The debate continues between two camps—the traditional vs. the reform—as to how children should be taught math. On one side are those who believe skills should be taught based on algorithms, formulas and step-by-step procedures. On the other side are those who think the more inquiry-based approach that emphasizes developing conceptual understanding and problem-solving skills is the key to success. My question is: Why does it have to be one or the other? Why can’t it be a combination of both?
Let me illustrate. My 2nd grade grandson walked to my house to show me how well he is doing in math class. He announced, “I have an ‘A,’ Gigi!”
“Wow!” I said, “Show me what you are learning!”
He told me he is learning how to add two-digit numbers, so I wrote on a piece of paper 45 + 23. He quickly wrote his answer as 68 and grinned. I replied: “You answered that one correctly. Good for you! But can I ask you some questions?”
“Sure,” he said.
“What does the 6 stand for?”
“What does the 8 mean?”
Another blank stare.
“How did you get that 6?”
He replied, “I added the 4 and the 2.”
I asked, “But what do the 4 and 2 stand for?”
He had no idea. Oh, sure. He added quickly, but he had no idea what he was adding.
It is obvious to me that skills are being taught, and I know he is taking timed tests, but what is going to happen when he gets to division and is faced with the problem 102 ÷ 3, and the only way he knows how to divide is by using the shortcut algorithm I was taught? “Three won’t go into 1, so put a zero on top. Multiply, subtract, bring down the 1 and 0, and so on.” He will memorize the algorithm, but he will not have a clue as to what he is doing. Can 100 be divided into three groups? Well, of course it can. If my grandson develops conceptual understanding of place value, dividing will be easy, and fractions and decimals will not be the nightmares of 4th grade.
The Elevated Math lessons were created using the philosophy that a balanced approach can be delivered through engaging, interactive technology. The lessons guide students as they develop conceptual understandings; provide algorithms, steps, rules and procedures; and present opportunities for students to further develop and practice skills in real-world problem solving situations. Doesn’t that make sense? Isn’t it all in the balance?
2 thoughts on “Teaching Math: It’s All in the Balance”
Perhaps if I can see a lesson I will better understand how it will develop a conceptual understanding.
I am looking forward to showing you the iPad lessons! Then, you will understand that the illustrations, models, and diagrams help students understand the processes and algorithms.!