WhatIsPreAlgebra < Kitchen

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Fuzzy math comes in another guise called CGI (Cognitively Guided Instruction), I just found out. http://www.minnewaukan.k12.nd.us/math.htm

Of course, everything is "research-based" as always.
-- Main.CharlesH - 31 Jan 2006


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However, Wikipedia's definition of <a href="http://en.wikipedia.org/wiki/Algebra">algebra</a> itself is: 
<blockquote>Algebra is a branch of mathematics which studies structure and quantity. It may be roughly characterized as a generalization and abstraction of arithmetic, in which operations are performed on symbols rather than numbers. It includes elementary algebra, taught to high school students, as well as abstract algebra which covers such structures as groups, rings and fields. Along with geometry and analysis, it is one of the three main branches of mathematics.</blockquote>

So the pre-algebra course overlaps with algebra to the extent that operations are performed on symbols rather than numbers.  

I think pre-algebra is just a name that's been stuck on a course regardless of whether it makes perfect logical sense or not. 


-- Main.TracyW - 31 Jan 2006


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The LA Times is running a story about the high rate of High School dropouts in the LAUSD.

Below are excerpts from their second article -- on the algebra requirement.

#AlgebraAnchor
The whole series is avaailable at www.latimes.com/dropouts, but may require site registration.

January 30, 2006    
THE VANISHING CLASS
A Formula for Failure in L.A. Schools
By Duke Helfand, Times Staff Writer

Each morning, when Gabriela Ocampo looked up at the chalkboard in her ninth-grade algebra class, her spirits sank.
Gabriela failed that first semester of freshman algebra. She failed again and again — six times in six semesters. And because students in Los Angeles Unified schools must pass algebra to graduate, her hopes for a diploma grew dimmer with each F.


"It triggers dropouts more than any single subject," said Los Angeles schools Supt. Roy Romer. "I think it is a cumulative failure of our ability to teach math adequately in the public school system."

In the fall of 2004, 48,000 ninth-graders took beginning algebra; 44% flunked, nearly twice the failure rate as in English. Seventeen percent finished with Ds.

Among those who repeated the class in the spring, nearly three-quarters flunked again.

The school district could have seen this coming if officials had looked at the huge numbers of high school students failing basic math.

Discouragement, Frustration

Birmingham High in Van Nuys......has a failure rate that's about average for the district. Nearly half the ninth-grade class flunked beginning algebra last year.

In the spring semester alone, more freshmen failed than passed. The tally: 367 Fs and 355 passes, nearly one-third of them Ds.

Like other schools in the nation's second-largest district, Birmingham High deals with failing students by shuttling them back into algebra, often with the same teachers.

Last fall, the school scheduled 17 classes of up to 40 students each for those repeating first-semester algebra.

The strategy has also failed to provide students with what they need most: a review of basic math.

Teachers complain that they have no time for remediation, that the rapid pace mandated by the district leaves behind students like Tina Norwood, 15, who is failing beginning algebra for the third time.

Tina, who says math has mystified her since she first saw fractions in elementary school, spends class time writing in her journal, chatting with friends or snapping pictures of herself with her cellphone.

Her teacher, George Seidel, devoted a class this fall to reviewing equations with a single variable, such as x -- 1 = 36. It's the type of lesson students were supposed to have mastered in fourth grade.

"I got through a year of Vietnam," he said, "so I tell myself every day I can get through 53 minutes of fifth period…. I don't know if I am making a difference with a single kid."

Eager to close this competitive chasm, education and business leaders in California sought to re-engineer the state's approach to math. They produced new math standards they believed would foster a "rising tide of excellence."

This meant teaching algebra earlier, as soon as eighth grade for some students, even if instructors questioned whether younger students could handle abstract concepts.
'I Give Up'

Whether requiring all students to pass algebra is a good idea or not, two things are clear: Schools have not been equipped to teach it, and students have not been equipped to learn it.

Secondary schools have had to rapidly expand algebra classes despite a shortage of credentialed math teachers.

The Center for the Future of Teaching & Learning in Santa Cruz found that more than 40% of eighth-grade algebra teachers in California lack a math credential or are teaching outside their field of expertise; more than 20% of high school math teachers are similarly unprepared.

High school math instructors, meanwhile, face crowded classes of 40 or more students — some of whom do not know their multiplication tables or how to add fractions or convert percentages into decimals.

Birmingham teacher Steve Kofahl said many students don't understand that X can be an abstract variable in an equation and not just a letter of the alphabet.

Birmingham math coach Kathy De Soto said she was surprised to find something else: students who still count on their fingers.

High school teachers blame middle schools for churning out ill-prepared students. The middle schools blame the elementary schools, where teachers are expected to have a command of all subjects but sometimes are shaky in math themselves.

At Cal State Northridge, the largest supplier of new teachers to Los Angeles Unified, 35% of future elementary school instructors earned Ds or Fs in their first college-level math class last year.

Some of these students had already taken remedial classes that reviewed high school algebra and geometry.

"I give up. I'm not good at math," said sophomore Alexa Ganz, 19, who received a D in math last semester even after taking two remedial courses. "I think I've been more confused this semester than helped."

Ganz, who wants to teach third grade, thinks the required math courses are overkill. "I guarantee I won't need to know all this," she said, perhaps not realizing that if she were to teach in a public school, she could be bumped as a newcomer to upper grade levels that demand greater math knowledge.

Administrators in L.A. Unified say they are trying to reverse the alarming failure rates of high school students by changing the way math is taught, starting in elementary schools.

The new approach stresses conceptual lessons rather than rote memorization, a change that some instructors think is wrong. New math coaches also are training teachers and coordinating lesson plans at many schools.

The simplest algebraic concepts are now taught — or are supposed to be taught — beginning in kindergarten.

Searching for a solution in its secondary schools, L.A. Unified is investing millions of dollars in new computer programs that teach pre-algebra, algebra and other skills.

Officials are considering other costly changes, including reducing the size of algebra classes to 25, launching algebra readiness classes for lagging eighth-graders and creating summer programs for students needing a kick-start before middle school or high school.
Go figure

Most Los Angeles ninth-graders find algebra difficult. A sample question from the algebra standards test:

A 120-foot-long rope is cut into 3 pieces. The first piece of rope is twice as long as the second piece of rope. The third piece of rope is three times as long as the second piece of rope. What is the length of the longest piece of rope?

A) 20 feet

B) 40 feet

C) 60 feet

D) 80 feet

*

Correct answer: C


Algebra test

A majority of ninth-graders in Los Angeles fail algebra or pass with a D grade.

Algebra grades of LAUSD freshmen in fall 2004:

C and above 39%

D 17%

F 44%

*

Sources: Los Angeles Unified School District, California Department of Education


-- Main.BenCalvin - 31 Jan 2006


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Chicago is going full steam ahead with fuzzy math. http://www.cmsi.cps.k12.il.us/ViewProgramDetails.aspx?pid=357

-- Main.CharlesH - 31 Jan 2006


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<I>It may be roughly characterized as a generalization and abstraction of arithmetic, in which operations are performed on symbols rather than numbers</I>

well, that's exactly the definition I'd read, in Hu I think (the Berkeley mathematician)...

-- Main.CatherineJohnson - 31 Jan 2006


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bad news about LA Unified

I <I>think</I> they're using Saxon - although they've apparently all messed around with Dolciani's algebra text that no one can learn anything from it

I'll try to find the Klein editorial

-- Main.CatherineJohnson - 31 Jan 2006


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I'm up extremely early because Andrew threw a massive temper tantrum at 6 am

Med changes

I've had it

-- Main.CatherineJohnson - 31 Jan 2006


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from [[http://www.csun.edu/~vcmth00m/lausd.html][LA Unified destroys Dolciani]]:

A copy of the LAUSD pacing plan for "Algebra I: Structure and Method" is included at the end of this letter.  It undermines the organization of ideas in this textbook, and it undermines the California Mathematics Framework and Standards.  We illustrate with some examples.

The two year pacing plan for "Structure and Method" calls for the quadratic formula together with completing the square of quadratic polynomials (in Chapter 12 of the textbook) to be explained to students before basic factoring techniques for polynomials (in Chapter 5), and before an introduction to radicals, including techniques for simplifying radicals (in Chapter 11).  This choice of ordering of topics is so mathematically unsound that it will most likely seriously undermine the ability of LAUSD math teachers to teach algebra in a coherent and meaningful way. It will reduce the learning of algebra to memorizing meaningless formulas without understanding.    In the words of the chairman of the Math Department of San Pedro High School (in LAUSD), Richard Wagoner: 
 

"First and foremost among the problems with the Pacing Plan is that 
it renders the textbook and all support materials useless and obsolete. 
The sequence is so seemingly random that students must jump back and 
forth between sections of chapters through most of the course. 
Therefore, all review materials, diagnostic tests, supplementary 
materials and enriched materials -- all of which are tied to the 
sequence as designed by the authors -- can no longer be used."

-- Main.CatherineJohnson - 31 Jan 2006


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<B>Ben</B>

Thanks so much.

The Photo Gallery is incredible.

Everyone should see it.

[[http://www.latimes.com/news/education/la-013006dropouts_day2-f,0,7232169.flash][photo gallery]]

Be sure to read the captions.

-- Main.CatherineJohnson - 31 Jan 2006


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Listen to this:

Teacher George Seidel left a 25-year law career two years ago, hoping to find fulfillment as a teacher at Birmingham High in Van Nuys. "I got through a year of Vietnam," he says, "so I tell myself I can get through 53 minutes of period five.... I don't know if I am making a difference with a single kid."

-- Main.CatherineJohnson - 31 Jan 2006


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<br />
http://images.barnesandnoble.com/images/4250000/4253890.gif
<br />

-- Main.CatherineJohnson - 31 Jan 2006


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terrific book (nothing to do with public schools or math)

-- Main.CatherineJohnson - 31 Jan 2006


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<B>Charles</B>

The word 'cognitive' is usually a warning sign, which makes things difficult since cognitive science is what I follow.

Piaget is a cognitive psychologist. I believe that's where the word typically comes from in constructivism.

-- Main.CatherineJohnson - 31 Jan 2006


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<i>In the fall of 2004, 48,000 ninth-graders took beginning algebra; 44% flunked, nearly twice the failure rate as in English. Seventeen percent finished with Ds.</i>

That's because in algebra 2 + 2 has to equal 4.  In English 2 + 2 can equal Walrus if that's what the teacher says.

In this school the real failure rate in English should probably be about 44% or higher too.

-- Main.KDeRosa - 31 Jan 2006


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<i>Officials are considering other costly changes, including reducing the size of algebra classes to 25, launching algebra readiness classes for lagging eighth-graders and creating summer programs for students needing a kick-start before middle school or high school. Go figure</i>

Seems like they're trying everything but what works -- teaching elementary math to mastery before teaching algebraic concepts.  It is exeedingly difficult to be this wrong accidentally.

-- Main.KDeRosa - 31 Jan 2006


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<i>The Photo Gallery is incredible.</i>

Once again the photos/illustrations tell the real story better than the article.

-- Main.KDeRosa - 31 Jan 2006


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After viewing the photo gallary, I just want to say OMG.  This article should be sent to every school board member pushing for "fuzzy" math.

I am a homeschooler, so I don't have a dog in this fight, but I have made the following observation over and over again..homeschooling parents rarely struggle with math curriculums.  You scour the homeschooling boards and you don't see post after post about failing math curricula.  We have our "visual learners" Math-U See "folks, we have our Saxon "school-at-home" types, and we have our "I don't care what they're doing in ps" Singapore users.  Homeschoolers struggle with finding the perfect.....SPELLING program.  

Seeing students in these photos who have been academically-abused for the first 8 years of their school lives just floors me. Really, this country doesn't need to worry about terrorist, we are destroying our country from the inside out.

Sad.


-- Main.NicksMama - 31 Jan 2006


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_After viewing the photo gallary, I just want to say OMG. This article should be sent to every school board member pushing for "fuzzy" math._

No, they'd say, "look at the board, these kids are trying to do algebra. What they needed was a constructivist education, not that soul-killing drill stuff."

The pictures are horrendous. I feel for the teacher, who is trying to pretend everything is okay.

-- Main.CarolynJohnston - 31 Jan 2006


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I look at those pictures and captions and everything points to how grades K-8 failed these kids. Lower schools do not want to hold kids back. One reason given for this is some study showing a higher drop-out rate for those kids who were held back. Duh! Keep passing them right along and you will have a 100% graduation rate.

At our public schools, they use the concepts of developmentally appropriate, full inclusion, and spiraling to justify this approach. They don't want classes/subjects to be filters. However, the filters are delayed until high school so they never see the product of their work. It's easy enough to blame the child, the parent, or society. By eighth grade many kids will decide that they are just not good in math, thereby completely letting the lower schools off the hook. High schools let the lower schools off the hook. They should be yelling and screaming at the lower schools.

My reaction is to tell people to look at the state tests and tell me what is so difficult that schools cannot succeed for most kids no matter what their parents or society does.



-- Main.SteveH - 31 Jan 2006


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<I>After viewing the photo gallary, I just want to say OMG. This article should be sent to every school board member pushing for "fuzzy" math</I>

No kidding.

It's incredible.

Here are all these teachers AND students saying 'He still counts on his fingers' &mdash; how can anyone NOT take seriously the absolute need to learn the procedures and algorithms of elementary math COLD. 



-- Main.CatherineJohnson - 31 Jan 2006


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COMMENT TO POST

I have made the following observation over and over again..homeschooling parents rarely struggle with math curriculums. You scour the homeschooling boards and you don't see post after post about failing math curricula. We have our "visual learners" Math-U See "folks, we have our Saxon "school-at-home" types, and we have our "I don't care what they're doing in ps" Singapore users. Homeschoolers struggle with finding the perfect.....SPELLING program.

(I'M WRITING COMMENT TO POST AS A KEY WORD SO I CAN FIND THIS AGAIN)

I had no idea homeschoolers didn't struggle over finding a math curriculum.

Of course, I didn't struggle.

There were two choices (that I knew of at the time), and I made the choice quickly once I saw both.

Now I <I>would</I> struggle. I'd definitely teach bar models no matter what.

But I may be finding I prefer Saxon, overall, to Singapore....

-- Main.CatherineJohnson - 31 Jan 2006


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<i>Here are all these teachers AND students saying 'He still counts on his fingers' — how can anyone NOT take seriously the absolute need to learn the procedures and algorithms of elementary math COLD.</i>

My kindergarten aged son gets embarrassed when he has to resort to counting on his fingers to solve an addition or subtraction problem.  You think these kids don't know that thye're not supposed to be counting on their fingers in high school?  I'm sure this is all part of the low self-esteem problem you get when you you can't do math.

-- Main.KDeRosa - 31 Jan 2006


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I might try to use both, frankly. 

When you're working efficiently at your child's pace, rather than at the pace of the class & the school with its many holidays & moments of lost instructional time, I think it would be easy to get through one Saxon book & two Singapore books each school year K-5 or even K-8.

-- Main.CatherineJohnson - 31 Jan 2006


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<I>Seeing students in these photos who have been academically-abused for the first 8 years of their school lives just floors me.</I>

It's very upsetting.

Because these kids - these young adults - really are suffering. You can see it in their body language.

This didn't need to happen.

-- Main.CatherineJohnson - 31 Jan 2006


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<I>They don't want classes/subjects to be filters. However, the filters are delayed until high school so they never see the product of their work.</I> 

Good point.

Somebody else gets to deliver the blows.

-- Main.CatherineJohnson - 31 Jan 2006


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My friend whose second grade daughter is good at math & likes the subject very much (dad is a computer scientist) says her daughter uses her fingers <I>and</I> her toes to do calculations.

She's got her in KUMON now, and the teacher told her she's adding practice in the algorithms.

-- Main.CatherineJohnson - 31 Jan 2006


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<i>Because these kids - these young adults - really are suffering. You can see it in their body language.

This didn't need to happen. </i>

This is the part that sticks in the craw the most when you read the comments left on the edusphere blogs by <s>clueless</s> apologist educrats (teachers, academisc, admins) who continue to deny there is a problem with the current system.

-- Main.KDeRosa - 31 Jan 2006


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<B>Carolyn & all</B>

What can a teacher in this situation do?

Is there anything at all?

I've thought about this a lot.....I've wondered whether you could recruit <I>some</I> of the parents to do volunteer remedial work with their own kids and perhaps with one or two 'study buddies' in the class.

If you're required, by your district, to get through X material even though the kids aren't prepared to do X material.....and you know they aren't prepared.....

Do you have options?

As a matter of personal philosophy, I generally believe there are always 'options.'

So I'm going to vote 'yes' here, just on principle, and say there's <I>something</I> a teacher could do beyond march through the material to the very best of his ability.

But what is it?

-- Main.CatherineJohnson - 31 Jan 2006


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One thing I know I'd do: I'd proselytize the hell out of these kids.

I'd tell them: 

Your problem isn't algebra.

Your problem is elementary math.

You could do algebra in a heartbeat if you'd learned elementary math the first time around.

I'd make them believe it, too.

-- Main.CatherineJohnson - 31 Jan 2006


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I don't know that that would <I>help</I>, but there'd be a couple of kids who took me up on it - there'd be a couple of kids who said, then or later, OK. I need to go back and learn fractions.

It's not my fault I didn't learn them the first time around.

But I'm the person who's going to have to fix things now. 



-- Main.CatherineJohnson - 31 Jan 2006


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<I>This is the part that sticks in the craw the most when you read the comments left on the edusphere blogs by clueless apologist educrats (teachers, academisc, admins) who continue to deny there is a problem with the current system.</I>

I know.

Because we are looking at pain.

These young people break my heart.

Every one of these young people can solve an equation like

3x + 2 = 32

Christopher <I>may</I> be able to do that now.

IF CHRISTOPHER WERE USING SAXON MATH HE'D BE ABLE TO DO THIS WITH EASE.

The only reason Christopher has found equations like this one hard is that the course moves way too fast with way too little practice.

-- Main.CatherineJohnson - 31 Jan 2006


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I suppose the crafty teacher could secretly teach elementary math in class instead of algebra.  It's not like these kids are in any condition to pass algebra anyway.  Of course, thne this teacher looks bad since his students are all failing algebra and some other teacher will get all the glory when they ultimately pass algebra.

-- Main.KDeRosa - 31 Jan 2006


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What can a teacher in this situation do?

Is there anything at all?

I've thought about this a lot.....I've wondered whether you could recruit some of the parents to do volunteer remedial work with their own kids and perhaps with one or two 'study buddies' in the class.

If you're required, by your district, to get through X material even though the kids aren't prepared to do X material.....and you know they aren't prepared.....

Do you have options?

As a matter of personal philosophy, I generally believe there are always 'options.'

So I'm going to vote 'yes' here, just on principle, and say there's something a teacher could do beyond march through the material to the very best of his ability.

But what is it?
................

My MIL taught math to middle school kids for 25 years.  She always complained about how ill-prepared they were for middle school math.  Her solution?  Get involved in designing the Standards of Learning (these were designed for the VA Dept of Ed. long before the NCLB laws were in effect).  She said that the elementary teachers needed to be held accountable and if it took standardized testing to ensure that the kids were learning and prepared for middle school, the so be it.  She is still a big supporter of state testing.  Late in her career, she ended up remediating high schoolers who counted on their fingers and didn't have their times tables down.  
 

-- Main.NicksMama - 31 Jan 2006


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<I>I suppose the crafty teacher could secretly teach elementary math in class instead of algebra</I>

jeez.....you know, you're right

talk about differentiated instruction....

if you've got anyone in the class heading towards being able to pass algebra, that group is going to be the minority

-- Main.CatherineJohnson - 31 Jan 2006


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<I>then this teacher looks bad since his students are all failing algebra and some other teacher will get all the glory when they ultimately pass algebra</I>

in this particular case, the teacher is teaching a class of kids who've already failed

there aren't going to be a lot of other teachers beating his numbers

-- Main.CatherineJohnson - 31 Jan 2006


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<I>She always complained about how ill-prepared they were for middle school math. Her solution? Get involved in designing the Standards of Learning (these were designed for the VA Dept of Ed. long before the NCLB laws were in effect). She said that the elementary teachers needed to be held accountable and if it took standardized testing to ensure that the kids were learning and prepared for middle school, the so be it. She is still a big supporter of state testing. Late in her career, she ended up remediating high schoolers who counted on their fingers and didn't have their times tables down</I>

good for her

did she share thoughts about handling these kids in her classroom?

-- Main.CatherineJohnson - 31 Jan 2006


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I'd love to hear something from Carol Gambill on this subject

remember, she says that her kids show up for 8th grade algebra not well prepared &mdash;

-- Main.CatherineJohnson - 31 Jan 2006


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[[http://www.kitchentablemath.net/twiki/bin/view/Kitchen/GambillMethodForTeachingAlgebra][Gambill Method & kids who aren't prepared for algebra]]:

<I>"Most students who enter my eighth-grade Algebra I or Honors Algebra I classes in September each year are ill-prepared to learn algebra because most of them have not fully mastered arithmetic. To make matters worse, I have too few class periods to teach them the entire rigorous course when one adds up the drug education activities, annual class trips, report card day, vacations, snow days, exams, and parent-teacher conferences. These restrictions demand that the students put in extensive quality time outside of class grappling with difficult problems and practicing for accuracy.</I>

-- Main.CatherineJohnson - 31 Jan 2006


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"To make matters worse, I have too few class periods to teach them the entire rigorous course when one adds up the drug education activities, annual class trips, report card day, vacations, snow days, exams, and parent-teacher conferences."

Here in Chicago you can add "restructured days" to the list of distractions. These days occur with great frequency. They are half-days that disrupt class rotation and regular teaching is impossible.

-- Main.CharlesH - 31 Jan 2006


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<B>Charles</B>

What is a restructured day?

Is it like a superintendent's day?

It really is shocking, the amount of lost instructional time.

Teachers here complain all the time, AND THEY'RE RIGHT

-- Main.CatherineJohnson - 31 Jan 2006


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On those days the kids are sent home around noon to subject teachers to "professional development." This usually worthless PD stuff is hugely costly. The Chicago school system is now running a $328 million deficit. From what I understand PD costs hundreds of millions. 

-- Main.CharlesH - 31 Jan 2006


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And meetings. Lots and lots of meetings.

They really should only count full days with the teacher when they're adding up the 180 days of school required. It would probably shock parents how few days in the year are actually spent with their teacher learning about core subjects.

-- Main.SusanS - 31 Jan 2006


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"It would probably shock parents how few days in the year are actually spent with their teacher learning about core subjects."

Even with the teacher instructional time is a shrinking commodity. The first activity of the day is handing out meal ticket. That often takes half an hour of prime time. I've known teachers who schedule an hour of SSR in the morning. More prime time lost. Then you have the dogma of non-instruction under the constructivist regime. Time filled with often trivial activities and projects.

-- Main.CharlesH - 31 Jan 2006


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<I>On those days the kids are sent home around noon to subject teachers to "professional development." This usually worthless PD stuff is hugely costly. The Chicago school system is now running a $328 million deficit. From what I understand PD costs hundreds of millions</I>

oh boy

another boondoggle

no vendor left behind

-- Main.CatherineJohnson - 31 Jan 2006


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<I>It would probably shock parents how few days in the year are actually spent with their teacher learning about core subjects</I>

I THINK Stevenson & Stigler came up with a figure of only 60% of class time actually being spent on academic activities.

IIRC

-- Main.CatherineJohnson - 31 Jan 2006


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<i>I THINK Stevenson & Stigler came up with a figure of only 60% of class time actually being spent on academic activities</i>

And how much of that 60% is spent on real academics?

-- Main.KDeRosa - 31 Jan 2006


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http://www.colby.edu/catalogue/0001/images/major/MA.gif

-- Main.CatherineJohnson - 02 Feb 2006


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<I>And how much of that 60% is spent on real academics?</I>

oh gosh

I hadn't even allowed that thought to surface in my mind.

-- Main.CatherineJohnson - 02 Feb 2006


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