Posts Tagged MATH EDUCATION

Common Core Math Expectations Are Only A Baseline

Published by EducationNews.org — There’s surprisingly little controversy over the meaning of “college-ready math.”  Ready for which college?

We’re going to discuss Common Core today, so take a chill pill.  I’m not saying CC presents nothing to be upset about, but getting upset just clouds clear thinking.

CC is by no means perfect, but it’s not Evil incarnate, either.  So let’s get to know it.  Finding the good parts will remind us that we don’t really want to return to zero accountability, or 50 definitions of proficient, such as we got from No Child Left Behind, or continued stagnant progress in the country’s educational achievement.  Most importantly, if not, Common Core, what?

Conveniently, the lead writers of the Common Core State Standards (CCSS) wrote two one-pagers that describe “The Shifts” in thinking that are at the standards’ philosophical heart.  If you look at no other CC materials, read these.  Even for educators, digesting the standards themselves is a daunting task.  So before joining one of the inflamed bandwagons out there, get a bit of grounding in original documents.  Many CC controversies are bogus hysteria — such as the standards requiring limits on bathroom time — but some are very real.

Using The Shifts’ math page, let’s examine the frequent accusation that CC “dumbs down” math expectations, in part by notrequiring Algebra I until the 9th grade.  This is a legitimate concern since Algebra II is generally the gatekeeper to all but the least selective colleges.  Historically, schools found that only by pushing Alg I into middle school would it give struggling math students, often low-income minorities, plenty of time to repeat math classes and still reach the “college-ready math” benchmark.  Not an insignificant worry.  Let’s consider it:

The philosophical shifts for math are organized under “Focus,” “Coherence,” and “Rigor.”  The first shift is this:

The Standards call for a greater focus in mathematics.  Rather than racing to cover topics in a mile-wide, inch-deep curriculum, the Standards require us to significantly narrow and deepen the way time and energy is spent in the math classroom.  We focus deeply on the major work of each grade so that students can gain strong foundations:  solid conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the classroom.

Admit it:  that’s not so nuts.

So let’s make three points:

1.  CCSS are about the timing of testing skills. 

Despite opponents claiming otherwise, standards are NOT a curriculum.  CC offers “exemplar” curricula suggestions — some truly bad — but by all means, ignore them.  The standards only identify when particular skills will be assessed.  Algebra I concepts won’t be tested until the spring of 9th grade.

But no standard prevents schools from offering advanced math to any and all students, so talented kids absorb the sequence of math skill-building that ends with Calculus as fast as their clever heads let them.  Shame on schools that don’t push all their kids to their highest potential.  Kids on a fast track will ace those Algebra I skills by spring of 9th grade.

2.  The CCSS are only a bottom line, a minimum guarantee.

There’s surprisingly little controversy over the meaning of “college-ready math.”  Ready for which college?  Because they range from community colleges to the Ivies.  A recently published research report, “What does it really mean to be college and work ready?” addresses the issue directly.  The NCEE researchers found that at any given time, 45% of all American college students are attending community colleges.  The great majority of these students bomb basic skills tests, especially in math, and end up paying for remedial classes that do not get them closer to an actual degree or certificate.  The report argues that the math needed for most of the Associate’s degree programs, as well as passing the Accuplacer or other placement tests are solid 8th-grade skills with a smidge of Algebra I and Geometry.

Algebra II is usually the gatekeeper to college, and often a high-school graduation requirement.  So schools race through a bazillion topics without ensuring that all kids acquire at least a solid set of practical skills.  The lack of those skills is wrecking the academic careers of largely low-income students attending community colleges.

3.  Redefine “college-ready” math to ensure all kids get the basics. 

I am totally gung-ho for the training that Algebra II offers the mind, but not at the expense of setting up those community college kids for success — never mind winning back the hearts of students who give up high school altogether or any dreams of post-secondary training.  After all, the NCEE report found that only about 5% of jobs require the skills in Algebra II and above.  We might have to be more specific about which-college ready we mean.

Yes, the lack of Algebra II would likely keep students out of highly-selective Ivies, but frankly, the kids I’m concerned about weren’t going to Dartmouth, Vassar, or Reed anyway.  By all means intrigue, cajole and push the low-income, statistically-least-likely-to-succeed kids so some of them get over the hump and into selective colleges.

But are we “dumbing down” or recalibrating “college ready” so tons more students could be prepared for an accessible success?  Again, nothing is stopping schools from challenging the daylights out of the students who can handle it.

Julia Steiny is a freelance columnist whose work also regularly appears at GoLocalProv.com and GoLocalWorcester.com. She is the founding director of the Youth Restoration Project, a restorative-practices initiative, currently building a demonstration project in Central Falls, Rhode Island. She consults for schools and government initiatives, including regular work for The Providence Plan for whom she analyzes data. For more detail, see juliasteiny.com or contact her at juliasteiny@gmail.com or c/o GoLocalProv, 44 Weybosset Street.

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Teach Real Algebra Instead of Wasting Time with Fun Apps

Published by EducationNews.org — “The student-engagement bandwagon has gone too far.”


Emmanuel Schanzer majored in Computer-Science at Cornell University.  With such a high-value degree, he knew he could sail into a lucrative, snazzy job.  But he was keenly aware that he was a C.S. hotshot (my word) because he’d entered college with good math skills already under his belt.  No one codes who doesn’t understand algebra — you know, the hard stuff that looks like a Slavic language with some numbers thrown in.  To get a lot more kids, especially ill-prepared urban kids, into the bright future that comes with computer science, someone had to build up their math first.

So later on, Schanzer would create Bootstrap’s curriculum.  Because — buyer beware! — most of the apps and programs that currently promise to teach kids algebra are fun, but a total waste of time.

“When you hear, ‘This is so amazing!  These apps teach kids to program!’  That’s snake oil.  Every minute your students spend on empty engagement while they’re failing algebra, you’re assuring that they’re not going to college.  Studies show that the grade kids get in Algebra I is the most significant grade to predict future income.”

A Man With a Math Mission

In college Schanzer searched for a way to improve math instruction through real programming, and found Program by Design (PxB, about which I’ve been writing for the last 2 weeks).  While excellent, it’s pitched too high, assuming strong math skills that challenged urban students haven’t yet acquired.  He vowed to redesign it one day — after cashing in on his computer-science degree.

But his years working in the tech sector were no match for his passion.  Plan “B,” then.  With an education degree in hand, he started teaching his beloved algebra in urban schools.  But the programming tools available to his students were maddeningly off the mark.  “First, none of the popular K-12 computer languages/teaching tools had anything to do with math, which seemed insane to me.  They had things called “functions” and “variables,” but they didn’t behave at all like the functions and variables students see in their math classes.  How’s that supposed to help them?  Students were expected to entertain themselves by playing with the tools, but it wasn’t clear what they were supposed to learn.”

“The student-engagement bandwagon has gone too far.”

“The goal is to help kids get the computer to do something, because there is an intangible value in being in control.  It’s engaging, no question.  So in the last 5 years, all the sexy languages are drag-and-drop programs, like Scratch and Alice.  I have enormous respect for these tools, as long as they’re a first step towards PythonJava.  But by themselves, they are a terrific answer to just one question:  How do we make it seem easy to code?”

Those programs have built-in blocks of code, represented by icons that kids can manipulate.  But kids don’t interact with the code itself, never mind write it or program.

“Typing code is hard.  If you forget a semicolon, the program doesn’t work.  So the supposition has been that if they play with a tool, it will help them later.  But that’s not programming and it’s not algebra.  Classroom time is valuable.  If you’re spending 50 hours in the course of a year “coding” in block language, you’re stealing time from real learning.  Students get an “A” in high school and then go to college and find programming is something else entirely, and get totally turned off.”

Bootstrap Is Born

Like a good Millennial, Schanzer founded a start-up to solve the problem.  Bootstrap’s programming language behaves like the algebra students learn in class, reinforcing honest-to-God algebraic concepts.  Yes, Bootstrap teaches kids the basics of game building, but only by teaching the math that supports the code.

The materials are free and online, though professional development is available.  Every lesson is cross-walked with the Common Core, assuring teachers that their efforts will result in real learning.  A growing library provides homework assignments and warm-up activities.  Teachers can use each lesson’s script until they’re familiar with the program.  And a pre and post-test measures the learning.

“Teachers know if it’s not real math.  You have to do things the way teachers do it in a classroom.  Bootstrap enforces mathematical behavior — same vocabulary, steps, style as a math book.  This is a math class.”  The fun video on Bootstrap’s homepage shows kids loving the approach.

As luck would have it, Schanzer found himself Boston’s subway one morning and noticed a guy, a German, working with Program by Design.  Lo!, the man was none other than Matthias Felliesen, creator of PxD.  With that chance meeting, Schnazer secured allies in his efforts to get math to urban kids.  Bootstrap started to take off.

And if a Bootstrap student starts to soar, a teacher can point the budding computer-scientist to PxD for more challenge, and a pipeline to college.

Schanzer is fulfilling his college-born dream to propel bunches of kids into bright futures at places like Cornell.  Absolutely, engagement is important.  But the key all along has been to shore up math itself.

Julia Steiny is a freelance columnist whose work also regularly appears at GoLocalProv.com and GoLocalWorcester.com. She is the founding director of the Youth Restoration Project, a restorative-practices initiative, currently building a demonstration project in Central Falls, Rhode Island. She consults for schools and government initiatives, including regular work for The Providence Plan for whom she analyzes data. For more detail, see juliasteiny.com or contact her at juliasteiny@gmail.com or c/o GoLocalProv, 44 Weybosset Street

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In US Schools, ‘Incorrect Answers are Un-American’

PPublished by EducationNews.org — Methods are about HOW to solve problems, not solving problems themselves.

Back in the 1990s, circumstances so maddened Dr. Matthias Felleisen, he felt forced to create Program by Design (PxD) to bring life back to computer science and algebra, both. Since then, thousands of students have used it to learn the elements of programming, with or without a teacher. Even I could understand its free, online textbook. The PxD target audience were first-year college students, but Felleisen’s team wanted it to be accessible to clever 10-year-olds. The NSF and other major funders continue to be impressed.

The final straw for Felleisen’s frustration was his children’s 10th-grade babysitter, when he was a young computer-science professor at Rice University. The girl was floundering miserably in math, as so many students do. He offered to help and found her gratefully receptive to his methods.

Felleisen is German by birth, so his own training was quite different than what’s available here. In the U.S., “Teachers hand students the functions, but students do not know where they came from or what they are, really. Algebra problems are terribly boring because teachers just use numbers. Algebra can manipulate pictures, or even words. I have nothing against numbers, but I asked if I could help (the sitter) make functions of her own that could that make a movie or a game.”

Animation helps beginning students see how math makes a computer DO something.

“Of course it worked with her, so I knew then that I could and should change algebra.”

“Multiple choice is about right answers.”

Felleisen’s much bigger issue were his frustrating college students. It seemed they’d been taught to drive straight to right answers with virtually no attention to the methods by which answers emerge. No real-world context engaged students in why the problems were intriguing — contexts like animation, Census data, aerospace calculations or video games. What really excites him are the methods or processes that help students work through problems. He gets impassioned, even a bit snarky about American teaching methods, using the word “boring” a lot.

“I grew up in Germany where I was taught by ex-engineers. They were excited because they had no limits on their imaginations. My textbooks were one-tenth the size of American textbooks. They just had the methods for how to solve problems. My math teachers put the subject in context.”

American textbooks, on the other hand, “are huge, filled with big color pictures of all kinds of objects that may convey the idea of a function (a manual meat grinder), or an alternative view of functions (an image of a graph and a rule with arrows in between). They might describe several uses of functions (economics, biology, or programming), often with one-page stories on a person. None of this reaches the kids. In particular, it fails to bring across why a functions are needed and how they are created systematically. Instead, they have pages of practice problems. My training had no multiple-choice. It was always about the method and not the right answer.”

Felleisen gives his students zeros if they get the correct answer, but don’t show work that lets him see their methods and thinking. They get full credit, though, “if your answer is wrong, but your methods are right and you made a small mistake. Yes of course I had math drill, but only early on, when I was very young. From then on it was all about the methods, for algebra, geometry…”

The drive to get the right answer seems to have wiped out most students’ sense of the possibilities and power of both math and the computer.

“A computer is a dumb piece of engineering.”

After the baby-sitter experience, Felleisen gathered a team to develop a curriculum that turned the computer into the learner. “The student, then, is the teacher who tells the computer what to do. The creative person is the student.”

In his own class, his first lesson teaches students how to get a computer to move a cat across a screen. The cat is on the left, positioned in relation to the “x” and “y” axis.

He says, “You construct a function from the little ingredients. When you understand the relationships in your function, the numbers are just incidental. Mathematicians know this. Functions are just little machines. They’re often written as tables where the function of time is to place the cat image at X distance from the right. Every time I make this picture I change the Time and the coordinates. Yes, these are numbers, but pictures are involved.”

Methods are about HOW to solve problems, not solving problems themselves.

So the driving question ought to be: what problem do you want to solve? What real-world context is engaging? When right answers become too important, math is all plug-n-play with functions and not creative acts of imagination.

Worse still, the bee-line drive to right answers cripples the American student’s imagination and appetite for solving problems in all sorts of ways. And that, in turn, produces way too many wrong answers on the all-important tests. Ironic, no?

Julia Steiny is a freelance columnist whose work also regularly appears at GoLocalProv.com and GoLocalWorcester.com. She is the founding director of the Youth Restoration Project, a restorative-practices initiative, currently building a demonstration project in Central Falls, Rhode Island. She consults for schools and government initiatives, including regular work for The Providence Plan for whom she analyzes data. For more detail, see juliasteiny.com or contact her at juliasteiny@gmail.com or c/o GoLocalProv, 44 Weybosset Street.

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Math-Haters Love Crunching Numbers for Business Plans

Published by EducationNews.org — For far too long, project-based or “constructivist” learning has been at war with the “drill-and-kill” focus on building skills first.  A balance is best.

Five high-school seniors cluster behind a pillar in a lecture hall at Rhode Island College.  Behind them is a movie-sized screen, and in front looms a modest but intimidating stadium of seats.  With the giggling and “Oh my God!s,” they’re reviewing the game plan for making their upcoming presentation.

To my eye, these students, urban and suburban, don’t seem academically challenged.  But none of them passed the math section of last fall’s state test, which is now a graduation requirement.  Fully 38 percent of RI’s seniors are at risk of not receiving a diploma.  The field refers to them as the “Level 1s,” the lowest test level, “substantially-below proficient.”

While some people vigorously oppose the requirement itself, others organized “cram camps” to give these students urgent-needed help.  The Northern Rhode Island Collaborative, an education-support organization, hired Christine Bonas to assemble educators to develop and deliver this two-week summer intensive.  An ex-math teacher herself, and now guidance counselor, Bonas gets both the academic demands and the kids’ lack of motivation.

Because whatever kept the kids from learning math before, they’re into it here.  The program is brilliantly designed.  Teachers spent the first day asking students what they don’t like about their community.  Answer:  plenty.

Okay.  So get into teams and pick one problem — like, no place for teens to hang out, bad public parks, a need for animal rescue shelters.  (Yes, many shelters exist, but so what?)  Then, build a business model with a plan that will solve the problem.  Don’t whine; take an entrepreneurial approach.  With your idea in hand, research the costs of rent, labor, utilities, equipment.  Prepare multiple spreadsheets that explain income and outflow, start-up costs and maintenance.  Develop “what if” scenarios for unanticipated expenses.  Talk to local business leaders, provided by the program, about your calculations.

Lastly, learn how to pitch your idea.  To add a competitive game element, local businesses pooled $1,000 seed money for the winning plan.  I’m at their pitch rehearsal, but superintendents and business leaders will evaluate the final presentations tomorrow.

The giggly group emerges and makes a thoughtful presentation.  Their business eliminates the hated condition of teens depending on family and friends for rides.  They show us an example of eco-friendly electric mini-buses that will take kids to the mall, their friends’ house, wherever.  The team wanted a cost-free service, but crunching the numbers ruled that out.  (A snootful of Reality is such a good lesson.)  Taking turns, students walk us through slides of spreadsheets that show us they’ve been steeped in manipulating numbers effectively.

Apparently, the these students’ final presentations were so good, the kids surprised even themselves.  Business planning gave them a real-world feel for what they could actually DO with math skills.  Bonas says “The light dawned on them that this is what math is for.”  Bingo.  This should have happened long ago.

Why can’t school be like this all the time?

Bonas was blunt.  “As a former math teacher, I can tell you that you’re handed a textbook and told how to do it.  We’re not able to think outside the box.”  Partly that’s a result of the way teachers are trained, and partly because districts have gotten more and more prescriptive for their teachers.  She says, “It’s a manufacturing process.  You’ve got too much to do and you’ve got to get it done.  You don’t have time to be a dynamic teacher.”  She explains that “project-based learning,” where students actively pursue a project of interest to themselves, takes more work to plan.

“To teach them a slope, we (math teachers) put a formula on the board, give them graph paper and show them the rise over run.  There’s always one kid who says, When am I going to use this?  The teacher says, uh, well, see that roller coaster?  Parabolas are how to keep them from crashing.  That’s no answer.  They don’t care.  But if you ask a kid to show me how your business is going to make a profit, they can show you time on the “x” axis and increase in cost on “y”, suddenly we’re looking at a negative slope.  Oh!, they say.  Because we’re teaching in context.  Parabolas have to have something to do with their lives.  Making a profit is something they can care about.”

For far too long, project-based or “constructivist” learning has been at war with the “drill-and-kill” focus on building skills first.  Skills are critical, but as Bonas notes, the kids don’t learn if they don’t care.  Learning can’t be either/or.  Get kids hooked on solving problems that matter to them, but stop them here and there to teach and reinforce the skills they need.  Both/and.  Bonas’ kids talked to bankers, attorneys, accountants.  As one girl said about these interviews, “They, like, so opened my eyes to how much detail you need to have.”  Of course details matter.  Dream all you want, but the math has to work.  Skills and projects need a healthy balance.

We’d have fewer “Level 1s” of all kinds if school were more engaging, creative, meaningful.  Bonas says, “I’m amazed by the growth I’ve seen in just two weeks.”  Now imagine the growth after a whole year of that.

Julia Steiny is a freelance columnist whose work also regularly appears at GoLocalProv.com and GoLocalWorcester.com. She is the founding director of the Youth Restoration Project, a restorative-practices initiative, currently building a demonstration project in Central Falls, Rhode Island. She consults for schools and government initiatives, including regular work for The Providence Plan for whom she analyzes data. For more detail, see juliasteiny.com or contact her at juliasteiny@gmail.com or c/o GoLocalProv, 44 Weybosset Street.

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Algebra Can Be Taught as Basic Software Programming

Published by EducationNews.org— Creative approaches to algebra — like using computer science and technology — can help improve math education outcomes.

 

Recently, in the New York Times opinion section, Professor Andrew Hacker asked, Is Algebra Necessary?

Surely he knew the educated, newspaper-reading public would revile him for such heresy.  He states obvious truths, however.  Algebra, and math requirements generally act as linebackers blocking “unqualified” kids from college altogether, and pushing large numbers of students who did manage to get in to drop out.  In high school and college, students fail math courses far more often than other subjects.  Hacker suggests colleges ease their requirements so mathematically-challenged “poets and philosophers” can thrive.

Naturally, the four zillion reader-comments passionately argue that algebra is necessary.  For good reasons.  Many howl that we’d be nuts to continue “dumbing down” the already-low bar that Americans set for most students.

But I applaud Hacker for sparking the conversation.  He’s right that math is a huge problem.   It begs creative solutions.

So let’s consider two complementary ideas.  One has a decent track record, and the another employs technology in a new way.

In the 1980s researchers provided hard data proving that requiring Algebra II blocked most minority and low-income students from any hope of college.  The College Boardresponded with a program called Equity 2000.  The 6 pilot sites included Providence, Rhode Island, where I was then serving on the School Board.

The idea was to eliminate all the “business,” “consumer,” and other dummy-math courses.  Put every 9th grader in Algebra I on the assumption that many could make it, given the chance.  Every high-school student would have 4 years to get through Geometry and the much-loathed Alg II.

Providence decided to back up even further.  All 6th graders went into Pre-Algebra, creating a year of preparation and even more time to plow through the traditional sequence.  If nothing else, the kids would get real math.

While kind-hearted, perhaps, the teachers’ hue and cry about the kids not being able to do the work only strengthened our resolve to raise expectations and boost kids’ opportunities.  All math teachers 6-12 got College-Board training — though surely not enough.

Still, two terrific unintended consequences emerged.

First, apart from the struggling students the program was designed to help, it was a godsend to the smarty-pantses.  My kids were going through the system at the time, so I saw for myself the Brown, Providence, and Rhode Island College professors’ kids, among others, happily booking through the sequence, finishing Algebra I in 7th grade and Geometry in 8th.  Those kids began 9th grade taking Algebra II.  The local exam school, Classical High, had to beef up its math program to keep up with them.

Secondly, teachers started creating classes of slower students who, while not mastering the prescribed full year of a math subject, still got credit for what they did achieve.  This allowed them to move forward, instead of flat-out repeating, which is such a drag — and an invitation to drop out.  Students in Providence’s large schools could be sorted into differently-paced classes, with names like Pre-Algebra Part II.  Kids got through the traditional sequence at varying rates, but as a result, many entered high school ready for Geometry.

And since their math courses were more rigorous, and at the same time more flexible, students failed courses at much less damaging rates.

Bottom line:  In time, Equity 2000 got many more urban kids into college.

But in truth, it only picked up the kids for whom low expectations were the only real problem.  It didn’t much change how math is taught.

The NY Times’ readers insisted on algebra’s importance to teaching logic, patterning, problem-solving, critical and analytical thinking — in other words, reasoning.  Absolutely true.

But the great majority of learners — estimated at two-thirds — need to wrestle with a real-world problem, and think it through, in order to grasp the abstract concepts embedded in the solutions.  Math instruction mainly focuses on the algorithms, formulae and procedures to get to right answers instead of thinking through problems.  Programs likeConnected Math make some attempt to use real-world problems to teach algebraic abstractions.

But my now-grown sons, two of whom became software developers, have been arguing since high school that learning computer software programming is essentially learning algebra, only infinitely more fun, interesting, and useful.

And lo!  At the Advanced Math and Science Academy (AMSA) in Marlborough, Massachusetts, every student 6 through 11th grade takes computer science, in conjunction with math and the sciences, where programming skills come in very handy.  AMSA had to invent the curriculum, because none was available.

Legions of students apply to this charter school, not because they adore math, but just to escape whatever school they would otherwise attend.  This forced AMSA to figure out how to intrigue the “poets and philosophers,” especially among the girls, who arrive full-on hating math and science.  AMSA’s been remarkably successful, enjoying off-the-map state-mandated math-test scores.

Equity 2000 was right-minded, but limited.  It needed far more tricks, options, and new approaches to lure students into the puzzles of mathematical reasoning.

And really, in this day and age, shouldn’t all kids start learning computer-science right about 6th grade anyway?

America’s K-12 educators can’t afford to keep lowering the bar.  Raise it, instead, by all means.  But get creative.  It’s 2012.  Can we really not see the value of computer science as a compelling teaching strategy?

Who are the slow learners here?

Julia Steiny is a freelance columnist whose work also regularly appears atGoLocalProv.com and GoLocalWorcester.com. She is the founding director of the Youth Restoration Project, a restorative-practices initiative, currently building a demonstration project in Central Falls, Rhode Island. She consults for schools and government initiatives, including regular work for The Providence Plan for whom she analyzes data.For more detail, see juliasteiny.com or contact her at juliasteiny@gmail.com or c/o GoLocalProv, 44 Weybosset Street, Providence, RI 02903.

 

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