Here is the problem from years ago:

Mrs. Mahoney went shopping for some canned goods which were on sale. She bought three times as many cans of tomatoes as cans of peaches. The number of cans of tuna was twice the number of cans of peaches. If Mrs. Mahoney purchased a total of 24 cans, how many of each did she buy?

David responds in the comments:

"My question would be, why would we want students to solve these problems? What would be the purpose?"

I find this an intriguing question.

The other day in my classroom the kids were doing problems from a problem solving workbook. Yes, I still cling to it but am phasing in more of Dan Meyer's kind of "conceptual problem solving". (I have written extensively, much of it based on his ideas, on this kind of problem solving, choose the tag "math" on this blog)

I have talked with my students a lot about the different levels of thinking in math and the importance of conceptualizing, relevance, real-life problems and computation in learning math. One of my best math students came up to me and complained about a problem in the book because it was irrelevant and had no real-life implications. Guess I reap what I sow. I looked again at the problem. Here it is:

"Four men were stranded on a desert island and collected some coconuts and then fell asleep. The first woke up hungry and ate 1/3 of the coconuts. The second woke up and had 1/3, the third woke and had 1/3 as well. The fourth woke and took his share. There were 6 coconuts left at the end. How many coconuts were left?"

My workbook is filled with these questions. How would you respond to this student? What came to mind and how I rationalized it to him was that really smart people like Einstein were famous for thought experiments like "what if we traveled faster than the speed of light", or "what if you were on a train moving 200 km/hr and a light was shined from a stationary source going in the opposite direction". These thought experiments have little relevance to many of us but they "are" useful to improve the reasoning power of our brains. They strengthen synapses which may benefit us in ways not apparent to us at the present time.

I added that by working on such problems in groups I was actually more interested in developing collaboration and communication skills than the answer to a somewhat irrelevant or unrealistic math problem.

As I tell my students, a reflective learner will have more questions than answers. Here are some of mine. It would be fun for you to help me with these!

How do you answer the tough questions about math in your class?

Do your kids ask them?

How do you teach math problem solving in your class?

Are traditional math problems an effective way to teach problem solving skills and strategies?

Do your kids show improvement in problem solving ability and/or computation skills because of traditional math problem solving?

Have you tried the kinds of techniques Dan Meyer writes about?

What kind of balance do you strike between computation/technique based math and conceptual real-life problem solving challenges?

Where do you get your ideas and activities for conceptual real-life, relevant math challenges?

What other methods do you use?

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