Math and Transitions
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My concern is that some students could and should be able to gain a certificate or, perhaps, even an Associate's without a knowledge of algebra.
I have a Ph D and slogged through three grad course in statistics. However, if you put a gun to my head and ordered me to solve an equation with two unknowns I would tell you to shoot me.
I was a Tenured Full Professor at the University of Nebraska as well, and managed world-wide customer research for IBM without knowing how to solve that sort of equation.
Perhaps, the problem is with the curriculum and not the learners.
Roger Berg
Plymouth, MA
Bravo, Roger. Just put me in the shooting line. I have made it very well thank you without the knowledge of math beyond basic algebra. I probably did have the knowledge at one time-but as the old saying goes..."use it or lose it" In most daily lives higher order math is just not necessary. Problem IS with the curriculum-not the learners...
Kathy Ellithorpe
Data released by ACE re the GED suggests that a 500 score equals the median for over 8,000 high school grads. Shouldn't community colleges be able to develop programs that lead to better jobs in a global economy without trying to have a fully-funded math department?
When I was with IBM (1999) another manager client confided that a manager across the hall asked her how much would be a 5% raise be for an employee earning $40,000? This manager was probably earning six figures ten years ago.
I am not advocating innumeracy but I am advocating programs that make demands that recognize the current world of work.
Roger Berg
nqr@max.com
And now they're talking about putting calculus on the GED??? I never went past geometry as a high-school sophomore, and as I tell my students, I have lived a long and happy life without math. That goodness, we have separate math teachers at my center!
Wendy Quiñones
Good morning!
What a great discussion! I've been attempting to follow it while balancing other things right now, and I'm so glad I have because many of the points that have been made really speak to our system of education delivery. How long has algebra been taught in 8th and 9th grades (after basic arithmetic)?
I'm passing along this link sent to me by a coworker on what's going on in K-12 with regard to teaching algebra. The link is for an algebra webinar, and it was in the EdWeek Update [1]
Cheryl Pyburn
Team Leader
Adult and Community Learning Services
Malden, MA
Hi Kathy, Roger, and everyone,
While I also am math challenged, and I feel competent in my daily math skills, I guess I would argue that all this depends entirely on the context and the needs of the student. There are an awful lot of careers and jobs that depend on the individual having a good command of higher order math, and there are a lot of people interested in this type of math (some who do not even realize it).
But perhaps this is what you are saying - that maybe if the curriculum were better constructed, like a ladder say, then the people who do want to pursue math will, and in greater numbers.
Is that what you're saying?
Thanks,
Marie Cora
Assessment Discussion List Moderator
And to support you, Marie, I come back to my pet obsession of the moment, which is the ACCUPLACER: without sound algebra skills, GED grads are doomed to the abyss of developmental math courses and/or an often futile struggle with college-level math. (See discussion thread entitled 'Accuplacer'.) Other states with different college placement tests have the exact same problem. So lament it or not, algebra is the world our students must be able to navigate through to access post-secondary education and training.
Tom Mechem
GED State Chief Examiner
Department of Elementary & Secondary Education
Commonwealth of Massachusetts
Tom, you articulated my own thoughts very well! Thank you!
GED level algebra is actually quite basic and is generally perceived as a fundamental math needed by all students. It has many simple, real-life applications even though some may not think of the calculations used as being algebraic, i.e. recipes, drug dosage calculations, purchasing, painting and wallpapering, etc. Teaching/facilitating the connection between algebra and real life applications often helps de-mystify algebra and decreases the angst that some students have when they "hit the algebra wall". Additionally and, in my opinion, as important, skills necessary for mastering algebra are among necessary 21st century skills, i.e.
problem solving
accessing, processing, and synthesizing information
critical thinking and reasoning skills
abstract thinking
self-directed learning, etc.
Just a few thoughts to offer....
Melinda M. Hefner
Director, Literacy Support Services
Caldwell Community College and Technical Institute
Hudson, North Carolina
Marie-Thank you so much for your comments. After a 23 year teaching career at all grade levels I do know that math as a whole is the subject we seem to struggle with the most. As an adult educator for the past 8 years, I know that math is the one subject that my students actually fear. Whether this comes from past experience, i.e. failure, or just plain old math anxiety - the one subject that adult learners almost always need the most help with is math. We start at the bottom of the ladder with them. My approach is actually one using the ladder metaphor. "If you miss a step on the ladder it's difficult almost impossible to make it to the next level."
As an educator (not a math major) I do wonder just how much math is enough math. Just where do we draw the line as far as math education goes in most career education? Is it valid to assume that a general business major needs as much math as an engineer? Or even the same kind of math? If a student learns that kind of math and does not use it on a regular basis, will he/she lose what was learned? It has been my experience that as adults we retain the kind of math that we use the most. Do we need to construct curriculum to address careers?
Kathy Ellithorpe
Math is the favorite subject of my children. One child went to University Laboratory High School in Champaign, Illinois where she came across math author Donald Cohen. He teaches math to children and has been successful in teaching them calculus at elementary level. His website is [2] Maybe we could use his strategy in adult education?
Barbara Jacala
Like it or not, colleges require a reasonable level of math including algebra for entering students. Otherwise they go into developmental math. So we should just "get over it" and figure out ways to teach this to GED and ESL students. If we want to change college admissions requirements, that's a separate crusade. In fact many people think they're too low - including me.
Forrest Chisman
Forrest, et al,
I am a good example of "beyond math challenged." I was the oldest person in my high school graduating class, primarily because of algebra and geometry. I started out in the university in zoology. I had to quit, because of failure to balance freshman chemistry equations and inability to take such required courses such as biochemistry and genetics. People kept saying that it was an "attitude thing," as I was already publishing in the field of herpetology, while still in high school. I was able to change majors to English/Spanish in the university and fortunately was permitted to substitute Latin for required math. I got my degree finally and after going into ESL didn't even think about graduate school because of the math portion in the GRE. I have had a very good career in ESL, have published articles and textbooks, done management work and am functional in several languages. Years after all of this started I was at a TexTESOL meeting in San Antonio and the subject was right and left hemisphere predominance. I took a test and turned out to be fourth from the end on the right side group of some 80 people. When they did a results analysis, it turned out that I was a creative person who saw things, including new languages, holistically before details registered properly. There is probably an empty spot on my left hemisphere area! This explained everything to my satisfaction. Left hemisphere predominant persons have step-by-step minds and become engineers, scientists, etc. Right hemisphere predominant people are abstract artists, natural musicians, etc. and learn everything differently. In a long career, I have fortunately never had to use anything beyond elementary arithmetic. My wife keeps the checkbook, as she is predominately on the left side, because even at that level I mess up. The problem is that we are in a left-hemisphere education system. One of the factors that should be considered is hemispheric testing of all school children and adults and adjustment of their curricula and goals. That could solve some of the problems. Persons who are in the middle of the right/left predominance usually do O.K. if they have motivation also. Persons who are far right or far left will all have some areas of weakness. By the way, I had some really competent math teachers and tutors, who I inadvertently drove crazy.
Ted Klein
www.tedklein-ESL.com
Ted,
Over 100 years ago the Committee of Ten decided that algebra and geometry developed "thinking muscles or skills" and should be part of the high school curriculum. Some people still subscribe to that outmoded theory. Now, Brain Science is in its infancy but we still know that there are many kinds of learners. The question remains are the "answers" of 100 years ago the answers for all learners today.
Must we place barriers that prevent learners form reaching their potential? What percentage of GED recipients finish community college (CC)? Without the math roadblock how many might finish CC? What percentage of CC students need math not arithmetic to succeed in their chosen careers?
One of my favorite New Yorker cartoons shows two 13 year-olds at their school lockers and one of them explains to the other, "The job I am going to have hasn't been invented yet."
Roger Berg
Senior Strategic/Community Planner
Literacy Program at the Plymouth Library
Plymouth, MA
Thanks Roger, great information. Who was the Committee of Ten?
Michael Tate
"National Education Association of the United States Committee of Ten"
Eliot, the President of Harvard with some other academics and some prep school headmasters decided what should be taught in high school.
In my opinion, most academics are hot to change others, but loathe to change what they do themselves. Old quip: It is easier to move a cemetery than change a college curriculum.
I have witnessed first-hand the horse trading that goes on when a new program or department major is developed. It is not pretty!
As someone else noted: Academic politics are so brutal because the stakes are so small.
Roger Berg
Senior Strategic/Community Planner
Literacy Program at the Plymouth Library
Plymouth, MA
How much math is enough? For adult education students, enough to get into college without placing in developmental math. Those who pursue majors requiring more math skills will take advanced math classes in college -- as they now do.
Forrest Chisman
How much math is enough? Getting into college without placing in developmental math is a pretty tall order. Many high school graduates are doing developmental math - so I sometimes wonder why we would expect ABE/GED students to get "enough math" in our courses to bypass developmental math.
I also wonder about the ladder metaphor. I appreciate the Adult Learning Standards in Washington state, which emphasize four components across all levels: numbers and number sense; patterns/functions/relationships; space/shape/measurement; data/statistics.
When I taught math, and realized that you can introduce basic algebra concepts to even the lowest level math student, while you're teaching arithmetic, that opened a whole new way for me to think about teaching and learning math. Learning the multiplication facts is useful, but not a gate-keeper to higher level math. You can approach learning the facts via the times table, which has an array of fascinating patterns. I really see math as recursive, versus a ladder.
Debbie McLaughlin
Seattle Central Community College
dmclaughlin@sccd.ctc.edu
Agreed Deborah...I am the mother of two relatively high functioning high school students. Both placed in developmental math at their chosen Universities. Both went to community colleges for recovery of their math skills and were glad for the opportunity. They needed it! I think it is a lot to ask a GED student-but what are the alternatives? What are the choices? We just don't seem to do a good job at math education or maybe it's more an issue of creating the necessary bridges from secondary to post secondary expectations. May be that's where the answer lies...
Kathy Ellithorpe
I agree wholeheartedly!
Cynthia Roe
Instructional Specialist, Adult Education Programs
Carroll Community College
Westminster, MD
Hi Forrest! Thank you for participating on the listserv and for your years of leadership.
With the technology we currently have, we could customize instruction for students (on-line or face-to-face). Then, I think Forrest's question would be appropriate.
When most of our schools are focused on standardization, "how much math" really is an accreditation question. We teachers and administrators decide for students. And, if what we do here in Washington is representative, if we err, we err on the side of too much math rather than just enough.
Here, we have decided that algebra 2 is the standard for every high school graduate. Do you see people in the near future needing that skill level? Is there a parabola in everyone's future? :) I'd really like to hear what you have to say about student assessment's role in program evaluation.
Michael Tate
Well, I think erring on the side of too much of any kind of education is always a good idea. After all, it's EDUCATION. But you're right that, in AE, the level of math taught is practically speaking a certification question: enough to get them into college for students seeking to make transitions, enough to help them handle VESL programs, if they go that way, etc.
With regard to student assessment and program evaluation, my views are TOO well published. See for example ANY of the reports that bear my name under the ESL section of the CAAL website (www.caalusa.org). Basically, I don't think there is any way in which we can know what we are accomplishing, let alone improve it, without longitudinal (5-7 years) records of student performance. And the only way to get THESE is by pre-testing on entry and post-testing at each semester break (or equivalent) and probably more often. Most standardized assessments aren't considered valid by their publishers until about 60 hours. But I find that many (most?) teachers don't think those tests accurately reflect what they teach and what students learn -- in part because of curricular differences, and in part because of inherent limits of the tests. I think they're right. Thus, many (most?) programs use locally constructed tests/metrics for program management purposes. I think that's okay as long as they are well-constructed to reflect curricula, and as long as the curricula are linked to some external validator (like state curricular guidelines and/or college entry requirements). I think it is very problematical if the program relies on individual teacher assessments alone. The teachers in a program should collegially agree on performance measures -- perhaps in collaboration with other local/state programs. At best that's a stopgap, however -- although it's better than the available alternatives. What we really need is a Manhattan Project to develop a more flexible assessment system (not a single test) for ALL of AE.
Forrest Chisman
We, at SABES (System for Adult Basic Education Support), have been working diligently to improve the teaching of math to adult learners and while I am far from an expert on math, I have learned a great deal from our math leaders regarding the usefulness of learning algebra. While on the surface it may appear that learning algebra is unnecessary in order to succeed in post-secondary education and in life, I have learned from our Math Leaders that in learning how to do algebra, we actually are learning algebraic thinking, which is a critical thinking and problem solving skill needed to succeed, not only in college, but in life. My non-expert take on this is that algebraic thinking will enable you work with a few unknown variables to figure out what might happen if x or y occurs. So beyond getting a GED and passing the Accuplacer, algebra serves a very important function. On algebraic thinking [3]
Carol Bower
Director, Northeast SABES
Northern Essex Community College
Lawrence, MA
Carol highlights a common perception among people who are less familiar with math - that algebra is working with unknown variables. It's true that much of the process of algebra deals with variables (known and unknown), but its underlying principles have to do with recognizing and finding patterns and making predictions based upon the patterns.
Knowing how to describe a pattern as an algebraic expression can be a very useful and sometimes enjoyable tool. But recognizing patterns and learning to make predictions based upon patterns have many applications beyond passing the GED and Accuplacer and other school situations.
Susan Kidd
ABE Professional Development Coordinator
State Board for Community & Technical Colleges
I used the following title a lot when teaching math: Helping Low Achievers Succeed at Mathematics (Derek Haylock & Marcel D'Eon, Springboards for Teaching). It's geared to the math of grades 2 - 8, and has a ton of interesting, engaging, hands-on activities for students. I still have materials I made based on recommended activities.
Debbie McLaughlin
Director of Basic & Transitional Studies
Seattle Central Community College
Hi Carol and other Listers:
Regarding math and SABES, here is an interesting take on the math dilemma from Tricia Donovan, also at SABES:
From Tricia:
(begin quote) I just read a piece by Arnold Packer (SCANS: Secretary's Commission on Achieving Necessary Skills) in which he argues that how we structure math classes and curricula needs to change completely -- he calls for Empirical Math -- learning math through projects geared to meet the roles we will play as adults in this country. He thinks it's more likely the majority will encounter spreadsheets than second degree algebraic equations, and he notes our lack of success with the math academic ladder proves that it's not working. As Einstein said (paraphrasing), 'The repetition of an unsuccessful action over and over again with the expectation of new outcomes is the definition of insanity.'
We shared some of the Packer piece in this quarter's SABES Math Bulletin. I'd come down on the side of those who think the type of mathematics we require is specific in its applications, and not of general use. Even those of us who succeeded grandly in manipulating symbols and expressions in Algebra II, Trig, and Calculus forget it all and wonder what it proved. I'm rambling, so will stop. Math Bulletin link [4]
SABES "Training Leaders in Adult Basic Education"
Tricia Donovan, Ed.D.
SABES CRC
World Education
44 Farnsworth St.
Boston, MA 02210
617-482-9485 x3785
Fax 617-482-0617
(end quote)
Cynthia Zafft
The comments regarding "how much math" are interesting and that's an issue subject to continued debate. I wonder, however, if it could become a moot point if we identified "GED" classes as Adult Basic Education classes and all prospective college students who don't fare well on the Compass or Accuplacer were referred to ABE, regardless of whether they have a high school diploma. Any student who doesn't score adequately on a college placement test could use this free service...and the additional academic knowledge. I'm not suggesting there's no place for developmental courses, but Adult Basic Education courses can be an important bridge for "good high school students" to gain college-level foundation skills.
I had the good fortune to attend the NCTN (National College Transition Network) conference in Rhode Island last November (2008)...a terrific opportunity to gain a wealth of knowledge on a range of topics within the transitions umbrella. In particular, the session by Pam Meader of Portland, Maine, entitled Algebra as the Gatekeeper, offered strategies for helping students develop algebraic reasoning and improving "sense making vs. symbol manipulation".
Additionally, Donna Miller-Parker and Sara Baldwin of South Seattle Community College gave an excellent session entitled Our Mission is Transition. They discussed the multi-level approach used in their basic education program to encourage students' transitions to further education, of which a student transitions portfolio was an important component. Faculty learning communities were also vital to their approach.
I wish I had more time to write on all I gained from the conference, but both of these sessions were exceptionally valuable!
Joyce Winters
Professional Development Specialist
NWRC/Owens Community College
Northwood, Ohio
Thank you, Joyce, for your kind words. I have been slogging through two days of comments and do need to address the algebra concerns addressed on this listserv. The Center for Occupational Research and Development states that algebra is the "language of technology". I believe algebra is critical for our adult students but the way that algebra is taught needs to be changed. As one person noted, we do not have to wait until a formal algebra class to introduce our students to algebraic thinking, patterns, and functions. Algebra needs to be applied, hands on and developed conceptually. Students need to be able to recognize patterns, derive formulas, understand rates, analyze trends, and construct graphs.
Case in point: I had a fisherman in my algebra class a few years back that needed to be retrained as he had broken his back and couldn't fish anymore. He received a letter from the government explaining how they were going to buy him out. It included a very complicated algebraic formula. Without some knowledge of algebra, this fisherman would have felt intimidated. Instead he felt empowered to at least question what the government was doing in this buyout plan.
Another student was involved in insurance and began to understand the various graphs from her company, especially involving rates of change. Still another finally understood statistical process control sheets she received from her worksite.
My point is without some algebraic understanding they received from my algebra course, they probably wouldn't have made those connections.
I teach for Portland Adult Education in Portland, Maine. In Maine, our adult education sites are connected to K-12 programs rather than community colleges. For our students we do offer two levels of algebra classes that students take either for high school credit or for college transitions. Students in our program who complete their GED are encouraged to take these classes particularly if they are college bound.
Most students who successfully complete our Algebra Part A and B courses have passed the Accuplacer Arithmetic and Elementary Algebra tests and start college level math courses at our community college.
The Adult Numeracy Network will be doing a day long presentation on algebra and algebraic thinking at the pre-conference session of COABE for any on the listserv attending COABE in April. NCTN will also be sponsoring a strand during COABE in which I will also address algebraic thinking.
Pam Meader
Past President of the Adult Numeracy Network
Portland Adult Education
Portland, Maine
In a previous post, Donna Chambers referred to Tom Mechem's identification of the math that is tested on the Accuplacer (see thread entitled National External Diploma Program). What are those, and how do we get that info?
Thanks,
Ramsey Ludlow
Oxford / Buckfield Hills Adult Education
South Paris, Maine
What Tom has done and what we can all do is look what is being tested on the Accuplacer (for example) or what is required in college math and make sure that our adult math curriculum is covering the gaps, between the GED or the NEDP (National External Diploma Program). For example, NEDP does not test for algebra, but rather tests for contextual real life arithmetic. When the learner sees x's and y's on a test, he/she is likely to "freak" even though they could answer a similar question if it was presented in a real life problem.
Our NEDP Plus will introduce math concepts the way they are offered on a standardized test. Exponents, variables, right triangles, and the quadratic equation are not currently required for NEDP, but will be covered in the NEDP/TTC (Transitions to College) in order to graduate. This is just an example and I am sure Tom could offer more.
Donna Chambers
Ramsey, et al.
Well, I can tell you what in my amateurish way I have done. For a number of years part of my job has been to make presentations to GED teachers and program directors regarding what skill sets are needed for success on the five parts of the GED tests. As you know, no one can see the GED tests, so it's hard for teachers to know what to teach or what it means that one of their students got a 410 on the Writing test, and so on. The GED Testing Service in Washington provides us with valuable information on the most-missed questions (based on their analysis of every test taken world-wide since January 1, 2002); we have the GED Item-Writing Manuals, which give valuable insights into the philosophy of how the GED questions are formulated; and we pester the GEDTS at every opportunity for more info. Teachers have found this to be valuable for the most part.
Lately I have focused more on the Math because it is the main reason for GED failures and it is far and away the main reason that GED grads end up in developmental courses.
Last spring, after it finally sunk in that GED grads were not getting anywhere near as far as they needed in post-secondary education, that a great majority were wallowing in (mostly math) developmental courses, that poor performance on the ACCUPLACER math test was one of the main reasons for that, and that there was no correlation between a GED math score and an ACCUPLACER algebra score, I took the ACCUPLACER Algebra test (something I recommend everyone interested in this subject to do). And I almost threw up, not just for myself, trying to battle through it, but for our GED grads, knowing what it was going to look like to them. So I took the ACCUPLACER dozens more times and I have put together another presentation for teachers and program directors which talks about the differences (in philosophy, in how the test is presented and taken, and in the skills sets needed) and starts the dialogue as to how we can create a GED math curriculum that prepares our students to pass the GED tests, do well enough on the ACCUPLACER to avoid developmental courses, and succeed in college Math classes.
(Here's a brief example: if the GED test wants you to use the formula for the area of a rectangle, it will create a "real-life" situation in a word problem, somebody building a patio or whatever, and the answer will be what our GED students consider an "answer," "460 square feet" or something like that. On the ACCUPLACER, the rectangle will have a width of "x" and a length of "x + 3," so the area will be (I can't type the exponent, but...) "x2 + 3x" and all the multiple-choice wrong answers will be in that form, more or less.)
These presentations have been great for me because of the tremendous enthusiasm and input from the teachers, "Well, here's a difficulty you present and here's how I address that in my class." And the discussion this week has been fabulous in that respect as well: so many dedicated people and so many fantastic ideas I can hardly steal them all.
If anyone were to e-mail me off-list, I could send you my PowerPoint presentation: one man's opinion, a work in progress, but perhaps food for further thought.
Tom Mechem
GED State Chief Examiner
Department of Elementary & Secondary Education
Commonwealth of Massachusetts
Thanks so much for your work and offer to share it, Tom. Has anyone also done this kind of work with the Compass placement test?
Joyce Winters
Professional Development Specialist
NWRC/Owens Community College
Northwood, Ohio
A couple of years ago a group of ABE math teachers from Washington State looked at the content of CASAS Life Skills and Employability, the GED and both the COMPASS and ASSET Numeracy/Pre-Algebra tests. If anyone would like to see the crosswalk they created, I'd be glad to send you a copy.
Susan Kidd
ABE Professional Development Coordinator
State Board for Community & Technical Colleges
Yes I would love a copy. I am part of an adhoc group in Florida and we are working on these issues.
Robin Matusow
Rehabilitation Instructional Specialist
Miami-Dade County Public Schools Regional Operations
Hi Robin:
I was wondering if the GED-Plus project in Florida is a resource for all adult education programs in Florida. Their website is a wealth of information on the model (e.g., implementation guide, newsletters, discussion board, etc.) and has a curriculum resource guide that is the biggest compendium of study skills I've ever seen.
GED-Plus College Prep Program website: [5]
Cynthia Zafft
My understanding is that it is available to any institution that wishes to adopt it. I would contact Bonnie Vondracek-Goonen at bv3008@aol.com to discuss it. She was one of the contacts for us in Miami. At this point I do not believe we have the program up and running.
Robin Matusow
Rehabilitation Instructional Specialist
Miami-Dade County Public Schools, FL
This has been an extremely useful and informative session -- in particular the discussions around the math issues.
I, like many GED teachers, was drawn to the field as a writer / reader / English major type. Teaching math has a way to recognize patterns - is very intriguing. I could see that some students would respond to that more than to the arithmetic approach. Success in life often stems from the ability to identify patterns in data and events, and then make decisions based on that new interpretation of information.
However, the texts that we use are not set up to teach math as skills in recognizing patterns. And that is an issue. Even people trained in math don't necessarily have the experience to explain how to recognize patterns. While McGraw-Hill and Steck-Vaughan have ancillary material around pattern recognition -- the mainstay texts focus on arithmetic and computation in the context of the types of real life problems that people face. Does anyone know how they are planning to address this issue?
I appreciate the links that different people gave us to websites that have that pattern recognition focus.
Also -- a great way to teach multiple variables -- is to set-up problems for selecting cell phone services.
Given the importance of this issue, I would like to suggest an independent session on how to assess progress (both for the teacher and for the student) in incorporating the pattern - recognition portion of algebra into the earlier ABE math courses.
Thank you all very much for an illuminating discussion.
Gail Bundy
Native American Multi-Cultural Education School
Denver, CO
