In this monthly column, we speak with a notable member of the mathematics education community about their work and their perspectives on the teaching and learning of mathematics. This month, we had the pleasure of speaking with Dan Meyer.
Dan Meyer taught high school math to students who didn’t like high school math. He has advocated for better math instruction on CNN, Good Morning America, Everyday With Rachel Ray, and TED.com. He earned his doctorate from Stanford University in math education and is the Chief Academic Officer at Desmos where he explores the future of math, technology, and learning. He has worked with teachers internationally and in all fifty United States. He was named one of Tech & Learning’s 30 Leaders of the Future. He lives in Oakland, CA.
First things first, thank you for taking some time out of your busy schedule for this conversation!
As Chief Academic Officer at Desmos, you spend a great deal of time considering the affordances of digital technology for the teaching and learning of mathematics, and designing tools that tap into these affordances.
The phrase ‘online learning tools’ evokes a diversity of conceptions and misconceptions; I wonder if you could address some of the latter. First, you have written that “the online medium is fundamentally connective and yet students often report feelings of social isolation” (Meyer, 2015a, p. iv). However, you have also argued that well-designed online tools can promote dialogue and collaboration, rather than isolation and individualization. How so?
[perfectpullquote align=”right” bordertop=”false” cite=”” link=”” color=”” class=”” size=””]”Whether we’re in the high-tech or low-tech space, if students are doing interesting, creative work, the teacher has the opportunity to turn it into a conversation.”[/perfectpullquote]For starters, whether we’re in the high-tech or low-tech space, if students are doing interesting, creative work, the teacher has the opportunity to gather it purposefully and turn it into a conversation. So we have to start by giving students more interesting online work to do than multiple choice and numerical response. That kind of work is useful for some purposes, but as far as dialogue and conversation goes, it’s bunch of wet twigs that won’t start a fire.Second, we have to realize that when students do something interesting digitally, they often try to share it. And that sharing stems from a natural interest in exhibiting something they’re proud of, but it’s also an interest in learning. In many cases, it’s an interest in learning what their peers think about a video or photo they’ve taken. Will it get lots of likes or shares or retweets? Will it make someone laugh?
We don’t exploit that interest in exhibition and learning with digital math tools. You create dull work and you share it with nobody but the machine. At Desmos, we seek to give students interesting work and put them in places to share it with each other.
Another fear related to online learning tools is that we are moving towards the obsolescence of teachers, who will be replaced by online programs that can provide instant feedback and the opportunity to move at your own pace (Khan Academy, for example, is viewed by some as an early glimpse into this future). What’s your position? In your view, what role does the (human) teacher play in the digital age?
At Desmos, we design our activities with the assumption that a knowledgeable teacher is in the room. We can’t realize our highest aspirations for student learning without teachers. We want to ask students questions that machines can’t easily grade (written responses and sketches of relationships, for example) and we want students to see connections and structure in the class’s thinking that machines don’t know how to generate. We need teachers looking at all the work students are doing on our dashboard and thinking about the kinds of questions they’ll ask about it. We envision productive human-computer partnerships of the sort we saw in the experiments of the late 1990s, where humans and computers working together in a chess match outperformed humans or computers on their own.
Related to your interest in supporting the teaching and learning of mathematics through digital technology is your interest in improving the teaching of mathematical modeling. You have written that you studied mathematics as a child and mathematics education as an adult because of powerful experiences you had of using mathematics as a model for the world around you, and would like students to have similar experiences (Meyer, 2015b). However, as you write, “modeling with mathematics […] [is] one of the practice standards most in need of explication. Five different teachers may have five different understandings of its meaning.” (2015b, p. 579).
What do you mean by mathematical modeling? How do your Three-Act Tasks, a framework which you introduced on your blog in 2011, engage students in the process of mathematical modeling?
[perfectpullquote align=”right” bordertop=”false” cite=”” link=”” color=”” class=”” size=””]”Students get very few modeling experiences, even from problems in textbooks that are labeled ‘modeling.'”[/perfectpullquote]Modeling is a constellation of verbs that include identifying essential information to a question, formulating a model that structures that information, using the model, interpreting what the model tells you, and validating your interpretation back in the world. It’s commonly seen as a cycle, where your validation underperforms your expectations so you circle back to your earlier assumptions and start again.Students get very few of those experiences, even from problems in textbooks that are labeled “modeling.”
The 3-Act Math project is not the final answer on mathematical modeling but it offers students some uncommon experiences. It uses digital media—photos and videos—to bring the world in from outside the classroom in ways that are more evocative than reading a text description on paper. A prismatic water tank filling up slowly—to take one example. It doesn’t explicitly state any given information, giving students the chance to think about what’s essential. And it also shows the answer to a question, allowing students to validate their modeling work more meaningfully than through an answer in the back of the book.
In Meyer (2015b), you argue that textbooks typically fall short of engaging students in mathematical modeling, despite their claims of doing so. Fortunately, you are not only interested in critiquing current resources—you have been working hard to improve them. You wrote in 2015: “I need a question to carry me through my thirties and I can’t think of a better one than, ‘What does the math textbook of the future look like?’” (Meyer, 2015c).
Beyond the missed opportunities to engage students in all of the processes of mathematical modeling, what are other critical shortcomings of many of today’s math textbooks? What is your (working) vision for how the “textbook of the future” will address these shortcomings and better support students’ learning of mathematics?
[perfectpullquote align=”right” bordertop=”false” cite=”” link=”” color=”” class=”” size=””]”The textbook of the future will need to offer students provocative encounters with mathematics that are impossible on paper.”[/perfectpullquote]The textbook of the future will need to offer students provocative encounters with mathematics that are impossible on paper. For example, on paper, we can present a scenario and ask students to sketch the relationship between two variables in the scenario. Say, the height of an airplane over time—rendering the world into math, basically. What’s impossible on paper and possible on computers is to then render math back into the world, to take the student’s sketch and show the airplane height based on that sketch. We need loads and loads of encounters with math just like that—provocative of mathematical thought, and impossible on paper.We also need to take advantage of the digital media’s capacity to connect people together. A digital textbook should display your thoughts to me and my thoughts to you. Digital media has mutability that paper doesn’t—so if you feel like my definition of a proportional relationship or yours has advantages over the textbook’s, you should be able to add it into your textbook permanently. If you feel like you could take a more interesting photo representing a rhombus than the one in the textbook, you should be able to add it.
This is the low-hanging fruit. I have no idea yet what’s higher up the tree until I clear what I can see first.
Lastly, I want to ask you about the affordances of digital tools for teacher learning.
You have often discussed the phenomena of blogging among mathematics teachers and the growing, self-driven community known as the Math Twitter Blog-o-Sphere (MTBoS), which connects thousands of mathematics teachers around the world who blog about their teaching practice and connect over Twitter under the hashtag #MTBoS. As Judy Larsen writes, “it is evident that they spend hours writing publicly about their daily practice, posting resources, and sharing their dilemmas with no compensation and no mandate” (2016, par. 6). To outsiders, this may be surprising: “If you had to go back in time and bet that one group of teacher bloggers would break out in these amazing spasms of collaboration, admit that math teachers wouldn’t have been your first or second guess” (Meyer, 2016).
In your view, why are mathematics teachers particularly interested in blogging and connecting online, and what draws you, personally, to blogging and the MTBoS community?
[perfectpullquote align=”right” bordertop=”false” cite=”” link=”” color=”” class=”” size=””]”The sky is blue. Water is wet. Math teachers own Twitter.”[/perfectpullquote]I have no idea why math teachers have emerged as the most productive community of educators online—an opinion I don’t think is controversial even among other kinds of educators. The sky is blue. Water is wet. Math teachers own Twitter. I’ve been a contributor for over ten years and I’m still confused. Happy about it, but confused.In those ten years, I’ve participated on Math Teacher Twitter for all kinds of different reasons. I needed resources. I needed community. I needed to process my thoughts in writing. I needed an audience in order to do my best writing. The consistent theme in my participation is the fact that my thoughts always seem perfect to me until they escape the vacuum seal of my brain. Once they’re out in the world, in a blog post or a tweet, that’s when I realize how much work they need. I can’t get that feeling any other way.
Interviewed by Ilona Vashchyshyn
References
Larsen, J. (2016). Negotiating meaning: A case of teachers discussing mathematical abstraction in the blogosphere. In Proceedings of the 38th Conference for Psychology of Mathematics Education – North American Chapter. Tucson, Arizona.
Meyer, D. (2015a). Functionary: Learning to communicate mathematically in online environments (Doctoral dissertation, Stanford University, California). Retrieved from https://searchworks.stanford.edu/view/11059115
Meyer, D. (2015b). Missing the promise of mathematical modeling. Mathematics Teacher, 108(8), 578-583.
Meyer, D. (2015c). What’s next for me: Desmos [Blog post]. Retrieved from http://blog.mrmeyer.com/2015/whats-next-for-me-desmos/
Meyer, D. (2016). How do you make a MTBOS? [Blog post]. Retrieved from http://blog.mrmeyer.com/2016/how-do-you-make-a-mtbos/