Author: Bon Crowder

  • Interview with Math Game Sokikom’s Founder

    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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  • The Order of Operations Explained: Exponents

    The Order of Operations Explained: Exponents

    This is the 3rd in the series The Order of Operations Explained. For the other articles in this series, click here to visit the introduction.

    Exponents are the second in the list for the Order of Operations (OoO).

    When we want to find the result of 32 x (2 + 7), we have no problem. We know to do parenthesis and then exponents, then multiplication.

    When you teach algebra, you’ll have to teach some distributing of exponents. But that’s still okay. And the rules of exponents are pretty straight up.

    So why a whole article on exponents?

    In the order of operations, the “Exponents” rule represents a bunch more than just superscripts or tiny numbers flying up and to the right of things.

    Roots are exponents, too!

    Tree Roots by Linda Allardice

    Not the ones from trees, but things like square roots and cube roots. Consider 9+2\sqrt9 + 2. You do the square root first because it qualified as an “exponent.”

    But if you had 9+2\sqrt{9+2}, the 9 + 2 is under the radical sign (the square root sign) so it’s bound together in the “Parenthesis” rule.

    This one isn’t that hard with arithmetic, but when you come to algebra and start “undoing” these things – it’s important to remember that roots fall into this category.

    Fractional exponents are exponents.

    This one seems pretty “duh” so it’s easy to see how they fall into the “E” of the order of operations. But what are fractional exponents really?

    912 means 99^\frac{1}{2} \text{ means }\sqrt9

    So fractional exponents are the same as roots.

    Note that some fractional exponents are roots and “plain” exponents all mixed up. Like this one:

    2723 means 2723 as well as (273)2.27^\frac{2}{3} \text{ means } \sqrt[3]{27^2} \text{ as well as } (\sqrt[3]{27})^2.

    This is a big fat full concept that needs a little more explaining. I’ll write more on these in another article.

    Logs fall under the E.

    Axe In Stump by caroline steinhauer

    As my algebra and computer math teacher in high school, Mrs. Kelley, used to tell us – logarithms are exponents. It took me a long time to figure out what the heck she meant. But when I did, I thought it was brilliant.

    This is a true statement: log3⁡9=2\log_3 9 = 2. Let’s analyze it.

    Based on the definition of logarithms, this means that 32 = 9. Which we know is true.

    Notice who the exponent is in this: 32 = 9: 2 is the exponent. And 2 is the same as log3⁡9\log_3 9 because the equals sign in log3⁡9=2\log_3 9 = 2 means “is the same as.” So the logarithm log3⁡9\log_3 9 is the exponent 2.

    Still with me? Either way, it’s okay. It’s a weird concept that I can go into detail in a video soon.

    The thing to remember here is that logarithms fall into the “Exponents” rule of the order of operations.

    So if you have log3⁡9+7\log_3 9 + 7, you have to do the log3⁡9\log_3 9 first and then add the 7 after.

    Want more on exponents?

    In the meantime, you can check out more than everything you always wanted to know about exponents on the Wikipedia Exponents page. Rebecca Zook created a great video on logarithms. And check out this explanation and problems to work on fractional exponents.

    And let me know what you think. Did I miss something?

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  • How to Quit Saying “I Hate Math”

    How to Quit Saying “I Hate Math”

    Is changing how you feel about math like changing who you are?

    My Little Brother is a licensed professional counselor. He often tells me that you can change your attitude by changing your behavior.

    Apparently the behavior-attitude door swings both ways. If you don’t want to do something because you feel frustrated, do it anyway and that will clear up the frustration.

    So that’s how you can get your attitude and your child’s attitude aligned with positive feelings of math.

    Stop saying angry math things.

    I’ve pointed out that the real place kids learn math is at home. And I’ve discussed why grown-ups should quit talking about hating math. But until now, I’ve never said how to do this.

    Because it’s easier said than done right? When you’re frustrated, or your children are frustrated, you’ve gotta say something. So you can’t “just stop.”

    HOW do you quit saying “I hate math” (when you really do hate math)?

    First, make a list of all the math things you do (download the handy helper here). Here’s a starter list for both you and your children:

    • I know how long it takes to get dressed and so I can calculate when I have to wake up in the morning.
    • I can figure out if our car is getting good gas mileage.
    • I can figure out if I have enough money saved to by a nice toy.
    • I know what I have in savings and if that’s enough to buy the fancy shoes I want.
    • I know how many minutes it takes me to walk to my friend’s house.
    • I know that riding my bike to my friend’s house is faster than walking.
    • I know that in the past I couldn’t reach the middle of the dinner table, and now I can – because my arms are longer.
    • I can figure out how much I’ve grown in the past year by looking at my growth chart.

    Copy your list and put it on the refrigerator, in the bathrooms, on the front door and next to your bed. When you find your child or yourself wanting to say, “I hate math,” instead say, “I can do math because __” and fill in the blank with something from the list. If you need to, continue like this:

    This particular math problem I’m working on is more challenging than what I already know, but it isn’t hard. I just have to figure it out. And since I’m smart enough to do all that other math, I can figure this out!

    The behavior of changing what you say will have a positive affect on how you and your children feel about math!

    Try it. Let me know how it goes!

    This article was previously part of a We Are That Family “Works for Me Wednesday” post.

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  • Math Game Review: Sokikom

    Math Game Review: Sokikom

    I’ve recently been playing a new math game called Sokikom (so-kee-kom). It’s an online social math game – yes “social” – for 1st through 6th graders.

    So far I love it. The only bummer is that Daughter is only 21 months old, so a mouse to her either squeaks or is edible. But I did have some older kids in my family play – and they’ve all enjoyed it!

    It currently has three games, Frachine, Treeching and Opirate, and various other perks and treats to help children with math. It’s officially launching next week and the folks at headquarters tell me there’s more to come – even after launch.

    Here’s a little info to whet your whistle for it:

    Frachine reinforces fractions.

    The fun part of this fraction game is you get to cut the pieces up while you play. So it isn’t just showing parts of a whole, but the child actively makes the parts of the whole.

    Treeching supports money, measurements, time, patterns and early algebra.

    Sokikom is full of surprises. Sometimes the answer isn’t in the form you’re expecting. At first glance, this challenge puzzle seems all about mouse control. But notice there isn’t a matching “12 months” on the tree. Instead you have to convert. This is a great opportunity for teaching units!

    Opirate reinforces operations and early algebra.

    This was my least favorite game of Sokikom – but only because my sister creamed me in it. (We used the online social part from our respective houses. Felt like being a kid again!)

    Opirate is a bit of a thinking-through game. You have to do the problem (in the cloud at the top of the screen), then find the solution on the map, then get yourself to the solution. The “X marks the spot” numbers keep popping up – so every new problem has the old X’s that you had before (if you can remember where) as well as some new ones.

    The Social Aspect

    Your children can “friend” other kids with whom to play. I’m not a Farmville or World of Warcraft person, but I understand the appeal. Playing 20 minutes a night with an online friend keeps kids connected and at home, safe.

    More Goodies for the Kids

    In Sokikom kids earn energy (which they need to play a game) and Soki-money. As they accomplish levels, they get awarded Soki-stars. The Soki-stars unlock clothing and accessories items they can “buy” with Soki-bucks to personalize their avatar – a popular element of any social game.

    For parents and teachers

    Parents typically read to children before bed. Sokikom is a way for parents to encourage a little bedtime math: do some Sokikom math for 10 minutes and read for 10 minutes.

    And since many households have multiple computers, you can play online with your child – even sitting next to him or her. What a great bedtime routine!

    Sokikom also has a robust infrastructure to track and manage the progress of each child:

    Are you ready for it?

    Sokikom has won numerous awards and is funded by the US Department of Education. From their literature:

    Sokikom is focused on five core tenets: provide social learning where kids help kids learn math; adapt to individual students’ needs and learning styles; encourage positive and safe competitive game-play, which leads to measurable improvements; and connect school and home to allow for continuous web-based learning.

    I’ve seen these in action with this game. I’m a hands-on kind of mom and teacher, and I’m very much into attaching math to anything we can. If your kids lean toward video games, Sokikom‘s a great one to use!

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  • Why It’s Okay to Add Denominators when Adding Fractions

    Why It’s Okay to Add Denominators when Adding Fractions

    I did some videos for avoiding finding a common denominator and why this trick works. Ever since then I’ve pondered what it would look like if you added without a common denominator.

    A mom on the Living Math forum was asking for advice on how to teach adding numerators and not adding denominators in fractions. So this topic is again in the front of my mind.

    First note, that you can add both numerators and denominators – this is called piecewise addition – but then you are getting into a whole new world of stuff. Actually, you’ll be experimenting with some goodies from Abstract Algebra (my field of study). We’ll talk about how and why this is good in a few paragraphs.

    What is adding fractions, anyway?

    For us in the “real world,” adding fractions is adding values that can’t be counted with fingers. It’s adding bits of things together – maybe whole things with bits, even.

    We have agreed to use things that look like

    some number on topsome number on bottom that isn’t zero\frac{\text{some number on top}}{\text{some number on bottom that isn’t zero}}

    to represent fractional pieces of a whole.

    When we add 12+14=34\frac{1}{2} + \frac{1}{4} = \frac{3}{4} we have said that our total is

    3 pieces of a whole pizzawhen the pizza is cut into 4 equal pieces\frac{\text{3 pieces of a whole pizza}}{\text{when the pizza is cut into 4 equal pieces}}
    Total: 3/4 of a “pizza” is blue.

    Quantity over value is important to young children.

    I remember taking money from Little Brother when we were kids. You might think I was stealing, but it was more of conning the innocent. He would have 3 dollar-bills. I would have 20 pennies.

    He would quite willingly trade his 3 monies for my 20 monies. For him, this was a matter of quantity. I knew the value, though. (Bad girl – sorry, LB I owe you. xo)

    This measuring of quantity, rather than value was important in LB’s development. Instead of someone teaching him how to measure value, he learned it through experience.

    This is why we should allow kids to add the denominators.

    Let’s use the example above and add the numerators and the denominators to see what that means.

    Adding 14+12=26\frac{1}{4} + \frac{1}{2} = \frac{2}{6} means that our total is

    2 pieces that we have6 pieces that were possible to have\frac{\text{2 pieces that we have}}{\text{6 pieces that were possible to have}}

    Notice here you can’t “reduce” the fraction – because this isn’t the value  as we know it.

    If you teach adding fractions using manipulatives or toys and allow adding denominators, soon your children will see that your   (on the top in the picture below) is very different than having their  , on the bottom.

    We have six total pieces.

    This will inspire them to work toward equality – and invent fractional addition (correctly) on their own!

    Tell us how it goes in the comments!

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  • Why Learning to Subitize Is Important

    Why Learning to Subitize Is Important

    Previously, I gave a definition and some resources for subitizing – assessing quantity without counting. The questions I posed in the previous article were

    • If you do it, how did you learn to do it?
    • How do we teach children to do it?

    Having thought a great deal about it, I wondered if it was even relevant to teach it. And Husband asked the question, “Don’t they need to count and know their numbers before learning to subitize?”

    You don’t have to learn to count to know “how many.”

    Although evidence indicates that subitizing and counting happen in the same part of the brain, you don’t have to know how to count to subitize.

    Subitizing up to 4 or 5 using recognition bypasses the “counting” of numbers.

    Daughter is currently subitizing 2 – without counting. I haven’t taught her how to count objects at home and they don’t do it at school yet. So she has no concept of one. But “two bows” (one for my hair and one for hers) is very important to her. Likewise “two bowls” (one with goldfish and one with Rice Chex) is an amazing thing.

    This article by Ernst von Glasersfeld explains how number words can be associated with the quantity without ever counting. Children give the appearance of counting because they’ve memorized the number words and they use the cadence to tap their finger on objects. But they’re usually doing this to be rewarded with praises and cheers. They don’t really understand the concept of counting. This is what I saw the little girl doing at the playground.

    It IS important for kids to subitize.

    What’s the point, anyhow? If I can quickly see 8 things  – does it matter? And is it important to tell the difference between 8 things and 9 things? If there are 8 hungry tigers heading for me and I subitize that there are 9, will it make a difference in how fast I run from them?

    I researched more and found out that  subitizing does matter to the understanding of numerical concepts.

    Subitizing 2 items and putting it with a subitzed 3 items can yeild the perceived 5 without ever knowing what addition is. And having the group of 4 items and seeing within it a group of 3 or 2, leads quickly to subtraction and division.

    Thus subitizing “teaches” various mathematical concepts without ever getting into the language or construct that grownups have put on it.

    So how did we learn it?

    My initial guess was that we’ve learned to do it the same way we’ve learned to read without sounding out the words. Over the years we’ve seen and counted many hundreds of bundles of 3 things that when we see another bundle of 3 things, we know there’s 3 of them.

    Upon further research I’m now of the opinion that I learned it from Ma saying to me “there’s three of them” while I looked at a collection of three objects. I bypassed the counting and went straight to learning the cardinality – with the help of grownups.

    The cliffhanger…

    So I’ve yet to answer the question, “How do we teach subitizing?” Alas, it’s coming. (UPDATE: it’s here, complete with downloadables!)

    In the meantime, where do you observe subitizing and does it seem important?

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  • The Order of Operations Explained: Parenthesis

    The Order of Operations Explained: Parenthesis

    This is the 2nd in the series The Order of Operations Explained. For the other articles in this series, click here to visit the introduction.

    I mentioned in the introductory article for this series that “the order of operations isn’t best practice for expressions involving variables.”

    When you involve a variable, you can’t just “do” the arithmetic. Like in the case of 2(3x + 4)=11. You can’t add 3x and 4 to get a result before moving on. You have to use the distributive property.

    And even the distributive property won’t work sometimes – as in the case of absolute values shown below.

    Parenthesis mean isolation.

    When we say “parenthesis” in the Order of Operations (OoO for short), we mean anything that’s grouped together and isolated. This could mean with actual parenthesis. This could mean [square brackets] or {curly brackets}.

    Although grownups seem to know that square and curly brackets are the equivalent of parenthesis, children don’t. This has to be said out loud.

    “Parenthesis” in the OoO can also mean |absolute value bars|. This one’s not so clear.

    When you try to solve the equation 4|2x+3|=20, you have to start with dividing by 4 to isolate the absolute value chunk. There’s not a “rule” for distributing the 4.

    (Although, it would be worth it, and fun, to see if your children can come up with some rules for distributing within absolute value bars. This would be some real mathematics at work for them – experimenting and discovering.)

    Tops and bottoms of fractions are implied parenthesis.

    It’s also the case that the numerator (top) and denominator (bottom) of a fraction are isolated places. These fall under the OoO as parenthesis.

    Check out this older video I did. It shows how this works with fractions:

    Parenthesis are for deviation from the other rules.

    David Chandler of Math without Borders commented this in the previous article of this series:

    The rule is to do higher level operations first. Use parentheses whenever your intention is to deviate from this rule.

    If you can focus on this instead of a mnemonic device, you can get students to internalize what’s going on with the OoO. It’s important, however, to make sure they remember about other bracket shapes as well as isolation.

    Let us know your tips and thoughts on the P in PEMDAS!

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  • Can You Teach All K-12 Math in 8 Weeks?

    Can You Teach All K-12 Math in 8 Weeks?

    Elizabeth, @Ser3nd1pity, tweeted an excerpt from a book by David H. Albert called Have Fun. Learn Stuff. Grow.

    Reading through it, the thought that came to mind over and over was, “Finally.”

    Here was my favorite part:

    …the subject matter itself isn’t all that hard. What’s hard, virtually impossible, is beating it into the heads of youngsters who hate every step.

    Indeed there is a gracious sufficiency of beating – and resistance – when teaching math.

    But everyone already knows math!

    In the book, Albert wrote:

    If you never teach a stitch of math, in a mathematical culture your kids will learn heaps of it anyway. …learning math along the journey is a difficult thing to avoid.

    You can’t not do math and exist. It’s like not breathing. Impossible.

    We survived for a very long time without the written word. But we’ve never existed without math.

    Early humans knew that to divide a chunk of meat between two people would yield too little:

    meat2<what I need\frac{\text{meat}}{2} < \text{what I need}

    He might not have have had the fancy way to write it – but he could learn how to write it in 8 weeks.

    Daughter playing with washers: counting them and learning math in her world.

    Can you teach all of K-12 math in 8 weeks?

    The short answer – it depends on to whom. In Albert’s article, he’s teaching children. You can totally do this with kids. And cavemen, I suspect.

    Grownups are a different story. Innumerate adults already have anxiety, anger or fear associated with math. There’s a whole lifetime of un-doing that would have to take place.

    But once you undo this, then the 8 weeks would work.

    The way I teach college classes is this: we’re going to spend 48 contact hours together – I’m going to wow you in ways you’ve never expected. When we’re done, you’ll be much calmer. You’ll be able to learn math much better, both on your own or in a classroom.

    I don’t force learning. I don’t even require learning. I let it happen. It’s the closest I can get, in the classroom, to what Albert is saying.

    Can you get closer to the 8-week method?

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  • What is Subitizing?

    What is Subitizing?

    Suzanne at Guided Math Study Group emailed me about subitizing the other day.

    I used perceptual subitizing to “know” that there were three green hair curlers here.

    Alas, I had never heard this term. So I did some research and thought I’d share what I’d learned.

    Subitizing is a way of instantly counting. In fancy math terms it would be getting to the cardinal number of a set (how many) without without going through the ordinals (counting each one’s position).

    There are two types, perceptual and conceptual. Perceptual is perceiving the number of objects immediately. Conceptual is putting a little effort into it.

    For instance, I glanced at the hot rollers Daughter had scattered on my side of the bed. I perceived there were three on the nightstand. But I had to do a little conceptual subitizing to arrive at the number of curlers on the floor (see the pictures).

    I had to mentally “chunk” these hair curlers into smaller perceivable bundles to conceptually subitize the number here.

    Here is a list of resources I found about it:

    In the next article, I’ll attempt to answer the two questions I see associated with subitizing:

    • If you do it, how did you learn to do it?
    • How do we teach children to do it?

    What do you think of these questions? Do you do it? Do you teach it?

    (By the way, it is pronounced with ooo – like “Ooo! Subitizing is neat!”)

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  • Counting Isn’t an Inherent Concept

    Counting Isn’t an Inherent Concept

    We spent our vacation a couple of weeks ago in central Texas. We had lots of fun – including lots of counting.

    One to one association of fingers to Discovery Toys’s Giant Pegboard pegs

    I noticed that some of the basic counting principles grownups know, aren’t inherently known to kids.

    I was observing Daughter as I was counting. She continued to look in deep concentration as I counted from one direction and then recounted from the other. Then I would rearrange the items and count them again. She was still enthralled.

    We teach our young children to count to 10, but never realize they don’t know what that means.

    Counting is a way to associate how much with a group of objects.

    If there are three things in a bundle, we associate the word “three” and the symbol 3 with that bundle. This number is called the cardinality of the set/bundle and means the number of things in it.

    My lone Calculus classmate in high school decided to create her own number system when we were freshmen. Everyone else laughed at her, but I got it. She was noticing that there was no rhyme or reason that we called a set of two objects “two.”

    We’ve decided to say out loud “two” and label it two and 2 and that means this many things: X X

    Counting is a way to order things.

    A bunch of things can be lined up and counted – even if they aren’t technically in a line. Each subsequent number is associated with another object. These numbers are the ordinal numbers. The final number that you count ends up being the cardinality of the set (from above). In this way you use ordinals to determine the cardinality.

    Counting is a way to compare one group of objects with another.

    Take two groups of objects. Pair one object from one group to an object from the other group – set them up in a one-to-one fashion. This shows that the two groups have the same number of objects. It doesn’t determine how many there are, but very young children don’t have to know the numbers to grasp the concept of “the same.”

    This eventually leads to the concepts of equality as well as less than and greater than.

    Counting isn’t dependent on which object you start with.

    This was the craziest concept for me. I noticed this when reading Brown Bear, Brown Bear one night.

    To mix it up (to keep my sanity) I would count the children in the book in differnet directions. After 3,000 nights of reading the same book over and over, something occurred to me. There is no reason for a 2 year old to know that counting in one direction will yeild the same number as counting in another direction.

    This is taught – not directly, but through experience. After counting a bazillion times, we eventually figure out that no matter which way you count things, you’ll get the same number.

    Well, unless Little Brother starts eating those things.

    Counting can be stopped and picked up where you left off.

    This is another concept that grownups “just know.” If you can mark your place (and Little Brother isn’t involved), stopping and coming back won’t change the result. This is the forerunner to addition, too.

    Counting is the foundation of all mathematics.

    This is the kicker. Counting is the beginning of it all.

    If you can get your kiddo to count, the rest is cake. And not just saying, “1, 2, 3, 4, 5, 6, 7, 8, 9, 10,” but really getting him or her to understand the totality of the concepts.

    • How much is there?
    • Is there an order?
    • Does one group have more, less or the same as another group?
    • Did the number of objects change when you counted differently?

    Grownups get it, but we aren’t born with it. Imagine that you don’t know these things inherently. How does that change the way you observe the world?

    This article was originally shared on Homeschool Creations.

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