{"id":3087,"date":"2024-03-15T06:47:00","date_gmt":"2024-03-15T06:47:00","guid":{"rendered":"https:\/\/www.terc.edu\/adultnumeracycenter\/?p=3087"},"modified":"2024-03-05T18:49:24","modified_gmt":"2024-03-05T18:49:24","slug":"one-right-answer-one-right-way","status":"publish","type":"post","link":"https:\/\/www.terc.edu\/adultnumeracycenter\/one-right-answer-one-right-way\/","title":{"rendered":"One Right Answer? One Right Way?"},"content":{"rendered":"\n

by Sarah Lonberg-Lew<\/p>\n\n\n\n

Does every math question have a single right answer? Many people would say yes. In fact, that\u2019s one thing that I\u2019ve heard people say that they love about math. There\u2019s no ambiguity. It\u2019s not a matter of opinion. The answer to 2 + 2 is 4 and that\u2019s the end of the story. It\u2019s clean and clear.<\/p>\n\n\n\n

\"ibuprofen<\/figure>
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In my work, my colleagues and I promote a different view of math\u2014that it is a flexible, creative, and sometimes messy environment, and that in the real world, there isn\u2019t 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\u2019t 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 \u201cbetter deal\u201d? There isn\u2019t a single right answer!<\/p>\n<\/div><\/div>\n\n\n\n

BUT<\/u> (I hear you cry), what about on the test<\/em>? On the test there is only one right answer, and it is important that students get it right! It\u2019s true. On the test, and in many other places, there is only one right answer, and it is<\/em> important to get it right. So, does that mean that math isn\u2019t <\/em>a flexible and creative subject? After all, if the answer to 2 + 2 is 4, it doesn\u2019t matter how I feel <\/em>about that. My feelings don\u2019t change the answer.<\/p>\n\n\n\n

But suppose I ask you how you know<\/strong><\/em> that 2 + 2 = 4?<\/p>\n\n\n\n

\"pause<\/figure>
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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?<\/p>\n<\/div><\/div>\n\n\n\n

What happened in your <\/em>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\u2019t thought of? Each of these pictures shows that 2 + 2 = 4, but they are not the same\u00a0pictures, and they don\u2019t reflect the same thinking.<\/p>\n\n\n\n

\"representations<\/figure>\n\n\n\n

When I say that math is flexible and creative, that doesn\u2019t mean I think that you can decide that 2 + 2 = 5\u00a0if that\u2019s what makes you happy. I don\u2019t 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 isn\u2019t a single right answer.) But even when there is<\/em> only one right answer, there isn\u2019t<\/em> a single right way to get to it, to reason about it, to visualize it, or to investigate it.<\/p>\n\n\n\n

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\u2019t 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\u2019t think in that one specific way\u2014and 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\u2019t 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\u2019 intuition and connections to their cultural traditions. When we insist on math being done in one particular way, we remove avenues to success\u2014we make it less likely that our students will find a <\/em>way to the correct answer because our focus is on memorizing THE way instead of capitalizing on our students\u2019 formidable mental resources.<\/p>\n\n\n\n

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\u2019t<\/a>). But that is not the same as there being only one right way. Math is<\/em> a flexible and creative subject, even when it comes to getting the right answers on a test<\/a>!<\/p>\n\n\n\n

(For more on the connection between equitable teaching and pushing back against \u201cone right way\u201d thinking, see this short video from Berkeley Everett.)<\/p>\n\n\n\n

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