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 21st-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:

Solve for x.

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, 21st-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 21st 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.

groomed for murder

Looking for a fun read with some mystery and a little sex? Look no further than Vivian Rhodes’ Groomed for Murder. Set in Los Angeles and written in a breezy style that fits the SoCal vibe, the book is marred for my ears by frequent sexist language and assumptions. Nevertheless, the plot is solid and the characters are well-formed. It’ll  hold your attention and keep you turning pages.

dataclysm

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When we are online, every like, every follow, every click is recorded and analyzed by the corporations, large and small, that rule the internet. They use these terabytes of data to market their products, to predict how new products will sell, and more. Exactly what other uses they make of the data, most of us don’t think much about,  but the corporations own it and we give them permission to collect and use it when we agree to their terms of service.

The fact that most of us don’t think about someone watching our online behavior is a central assumption in Christian Rudder’s book, Dataclysm, made explicit by the subtitle Who We are (When We Think No One’s Looking). Using that premise, Rudder analyzes the clicks, messaging behavior, and survey results from the online dating site OkCupid, as well as few others. He has access to this data because he is a founder of the site and knows other people in the field. He leverages this privileged information into a book length speculation about what the data means.

Some of Rudder’s observations are well-considered and interesting. Some are less profound. At times I think Rudder jumps to erroneous conclusions and I’d wager a significant amount of money that any thoughtful reader of the book will agree with Rudder sometimes and disagree at others, depending on the specific context. Probably most readers will be occasionally offended by the book. But despite the fact that his ideas are often not fully supported by the data, they are also not fully contradicted by the data. So, even when you disagree with his conclusions, you have to admit he could be right. We just don’t know.

Overall, that makes for a provocative book that opens the imagination for the kinds of knowledge we could gain with careful analysis of the vast quantities of data we, as a global internet society, are collecting.

But beyond agreeing or disagreeing with Rudder, I have a more fundamental issue with Rudder’s approach to the data. He writes,”As far as I know, I’ve made no motivated decision that has bent the outcome of my work.” With this sentence he claims that he uses no theory to reach his conclusions, as if, somehow, he just lets the data talk and listens carefully, transcribing the data’s proclamations accurately.

I don’t think Rudder is naive, but I can only take him at his word. As any scientist or thinker knows, it is impossible to be theoryless. So, to claim explicitly to be theoryless means either he doesn’t know what theory or theories are guiding his decisions or he refuses to tell us. Either way, it is a deep flaw in the book that the reader doesn’t know the theoretical approach taken by the author.

Read the book for some interesting applications of descriptive statistics (and, typographically, for some great use of the color red!). But read with a skeptical mind.

 

the last detective

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If you like a mystery in the English style (think Midsommer Murders), then The Last Dectective is right up your alley. Smoothly written, with interesting characters and some unexpected twists, the novel is a solid contribution to the genre. Themes include the conflict of the technology with “old-fashioned” smarts, trouble with authority, and the use and misuse of police power.

brown is the new white

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Brown is the New White is the most hopeful, optimistic book about politics in the US I have read. Phillips’ subtitle captures his main argument, made concrete in his first chapter and backed up by thorough evidence: people of color and progressive white folks are the new electoral majority in the US and, if we organize and take advantage of that majority, we can change the course of the nation, making it a better place to live for all.

Phillips’ prime example is the election of President Obama. Through a careful analysis of the voting trends, he shows that the new majority elected the President and debunks the myth that of a backlash against that mandate in the off-year elections. He demonstrates that the Democratic losses in the US House and Senate were, instead, the result of the new majority not voting in those off-year races, precisely because the Democrats failed to engage progressives on the issues they care about.

In addition, Phillips looks at the history of White privilege in this country and how both the major political parties continue to dedicate the vast majority of their energy and resources to winning the White vote, despite the demographic shifts we are experiencing. He shows how those shifts are rooted in the anti-discrimination, voter rights, and immigration policies enacted in the 1960s, now coming to fruition. And, importantly, Phillips outlines the policy priorities for the new majority, the issues that will energize and bring progressive voters to the polls.

Brown is the New White is not a Pollyanna look at the US — there is chapter entitled “Conservatives Can Count” toward the end of the book that warns the other side is aware of the same trends he outlines and is moving to attract those voters as I write — but it is unrelentingly hopeful. When I saw Phillips speak in person, I asked him how he maintains his optimism in the face of so much cynicism in today’s political landscape. Without hesitation, he explained that 16 million Americans have health care today that didn’t eight years ago, that unemployment is down across all demographics, that life for regular folks all across the country is better today than it was before we elected President Obama. The trends, he said, are up and there is every reason to believe that we can continue to improve.

old school

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Stories are important to me. I think stories are important to most people. We use them to share our days, our lives, and our histories. Stories entertain us and help us know who we are and where we came from. And the stories we tell about ourselves, together with the stories that are told about us, can become who we are in the minds of others. If those stories are not true, they can get us into trouble. But not always.

Uncertainty about the power and effect of stories, the way stories define or don’t define our identities, is a major theme in Old School (Tobias Wolff, 2003), a novel told in a series of short stories that seem like chapters until the last chapter/story, which is only just connected to the rest of the book. It feels like Wolff calling attention to the structure of the book by taking us out of the narrative flow. Only then do you go back and realize that each chapter could stand alone, that, in addition to being about stories, the larger book is made up of a series of smaller stories.

In addition, large portions of the novel are dedicated to talking about writers and the stories they write. So on many levels this is a story about stories. It is like poems about poetry, a cliché that, in this case, does not lessen the power of the product.

The power comes from the sharp, clear prose. To call the prose sparse would be too strong. Efficient is too utilitarian. Elegant and beautiful miss the mark as well. It’s one of those moments when you just want to say it is good writing; you know it when you see it. The writing is good enough to make a story about privileged white boys in a small private boarding school on the east coast in 1960 compelling – and for me, that’s saying something. Themes that include social class, passing for white privileged, the relationship between sons and fathers, community, and integrity also help.

But even as Wolff marshals the power of stories to define ourselves, he also questions it to the point of asserting that we become who we are without realizing it. For himself, that means “the life that produces writing can’t be written about.” Not because language is incapable of capturing it, but because “it is a life carried on without knowledge even of the writer, below the mind’s business and noise.” Therefore, “no true account can be given of how or why you become a writer, nor is there a moment of which you can say: This is when I became a writer.”

For Wolff, it seems, we tell stories about this or that moment in our lives, pretending they are turning points. But in fact these are fictions and the truth of our selves is “in deep shafts where phantom messengers struggle toward us, killing one another along the way; and when a few survivors break through to our attention the are received as blandly as waiters bringing more coffee.”

Old School shows how stories help us feel alive and wise and full of energy to rise above that blandness, while simultaneously recognizing their limitations. They are crystals of knowledge we can hold and dissect and talk about. They help us remember and think about ourselves. Wolff’s ranks among the best at all these.

100 top novels — 15

New addition: Old School (#50), by Tobias Wolff

1 One Hundred Years of Solitude – Gabriel Garcia Marquez
2 Beloved – Toni Morrison
3 To the Lighthouse – Virginia Woolf
4 Mrs. Dalloway – Virginia Woolf
5 Molloy – Samuel Beckett
6 Lolita – Vladimir Nabokov
7 Underworld – Don DeLillo
8 Middle Passage – Charles Johnson
9 White Noise – Don DeLillo
10 Middlemarch – George Eliot

11 Wuthering Heights – Emily Bronte
12 Suttree – Cormac McCarthy
13 Housekeeping – Marilyn Robinson
14 Love in the Time of Cholera – Gabriel Garcia Marquez
15 The Brother’s Karamazov – Fyodor Dostoyevsky
16 The Plague – Albert Camus
17 Heart of Darkness – Joseph Conrad
18 Darkness at Noon – Arthur Koestler
19 Lord Jim – Joseph Conrad
20 The Poisonwood Bible – Barbara Kingsolver

21 The Great Gatsby – F. Scott Fitzgerald
22 Native Son – Richard Wright
23 All Quiet on the Western Front – Erich Maria Remarque
24 Jane Eyre – Charlotte Bronte
25 On the Road – Jack Kerouac
26 The Invisible Man – Ralph Ellison
27 Ceremony – Leslie Marmon Silko
28 Wolf – Jim Harrison
29 Narcissus and Goldmund – Herman Hesse
30 The Master and Marguerita – Mikhail Bulgakov

31 Blindness – Jose Saramago
32 A House for Mr. Biswas – V. S. Naipaul
33 Written on the Body – Jeanette Winterson
34 The Glass Bead Game (Magister Ludi)- Herman Hesse
35 The Grapes of Wrath – John Steinbeck
36 Blood Meridian – Cormac McCarthy
37 The Intuitionist – Colson Whitehead
38 The Bone People – Keri Hulme
39 Of Mice and Men – John Steinbeck
40 The Tin Drum – Gunter Grass

41 Pride and Prejudice – Jane Austen
42 One Day in the Life of Ivan Denisovich – Alexander Solzhenitzen
43 Gravity’s Rainbow – Thomas Pynchon
44 Motherless Brooklyn – Jonathan Lethem
45 Americanah – Chimamanda Ngozi Adichie
46 The Brief Wondrous Life of Oscar Wao – Junot Díaz
47 1984 – George Orwell
48 The Fortress of Solitude – Jonathan Lethem
49 To Kill a Mockingbird – Harper Lee
50 Old School – Tobias Wolff

51 The Uncomfortable Dead: (what’s missing is missing) – Paco Ignacio Taibo II & Subcommandante Marcos
52 Huckleberry Finn – Mark Twain
53 Mao II – Don DeLillo
54 Catcher in the Rye – J. D. Salinger
55 A Confederacy of Dunces – John Kennedy Toole
56 The Scarlet Letter – Nathaniel Hawthorne
57 Frankenstein – Mary Shelley
58 Anna Karenina – Leo Tolstoy
59 As I Lay Dying – William Faulkner
60 The Red Badge of Courage – Stephen Crane

61 A Tale of Two Cities – Charles Dickens
62 Neuromancer – William Gibson
63 For Whom the Bell Tolls – Earnest Hemingway
64 Generation X – Douglass Copeland
65 Brave New World – Aldus Huxley
66 The Chosen – Chaim Potok
67 Doomsday Book – Connie Willis
68 Corelli’s Mandolin – Louis De Berniere
69 Fall on Your Knees – Ann-Marie MacDonald
70 Middlesex – Jeffrey Eugenides

71 The Dog of the South – Charles Portis
72 All the Pretty Horses – Cormac McCarthy
73 Dr. Zhivago – Boris Pasternak
74 The Crying of Lot 49 – Thomas Pynchon
75 Fahrenheit 451 – Ray Bradbury
76 Gorky Park – Martin Cruz Smith
77 White Teeth – Zadie Smith
78 The Stone Canal – Ken MacLeod
79 Schizmatrix – Bruce Sterling
80 The Left Hand of Darkness – Ursula K. LeGuin

81 The Loved One – Evelyn Waugh
82 The Metamorphosis – Franz Kafka
83 The Fall – Albert Camus
84 Vineland – Thomas Pynchon
85 Straight Man – Richard Russo
86 A Small Death in Lisbon – Robert Wilson
87 Disgrace – J. M. Coetzee
88 Kindred – Octavia Butler
89 The Road – Cormac McCarthy
90 The Palace of Dreams – Ismail Kadare

91 The Street – Ann Petry
92 The Feast of Love – Charles Baxter
93 Fear of Flying – Erica Jong
94 Clockwork Orange – Anthony Burgess
95 The Old Man and the Sea – Earnest Hemingway
96 The Star Fraction – Ken MacLeod
97 He, She, and It – Marge Piercy
98 The Dispossessed – Ursula K. LeGuin
99 The Shipping News – E. Annie Proulx
100 The Parable of the Sower – Octavia Butler

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