“Is that the right answer?”
Students ask me this question often when we first start working together. They are programmed to think that the goal of doing math is getting the correct answer. After working with me for a while they learn that the process of solving a math problem is just as important - maybe even more important - than getting the answer.
Don’t get me wrong. I certainly want students to add, subtract, multiply, and divide accurately. These are important skills but more importantly students need to know which operation to use and why.
Well constructed word problems are a way for students to apply math skills and concepts in real life situations. They are often a challenge for students because first and foremost word problems are reading questions.
If students struggle with reading, they will have difficulty with word problems. We see this when they pluck numbers out of the word problem and just “do something” with them.
That’s where numberless problems come into the picture. A numberless word problem is exactly what it sounds like - all of the numbers have been removed from the word problem. When students first read a numberless problem their first reaction is to tell me they can’t answer the problem.
I tell them that they can’t get a numerical answer but they can come up with a strategy for answering the problem.
To do this they have to read the problem slowly and maybe more than once or sentence by sentence, think about the situation and the actions taking place, determine what information has been given and what they still need to know, and understand what unknown they are being asked to find. They have to figure out a strategy and the steps needed to find the unknown.
Sometimes, I’ll reveal the numbers and have the students complete the problem using the strategy. It’s a way for them to test if they chose the correct strategy.
Other times, I’ll put the numbers back into the problem and ask them to show me the process for answering the question but not have them actually do any computation.
Still other times I won’t provide any numbers and we’ll wrap up right after writing out the steps.
This approach to word problems is new to many students and is uncomfortable at first. It takes perseverance and the acceptance that they may have to try a few different ways to arrive at a strategy that will result in the unknown. In other words, students will experience productive struggle.
Watching and learning how students approach word problems gives me so much more information than looking at whether the numerical answer is correct. What do they do when they are stuck? Do they make sure they have answered the question? Is there another step to the problem? Can they explain why they chose one strategy over another? Do they check if the answer makes sense? Ultimately, my goal is for students to learn how to learn and how to help themselves.
Check out this post for more information about how I approach my role as a tutor.
By focusing on the process and not the end product, it shows students that math is more than being “doers of math”. I want them to strive to be “thinkers of math”.
So that’s the reason I don’t always have students “finish” word problems. Let me know in the comments what you think about numberless word problems and how you use them.