Think back to your math education, did you learn the steps required to add numbers? To subtract numbers? Did you learn another set of steps for how to add and subtract fractions? How about a procedure for how to add and subtract negative numbers? Were each one of those procedures different and specific to the "type" of number you were adding or subtracting? What about as you got older? More procedures? Were you successful? If so, you likely had a great capacity for memorization. The ability to memorize multiple steps and multiple procedures and know when to apply each of those procedures. What happened when you forgot just one step? The procedure failed to produce the correct answer. Were you ever frustrated because you couldn't figure out why it didn't work? No? How about your classmates? Any of them ever confused? Don't know? Try this, survey one hundred adults. Ask them, were you good at math in school? Did you love math? Did it make sense? I guarantee the majority will have a negative response. Our generation is full of math haters. Think about it, you would never hear someone say, I'm just not a literacy person, reading was always hard for me. On the contrary, I'm just not a math person, it never made sense... that's common place, socially acceptable. I was never taught to make sense of numbers, I was taught one way to solve every problem, every problem had ONE way, memorize these steps and you will be able to solve this problem. Sorry if you can't remember the steps. This is how we do it. I was robbed. I was not taught to persevere and try to make sense of the problem... who cares what it means, here's how you do it, just do this.
Hold on, why am I crossing out this number and changing that one?
Because you don't have enough to take away. Just do it!
But wait, I have 453 and I'm just trying to take away 17 I think there is more than enough to take away.
No you can't take 7 away from 3... Just cross out the 5. Just do it!
But wouldn't 3 take away 7 be negative...
NO! You can't take a bigger number from a smaller number, sit down, JUST DO IT MY WAY!
Hold on, why do I have to have common denominators?
Because you can't add apples and oranges! Just do it!
But... but... If I add 2 apples to 3 oranges I get 5 fruit...
Stop being sarcastic! Sit down, find common denominators... JUST DO IT!
I was wondering... why do I have to flip the fraction upside down if I'm dividing?
It's not your place to reason why, just invert and multiply! JUST DO IT!
Don't get me wrong, like some of you, I had a high capacity for memorization. I just did it, I memorized and memorized and very rarely made mistakes. I graduated in the top 3% of my almost 400 member class and I went on to high levels of math in college and was quite successful. Now, I'm a math specialist. It's what I do. I have spent four years studying and researching math instructional methodologies. Nothing but math every day for 4 years. Do you know what I've discovered? I didn't have any conceptual understanding of math. That made me angry. I have learned more about numbers and how they work in the last four years than I learned in my 19 years in public and post-secondary education. I have also learned how to help young students make sense of numbers, using their own innate understandings, their own built in mathematical ability. I have learned how to start with what they know, and what they understand and refine that into efficient strategies. In addition, I have also learned that it takes time. I must first allow them to be creative with numbers before I push my own ideas of how they "must" solve a problem. If I have patience and let them make sense of it, they will adopt the most efficient method, and they will become successful in math, not only knowing how to do it the way we learned it, but why that way works and when it's the best strategy.
The "new" methods you're seeing are not being taught. They are methods that students naturally invent. Just the way that mathematicians invented them before our formal mathematics system existed. Believe it or not, simplicity and efficiency are at the forefront of our classroom discussions EVERY day. We are guiding students through their own sense making methods not only to understand numbers and operations but to find the most efficient methods for each problem.
I understand your frustration. I was frustrated at first too. Remember, this is not the way I learned it either. Please be patient. Please reach out to your school's math leaders to help you understand. Please don't rob your child of the opportunity to make sense of math. We are trying to develop math lovers, problem solvers, and creative thinkers. How can that be wrong?
Lover of math and children