Question: If you didn’t know the procedure for addition or multiplication, and lacked numeracy skills, could you catch the errors in the calculations shown here?

This is what happens when you teach computations instead of reasoning. Anyone who looks at 14 x 5 and gets 25 does not have basic numeracy and estimation skills developed, and quite possibly has never used real objects to do multiplication before. The error is not primarily in the calculations that they are doing but in the system that leads them to trust their calculations more than their common sense and intuition about the problem they are working on. This kind of error happens independently of the tool used. If you don’t believe me that students can make similar computational mistakes using a calculator, ask math teachers how often they see 4/8 = 2 and other similar mistakes.

A mathematics curriculum based on the ability to do computations and not solve problems is flawed in my mind. We should focus on mathematics as a tool, rather than mathematics as a goal.

I agree completely with your last sentence, David, “A mathematics curriculum based on the ability to do computations and not solve problems is flawed in my mind. We should focus on mathematics as a tool, rather than mathematics as a goal.” Unfortunately, we alienate 80% of students who get trapped in the mechanics of mathematics, rather than the higher level problem solving skills needed in life. While students should develop number sense through a discovery process, once the concept is grasped, it can easily be replaced with technology such as calculators, spreadsheets, etc. Not doing so limits innovative thinking in students by making them perform boring computations replete with the potential for minor errors that make them feel inadequate mathematically. If we let go of this antiquated view of mathematical proficiency, we could unleash so much potential for good upon the world.

Yeah, in my mind, I’m really okay with students using a calculator to do computations, but they need to understand how the computations work and how to judge the size of their answers quickly, so they can easily spot mistakes they’ve made, just in entering the numbers into their computational tool.

An algorithm, like the ones shown in the video, is just a computational tool, just as a calculator is a computational tool. Neither enhances understanding of the problem, which in this video is to determine how to fairly split the money.

Bravo! LOGIC should be the main focus of mathematical education, not computation! Students need to know how to ask good questions, and check the reasonableness of answers!