I’ve “talked" about the differences between real life math and book math before. Turns out it’s not just me who is seeing the significant differences between them. There is a wave starting out there somewhere in the scientific community to eliminate math as a required subject and instead offer it as an elective where the material covered is more math games than math “work”.
The idea is that the math, as it is being taught, is so far out of one's daily reality, so sterilized for mass consumption that is it isn’t teaching our kids workable, usable real life math anymore. Beach works every day with REAL money, fractions, measurements, equivalents, and time/elapsed time. She doesn’t need a workbook of story problems to understand how math works out in the world.
In school, there isn’t enough hands-on exploration or real-life practice and applications. Too much memorization and not enough messy trial and error. The end result is the learning isn’t deep enough. The students come away knowing a thin layer of rules or facts that if not practiced will slowly erode over time. It also makes math "not fun". Really?! Math is a ton of fun!!! AND it sets kids up to fail. They think they aren't good at math. Nope, we as a "system" aren't good at teaching it.
When we decided to do a course on Algebra she had a ton of fun working the “puzzles” as she called them. She never allowed me to give her rules to blindly follow. I had to prove each one to her. Then she had to prove them to herself before she would use them.
In our push to finish The 6th Grade, we needed to get back to fractions. Why yes, I do teach Algebra before adding and subtracting, multiplying and dividing fractions. Guess what? It was awesome because now she uses the tools she gained in Algebra to solve fractions.
Back to the point. What I realized, was just like Algebra, I couldn’t simply give her the rules. Telling Beach, “Crisscross Applesauce” I might as well go outside and smash my head into a brick wall! “But why?” “That’s the rule.” “Why?” “Because, it’s how it works.” “But why does it work?” ~i don't know, it just does...
I realized there was only one way to do this we were going to have to play around with fractions until the rules showed themselves to her. It shouldn't be too long she already does conversions and addition of all sorts of fractions in real life. (There is that word again, REAL). So I threw out the fractions workbook and began looking for math games with fractions or those that I could adapt to using fractions. Then we pulled out the fraction circles and we got down to play, I mean work, no play. Here is one of the games we played yesterday.
A fun upgrade on the card game WAR: Using a deck of cards with the face cards removed and something to act as a fraction line you can play Fraction War. The players must decide which one has the larger fraction based on the 4 cards played (2 cards each, 1 numerator & 1 denominator). The winner gets to keep all the cards. The player with most cards at the end wins.
With the goal of fostering a deeper understanding of what is going on, we added mathematical proofs to the game. Using the fraction circles each player had to prove the value of their fraction.
Next to make it more challenging; add a second deck of cards (face cards removed) and deal each player 2 fractions (4 cards to each) and add in a mathematical operation (addition, subtraction, multiplication or division) before comparing the value against the other player's cards. Same rules apply the player with the larger sum/product wins the cards and the player with the most cards at the end wins the game.