September 24, 2019
For the past 5 or so weeks, I have been learning about disciplinary literacy. After reading article after article and having class discussion after class discussion about how wonderful disciplinary literacy is and all the amazing benefits of it for students, I was still a bit skeptical on how disciplinary literacy can be implemented or even be beneficial in a Mathematics class. If you have not read my previous blogs, here is my own definition of disciplinary literacy so the rest of this blog makes sense to you. Disciplinary literacy is using reading and writing in any content area (Mathematics, Social Studies, Science, etc.) to move the students’ thinking to a new level. Rather than the students simply learning the content, the students are using reading and writing to fully understand the content. In other words, the students are pushed to think like a mathematician, historian, scientist, etc. With that definition in mind, in regard to mathematics, I could not help but wonder how can reading and writing can be incorporated into math? Isn’t it as simple as just solving a problem correctly and then moving onto the next problem? If I got the right answer, is that not enough to prove I know the content? Through my own recent experiences as well as information presented in an article, I was proven wrong on this matter.
Before I dive into the article I read today regarding disciplinary literacy in mathematics, I would like to share a personal experience. As a future Middle-Level Education teacher, I am currently in classes all about how to teach mathematics in the middle-level grades. In these classes, we learn the concepts that the students will learn in mathematics and then we learn how to teach those concepts. This past week, my class was assigned our first homework assignment. This assignment was all about comparing fractions. This seems like a walk in the park right? Well, that’s what I thought at least. My first question asked me to determine which of these two fractions was the greatest: 5/6 and 7/8. Simple right? I could make a common denominator, I could convert them into decimals, or I could even cross-multiply to compare. Well, the very fine print of that problem said, “You can only use mathematical reasoning to answer. You may not use common denominator, decimals or cross-multiply.” Instead of using math, I had to think and write which fraction was greatest using only my logic. Therefore, I had to use disciplinary literacy to explain why the one fraction was greater than the other. This truly through me for a loop as every problem of that assignment had me explain why I got the answer that I got, and why the formula or tactic I used worked. A homework assignment that could have taken me 30 minutes using what I learned in 4th grade actually took me almost 4 hours to complete because I had to think like a mathematician to understand why the math I was doing to get the correct answer worked.
This homework assignment really opened my eyes up. Not only was I introduced to what disciplinary literacy can look like in a mathematics class, but it also made me realize that I really was not too sure as to why the math led me to get the right answer. All throughout my schooling in math, I was only taught how to solve math problems. Give me any two points on a line and I could plug and chug until I told you the slope of that line and the equation of that line. Yes, that’s great that I mastered this skill, but truthfully, I never knew the reasoning behind what I was doing, and I think that it is a big problem. I find it almost embarrassing that a senior in college had to truly had to stop and think why I am able to cross-multiply to show which fraction is the greatest. I do not think that fault is my own or even my various math teachers’ faults. Rather, I just think we, as teachers, need to shift the focus in math to guide students to understand the reasoning behind the math they are doing. Now, I understand the importance of disciplinary literacy in math, and I see how it can most definitely be beneficial. As a future educator, I do not want my students to fill the blanks in a formula to solve an equation. I want them to understand why that formula works. And, I think the best way to do this is to have the students write out a reasoning to the math they are doing to encourage them to think like a mathematician.
This leads me into the article, “A Literature Review on Disciplinary Literacy: How Do Secondary Teachers Apprentice Students into Mathematical Literacy” by Ann Marie Hillman. While this article tends to focus on the secondary grades, I think that the strategies that Hillman suggests for teachers to use to incorporate disciplinary literacy in math can also be used in the elementary and middle-level grades with a little bit of tweaking. At the end of the article, Hillman gives some implications on how disciplinary literacy can be implemented in math. Her first implication is to encourage teachers to “ask probing questions” as this “deepens students’ understanding” (Hillman, 2013, p. 403). The more difficult a question asked by the teacher is, the deeper the student has to think which leads the student to a stronger understanding. Hillman also puts a heavy emphasis on students verifying their answers to a problem. She says, “Another implication is that mathematical literacy lends structure to children’s reasoning, particularly in a way student verify their solution… Teachers can help students construct mathematical understanding by requiring them to share their reasoning and verification processes orally or in writing” (Hillman, 2013, p. 403). However, Hillman suggests that writing may be the better way to share reasoning and verification. She then gives several ways that students can write their reasoning which include: double-entry diaries (one side shows the math while the other side shows the written reasoning), diaries (students explain their reasoning to all problems in an organized way), and triple-entry diaries (the same as double-entry, however the third column is for students to write down another way a peer solved the problem different from their way) (Hillman, 2013, p.404). All of these strategies, and many more, incorporate disciplinary literacy into mathematics. These all encourage to students to understand the why behind the problem and turns every student into a little mathematician!
Reference:
Hillman, A. M. (2013). A literature review on disciplinary literacy: How do secondary teachers apprentice students into mathematical literacy? Journal of Adolescent & Adult Literacy, 57(5), 397-406.
Happiest Teacher on Earth 
Your post was really thought provoking for me. I love how this class applies to our other classes and gives us connections to make. I agree that the homework where we weren’t allowed to use our mathematical algorithms was difficult. I know how to get most of the answers in math, but my “reasoning” is probably going to be a function that I learned from pre-historic times and I have no idea why this exact algorithm works. It just does. I do also like the article you cited in your last paragraph. It seems like something our professors right now are having us do in a way when we are reflecting on a student’s work. We have to explain THEIR thinking, which makes us reflect on our own. The journaling is not something I have done for a math class before, though I think it is a great idea for someone in math who would like to incorporate more disciplinary literacy. So do you think when the students do their work on the whiteboard upfront and are asked to explain how they got what they got is disciplinary literacy? It isn’t reading and it isn’t writing, but it is speaking, which doesn’t fit in with your definition of disciplinary literacy.
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It is interesting that your homework assignment started with a question that you were not allowed to use traditional math techniques to solve. This is a cool idea because it makes students think in a nontraditional way, but it is still related to math and the topic of fractions. I would be interested in giving my future students an activity like this because it will stimulate their brains to find a solution to the problem in a new way. This would also be good for students who are less interested in the field of mathematics. Students who are more “right-brained” or interested in writing, theater, or art might enjoy this kind of activity more than a traditional worksheet because it allows them to think outside the box. The more a student is interested in the activity, the more they will engage, and the more they will understand about the topic.
With this, I like this idea for a lesson because it could open up the floor for discussion. You could send your students home with this assignment giving them the chance to work out the problems on their own. Then the next day you could have students get into small groups to discuss how they came to a solution for each of the problems. Group discussion is an amazing way to help students further their understanding of the topic because discussion forces the students to explain their thought process.
I had never thought about how I would implement group discussions or disciplinary literacy skills into a math classroom, but I really like this idea.
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One thing you brought up caught my attention. The example that you stated was that you had to write and explain the problem based on math background knowledge. I found this example to be a good set up to accompany the rest of your blog. The diaries and double entry columns seem like a good way for students to be able to see both sides and also see the connection between the explanation and the actual math problem. One point you brought up “Rather, I just think we, as teachers, need to shift the focus in math to guide students to understand the reasoning behind the math they are doing.” is a good way to think about how to apply this into the future. This mind set could help students get a deeper meaning to math and might help more students have better feelings about math in general. I also think that this allows for students to know why they are doing the math instead of thinking “why am I learning this if I’ll never learn it”. I think this mindset extinguishes their love of learning. While I agree that this can be helpful and is a good idea, how can we get struggling students in elementary school to be able to do this? I find that when I am in math, I have a hard time explaining a topic that I was not strong with to start. Although I do feel like this is due to how I was taught math when I was younger. How can we make sure that writing out math helps the students instead of further confusing the students? Overall, the points you brought up were strong and I feel that if you apply these new tools in disciplinary literacy it will help students dig deeper into math and have a better understanding.
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As being a future teacher myself, I have personally reflected on my own learning just as you did in this blog. I feel I saw the light bulb go off in your head as to why we are learning methods in class. The goal behind learning the reasoning is not only helpful for the students, but for you to be a successful teacher. In a sense, the way you communicated in this blog was disciplinary literacy as you are becoming an expert of a future teacher! However, to get back to what I was saying, by you learning the reasoning allows you to be a better teacher because you can further explain the problems to the students. In turn, you hope they absorb the explanation so they can become an expert of the math (or whatever subject) as well. Essentially, as we are learning all the methods and reasoning, we hope to be able to explain problems well so that the students can learn and absorb the information. I think you make a great suggestion where you state that students will, “write out a reasoning to the math they are doing to encourage them to think like a mathematician”. I think this is a fabulous idea to incorporate into your math classroom. This will really get the students to think why they are completing the math problems and where all the number came from. I think this is a great first step to include and I encourage/challenge you to continue to think of ideas of how to incorporate disciplinary literacy into a math classroom.
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You raise some extremely interesting points in this post. The experience you described having in math classes growing up is very similar to my own experience. We were never tasked to write out answers to open-ended questions on how to get a certain answer, we were simply asked to know the answer. Writing out and explaining how you were led to an answer even as simple as what is greater between two fractions, makes you truly think about what you’re doing and why. That is something that is lacking in math classrooms. Students are not able to explain how they solved a problem or what use the answer could be put towards. Math class treats students like robots and that is why we need to integrate these practices shown in the video and in your experience with your homework assignment in our classrooms.
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