Posts Tagged algebra

The Education Non-System Sets Kids Up for Failure

Published by — Educators at different levels are not talking to one another, hence a huge disconnect between high school and college.

While debates about standards still burn out of control, “readiness” has become a hot topic.  Wherever the standard or benchmark lies, what does a kid need to be ready to meet it?  What prepares a kid to be work-ready?  Ready for college?  Ready for high school?  We’ve hit a wall with beating up kids, teachers and schools for failing to meet standards, so now pundits are looking upstream to understand what could be improved before students drop out of high school or post-secondary training.

In May 2013, the National Center for Education and the Economy published a report called What Does It Really Mean To Be College And Work Ready?  As they searched for answers to their question, they found endless unsubstantiated opinions.  Employers, Higher Education and even folks on the street have very strong feelings about the skills necessary to the adult work world, or the training grounds that eventually lead to said world.  Such feelings abound because even with America’s high unemployment, many jobs go unfilled for lack of qualified workers, while low-skills jobs, like old-style factory manufacturing, are drying up.  The U.S. way outspends all other developed nations on K-20 education, so why aren’t more youth ready to be successful in the modern economy?

NCEE contends they found virtually no research on the subject, so they conducted their own.  They focused on the English and math skills necessary to be ready for community colleges because at any given time, roughly 45 percent of America’s college students attend community colleges.  For many students, these are the gateway to a 4-year degree.  And they offer the bulk of initial vocational and technical training, “for everyone from auto mechanics and nurses to emergency medical technicians and police officers.”  The report asserts that without the skills to complete at least a 2-year certificate or degree, young people will struggle to keep a family out of poverty.

Standards exist along a continuum. 

We would love for all kids to be medical-school ready, but let’s walk before we run.  College drop-out rates are alarmingly high generally, but community colleges experience the greatest losses.  “College for all” is not practical or helpful.  But all students should be at least community-college, which is to say, workforce ready.  Currently, we send a high proportion of badly-prepared students off to borrow and spend tuition money before they drop out, inadvertently creating a crisis of debt and wasted human capital.

(At the other end of the standards spectrum are the utterly-neglected talented kids.  They deserve our — my — attention, but not today.)

Community colleges often replicate the bad Literacy habits of high schools. 

NCEE found that community colleges generally require texts that are of an 11th or 12th-grade reading level — not highly demanding — but that high-school graduates struggle with them nevertheless.  Most importantly to my mind however, “students are not expected to make much use of those texts.”  Apparently, the days of ubiquitous essays and book reports, using texts that teachers know well, have given way to what’s known as “high-engagement” reading — think the “Twilight” series — and maybe writing a “reflection” paragraph.

Writing itself teaches reading, literacy and thinking.  Learning to write unpacks the structure of language and teaches how to use evidence to build an argument, to make a point.  The advent of computer-scored tests has been no favor to writing which can only be assess by capable readers and editors.  Grading papers has always placed a heavy load on English teachers, eased only when schools were clever about ways of giving them extra time to grade work and coach students directly.

But from the first job-application cover letter to the world of work itself, writing skills are deal-breakers.  Kids aren’t ready because the system didn’t get them ready.

K-20 needs to re-think the Algebra I through Calculus path.

Nor is the system serving them with math.

NCEE argues that many students and career paths depend on “middle school mathematics, especially arithmetic, ratio, proportion, expressions and simple equations.”  Also critical to community-college career tracks are subjects that are “rarely, if ever, taught in American elementary and secondary schools, including complex applications of measurement, geometric visualization and schematic diagrams.”  But Algebra II is the gatekeeper to college admission to any but the least selective college.  So students get pushed through the traditional track without ensuring the solidity of middle-school foundations.  Kids can’t build high-level mathematical skills on educational Swiss cheese.  That’s the system at work, setting a lot of kids up for failure.

Mind you, all students should be encouraged to shoot for the Calculus goal because math trains the mind in useful ways, including “modeling” or the ability to frame a real-world problem in mathematical terms.  But unless the 8th-grade skills are strong, why bother?

Identifying a basic platform — call it “community-college ready” — is not a dumbing down because it’s only the guarantee of the basics.  Currently we aren’t giving kids the basics, never mind a strong sense of what the future has in store for them.  Selective colleges and employers are not going to put up with cheesy work.

Most impressive to me was NCEE’s image of a so-called system that is really fragments, sections not particularly talking to one another.

Julia Steiny is a freelance columnist whose work also regularly appears at and 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 or contact her at or c/o GoLocalProv, 44 Weybosset Street.


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Teach Real Algebra Instead of Wasting Time with Fun Apps

Published by — “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 and 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 or contact her at or c/o GoLocalProv, 44 Weybosset Street

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The Man Who Made Algebra Child’s Play

Published by — Dr. Henry Borenson wants kids not just to know algebra, but to like it.

Dr. Henry Borenson began his career as a math teacher at Stuyvesant High School in New York City.  Like Boston Latin, Stuyvesant uses an exam to cream the best public-school students.  For those smartie pantses, algebra was a breeze.  Borenson’s biggest problem was the constant need to invent intriguing work to challenge his kids.

Then he took a job as Math Supervisor in another state.  As such, he descended from the lofty reaches of gifted-and-talented programs and became responsible for teaching, well, the rest of us.  Like so many young students now as well as back in my day, I developed a profound algebra-aversion.  It made me feel so hopelessly inept that I narrowed my college search to those that would not make me take math.

Borenson explains, “The way algebra was traditionally taught involved memorization without understanding.”  Well, not understanding makes anyone feel stupid and totally turned off.  No wonder many kids don’t like math.

Patricia Scales, the principal of the school I visited for last week’s column on this subject, explained, “We hurry kids along when we really need to slow down and teach process and understanding.  Only by getting solid foundations of a skill can they get to the next level, which takes time.  But if you have them do it by rote, they don’t understand and they’re not thinking.”

Especially with the testing insanity of the last decade or so, teachers want to help their students arrive at correct answers absolutely asap.  So math instruction often regresses to teaching rules — algorithms, formulae, tricks, rote.  Which is boring.

Of course, many math teachers don’t themselves have deep understanding that they can pass on with confidence.  They too mainly learned the rules.

Borenson says, “The focus of my entire career has been on the teaching of math.  Already 25 years ago, I was looking to make algebra more visual to support understanding.  I wanted to demystify the meaning of equations by representing them physically.”

His first effort was a crude system of letters and pictures designed to help a disengaged 8th-grade class.  “These visualizations allowed the weakest student in the class to solve advanced mathematics problem.  To her it was instantly obvious.  Clearly algebra needed to be more concrete so kids could get used to it and like it.”

That early work evolved into what became his life’s brainchild:  Hands-on Equations.  Designed for students grades 3 – 8, and struggling high-school students, the program has kids build equations, literally, with chess-like pawns representing the variables and numbered cubes.  (A child demonstrates how to do it here.)

Borenson says, “Pawns and cubes are much friendlier than x and y.  Kids can see that you can’t combine a constant (number) and x.  Each lesson introduces only one more concept, and the sequence of lessons provides building blocks for young learners.  Hands-on Equations is designed to give kids a head start before taking a regular algebra class.”

He adds, “When a kid is working on a video game, they don’t ask, when am I going to use this skill?  The reason they always ask what algebra is good for is because it’s boring.  They don’t understand what they’re doing, and they’re not successful.  Video games require strategic thinking; Hands-on Equations does the same.”

Helping kids feel confident about their ability to think through a problem sets them up with good attitudes.

Hands-on Equations is not new, but it’s still too much under the radar.  Over the years, tons of research has supported the program’s success with inner city kids, English language learners, special needs students, indeed, all kids.  In video testimonials, math teachers and researchers both report the same experience I had at Patricia Scales’ school, watching light bulbs popping over the kids heads.

Hands-on Equations was voted the #2 most downloaded math program for the i-pad.  Borenson argues that no other actually teaches algebra.  “In most math apps, the child knows he’s right because the program says ‘Terrific!’ or ‘Good Job!’ or something. Scientific American gave one (program) a top rating that can’t teach algebra because there is no way for a child to check his answer.  That’s enabling.  The fancy graphics are not teaching a kid to solve the problem on his own.”

The program is gamelike, but without points, winning or racing.  Kids learn math rules as “legal moves,” in the language of video games.

Borenson’s colleagues offer professional development for the use of the program.  But honestly, he and the teachers I met believe that the manual supplied with the kits provides all a motivated teacher needs to know.  The kits themselves are relatively inexpensive, and Borenson is negotiable when schools are seriously strapped.  A book of word problems supplements each lesson, to keep the more advanced kids challenged.

It’s rare for me to laud a marketed product.  But Hands-on Equations certainly would have cleared up my problems with algebra, perhaps opening up my college search.

Borenson says, “The point is to get kids used to algebra so they like it.  It’s important that they develop positive attitudes towards math.”

Surely improved attitudes would work wonders on kids’ anemic math achievement.

Julia Steiny is a freelance columnist whose work also regularly appears at and 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 or contact her at or c/o GoLocalProv, 44 Weybosset Street, Providence, RI 02903.

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5th Graders Having a Blast with Algebra

Published by —  Making algebraic variables child’s play

I was forewarned, but still, it was a lovely surprise to spend a solid hour with a class of students constantly popping off with “I got it!”  And “Ooooohhhhh!”  And “I see!”

These yelps of satisfaction sound just like the ones you hear from boys playing video games.

Except that this is math class at Dawson Elementary School in Holden, Massachusetts.

No, worse:  it’s algebra, the academic subject that more than any other strikes fear in grown-ups’ hearts.  But these are 5th graders.  And some are struggling learners.

The lesson is plenty rigorous, as you’ll see.

But the kids get a useful assist from the “manipulatives,” concrete objects — pawns and blocks — that support a program called Hands-on Equations.  Kids use the objects to build and break down algebraic equations.

Six years ago, teacher Lori St. Germain jumped at her district’s offer to train her in Hands-on Equations.  She shrugs, “I was always interested in algebra.  So I took a one-day, easy training, and later showed it to the other 5th grade teachers who were able to pick up the rest on their own.  For a while we were sharing one set.”  Each now has her own.

St. Germain also acquired the digital version so she can demonstrate the day’s concept on a whiteboard.  Students talk her through moving the pieces to solve the problem.

They start with a warm-up:  2(x + 4) + x = x + 12.

On the board, and in a packet in front of each students, are red cubes showing the constants, or actual numbers.  An oversized blue pawn represents the oft-feared “x.”  Kids build their equations on a “scale,” really a laminated placemat with a picture.  The fulcrum is the equals sign.

Borrowing from game language, “legal moves” are the mathematical rules for how to make an equation balance. The equivalent of winning is solving for “x.”

St. Germain reviews a recent lesson about how to handle multipliers that are outside parentheses.  With the kids’ help, she builds two versions of x + 4, one on top of the other, on the left-hand side of the scale.  And adds the extra x.  On the other side, they put a pawn and a cube marked 12.  Kids whittle down the equation by subtracting equally from both sides, first a pawn and then the value 8, from each side.  What remains are 2 pawns on the left and a 4 on the right.

“So what’s x?”  The kids shout “2!”  The visual makes it painfully obvious.

“Let’s check our work.”  Again, the kids talk their teacher through plugging 2 into the places where the x had been.  It’s become a simple arithmetic problem.

After teaching the new concept, St. Germain cuts them loose to work the problems out on their own.  The worksheets each had four examples of the new problems, six from recent lessons, and ten review equations on the back.  Math smarties finish quickly and go back for sheets of word problems.

St. Germain explains, “Some kids can see the problem in their heads and don’t need the manipulatives.  Some just draw.  Eventually you want them all to solve without the manipulatives, making drawings or using letters.  But the one or two who still need the manipulatives in June will have them.”  The objects wean the kids from concrete to abstract, the way training wheels support learning to ride a bicycle.

Several kids struggle.  St. Germain hovers nearby, helping.  After she got a lollygagging, impeccably-dressed girl through the first problem successfully — with one of those big “Ohhh!”s — the little fashion-plate quit fooling around and got to it.  By the end of class, she was proudly booking through the practice problems.  She nudged her neighbors for clues here and there.  A little lazy, but she was getting it.

St. Germain’s colleague Marie Horton says “This program takes a complicated concept, like a variable, and turns it into something they can take apart and put back together.  Like a puzzle.  So this is incredible for 10, 11-year-olds because of how much it makes them think.  They get such a sense of pride instead of looking at a problem and rejecting it as ‘stupid.’  Kids go at their own pace, so the learning is differentiated.  But the best part is seeing the little light bulbs pop, that sense of happiness.”

That is the best part.

At one point, St. Germain firmly told a squirmy boy to look her in the face.  She had to ask him twice, but he finally swiveled around and complied.  Without impatience, she repeated a sentence she’d already said several times during the lesson.  This time, not only does he get it, but a chorus of eavesdroppers who’d been struggling with their own work bellowed their version of “Oooooohhhhh!!!”

That’s what algebra class looks like when we’ve got it right.

Next week we’ll meet the program’s inventor, Dr. Henry Borenson, to understand the thinking that went into this work, the only algebra manipulatives program to merit a patent.

Julia Steiny is a freelance columnist whose work also regularly appears at and 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 or contact her at or c/o GoLocalProv, 44 Weybosset Street, Providence, RI 02903.

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