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Michelle Pacansky-Brock had my attention from the first paragraph of the introduction, where – in response to comments like, “Students today are so unmotivated,” “Students today don’t care about anything but their grades,” and “Students today feel entitled and aren’t willing to work hard” – she asks, “Are our students the problem? Or is it our [higher education’s] instructional model?” By shifting the responsibility to us, teachers and colleges, she wins an ally with me.
The foundation of her work is the idea of moving from “teaching to learning,” a phrase taken from a 1995 article by Barr and Tagg that, in part, means students learn more when they are active participants in their learning, rather than passive listeners to their professors. In addition, Pacansky-Brock leverages John Medina’s Brain Rules, focusing on three that she believes are “relevant for 21st-century college educators”: exercise boosts brain power; sensory integration; vision trumps other senses.
Not only, she argues, can technology help make learning more “brain-friendly” through strategies like those, it’s also the language that today’s college student speaks. Citing numerous statistics – like, 85% of 18-29 year olds in the U.S. have a smart phone – Pacansky-Brock supports the idea that “’online’ is a culture to young people. Yet to most colleges, it is a delivery method.” In sum, teaching with emerging technologies makes sense on a lot of levels and most colleges are behind the curve.
What follows is mostly practical advice for getting on the technology bus, based in experience and experiment. As a classroom teacher at both community college and state university levels, Pacansky-Brock been willing to try a lot of things. Readers benefit by learning from both her successes and failures.
Chapter one discusses the basics of preparing your students for a participatory classroom that uses significant technological tools. Because “students are trained to expect” a hierarchical classroom environment, “when an instructor embarks upon an instructional model that assumes a flattened relationship between student and instructor, like the flipped model, the must be communicated and discussed so it’s clear to students.” They need to understand why you are doing what you’re doing and how the pieces fit together to create the community of learners that you are trying to create.
This first chapter also includes issues like classroom philosophy, community ground rules, student privacy, copyright in the electronic world, and even a bit on the linking versus embedding in your online materials. Chapter two spends more time on participatory pedagogy and some basic tools you can use to foster it. In chapter three, she spends time on the “essentials” – smartphone, webcam, microphone, screencasting software, online content hosting, and more. Chapter four goes into more detail about tools for creating compelling visual content, from infographics to video conferencing to a “liquid” syllabus. Chapter five delves into the tools for participatory learning, including social media, online bulletin boards, online meetings, digital polling, and more on content curation. Through it all, Pacansky-Brock shares what she does, elaborates other options, and discusses the pros and cons of both. Her ideas, tips, and stories make what might seem like a list of apps into something like an annotated bibliography.
The book’s last full chapter is an extended argument for the potential of the internet to innovate and create new and better learning opportunities for students. Pacansky-Brock advocates against using your college’s Learning Management System (LMS) and describes her own evolution on this topic:
When I started teaching online in an LMS, I was disappointed in the quality of the learning environment I had developed for my students and felt constrained by the features available to me. By experimenting with new tools, I discovered different ways of engaging my students and opportunities for being present in their learning. But I still felt the need to use an LMS, largely because of concerns about violating the license for the images included in the textbook I was using, as well as my (former) institution’s expectation for faculty to teach with institutionally supported technologies. I imagine many instructors can relate to that experience.
I certainly can. But there is more. The extensive use of the LMS in higher education, she writes, “may be contributing to a gap between the skills college graduates need and the skills they have.” The LMS provides privacy, control, and less distraction, but it cannot keep up with the speed and scale of innovation on the open internet. Using an LMS also prevents students from developing a professional web presence. In fact, content developed by students during the course disappears when the course is over – essentially, their work inside the LMS is disposable. Working in the open internet can motivate students to produce higher quality work, because after all, “the internet is forever.”
Pacansky-Brock does not think the internet is a panacea for educating students. She sees the advantages and disadvantages of learning through the internet and believes that technology can be used to make learning more human and more participatory. She is thoughtful and thought-provoking – as a teacher, I was constantly taking notes for my own classes, sparked by ideas and stories in the book. I will be referring to it frequently as I continue to refine my teaching practice.
You can find out more at: http://teachingwithemergingtech.com/
Before the 13th century AD, math was done in sentences, sometimes called “rhetorical math.” The symbols we currently associate with math began to emerge in the Arab world during the 13th, 14th, and 15th centuries. By the 16th century, French thinkers were developing a fully symbolic system.
The advent of symbolic algebra changed the way we think about, learn, and do math. It also changed the kinds of problems that were doable by the lay mathematician with a basic education. Electronic calculators made arithmetic with large numbers more accessible, but didn’t fundamentally shift the way we think about math or learn it. (There is still plenty of debate in math education circles about the appropriate use of calculators in the curriculum.)
Today, computer technology is slowly altering math and math education, but especially in math education that potential is only beginning to be realized. Much of what we do with computers in math education mimics books, except in more color and with occasional hyperlinks. While there are folks taking advantage of multimedia presentation (think video, interactive sliders, etc. – for instance, the folks at Desmos are doing some great work), I have yet to see computers fundamentally and broadly change the way we teach math in the way that symbolic manipulation on paper did.
One option is to let the internet provide the kind of instructions that we’re used to seeing from teachers. Sites such as Khan Academy and publishers like XYZ Textbooks provide videos with multiple examples worked out slowly and carefully. Students can watch them on their own time, as many times as they want, stopping and starting and rewinding as they need. In class, teachers can clear up misconceptions and extend ideas already developed at home.
This “flipped classroom” model, however, assumes students can access the internet at home, an assumption that is often wrong and disadvantages those with the least (Is Digital Equity the Civil Rights Issue of the Day?). Add to that the fact that desk tops are giving way to small screens and it’s clear we must make sure we are making mobile-native, or at least mobile-friendly, education sites and activities. Even then, folks living in or on the edge of poverty often lose their access.
With this as context, consider Keith Devlin’s Mathematics Education for a New Era. In it, Devlin pulls together a career as a math educator and a love of video games to suggest a way for math and math education to evolve for the 21st century and beyond.
Devlin starts by discussing what he calls eleven principles of an ideal learning environment – like “the learning environment should be as similar as possible to the environment in which people will use what they learn” and “there should be sufficient ‘cost’ to getting something wrong to motivate correction, but not so great that it leads to the student losing heart and giving up” – ideas I think most people would agree with. With that basis, he tries to show how video games fit the principles very closely, even to the point of calling the next chapter “Euclid Would Have Taught Math This Way.” Part of this argument involves discussing the 36 principles of education that go into video games according to James Paul Gee (professor of education at Arizona State University) in his book, What Video Games Have to Teach Us About Learning and Literacy. Devlin goes on to discuss various aspects of math education and finishes by advocating for a math pedagogy that is part “flipped” and all carefully thought out to create optimal learning for each individual student, taking advantage of whatever methods are best for what’s being taught.
I find Devlin’s ideas compelling. Use computers and computer games to do the things they are good at: repetition and drilling (when appropriate); motivation and story. Continue to respect the relationships between teachers and students in a thoughtful system that supports students in the ways that they most need it. He is not arguing that that video games should be the sole way to teach math, or even that it is the best way. Instead, he believes that well-designed math education video games could be a powerful addition to school, home, textbooks, and the rest of the math educational apparatus.
He also makes some useful observations and distinctions for math teachers (like myself):
- The phrase “’do math’ is all too frequently taken to mean mindless manipulating symbols, without the full engagement that comes with genuine mathematical thinking.” In fact, Devlin points out, “skills are much more easily acquired when encountered as a part of mathematical thinking.” But he reminds us, “mathematical thinking is not something the human mind finds natural.”
- Anyone trying to teach math should design situations for students that promote mathematical thinking and expect to need to help them, while always remembering that “attempts to understand what it all means at too early a stage can slow the learning process.” In fact, “full conceptual understanding, while desirable, is not strictly necessary in order to be able to apply mathematics successfully.” Often what is needed in the short term is “functional understanding”:
Calculus is in many ways a cognitive technology – a tool you use without knowing much, if anything, about how it works. For example, few people know how an automobile engine or a computer works, but that does not prevent those people from becoming skillful drivers or computer users. Successful use of a technology does generally does not require an understanding of how or why it works.
I realize all of this is a pretty big pill to swallow for many of us, especially those, like me, raised on endless worksheets of drill, without motivation except a task master with a real or metaphorical ruler ready to slap the idle hand. But computers are changing many aspects of our life, for better or worse, and I don’t think that’s going to stop. Instead let’s figure out how to use them well, for the good of the generations to come. I think that’s what Devlin is trying to do. If it’s not the “right” answer, then it’s a pretty good try.
I’ll leave you with a long quote from the book’s opening chapter that I think captures some of Devlin’s vision and passion:
When people made the first attempts to fly, the most successful machines for transport were wheeled vehicles, and the only know examples of flying creatures were birds and insects, both of which fly by flapping wings. . . but that doesn’t work for humans. The key to human flight was to separate flying from flapping wings, and to achieve flight by another means more suited to machines built from wood or metal. . . .
Putting symbolic expressions in a math ed game environment is to confuse mathematical thinking with its static, symbolic representation on a sheet of paper, just as the early aviators confused flying with the one particular representation of flying which they had observed. To build truly successful math ed video games we have to separate the activity – a form of thinking – from its familiar representation in terms of symbolic expressions.
Mathematical symbols were introduced to do mathematics first in the sand, then on parchment and slate, and still later on paper and blackboards. Video games provide an entirely different representational medium. As a dynamic medium, video games are far better suited in many ways to representing and doing middle-school mathematics than are symbolic expressions on a page. We need to get beyond thinking of video games as an environment that delivers traditional pedagogy – a new canvas on which to pour symbols – and see them as an entirely new medium to represent mathematics.
I am currently on sabbatical till January, 2018. During my sabbatical my primary work-related responsibility is to complete a research project.
In my research project I’m trying to pull together three areas that I have worked in over the course of my career as a community college math teacher: math education, multicultural education, and online education. My initial research has found that, while there is literature in the overlap of pairs of these (math and multicultural, math and online, multicultural and online), there is little where the three areas intersect.
If further research confirms that little or no work has been done in these area, then this niche needs to be filled. The importance of better math education is well-documented. As our college student population increasingly diversifies, the need for the still majority-white teaching profession to understand how to better communicate with students of all backgrounds is more crucial than ever. And, though I don’t think technology is the answer to all educational problems, we would be foolish to think that online education is going away; on the contrary, the private-sector is pushing that way, legislatures have visions of the savings it can produce, and students are demanding the flexibility of learning on their own time and from where ever they happen to be.
I’d love to collaborate with others on what I think is a critical confluence of research and practice. If you’d like to work together, or if you know of work in the intersection of math education, multicultural education, and online education, I’d like to here from you. Please comment here or contact me at: email@example.com.
For every 100 Chicana/o children who enter elementary school in the United States, only 26 enroll in college and only 7 of those graduate—this according to U.S. census data, which also shows that some other groups go to college and graduate at significantly higher rates. On Friday, September 21, Dr. Tara Yosso spoke about this issue at the City College of San Francisco, and about what the college might do to improve the success of all its students.
Growing up in San Jose, CA, Yosso saw first hand the difference educational opportunity and access can make when her parents moved into a different neighborhood so she could attend a “good” school; many of her friends attended other, “not-so-good” schools. The differences were obvious: she was preparing for college, while her friends were on the vocational track—college was not an option; she was taking honors and advanced placement classes; her friends were in special education.
Her work today is inspired by the inequities and injustices she saw there, but its theoretical foundation is Critical Race Theory, which, according to Yosso, has four major tenets:
• Centrality, permanence, and pervasiveness of race and racism in the U.S.
• Challenge to dominant ideology, which centers on and generalizes the experience of white males.
• Commitment to social justice.
• Emphasis on experiential knowledge.
Using this theory, Yosso discussed “majoriatarian” stories versus “counterstories.” Majoritarian stories “recount the experiences and perspectives of those with racial and social privilege” (e.g. “All students enjoy access to same educational opportunities and conditions from elementary through postsecondary school.”). Counterstories “recount the experiences and perspectives of racially and socially marginalized people” (e.g. “Chicanas/os experience severely inadequate schooling conditions and restricted academic enrichment opportunities.”).
Race often informs majoritarian stories, which make “Whiteness, academic English, and middle class ‘values’” the standard by which all are measured. This leads to “cultural deficit thinking.” In the context of the work that Yosso does with the Chicana/o community, cultural deficit thinking
asserts that Chicana/o students lack appropriate cultural and linguistic attributes necessary for school success, blames Chicana/o parents for socializing children with inadequate skills and knowledge, and assumes Chicana/o families do not prioritize (value) school and do not instill high aspirations in their children.
But because a student doesn’t speak academic English does not mean she doesn’t have language skills; in fact, she may be bilingual and may be translating for her parents or grandparents every day. Because parents don’t come to PTA meetings, does not mean those parents devalue education; on the contrary, parents are often working a second job—which prevents participation at school events—so that their children are fed and housed. Such parents frequently exhort their children to excel in school so that they do not have to work as hard as their parents.
Yosso calls cultural deficit thinking “the most profound and persistent form of racism in schools” today. To combat this pervasive ideology, she calls attention to the “array of knowledge, skills, abilities and networks possessed and utilized by Communities of Color to survive and resist racism and other forms of oppression.” Calling this array “community cultural wealth,” she breaks it down into “aspirational capital, familial capital, social capital, linguistic capital, navigational capital, and resistant capital.” Yosso asks two important questions:
• How can community colleges cultivate the aspirational and navigational capital of Chicana/o students?
• What does it mean for colleges to foster a positive campus racial climate?
Yosso believes that by acknowledging the cultural wealth of our students and by creating space for that wealth in our classrooms and offices we can make a difference. Community colleges can play a crucial role in increasing the success of all students in the educational pipeline.
Yosso is Associate Professor of Chicana and Chicano Studies at the University of California, Santa Barbara. Her book, Critical Race Counterstories Along the Chicana/Chicano Educational Pipeline (Routledge 2006), analyzes Chicana/o experiences navigating through structures, practices, and discourses of racism from elementary through graduate school. Yosso’s current research projects address racial and gender microaggressions, community cultural wealth, campus racial climate, and entertainment media portrayals of Latina/o students.
The chart below is taken from Yosso’s book. Statistical sources are the U.S. Census and the National Center for Education Statistics.