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# Category Archives: education

## the new jim crow: mass incarceration in the age of colorblindness

In *The New Jim Crow*, Michelle Alexander traces the history of racialized control in the US – from slavery, to Jim Crow, to mass incarceration – pointing out the similarities and differences, particularly between the Jim Crow of the early and mid-20^{th} century and the mass incarceration of African-American and Latino men in the present day.

Jim Crow – which had replaced slavery as the method of reinforcing white supremacy in the US – was a system of laws and practices that made black people into second class citizens unable to vote, to serve on juries, to live in white neighborhoods, to go to school with white children, to use the same bathrooms as white people, or to participate in white society in a myriad of other ways. When it began to crumble in the face of the civil rights movement in the 1950s and 1960s, there was a period of relative hope for racial equality for African-Americans that included more decent-paying jobs, educational opportunities, and more.

The time of promise was short-lived. Alexander argues that the War on Drugs is the mechanism that was and is used to replace Jim Crow by imprisoning of huge numbers of men of color and reinforcing what she calls the “caste system” in the United States. The War on Drugs was initiated by President Reagan in 1982 despite the fact that at the time “less than 2 percent of the American public viewed drugs as the most important issue facing the nation.” Money for drug enforcement skyrocketed. “Department of Defense antidrug allocations increased from $33 million in 1981 to $1,042 million in 1991. During that same period, DEA antidrug spending grew from $86 to $1,206 million, and FBI antidrug allocations grew from $38 to 181 million.”

Because “police can stop, interrogate, and search anyone they choose for drug investigations, provided they get ‘consent,’” racial biases have free rein. In fact, police are allowed to rely on race as a factor in selection whom they stop and search (even though people of color are no more likely to be guilty of drug crimes than whites) – effectively guaranteeing that those who are swept into the system are primarily black and brown.

“Human Rights Watch reported in 2000 that, in seven states, African-Americans constitute 80 to 90 percent of all drug offenders sent to prison. In at least fifteen states, blacks are admitted to prison on drug charges at a rate from twenty to fifty-seven times greater than that of white men.” In that same year, African-Americans were admitted to prison at a level “*more than twenty-six times* the level in 1983. The number of 2000 drug admissions for Latinos was twenty-two times the number of 1983 admissions.” (Emphasis in the original.) By comparison, “the number of white drug admissions was eight times the number admitted in 1983.”

After arrest, prosecutors can overwhelm defendants with extra charges for which they have no evidence in an often successful attempt to get them to accept a lesser, but still felonious conviction. Because of harsh sentencing laws, “drug offenders in the United States more time under the criminal justice system’s formal control – in jail or prison, on probation or parole – than drug offenders anywhere else in the world.”

Predictably, the prison population exploded: “In 1972, fewer than 350,000 people were being held in prisons and jails nationwide, compared with more than 2 million today [2012].” They are disproportionately black and Latino. “One in every 14 black men was behind bars in 2006, compared with 1 in 106 white men. For young black men, the statistics are even worse. One in 9 black men between the ages of twenty and thirty-five was behind bars in 2006, and far more were under some form of penal control – such as probation or parole.”

This despite the fact that crime rates in the US remained flat or even fell during this time. Moreover, study after study show that crime rates are roughly equal across racial groups. It is not that black and Latino men are more likely to commit crime. It is that they are more likely to be targeted for arrest, more likely to be convicted, and tend to have longer sentences when convicted.

Once convicted, discrimination that is remarkably similar to Jim Crow segregation is legal and encouraged. A system of laws and practices denies felons the right to participate in society, even though they have “paid their debt.” “The vast majority of convicted offenders will never integrate into mainstream, white society. They will be discriminated against, legally, for the rest of their lives – denied employment, housing, education, and public benefits.” Felons cannot vote or serve on juries. Felons cannot apply for federal low-income housing. They are not eligible for most financial aid for college. It is legal in almost all states to deny jobs to the formerly-incarcerated, and they are barred from obtaining many licenses to open businesses of their own. Even in states where convicted felons are eligible for some of these right, they are shackled by legal fees and paperwork requirements that make exercising those rights all but impossible.

Alexander is clear and thorough and thoughtful. The statistics she cites are useful and compelling. Her arguments are logical and compassionate. If at times I felt overwhelmed by the book, it speaks only to its power.

Her goal is not to propose remedies, though she does begin to discuss them at the book’s end. Instead, I think her goal is to show how the system of mass incarceration is one of the biggest, if not the biggest civil rights issue of our time. In this, I think she succeeds.

When she does discuss remedies, she brings in the vision of Dr. Martin Luther King Jr., who called for a shift from civil rights to human rights. Alexander, in turn, suggests that we unify across racial lines, not by ignoring our differences or pretending that we don’t see the color of each other’s skins, but by recognizing and acknowledging the humanness that we all possess. We can no longer accept the “racial bribes” we are often given, the crumbs that put most whites, even if they live in abject poverty, above most people of color. Some people of color benefit, too, but at the expense of everyone else. Alexander argues that a more just and better world could exist if we reject those bribes and form a coalition that recognizes the common human needs we share and are systematically denied. Together we could be more powerful and build a society that benefits all the people, rather than just a few.

As I read this book, I repeatedly thought that a similar analysis needs to be done of many of our institutions so that we can understand and deconstruct the ways that all our institutions disadvantage people of color, women, and others. I thought particularly of the ways that higher education pushes out people of color and poor folks, sending them the message that they don’t belong there. Perhaps someone is already working on these books. I hope they are, because I believe that knowing and understanding these issues can help us create a more just society.

## humanizing online learning

As part of my research, I’ve stumbled across the work of Michelle Pacansky-Brock and what she calls “humanizing” online learning. She has created an infographic summarizing “How to Humanize Your Online Class“:

Pacansky-Brock’s work dovetails nicely with the work of Drs. Luke Wood, Frank Harris III, and Khalid White. In their book, Teaching Men of Color in the Community College (there’s also an online course with the same name), they stress teacher-student relationships that include positive messaging, authentic care, and intrusive interventions. They also point to the importance of high expectations and high support in the context of relevant content, critical reflection, collaboration, and performance monitoring. While that’s a lot to take in, I thought Michael Smedshammer’s approach in his Online Teaching Conference presentation, Five Ways to Leverage Your LMS to Improve Student Equity, put it succinctly: “Put relationships before pedagogy” and use “intrusive pedagogy.”

For me, this means it’s the teacher’s responsibility to reach out to our students. We cannot just offer to meet with students or put the invitation out there. We need to schedule times with our students and seek them out if they don’t show up. This is especially important for those students who need the most help and may be most embarrassed to asked for it.

In my own experience as an online and hybrid teacher building the relationships is the most difficult part, particularly because it’s one of the strengths I bring to my face-to-face classroom. Online and hybrid instructors typically see our students much less often than our in-the-classroom colleagues. We have to create human presence through the internet. When I started teaching online, I not only didn’t know how to be “present” remotely, I wasn’t very comfortable with trying. It felt completely alien and weird and the opposite of personal. I had to learn to get over myself. No matter how accomplished I was in the classroom, I had to adapt to the new environment. I had to get out of my comfort zone and do the things that my students needed. The resulting experiments have not been perfect, but I’ve learned a lot.

Here’s some concrete ways you can make your presence more real for your students online. You can use these to show who you are and to demonstrate your passion for your subject and for teaching. (Many of these ideas are gleaned from Pacansky-Brock and Smedshammer, as well as Fabiola Torres):

- Embed video of yourself in your syllabus
- Use icebreakers
- Offer online office hours using Zoom or Google Hangouts
- Use a texting service like Remind:

Email is old-fashioned. There’s no better way to reach your students than on their phones. I now require my online and hybrid students to sign up to receive texts from me. Even though I give them the option to talk to me about why they don’t want to get those texts, not one student has asked to get out of the requirement. Far from being intrusive, most students seem to appreciate my texts and see it as sign that I care about their success. - Post weekly or more frequent videos in your course:

Encourage students and let them see your normal or even geeky self. Torres calls these “learning nudges.” You can use QuickTime or iMovie or any number of other applications. - Respond to student work with a video — this is really easy inside Canvas. There should be a button to press under the box for assignment comments that allows you record and post a private video right inside the LMS.

## mathematics education for a new era: video games as a medium for learning

Before the 13^{th} 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 13^{th}, 14^{th}, and 15^{th} centuries. By the 16^{th} 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 21^{st} 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.

## sabbatical project – 1

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: hhuntsman@gmail.com.

## what’s so important about algebra?

Every student in the US has to learn algebra. If this statement is an exaggeration, it’s not much of one. Almost all students take at least two years of algebra before graduating from high school and millions take it again in college. In addition, algebra skills are required in most science, engineering, and other course. But as technology evolves and what it means to be an educated person changes, I think it’s time that we think about why we teach algebra and the way we use it in education. In particular, I think it’s time we stop making algebra skills a barrier to success in college.

Now don’t get me wrong – I love algebra. Really. It’s a beautiful achievement, solving problems that challenged humanity for centuries. It’s also fun, and, as a math teacher at a community college, I enjoy supporting people as they learn algebra’s intricacies. I hope algebra is always available for those students who want to study it. However, if we’re honest about the knowledge and skills needed by 21^{st}-century graduates, workers, and citizens, algebra does not rank high on the list. Even in the technical fields, I seriously question how often algebraic skills are actually required.

The issue is especially relevant in the community college setting because large percentages of incoming students are placed into developmental algebra courses, or below. These are the same courses most of us took in high school, but students have trouble retaining the algebraic skills they learned, especially if those skills aren’t related to their majors. As a result, many students struggle to learn algebraic content that, if they’re not going on to calculus, they don’t need for their next courses – topics like factoring polynomials and solving rational equations with variables in the denominator and synthetic division. The data reveal that students who place into algebra or below are very unlikely to ever pass college level math. And because first-generation college students and students of color are placed disproportionately into low-level math courses, the algebra barrier perpetuates educational and economic inequities.

For all these reasons, in 2010 I partnered with a colleague to develop a new course designed to prepare students who were going on to take college-level statistics. The fact is that relatively little algebra is needed to learn statistics and we thought we could help students succeed in statistics using a different kind of course, a course containing only the algebra students would need for statistics. We hoped to help the majority of students who aren’t heading toward calculus and who need statistics to complete their associate degrees and transfer to four-year colleges.

Fortunately, we were not the only ones working on this idea and we learned a lot from professors at other community colleges already trying this approach. (Learn more about the “pre-stat” community at: http://accelerationproject.org/.) With their help we were able to create our course, called Preparation for Statistics, and piloted it in Fall 2011. In the course, we asked students to engage with real data, using statistical ideas in an interactive and constructive teaching and learning style. We even helped them create their own surveys, collect data, analyze the data, and present it to their classmates. It was work to teach this way, but it was also the most fun I’d ever had in class.

Most important, it worked. Data from our college, combined with other colleges teaching similar courses, show that students from pre-statistics courses are successful in college-level statistics and that they are much more likely to complete their math requirements than students that who took the traditional algebra sequence. The evidence also suggests that the courses helped close achievement gaps for underrepresented students. (http://rpgroup.org/system/files/CAP_Report_Final_June2014.pdf) At our college, the evidence was strong enough to expand beyond the pilot stage. Each year we were helping hundreds of students reach and succeed in statistics.

If taking algebra in college is not necessary for success in statistics, what about other math courses? What about science courses? Isn’t algebra the mathematical foundation of modern science?

Questions like these got me thinking about mathematical prerequisites for general education science courses. These are the science courses that non-science majors usually take to satisfy the science requirement for their degrees, things like astronomy, biology, geology, geography, and basic chemistry and physics. I looked for studies of math prerequisites in courses like these, but have yet to find one (if you have one, I’d like to see it). The marked lack of statistical evidence that either supports or refutes the need for math prerequisites in science courses (or any courses, for that matter) is telling. At my college, most of these courses do not have math prerequisites, precisely because they want to attract non-technical majors to the courses (some of the courses advise completion of algebra, but don’t require it).

I did find some unpublished data, collected at my college and two other California community colleges that offer pre-statistics courses. Aggregating the data from all three colleges, students who took pre-stats courses before statistics were almost exactly as successful in their general education science courses as students who took the traditional algebra preparation for statistics (84% vs. 83%). Even disaggregated, the difference between the success of students at each college was never greater than 10 percentage points and the college (my own) with the lowest success rate for pre-stats students in GE science courses was still 72%, compared to 78% success for their traditionally algebra-prepared peers.

These results beg the question of how students without as much algebra are doing so well in general education science courses. One answer, suggested and bemoaned by some, is that instructors of those courses are reducing the mathematical content of the courses to accommodate students who haven’t had algebra since high school. Another potential answer is that, since almost all students took algebra in high school, a little reminding and prompting enables students to use algebra to the extent that they need to solve the problems.

While both of these are possible, I have yet to see any data that support those answers or any other. In the absence of evidence, I think it much more likely that the real skills needed to do well in general education science courses are things like numerical literacy, critical thinking, the ability to connect evidence to an idea, and academic skills like going to class, reading your book, taking good notes, turning in your homework on time, and, perhaps most important, belief in your ability to succeed. All these skills are taught in both algebra and pre-statistics courses; my experience is that more attention is paid to them in pre-statistics courses than in algebra.

But, what if it were true that science instructors have reduced the algebra content of their classes? Would this be a problem? I say, no. From my perspective, science classes exist to teach science concepts, not to test students’ algebraic knowledge. If, indeed, science teachers are making science concepts more understandable for students with less algebra experience, that would be a testament to the quality of their teaching ability. As I like to say, it’s easy to make an idea complicated and hard to understand; the difficult task is to make ideas simple and clear.

We have been making most science and math courses harder to understand by forcing algebra into them, even though it’s not needed or needed only minimally. For example, in a physics class the height of an object thrown in the air can be modeled quite well by a quadratic equation. Understanding of the scientific principle is demonstrated by setting up the equation. Solving the equation is purely algebraic, but most of the time these “physics” problems aren’t correct until the equation has been solved. In a science class, the science concept should be the primary goal. Solving the equation by hand should be less important, especially when computers with powerful solving algorithms are so readily available.

Here’s another example, from a geometry course:

The geometric concept being reinforced is that the sum of the angles in a triangle is always 180**°**. But, in order to solve the problem, you have to perform some algebra. We don’t need algebra to understand the geometric idea, but if a student can’t do the algebra they won’t get the problem right.

We force students to do similar (and often more complicated) algebraic manipulations in chemistry, biology, oceanography, geography, economics, trigonometry, calculus, statistics and many others. In my experience it is algebra that trips up most students in these courses, not the non-algebra content. Limits, differentials and integrals are challenging ideas in calculus courses, but factoring from beginning algebra is frequently the biggest barrier to completing a calculus problem.

Of course, reinforcing algebraic skills throughout the math and science curriculum is not necessarily a bad thing, but I think too often we do it because that’s the way we were taught, not because of any considered pedagogical reasons. The cost of this decision is high because algebra courses and algebra’s continued use throughout the curriculum is, as I mentioned earlier, so often a barrier preventing students’ success.

And, while algebra can teach attention to detail, mastery of algorithms, symbol manipulation, logic, critical thinking, problem solving, teamwork, numerical literacy, and more, there are other ways to teach those same skills. My experience teaching pre-statistics suggests that we can teach those skills as well or better outside of the abstract context of algebra.

Higher education is changing at an unprecedented pace. These changes are driven partly by increases in the percentage of the population who go to college, partly by pressures from the federal and state governments for more return on their education dollar, partly by employers’ demands for well-prepared, 21^{st}-century graduates, and partly by huge technological advances. In mathematics, the traditional algebra and geometry sequence, familiar to most of us from our own mathematical careers, is being questioned. The algebra sequence, after all, is designed to prepare students for calculus and beyond. But in a world where the most students are not seeking science, technology, and engineering degrees, do we really need to prepare all students for calculus? I don’t think so and I’m not alone. According to the 2015 report *Degrees of Freedom: Diversifying Math Requirements for College Readiness and Graduation*, “Alternatives emphasizing statistics, modeling, computer science, and quantitative reasoning that are cropping up in high schools and colleges are beginning to challenge the dominance of the familiar math sequence.” (http://edpolicyinca.org/publications/degrees-freedom-diversifying-math-requirements-college-readiness-and-graduation-report-1-3-part-series) These alternatives are emerging because the knowledge and skills needed by informed citizens of the 21^{st} century can be taught as well or better in other ways and because the cost of continuing to insist on algebra is too high.

I’m open to being persuaded that algebra is as important for college students as we have made it. But, to change my mind, you’re going to need to show that the benefits of algebra are algebra’s alone and that they outweigh the costs of forcing everyone to do it.

## It’s on math teachers to change society’s attitude toward math

The two most common responses when I tell people I meet that I’m a math teacher are:

- People tell me how much they admire and even like math;
- People tell me how bad they are at math, squirm uncomfortably, and kind of sidle away.

In the second, much more common option, I seem to represent all the inadequacies they have felt about math for much of their lives. They try and fail to put on a polite face, instead looking at me as they would a particularly disgusting plate of food. It’s an occupational hazard to have these awkward moments at parties.

Both responses more or less make an assumption that I love numbers and all things numeric. But, as much as I enjoy learning about and teaching math, I don’t love numbers. I love people and ideas. For me teaching is pretty close to a perfect combining of these two: I get to talk to people about ideas. Teaching statistics, in particular, is about helping people sort through all the individual stories they know, looking for a trend or trends; students learn to organize and communicate about data, helping them make decisions in the world.

And as a teacher, the stories my students tell me about struggling with math and with education in general are often heartbreaking. Everyone has a math autobiography, too often filled with a teacher or relative who said something like “math is hard and it’s not for everyone” — a backhanded way of saying telling the student he or she doesn’t cut it. Sometimes it’s more direct (“Math is not your subject” or even “You’re not smart enough to do math.”) and usually these messages are delivered to children at ages 8, 9, or 10.

Another common narrative is of the young person who enjoys math till a certain class or till a certain teacher — frequently around 9^{th} or 10^{th} grade — where the student gets the message that they have “reached their math level” and anything beyond it is impenetrable for their meager talents.

There are, of course, many other stories (and I invite you to share yours in the comments) and this kind of introduction often leads people who are pro-math-and-science to exhort our society to change its attitude toward math, moving to a more math-positive message for children or to calls for increased time and emphasis on math in school. And while that would be nice, I don’t think it’s the job of society to change its attitude toward math and science. I think it’s the job of teachers to change society’s attitude.

Clearly, many people have been trying for generations to do just that, so I’m not suggesting I have all the answers or that I know what everyone should do. But I would like to share some of my experience co-creating a math course using the principles of backward design, just-in-time remediation, attention to the affective domain, and the assumptions that students are capable of high-quality work and that context is important for learning.

Three years ago, a colleague of mine and I set out to create a course that would prepare students to take college-level statistics using these principles. Unlike myself, my colleague was an experienced statistics instructor and as we talked about what to put in the preparatory course and explored the curriculum together, I constantly asked “why do we cover that topic?” and “what’s the purpose of that skill?” To her credit, she never responded that we do it that way because we always have. She never said “trust me.” She always gave me a good reason — or we tossed out that topic. The result is a course in which, unlike every other math course I have ever taken or taught, there are no extra topics; that is, in our course (“Preparation for Statistics”) every topic and every activity and every assignment are directly relevant to preparing students for the next course.

And while statistics is in general easier to contextualize than algebra, if a student does ask why we are studying a particular topic, the answer is always, in addition to any other uses, that it will be used again next semester.

This intentionality about everything we do in the class creates more buy in for students. Combine it with the assumption that students are capable of doing the work and the practice of appropriate support and we have a course that alters students’ perceptions of math (toward being more useful to them) and of themselves (toward being capable of understanding and using math).

For generations math teachers have debated amongst themselves and with others about the best ways to justify and explain the importance of mathematical education, with more and less success. Arguments about the development of problem solving and reasoning skills assume a privileged place for math that is disciplinarily arrogant and willfully ignorant (or even insulting) of the intellectual rigors in every other discipline. Discussions of the utility of skills such as factoring polynomials, solving inequalities, and calculating the volume of a frustum (much as I enjoy these topics) are unconvincing and potentially disingenuous.

It is our job to do better. And from my experience, when we do a better job of connecting what we’re doing in class to something the students want to know, the students respond with curiosity and engagement — the kind of engagement that leads to empowerment, learning, and a new attitude toward math.

And when that happens, people no longer have feel that sinking feeling inside when they see some numbers in an article they’re reading, they no longer have to cringe when they meet a math teacher, and my social life gets a little less awkward.

(*Big ups to the work of the California Acceleration Project and its founders Myra Snell and Katie Hern – my work and the assumptions it’s based on could not have happened without their leadership, intelligence, and support. Snell and Hern are among the finest educators I know.)

## oh, and entitlement

Here’s a cartoon that, not only does nothing to refute my argument in the previous post, it also speaks to the entitlement the folks coming out of college appear to have. The not-so-subtle subtext is that getting a job and life in general after college is supposed to be free from pain and misery. Wasn’t my experience and wasn’t the experience of most people I know.