IMHO, the main reason why people flunk algebra is because of the almost exclusive symbols-only approach to algebra. Here’s a comparison: think money.
When we learn about the U.S. money system, we use all of the following, starting with some of the following as early as age 2 or 3:
• real object: coins – pennies, nickels, dimes, quarters, etc. – and bills;
• concrete objects: play coins and play currency, including Monopoly money;
• equivalent real objects: 1 penny buys 1 chocolate football;
• verbal descriptions: “Son, you can earn 5 pennies if you put away all the basement toys before lunch” – “Dad, I found a quarter! That’s 25 cents, right?”
• written symbols for money: 5 = 5 pennies = 5¢ = $0.05; 1 quarter = 25¢ = $0.25 = 5 nickels; 7 dollars = $7 = $7.00 = 700¢.
Now… think about learning money using only the written symbols.
That’s essentially how most people learn algebra – using only the written symbols. And that’s why too many people bomb algebra.