The problem with story problems
For this week's blog post I picked the following article out of one of Rethinking Classrooms Magazine series titled “The Problem with Story Problems”. I have linked the entire article above if anyone would like to read. Immediately when I saw the title I was dragged in. As a math educator countless times I have asked where I can make an impact in students' lives as it relates to social injustices in the field of mathematics. I understood my role as a member of a school community but I always struggled with my role in math. This article helped me to find where I could integrate conversations about social injustices in my classroom. The answer is word problems. One of the beginning quotes in the article reads “...too often the assumptions inherent in story problems perpetuate consumerism, reinforce racist and sexist stereotypes, and maintain classism and unsustainable approaches to the Earth” (Bright, pg. 15). This led me to start thinking in what ways? What types of problems are these scenarios created? How can students become aware of the injustices being asked of them to solve?
So often word problems ask the question of buying or consuming items. The basic one we ask students in grade one goes along the lines of, “You have $20 to spend at the store which of the following things can you buy given these prices”. There would be a list of items and students would pick based on the money that they had. It seems harmless and something a student would think to do with birthday money or allowance money. Yet, it empowers the idea of consumerism and economic status. From a young age students are being pressed into the idea of always spending money to buy new and improved things. Save save save to spend spend spend. We are indirectly encouraging kids that they need to spend the money that they have. One of society's structures, that the more things you own the better off you are, the higher you rise on the totem pole. Not only does the problem encourage consumerism, but it also glosses over economic status. Student’s families may not have $20 to give their child to buy items at the store for leisure. The families of the students may need all of their earnings to pay the bills because they are just making ends meet. This would make the problem completely irrelevant for some students and not approachable in solving. Yet, those of us in power would think nothing of the word problem.
The example and scenario I have provided above is just one example that you see countless times in math textbooks. Consumerist driven questions where students are being asked to consider spending money on particular items. Many times the items are not needed items, but they are wants or leisure activities. Another example that came from the article reads, “An orange grower in California hires migrant workers to pick oranges during the season. He has 12 employees, and each can pick 400 oranges per hour. He has discovered that if he adds more workers, the production per worker decreases due to lack of supervision. When x new workers (above the 12) are hired, each worker picks 400 – 2x2 oranges per hour” (Bright, pg. 16). The second I read this problem my mouth gaped. I am unaware of the year in which this story problem came from and how relevant it is to textbooks currently. This problem explores how to undermine already oppressed workers by paying them low wages for their hard working efforts. It leads the reader to begin thinking that the owner's objective is to maximize profit at the expense of dehumanizing migrant workers. There is an additional snippet from the problem that poses the idea that migrant workers are untrustworthy. It is creating stereotypes that the reader will begin to own as truth when in reality it is completely inaccurate and faulty information. It goes back to Johnson’s privilege and power. The story problem is naming a stereotype that exists and is enabling students to perpetuate the idea back into society in other potentially more harmful ways.
I was nosy to see if the curriculum I use in my school had word problems that enabled social injustices. It did not take me long to find one example. I am sure that there are countless more and more than I would ever hope to find. The one I found reads, “Meredith is given a $50 monthly allowance to buy lunch at school. Any remaining money can be spent on entertainment. Meredith would like to have at least $12 left at the end of the month to go to the movies with her friends”. The problem continues on with how much a lunch costs and poses the idea of how few lunches can she buy in order to have enough money left over. This implies that students would know what it feels like to have an allowance of $50. I am not sure about anyone else but I sure know that I didn’t get a $50 monthly allowance, regardless of if it was for lunch. The problem is also encouraging the idea of malnourishing your body in order to go see a movie. Something isn’t right about that. We know that eating disorders is one of the leading causes of death in adolescents and this word problem is encouraging just that. All at the expense of being able to spend money on leisure activities enabling consumerism.
Having seen this problem and the misleading damage it may cause to adolescents makes me think about what next. What can I do to change this? Well I could just not use that problem, whip my hands clean and move on. Until I come to another problem and another and so on until now it becomes irrelevant to even use the curriculum. The article poses a better solution. We ask students to think critically and create a space for students to say “Wait, that’s not right” or “This problem reinforces (insert social injustice)”. In order for students to be able to name these ideas, it requires the educator to model first. There should be a lesson that talks about what our math word problems really convey to us. What is our role as the mathematicians to change these problems so that they are more equitable for us to use in the classroom. I think this is where we can give students a voice and allow them to speak on the wrong doings of those in power. They can name that what exists in their math word problem is not okay. As a result, we (educators) can instead empower our students to rewrite the problems to fit a more just world that we want to exist in. There is one final quote that I want to end with from the article that reads, “As mathematics educators, we’ve been encouraged to ignore many things. We’ve been taught that we are exempt from responsibility—that math is value-free” (Bright, pg. 19). Math is clearly not value free and instead the wrongful, persuading ideas of those in power can be shaped to better educate students mathematically and as better human beings.
Hi Noah,
ReplyDeleteI was wondering what direction this would go with math because I also didn't think that there were many problems with word problems, but clearly, I was wrong! It can be really difficult to notice this kind of bias in word problems, but it is super pervasive. Thanks for sharing!
Hi Noah! This article was super shocking to learn about. I wish I could remember any I had growing up that stuck out but I feel like problems included someone with a non anglo name. I wonder if that was in relation to the rest of the question and added a negative connotation or if I'm thinking too deep. Anyways, great insight!
ReplyDeleteNoah, I loved reading this blog and you unpacking the issues with how we position these "real world" scenarios in math problems. I am NOT a math teacher so I have no idea how this would actually work, but I used to spend a lot of time working with statistics and trends, and always thought about how much math I would use when the annual RI Kids Count Factbook (https://rikidscount.org/factbook/) would come out. Have you ever thought about using that with your students? I don't know the topics they're covering, but you could graph data, design algebraic equations around city/town funding, etc. Could be an interesting way to integrate social justice into the math class.
ReplyDeleteTom, thank you for this insight. I think it would be extremely powerful to integrate into the classroom. I think students would be driven to be working with relevant data from their own community!
DeleteHi Noah,
ReplyDeleteI really enjoyed your blog and the article. Wow! So much for teaching through relatable real life experiences. I don't remember my kids having word problems like these but perhaps they did (most likely my oldest) and I just didn't recognize the bias and social injustice the same way I do now. I hope not. I'd be interested as well as to know the timeline of the math problem about migrant workers. I tried researching a little and saw variations of this math problem used through 2010s which to me doesn't seem that long ago which makes me feel it is even more wrong! I did want to share this little story- Although I was never given a $50 monthly food allowance (I think I received free or at least reduced lunch), my husband was given a monthly lunch allowance when he was a child in the Azores. His mom would give him the money at the start of the month when she received her pay. His Dad was a drinker and although he worked, was not a very good provider so Mom carried the family financially. My husband would spend very little, rationing money for lunch, often going without. He knew his mom would run short on money before the month was over so he saved all that he could to give back to her. Sad story...but it shaped him to be the man he is today.
Hi Noah, as a fellow math teacher, and as someone who studied business and worked in business for years, this really stuck with me. I have always liked applied "Real-World" math and use this to teach, whether it's in my Algebra class or in my enrichment classes. It is interesting how much implicit bias there is in these word problems. $50 may not be much money to some of us, but to some students, especially for an allowance, that is not reasonable. Also, I like your example of the migrant workers with the implicit bias that they aren't trustworthy, with the goal to pay them as little as possible to get the most return from them. Profits above everything. I will try to be more careful with my examples, but as you pointed out, many of these are in our curriculums.
ReplyDeleteHi Noah, thanks for sharing. This really made me think~ I did not really how much bias is in word problems. It can be hard to recognize, but the bias is there. Your schools $50 allowance problem was a prime example of social injustices within word problems.
ReplyDeleteHey Noah, I really liked your reflections on story problems because I do think that the way that these have been traditionally taught has been unjust even though it may not be immediately noticeable. This makes me think about the way story problems are taught in my school. I work for a charter network who has fighting against racial inequity in their mission statement. With story problems, teachers intentionally rewrite them to make them relevant to scenarios the students would go through. This includes changing the students name in the problem to one in your class, and the objects that they are doing an operation to ones they actually would in real life. We always change the objects to Pokemon Cards or Kpop Demon Hunters stickers so that students can be more engaged and they can see themselves more in the story problem. I also think they with story problems, it is super important to have explicit vocabulary instruction associated with the problems, as MLLs may not be able to access the problems and show their math skills if they cannot access the language used in the problem. I just figured to share these in addition to consider when trying to be more equitable with teaching story problems.
ReplyDeleteHi Noah, thank you for your reflections. They really made me think about how there are biases in story problems and if we don't unpack these, then we are doing disservice to our students. This made me connect this to how we change and adapt story problems to make them culturally relevant for students as well as accessible.
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