Our immediate past gives us insight into where AI is going with children's mental abilities. I am thinking about is calculators.
Calculators came into their own in the 1970s. So by the early 1980s, I used a financial calculator in the MBA program where probability calculations are a part of marketing strategies. I remember what a labour-saving tool it was.
Calculators became ubiquitous in the 1990s in classrooms. There was doubt that students could maintain a high level of skill while relying on calculators to do basic arithmetic. That controversy still exists. Articles say progress has not been made in integrating calculators with mental arithmetic. Studies show that heavy reliance on calculators leads to declines in student mathematical skills.
So I went searching for more and found a edutopia article on using calculators to deepen students' engagement with math HERE. I found it engaging for me, too.
"PERCENTAGE
In this lesson, I always begin by telling students that I’m going to give them several percentage problems as well as the answers. The first thing students wonder is why I would give them the answers. Aren’t they supposed to figure those out?
Not in this case, I tell them: The goal is not to get the answer, but to figure out how the answer was gotten. The first problem we tackle is pretty simple: What is 50% of 24? The students can usually shout out “12!” before I finish writing the problem on the board.
“Excellent!” I respond. “Now, how could you figure that out on a calculator?”
At that moment, students grab a basic four-function calculator. I walk around and have students show me their methods, and I tell them that dividing 24 by 2 is not what I wanted.
“But 50% is half,” they protest. “So you divide by 2.”
“Certainly,” I say. “But we’re not always going to have something as nice as 50%, so we have to find a different way.”
Exasperated, my students try to figure out what I want. After letting them engage in productive struggle, I guide them toward the idea that we can use the numbers 50 and 24 to reach 12. Soon, they’re getting ideas like multiplying the numbers, resulting in 1,200.
“That’s kind of like 12,” someone will say. “But I have to get rid of these zeroes.”
My students start figuring out that to reach the answer, we can multiply the percent by the whole number and then divide by 100. Some students even propose that you just turn one of the numbers into a decimal before multiplying (50 times 0.24 or 0.50 times 24). Others say that you put a decimal point into both numbers, but only one digit in each (5.0 times 2.4). Some suggest using the % button on the calculator, which would also turn their number on the screen into a decimal. I then have students provide conjectures about why all of these strategies work and what they have in common.
Soon, my students are engaging in a mathematical discussion about relationships between decimals and percents, how the number 100 is inherent to all of the calculations, and how 50%, 0.50, and ½ are all the same thing.
I continue the lesson with more complicated problems. Trying to solve something like 17.35% of 8.4 using paper and pencil is overwhelming—but with calculators, my students approach even seemingly scary problems like this with confidence, armed with the knowledge that the relationships remain constant regardless of the complexity of the numbers. Using ideas like percent-decimal equivalence—as well as efficient algorithms like “% × n ÷ 100”—my students develop, with the help of calculators, conceptual understanding and procedural fluency."
Isn't this a masterful sculpture on the landscape. This is at the Week 1 winning Trillium garden in Grimsby.
