Preventing Students From Saying, "I'm Not Good At Math."

  

                                         Photo courtesy of: www.motherpedia.com




   Here I am writing as the summer semester winds down and I find myself again thinking of my future students.  When you pursue an Elementary Ed. Degree, you know that your license will be a K-6 license, which means that I could one day have a classroom filled with five and six-year-olds or a classroom full of twelve and thirteen-year-olds, or any age in between.  Whatever the age, as their teacher, how will I help my students to engage in math?  to feel confident and competent in it?  to be interested in it?  to, dare I say, enjoy it?
   There are many articles out there about math and kids, most echo what we already know as students and parents of students.  What I know is that I will need to be proactive about both easing my students' math anxieties and encouraging them to embrace the math concepts that I am trying to teach them.
   We all have at least one memory of being called on in class, or worse yet, called up to the chalkboard and not having the correct answer to a math problem.  Those types of scenarios do not help students to feel comfortable with math.  Public embarrassment is not a good way to instill confidence in a child.  Confidence is key when it comes to math.  When a child believes that he or she is capable of coming up with the correct answer, or is at least comfortable asking questions that lead to that end, math becomes enjoyable.
   Not only do teachers need to provide many opportunities for students to be successful and to gain confidence in their own abilities, but we also need to make sure that our lessons are relevant to the real lives of our students.  How many times have I heard my teenagers ask disgustedly," When am I ever going to need to know this?"  We need to show our students that math is useful in everyday life.  If we don't, we lose their attention.  Lessons need to be linked to things that matter to them so that they care about what they are learning and see its purpose.  Annie Murphy Paul echoes these sentiments in her blog post entitled, "How Do You Spark A Love Of Math In Kids."
   Math is all about knowing the formulas, recognizing the patterns, making note of previous learning and knowing which strategy to "pull out of the toolbox."  It will be my responsibility as a teacher to help my students to do just that.  I hope to help them to love math in the process.

Teaching Children About Fractions

   The neat part about being in math classes right now as I pursue my Elementary Ed. degree is thinking about how I will apply what I'm learning to my future classroom one day.  How do I take this information and prepare to present it to my students in ways that they can understand and actually use in their real lives?  How will I break these large mathematical concepts down into smaller bite-sized chunks for them?  For example, how do we teach young children about fractions?
   Even children of very young ages can understand the idea of "half."  "Give half of those animal crackers to your brother..."  "Here, we'll split the pile of Legos in half so that you can both build with them..."  Half is pretty understandable, but what about more complicated fractions?  For example, which is bigger, 1/8 or 1/4?
   I guess I have a bit of a theme here lately with references to food.  I didn't intentionally do that, but here I go again.  In the classrooms that I work in as a Para Educator, I find that food can be very helpful when discussing fractions.  A Kit-Kat bar works nicely to show fourths since it is conveniently packaged as one chunk of chocolate that can be broken apart quickly and easily into four separate but equal parts.

  We can show our students that one of the four smaller bars is one fourth of the whole candy bar.  Simple enough.  The fun part is to lay another Kit-Kat bar under the overhead projector so that the children can watch each "fourth" being cut in half.  Now the candy bar is divided into eighths.  This makes it easy to see that you would rather have one fourth of the candy bar than one eighth.  Children tend to think that the bigger denominator must be a bigger number.  This visual helps them to understand what fractions mean.  Would they rather have 4/8 of a candy bar or 4/4?
   Another idea that makes learning about fractions easier is the use of pizza.  We can cut one pizza into eight equal pieces and another into sixteen equal pieces.  Then let the fun begin.  Which is more? 4/16 or 2/8?  There are some surprises for children when working with fractions.  Even those children who are not typically visual learners benefit from visuals when it comes to fractions.
  I found an interesting article from the U of M titled, "Teaching About Fractions: What, When, and How."  The article states that we need to let our students use manipulatives and give them many opportunities to explore fractions in hands-on ways.  It doesn't always have to be food.  It can be blocks or coins or paper cut into equal parts.  (Kids do get excited about getting to eat an 1/8 of a Kit-Kat during math, though.)
   Here is one example of a neat manipulative for learning about fractions:

Following the Recipe

      I like to bake.  Actually, I really really like to bake.  It's one of my only hobbies that finds me indoors now that I think about it.  I'm not one of those bakers, though, who can just whip up something delicious without a recipe in front of me.  I like recipes.  I know several women who can rattle off the recipes for their favorite treats off the top of their head with 100% accuracy.  I have always marveled at that ability because I do not have it.  I've been using the same chocolate chip cookie recipe since I first learned to bake about thirty years ago and I am not even close to having it memorized.  I wouldn't even try.  I get that little recipe card out and follow it each and every time.  Maybe the recipe card is my security blanket.  I don't know.
   What I've realized this summer while taking these math classes is that math is a lot about knowing the recipe.  In the language of mathematics, the "recipe" is called a "formula," but it's really the same thing.  If you don't happen to have the formula memorized, you simply need to remember that there is in fact a formula and then use it.
   There have been many times over the course of these past several weeks that I have read and then reread a homework problem, wondering how in the world to even begin solving it.  I've started scratching out some preliminary guesses as to how to plug in the information that's given and then realized, "Hey, there's a formula for this!"  It's amazing how even the most difficult of problems can be solved with the formula that was designed specifically for that purpose.
   If you want to figure out the volume of a pyramid or cone, you'll want to know that V=1/3 bh.  If you want to be able to figure out the value of each interior angle of a polygon, you'll want to know that the formula (n-2) x 180/n is the one that you need.  The "n" is where you plug in the number of sides of the polygon that you are working with.   For example, if you are figuring out the interior angles of a square, you'd plug the number 4 for the four sides into the spot in the formula where the "n" is.  (4-2) x 180/4 will give you the answer of 90 degrees.  Pretty neat.  Try it for a hexagon, an octagon, or even a 22-gon and you'll soon have your answers.  Try it without the formula and you won't get very far very fast.
   Do you remember hearing the formula for slope: "rise over run?"  That's an easy one to remember.  How about that area of a rectangle is "length times width?"  Could you memorize the formula for the equation of a line from two points, though?  What about the distance formula show below?

   Not only do we need to know these formulas in order to "know" math, but we also need to understand the order of operations.  We again need to follow the recipe.  When solving an algebraic equation, which part do we start on?  Here's a handy little tool courtesy of coolmath.com for that:

   If you don't know to do the part of the problem that's in parentheses first and to do all multiplication and division before you do any addition or subtraction, you'll just make a big mess of the problem and end up with the wrong answer.  Like I said, it's a lot like baking.
   I have found that knowing the formulas is empowering.  Knowing that there is a formula to plug the numbers into is empowering.  Solving the problem with a correct answer at the end is satisfying much like biting into that warm perfectly baked chocolate chip cookie is satisfying.  If I'm being honest, I enjoy the cookie a little bit more than the math problem, but you get my drift.

 photo courtesy of www.meals.com