Saturday, June 2, 2012
Out with the Old, in with the New?
Over the last cupe of decades, the general populus heard whispers - "are you using the New math?" Old Math vs. New Math?? Ok, I know it's a little overwhelming and confusing. I will try to explain a bit about the Old and New ways of approaching Math, but don't worry....even the experts agree the 'New' way doesn't work well.. I both love and love to hate the new math program. Has anyone heard of an 'Integrated' classroom? Or a child complain, "when will I ever use this in real life!" well New Math attempted to address these, they also tried to move past the basic computation skill we grew up with and moved toward advanced deductive reasoning. In our books and homework, back in the day of our childhood, we had line after line of the exact same type of problem working one type of process - this was in the hope of achieving wrote memorization of specific math facts. A child first learned to count. They then learned to add. Oce they had memorized adding, they moved on to subtracting. I've said it before, but old math was made difficult once a student approached algebra. This is because Old Math treated numbers and number manipulation as concrete facts. But, once a student starts algebra, they were told no, numbers can be molded and manipulated, they are NOT concrete. What I mean is, in the Old way: a student learns to count, they can recognize the shape of a 3 and a 4. Once they had mastered counting, they moved onto addition. They were told 3 + 4 = the shape the student recognized as a 7. Then the student eventually moved on to multiplication. They would see the shape 3 multiplied by 4 and they would recognize they equal 12. Once fractions were introduced it became overwhelming...why? Well we had spent years using those real numbers to achieve an answer. But in fractions you deal with the abstract - remember LCD (lowest common denominator)? We tell them, oh just multiply the fraction by 4 then solve the problem....but the student stares at the page and can't comprehend - you have changed the fraction, how can that get to the right answer? You can't just change shoes into umbrellas! They had no way of understanding that numbers, shapes, anything related to math is NOT concrete. A 3 is never just a 3, it can equal 1, 1, 1; or 4p=12 they both equal 3 but really 3 is just a label. New math attempts to start a student thinking of math as playdough or Legos. If you have a huge bucket of Legos you can choose to build a castle or a car - but they are still Legos you are using. New math attempts this, so kids learn that they can do a million and one things - but they are still just working with quantities and labels, in other words MATH! In my opinion, New Math can be summed up in one term - Discussion. New math is less about finding the RIGHT answer and instead is more about what path the student decided to try to take to achieve the problem. Some parents think we do not teach the students the pencil-and-paper shortcuts we learned when we were younger. We DO teach them, but we just don’t rush into it. We would rather students do things the long way first! Why, you ask? Our math programs must build a foundation of conceptual understanding first before the algorithms are introduced. In other words, we have to work concretely and manipulatively first. Students today use concrete, hands-on materials when they encounter new concepts. Later they will learn the symbolic shortcuts we used when we were younger. It is more important that students DESCRIBE AND DEMONSTRATE how they went about solving math problems instead of focusing on getting the correct answer. Research shows that students’ working together helps with their understanding. When you walk by a small group trying to discuss ways to figure out an answer, you hear: “I have an idea”, “Wait, wait I got a different plan”, “Let’s try your way, then my way”, and “But that does not make sense!” During group problem-solving, teachers are actively listening to students’ reasoning which, in turn, helps them better understand the students’ thinking. Keep in mind that there is still time in the classroom for students to work independently and teachers know how important it is to work independently. So, what's the downside of this new math? Well, there are sometimes too many choices! It can frustrate some minds when you say - there is no right or wrong way of finding the answer. It can be overwhelming to some, to look at an equation but not knowing which path to take to solve it and instead hear the teacher say, which one do you want to try? I think the key to success will be somewhere in the middle, giving instruction on one path at a time working mastery, but reminding the student that there are tons of ways of working with numbers!! Here are some websites: http://everydaymath.uchicago.edu/parents/ http://www.math.com/homeworkhelp/EverydayMath.html https://www.wrightgroup.com/parent_connection