Dietiker, L. (2015). What mathematics education can learn from art: The assumptions, values, and vision of mathematics education. Journal of Education, 195(1), 1–10. https://doi.org/10.1177/002205741519500102
Dietiker draws on Einser’s (2002) idea of applying an artful lens to some educational challenges to develop art-based learning in math education. Dietiker focuses on connecting the mathematics learning with storytelling by creating a sequence of tasks in story form from a Grade 7 math textbook. This approach transfers the abstract math concepts into “verbal art” so readers/students can be inspired through the interpretation of the stories. “Math stories” start from:
1) The beginning (introduction of the story and discussion of what happened)
2) Problem-solving (try the games and activities with classmates or teachers)
3) Make a decision (analyze the information and use critical thinking)
4) A resolution (predict or get the results)
STOP 1: “Stories integrate both logic (e.g., Does the story make sense?) and aesthetic (e.g., Does the story move me to continue reading?). While each of the other art forms offer elements of value that draw attention to particular aspects of mathematics, a narrative perspective also combines the temporality (i.e., how a story unfolds) and the message (i.c., the moral of the story) of curriculum. Stories conjure fictional worlds for which truth is self-contained, much like mathematics.”
Many people assume math is the opposite of the arts/literature. I guess one of the reasons is that in our education system, we tend to separate STEM from the arts (like how university degrees are designed). However, Dietiker argues that stories contain both logic and aesthetic parts, and the logic part has the same nature as doing math. I totally agree with this since all the fictional stories designed by the author must have a reasonable plot in order to make sense to readers. This is similar to doing math, where each step must flow reasonably.
STOP 2: “The meaning and effect of sequential temporal experiences have been theorized and rigorously studied in terms of novels and short stories alike but have so far been ignored in regard to mathematics instruction. Although it may be unorthodox to consider mathematical objects and activity in these novel ways, conceptualizing the unfolding of mathematical content in a textbook as a mathematical story allows new questions to emerge.”
When I read the idea of connecting math to stories, I immediately recall the novel “Mr. Tompkins in Wonderland”. If you are familiar with physics education, this is a great book that teaches physics concepts through stories --- a physics version of “Alice’s Adventures in Wonderland”. Mr. Tompkins, the protagonist, entered a strange world where all the physics laws are visible and exaggerated. I have to say I had a lot of fun reading this book when I was a child, and this is definitely something that encouraged me to go into the physics field (plus I’m a big fan of sci-fi novels and movies in general). From my own experiences, I can tell the power of storytelling. Stories in math are something people always ignored, as Dietiker said, but they may have great potential to benefit students’ learning.
Questions:
1. Is reading skill essential in doing math? If so, what can we do as math teachers to help students improve their reading skills (especially for English-learning students)?
2. Why do students always find word problems hard to understand? Will “math stories” help students better understand the concepts?
Activity:
For this week’s activity, I want to try something similar to option b) Ali and Colin’s activity.
One of the examples I have is to try the base of 4 and do a growing base in tiles activity. I will create 3 tiles: large, medium and small, as shown in the picture.
Then, students can try a drawing task. For example, represent 27 in base 4.
Exponent calculation and factoring are big parts of Math 10, and I have found that many students have difficulty understanding those two topics. This is just an initial idea of connecting the concepts with drawings. I’m thinking about whether I can develop from the tile drawing to create a factoring activity for students to do.
I do not know why word problems are such a difficulty for students. Reading comprehension is certainly part of it, and the challenge is increased for language learners. Another part of the difficulty is needing to determine the solution path. I have noticed that my students do very well when they know which procedure to apply to solve the problem. This is because many of them have memorized procedures.
ReplyDeleteWhen working with word problems, the solution path is often less clear. Or there may be multiple valid paths. This, coupled with student anxiety of "getting it wrong" causes a big road block for many where they are not even sure how to begin.
To answer your other question, I am going to push against it a bit and say that it may not be my responsibility as a secondary math teacher to improve reading skills. Now, I certainly model strategies and how to find the important information and convert this to "let" statements and diagrams and equations. I am generous with my language learners in provided help with understanding questions (especially during assessments) in order to lower this barrier.
One idea is to decouple the reading and instead of a written paragraph present the word problem (or scenario or story) orally. Then allow students to work in groups as they work out what the information provided means. Sometimes I will intentionally leave out an important part (like an ill-structured problem) to force them to work this out also. It is the same thing, but somehow less intimidating than a problem written on the page.
Your post reminded me of a Grade 7 lit/num block I taught a few years ago. As our culminating project, we read Math Curse by Jon Scieszka, and then in small groups students created their own “math curse”-style stories. Each group designed a character(s) who moved through their day, and each page had to include a math problem connected to that part of the story. One problem per chapter of our math text. They illustrated the characters and turned them into children’s books. They were definitely engaged, but more than that, it helped them see that word problems are actually how we encounter math in the world. Math doesn’t usually show up as a naked equation, it shows up embedded in situations. It also reminded me that we need to be better about making those situations realistic. As we’ve talked about before in our cohort, no one is out there buying 76 watermelons.
ReplyDeleteAs for why students find word problems hard. I think part of it is that we often treat them as decoding exercises instead of stories. Students scan for numbers and keywords rather than trying to understand the situation. I’ve really noticed this shift when I use numberless word problems. (https://numberlesswp.com/) We read the scenario first with no numbers at all and just talk about what’s happening. Who’s involved? What’s the problem? What information might matter? Only after we’ve made sense of the context do we slowly add the numbers back in. It forces students to focus on meaning before computation.
I wonder if “math stories” work in a similar way. They invite students to care about what’s happening rather than hunt for the numbers. If they’re invested in the character or the situation, maybe they’re more likely to make sense of it instead of just looking for a formula.
A numberless word problem is such a great idea! I have used one before and it really threw my students for a loop!! My students are very good at memorizing procedures, but often do not know what to do when they cannot instantly recognize and execute the needed procedure.
DeleteI appreciated your focus on narrative as structure rather than decoration. The idea that stories hold both logic and aesthetic tension feels like such an important reframing. We so often treat story as a hook, something to “engage” students before the real math begins, but I’m drawn to the idea of using story as the structure itself. When an idea unfolds over time within a narrative, it shapes and deepens understanding, much like the arc of a novel.
ReplyDeleteI haven’t read Mr. Tompkins in Wonderland it myself, but I’m now seriously considering sharing it with my new physics teacher because it seems like such a powerful example of how story can make abstract ideas feel internally coherent. I’m curious, would you recommend a particular edition? I noticed there are a few versions available, and I’d love to know which one you think would be the best entry point.
You raised such an important question about reading in mathematics. I agree that mathematical reading is its own literacy. It’s not just about vocabulary; it’s about tracking relationships, conditions, and constraints across sentences. For English learners especially, slowing down the sequencing , maybe even storyboarding a problem before solving it, could make the structure visible. That feels like a way to bridge narrative comprehension and mathematical reasoning rather than treating them as separate domains.
I also really like your base-4 tile idea. Representing 27 in base 4 through growing units makes exponents visible instead of procedural. There’s something powerful about seeing 16s, 4s, and 1s as nested structures.
Your post really made me think about how we choreograph mathematical over time, not just what tasks we choose, but how they unfold.
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DeleteHi Tracy, I'm glad you are interested in Mr. Tompkins stories. The original one was published in the 1940s, and the most up-to-date is called "The New World of Mr. Tompkins" (published in 1999) with modern physics analysis. I would recommend the up-to-date one since it covers some modern physics theories as an extension of the original work.
DeleteInteresting to think about mathematical stories, and then word problems. Are they the same thing, or closely related? As stories go, word problems are pretty poor-quality stories: no character development, no plot, no suspense, not much in the way of setting or action... ! I actually wrote my PhD thesis on word problems (published as a book called A Man Left Albuquerque Heading East), and there is a lot to consider with these odd little stories!
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