in any way than other “non-mathematician” parents?

    Jennifer: We play games. I probably view play differently than a lot of parents – but probably similar to many teachers, no matter their subject of expertise. I am all about learning, and it is hard to turn that off, even at home.

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

    Jennifer: Yes. Anytime some kind of math problem arises, I always ask the girls about their thinking, because I am very interested in how they arrive at answers.

    At dinner, one daughter noticed that her tortilla chip was in the shape of a trapezoid, so we had a great conversation that night about trapezoids. We have a “pi” pie plate, so both girls already know a little bit about pi. They definitely call an “oval” an ellipse and a “diamond” a rhombus. They have called their blocks by the appropriate solid names, such as cylinders, prisms, and pyramids, since a very early age.

    When the 9 year old missed a question on her state practice test about perspective drawing, instead of just telling her the correct answer, I got out the stash of Unifix cubes at our house to make her build the drawing with the cubes. She completely understood after doing so – and asked me to make up some more questions for her because she enjoyed working through the problems with the manipulatives. Both daughters play with my TI-Nspire™ CX handheld. They love making shapes, measuring their parts, and making them different colors.

    MathFour: I had to google that one – fancy device!

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

    Jennifer: Not yet…I’m not sure I will handle it well. But I am hopeful that since my goal is not just calculating math but understanding math, they can at least appreciate my passion for it, and I will honor their passion for another subject, if the need arises.

    MathFour: How do you think you’ll handle it if you find your self in disagreement with one of your children’s math teachers?

    Jennifer: I’m not sure I will handle it well if it does happen, but so far, so good. I am lucky to teach in a great school district with great support for teachers at all levels, so I will keep my fingers crossed!

    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?

    Jennifer: Having teachers who are experts in mathematics at all grade levels.

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

    Jennifer: I see teachers who are willing to use technology to engage students in the learning and understanding of mathematics, teachers who are learning alongside students (often because of and through technology), and teachers who are willing to give up some of their control over the classroom to create a classroom that is truly interactive.

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

    Jennifer: I have been amazed at some of the mathematics that my students are learning in the computer games that they play. So while I realize that some students go overboard with the time that they spend in front of their electronic devices, find a way to encourage them to explore mathematics through tools that do interest them.

    MathFour: Wonderful, Jennifer, thank you so much!

    How ’bout You? It’s back to school time – do you have any questions for a super technology oriented math mom? Ask them in the comments!

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  • Cuisenaire Rods Go Pythagorean!

    Cuisenaire Rods Go Pythagorean!

    I’ve been playing with the lovely Cuisenaire Rods for a few weeks now. I made the (fortunate) mistake of creating this flower in a past article about coordinate pairs.

    The mistake was that I would eventually have to come up with the coordinates for this thing. Fortunate because it gives the MathFourTicians out there something else to teach with the rods!

    The center of the flower is the place to start.

    Since all the “petals” are attached to the center, that’s probably the best place to begin.

    I converted to something I could see.

    Since everything is tiny (1 cm), I went to a bigger setup. And some of the coordinates were easy to pick out. So I put those in the big grid, too:

    And then I started to do some work…

    Next I considered what I was really dealing with: a square. And each side was 1 cm.

    According to those crazy Pythagoreans, the diagonal measures 2\sqrt2:

    So half the diagonal is 22\frac{\sqrt{2}}{2}:

    I went back to the big grid.

    When I put this information on the big grid, it looks like this:

    Doing some arithmetic and geometry, I get:

    Using my very cool TI-30 calculator, I get that 22−12≃0.2\frac{\sqrt{2}}{2}-\frac{1}{2}\simeq0.2.

    I can accurately name the points!

    Knowing that each corner pokes out roughly 0.2, I can calculate the coordinates:

    From this I can create the ordered quadruples as described here for the petals of the flower. But at this point I’m pretty much needing a break. So I’ll leave that for next time.

    Whatcha think? Fun? Share your thoughts in the comments and on Twitter:

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  • Long Division with Sumology Number Tiles

    Long Division with Sumology Number Tiles

    A few articles back, I published a video called Long Division with Playing Cards.  I did it super-fast in response to a comment at  Living Math Forum.

    I’ve pondered this a bunch since then and decided I like the idea, but the playing cards are too cumbersome. I ran across a game called Sumology (from Simply Fun) at the Texas Home School Coalition Convention. The heavens parted and angels sang.

    Or at least my heart started beating and my head started spinning.

    So here’s the same teaching method, but with a little more pizzazz and a couple of free downloads:

    What do you think? Will your child like it? Please share your thoughts in the comments.

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  • The Math of Parenting

    The Math of Parenting

    Today’s article is from Laura Laing, author of the book Math For Grownups and publisher of the website of the same name.

    So you think you don’t use math on a daily basis? Think again.

    You may not be solving for x, and the distance formula may not roll off the tip of your frontal lobe—mainly because you haven’t used it in years and years. But if you can put “parent” among your titles, you do math. I promise.

    Just look at a typical day:

    6:35 a.m.

    Your darling daughter went to bed late last night. Seems that she couldn’t pull herself away from the most recent novel she’s devouring, and she had to finish, “just one chapter.” Problem is, she’s a bear to wake up when sleep deprived, and she’s got an 8:00 checkup at the pediatrician. She can usually get ready in about 45 minutes, and it takes 15 minutes to get to the doc’s office. How much longer can you let her sleep in?

    9:03 a.m.

    Check-up is done, and you’re waiting to pay the bill. You’ve got $33.65 in your wallet and a $25 co-pay. But after a morning of running errands, you’ve promised dear daughter lunch at the local fast food place. Should you use your cash for the co-pay or pay with plastic?

    11:21 a.m.

    At the grocery store, you’re deciding between three brands of ketchup. One is on sale for $2.27. For another, you have a 50¢ off coupon. And the third is a smaller container for only $1.49. Which one should you buy?

    12:08 p.m.

    At Burgers ‘R’ Us, your daughter has requested the chicken nuggets and a drink – no fries! You’d like to eat the fries that come with her kids’ meal, but you’re not sure you can afford the calories. Luckily, the restaurant has a handy sign displaying the caloric values for each menu item. What can you order to go with her fries that won’t force you to eat only carrot sticks for dinner?

    1:31 p.m.

    You need to fill up, and you have your choice of gas stations. One offers regular unleaded for $3.27 per gallon, plus a free car wash (a $10 value). Another offers $3.15 per gallon—no car wash. Which station offers the best deal?

    2:47 p.m.

    It’s time for your daughter to practice piano—a task that she hates. You thought the practicing contest that her teacher started would give her the motivation to practice every day. Nope. So today, she’s going to try to catch up on the days that she slacked off. She’s expected to practice a total of 15 minutes a day, but she’s only practiced a total of 25 minutes for the week. Her lesson is tomorrow. How many more minutes does she need to practice to please her teacher?

    5:32 p.m.

    Time for dinner, and you’re exhausted. Instead of making a meal from scratch, you decide to order from the local pizza joint. Your daughter wants plain cheese, your husband wants pepperoni and sausage and you want a veggie pizza. What’s the most cost-effective way to order dinner?

    8:35 p.m.

    Thankfully, your daughter has crashed early, meaning she can catch up on the sleep she lost last night. If you wake her up at 7:00 a.m., how much sleep will she have gotten?

    Typical day? Perhaps. Typical math? Definitely.

    So the next time you think, “I can’t do math,” keep in mind the number-based tasks that come across your path on a normal day. You might be surprised at what you accomplish without even thinking about it.

    Where is the math in your day? Tell us in the comments!

    Laura Laing is the author of Math for Grownups, a funny and accessible look at how the over-18 set uses math in everyday situations. While this post is not based exactly on a day out of her life, it could be. She is a freelance writer and the parent of a pre-teen in Baltimore.

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  • Mathematician Parent: David Wees

    Mathematician Parent: David Wees

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

    I am quite excited to feature David Wees who teaches at Stratford Hall in Vancouver. David and I have been on numerous #mathchats together and I’ve found him engaging, fun and knowledgeable. He publishes the website The Reflective Educator (formerly 21st Century Educator).

    MathFour: Thanks so much, David for taking the time to answer some questions. First, can you share some more about your degree and career? How long have you been in math?

    David: I have a bachelor of science in mathematics with nearly 60 credits in honors level mathematics. I finished my degree in 1998, but have never been officially a mathematician. Instead, I teach mathematics in middle school and high school, and have recently moved into a new position as a learning specialist for technology.

    MathFour: Tell me about your family – how many kids do you have and how old are they? How do your family members feel about math?

    David: I have a wife, and a nearly 5 year old son. My wife found math to be painfully difficult for her entire career, but hides it well around our son. My son loves math. He recently confided in me that he knows math only slightly less than me, but that I know more technology, and he knows more science.

    MathFour: How cute! And great that your wife tries to keep the math environment positive.

    Do you have any worries about your son academically? In particular, do you think he will do better in math than in other subjects?

    David: I have no concerns at all about my son academically. He is bright, creative, and independently minded. He will almost certainly do better in math than his other subjects. Today he ripped a book because the “binding was loose.” So we told him to find $11 dollars in his piggy bank. He pulled out five $2 coins and one $1 in about a minute, carefully counting by 2s for the first $10, and then adding another dollar.

    MathFour: How do you play with your son? Do you inject math a lot?

    David: I think we play ordinary games, with some exceptions. Certainly we include mathematical play in our sessions. We count everything, and introduce different ways of counting. We play dice games and practice adding small numbers. We stack blocks in patterns. I’ve also recently introduced a “how can we get this number game.” For example, “How can we get 5?” My son responded with “1 and 1 and 1 and 1 and 1 makes five. Hrmm. 2 and 3 makes five. 4 and 1 makes five.”

    MathFour: Great game!

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

    David: Definitely. We spend much more time talking about numbers than other parents do.

    MathFour: Has your son ever expressed negative thoughts about math?

    David: I’ve not noticed any negative thoughts from my son on math, with the exception that he thinks I know more math than he does. He did ask me today about the odd, even pattern. “Why does it matter if a number is odd or even?” I told him it helped us know quickly if we could split the number into two equal parts. I don’t think he was terribly impressed by that explanation.

    MathFour: LOL! I guess that is a little unimpressive.

    Your son is almost five, so I’m guessing he’s not had many math teachers. Do you anticipate you’ll ever disagree with any of his math teachers? And what do you think you’ll do if that happens?

    David: My son is just starting school. As I work at the same school as he will be attending, I will have to handle disagreements with his math teachers very carefully.

    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?

    David: Mathematics, as it is usually taught, is neither interesting or relevant to students. Given that relevance and engagement are key to deep learning of a subject, it pretty much means that in most generations of people, the vast majority of them lack any functional numeracy.

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

    David: These types of conversations are amazing in my mind. I love that I can speak my mind about problems in math education and not have everyone jump down my throat.

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

    David: Count lots. Play number games early. Treat learning mathematics as important as learning how to read. Spend time playing and learning early math with your kids. Don’t let your kids learn that worksheets and rote memorization are math.

    MathFour: Wow, that was awesome, David! Thanks so much for your time and sharing with us.

    How about You? What are your questions for David? Ask them in the comments. And don’t forget to check out all the great stuff on his website!

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  • How to Teach Right Triangles when Crossing the Street

    How to Teach Right Triangles when Crossing the Street

    This morning Daughter and I went to the gym.

    When we crossed the street, I exposed her to undo risk by crossing at an angle.

    So on our way out, I explained to her that we were walking a little further to get to the car this time. And we would minimize the risk of getting hit by a car by taking the longer route.

    (Of course she’s not yet two, so she really didn’t care. But it was important for me to say.)

    Crossing at an angle is shorter than going straight across.

    People most often cross the street at an angle. Intuitively we know it’s shorter. Look at the tiny person in this picture. He needs to get to the front door of the store.

    It’s five yards to go at the angle, while if the little guy walked straight across then up, it would be seven yards.

    Suppose walking one yard takes 5 seconds. It will take the little guy 15 seconds to cross the street straight across. (And with a toddler, it does take 5 seconds to walk a yard.)

    Then he has to walk the four yards along the side to the door. Which means his total time is

    3 yards across at 5 seconds per yard = 15 seconds

    4 yards up at 5 seconds per yard = 20 seconds

    Total walking time = 35 seconds

    If he went at an angle, it’s 5 yards total (by the Pythagorean Theorem).

    5 yards diagonally at 5 seconds per yard = 25 seconds

    Total walking time = 25 seconds!

    Crossing at an angle puts you at risk for longer.

    For the pedestrian in a hurry (and wearing the shirt that reads “Safety Third”) the angled route is the way to go. But for a parent with toddler in tow, minimizing risk is a better option.

    If the little guy were to cross at the angle, he’d be in front of the oncoming cars for 25 seconds. If he were to take the route that is longer overall, he’d be in front of oncoming traffic for only 15 seconds.

    The car doesn’t care what angle you’re walking, it can squish you pretty easily either way.

    Not to mention he keeps the driver happy.

    Getting out of the driving area faster means keeping the driver happy. That might not be your goal, but adding some cosmic happy juice into the world of drivers never hurts.

    Plus, if someone were to “hypotenuse you” by taking the angled route when you were driving, wouldn’t you get a little annoyed?

    Next time you practice safety, practice math!

    So be safe. And tell your children why.

    It’s all about the math!

    Share your thoughts in the comments.

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  • The 1-2-3 Song

    The 1-2-3 Song

    Part of the Count 10 Read 10 series to help parents connect with kids through math a little each day.

    Did you know that the alphabet song, Twinkle Twinkle Little Star and Baa Baa Black Sheep are all the same tune!?

    Well, now there’s another!

    Thanks to all the great folks who have public domain images out there that I could use for this.

    Specifically

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  • How to Integrate Math into Geography

    How to Integrate Math into Geography

    Everyone’s getting back into the schooling groove. So twitter is filled with questions like Cara’s:

    And since my world revolves around math, here are my thoughts.

    Use the Four Color Theorem (but don’t say it out loud).

    The Four Color Theorem says that if you only have four crayons, you’re good to color your map and not have any colors touching. (That’s the he kiddo version of the theorem.)

    So get out your google and print out some map coloring pages. Choose ones with lots of borders. (As fun as it is to color Texas as a whole, use a map of Texas’s counties.)

    Caution: don’t tell the children they’ll be using math. Let them figure it out.

    Now it’s coloring time!

    And here’s the challenge: color the map with as few colors as possible so that no two touching territories have the same color.

    While they color, you can talk about the names of the locations and some of the details. Even have them label them.

    Once they finish coloring, have them remember how few colors they used.

    Next time you talk about this map, ask them to use one less color than they did before. Continue labeling and discussing the locations.

    After a while they’ll figure out that they can’t do it with three, but they can do it with four.

    Shower, rinse, repeat.

    From the Texas Environmental Education Providers (how cool is that!)

    Kids are experimental. And they don’t believe that what works once, automatically works again (that’s why they drop Cheerios on the floor over and over and over again).

    So you can do this with the next map when you’re ready to go to another part of the world.

    Indeed, they’ll eventually figure out that four is the magic number. Then they can google it and learn all about the theorem!

    How about it? Did it work? Share your experiences in the comments.

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  • Wordless Wednesday: An Example of Count 10 Read 10

    Wordless Wednesday: An Example of Count 10 Read 10

    In an attempt to join the Wordless Wednesday crowd, I’m sharing this photo. But as you can see, for MathFour.com, this is only a Somewhat Wordless Wednesday.

    Before this photo we were discussing size of shirts – a numeracy concept that is visually displayed through the inability for grownups to fit 4T nightshirts on their bodies. Count 10 Read 10 is part of our family’s afterschooling routine.

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  • Finding Patterns in a Lokta Paper Blank Book

    Finding Patterns in a Lokta Paper Blank Book

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

    For my 40th birthday, I bought myself this beautiful Lokta paper book from a fabulous little store in the Houston Heights called Write Now!

    It has circles on it – one of my “things.” I love circles. But then I saw how the colors were laid out.

    “Holy cow! This is a teaching opportunity!” I thought.

    And it got even better at the Texas Home School Coalition’s convention this last week. I shared it with former math teacher and now-homeschooler Sharon Brantley and she saw even more goodies in it!

    You can use it to teach math!

    Anything that has more than one aspect/characteristic/color (pretty much everything) can be checked for patterns. Patterns are an essential, perhaps even the most important, building block for mathematical thinking and development.

    Here’s what you can see in this book cover:

    Connect the green dots and you get a square. (Also the yellow dots.)
    The pink dots form a line and then the one dot off to the side can make a perpendicular line to the other line. (Purple dots, too.)

    These blue dots make a funny little shape.

    But wait! There’s more!

    What Sharon pointed out to me was that you can draw an L from any dot to another dot of the same color!

    Optional: This “L” thing links directly to the slope, by the way. Between any two points of the same color, the slope is either 1/2 or -2. Cool, huh?

    Where do you see patterns in your world? Share it (and a link to the picture) in the comments!

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