One Right Answer? One Right Way?
by Sarah Lonberg-Lew
Does every math question have a single right answer? Many people would say yes. In fact, that鈥檚 one thing that I鈥檝e heard people say that they love about math. There鈥檚 no ambiguity. It鈥檚 not a matter of opinion. The answer to 2 + 2 is 4 and that鈥檚 the end of the story. It鈥檚 clean and clear.
In my work, my colleagues and I promote a different view of math鈥攖hat it is a flexible, creative, and sometimes messy environment, and that in the real world, there 颈蝉苍鈥檛 always one right answer. Consider this situation: I can buy a bottle of 500 doses of ibuprofen for $16.99 or a bottle of 100 doses for $8.49. Textbook math says that I should buy the bigger bottle because I get more than twice the doses for about twice the cost, but my real world math might say that I can鈥檛 afford to spend $16.99 right now or that the pills in the bigger bottle would expire before I used them all. So, what is the right answer to the question of which bottle to buy? Should I still go for the 鈥渂etter deal鈥�? There 颈蝉苍鈥檛 a single right answer!
BUT (I hear you cry), what about on the test? On the test there is only one right answer, and it is important that students get it right! It鈥檚 true. On the test, and in many other places, there is only one right answer, and it is important to get it right. So, does that mean that math 颈蝉苍鈥檛 a flexible and creative subject? After all, if the answer to 2 + 2 is 4, it doesn鈥檛 matter how I feel about that. My feelings don鈥檛 change the answer.
But suppose I ask you how you know that 2 + 2 = 4?
Pause for a minute here and see if you can come up with an answer. Can you make a convincing argument that 2 + 2 = 4?
What happened in your brain? Did you hold up two fingers on each hand and then count to see that there were four all together? Did you picture starting at 2 on a number line and then taking two steps forward to land at 4? Or maybe you pictured starting at 0 and taking 2 steps and then 2 more steps. Maybe you thought about asking what number you could add to 2 to get to 4. Did you picture two groups of two objects? How were they arranged? Did you think of real objects or abstract representations? Did you actually take out concrete objects? Did you do something else that I haven鈥檛 thought of? Each of these pictures shows that 2 + 2 = 4, but they are not the same聽pictures, and they don鈥檛 reflect the same thinking.
When I say that math is flexible and creative, that doesn鈥檛 mean I think that you can decide that 2 + 2 = 5聽if that鈥檚 what makes you happy. I don鈥檛 deny that there are some situations where it is vital to get exactly the one right answer. (And there are also many where there really 颈蝉苍鈥檛 a single right answer.) But even when there is only one right answer, there 颈蝉苍鈥檛 a single right way to get to it, to reason about it, to visualize it, or to investigate it.
What is the value of being able to think about a math question in more than one way when we already know that there is a procedure in the textbook that works every time? Isn鈥檛 it simpler if everyone learns to do math the same way? The procedures in textbooks work, but they also reflect a particular way of thinking, a way of thinking that belongs to a long tradition that is firmly grounded in the dominant culture. Those procedures work, but insisting that they are the best or only way to solve problems excludes people who don鈥檛 think in that one specific way鈥攁nd when you consider all the ways there are to think, that is probably a lot of people. And it is more likely to be those people who don鈥檛 come from the same cultural tradition that the textbooks came from. When we insist on math being done a particular way, we can squash students鈥� intuition and connections to their cultural traditions. When we insist on math being done in one particular way, we remove avenues to success鈥攚e make it less likely that our students will find a way to the correct answer because our focus is on memorizing THE way instead of capitalizing on our students鈥� formidable mental resources.
Yes, it is true that there is only one right answer on the test. It is true that many mathematical questions have only one right answer (and many don鈥檛). But that is not the same as there being only one right way. Math is a flexible and creative subject, even when it comes to !
(For more on the connection between equitable teaching and pushing back against 鈥渙ne right way鈥� thinking, see this short video from Berkeley Everett.)
Sarah Lonberg-Lew has been teaching and tutoring math in one form or another since college. She has worked with students ranging in age from 7 to 70, but currently focuses on adult basic education and high school equivalency.
Sarah鈥檚 work with the聽听补迟听聽includes developing and facilitating trainings and assisting programs with curriculum development.聽She is the treasurer for the聽.