|Home | Textbook | Newsletter | Discussion Forum | Contact
 Time to Refocus Intermediate Algebra
We need to invest in education ... the number of schools rated "Failing" is
sky rocketing ... (college) remedial programs in reading, writing, and math
has become a growth industry ... large percentage of high school graduates are
not prepared for college work ... City University of New York (CUNY) spent $33
million last year on remediation ... the United States has declined from first
place to eleventh among developed countries in terms of the percentage of
colleges graduates in its population ... the list of doomsday statements goes
on and on. From the President to the Halls of Congress to State Houses to
local School Boards, educational policy (or lack of) is high on the priority
list of concerns.
While the numbers of high school students who are well prepared for college work continues to rise, so do the numbers of
students who begin their college experience taking developmental courses.
The New York Times recently (March 4, 2011) published an article on
developmental education at community colleges. Speaking of CUNY's six
community colleges, the article stated that "About three-quarters of the
17,900 freshmen at the community colleges this year needed remedial
instruction in reading, writing, or math." Nationwide "The knowledge gap at
community colleges is increasingly being recognized as a national problem.
About 65 percent of all community college students nationwide need some form
of remedial education with students shortcomings in math outnumbering those in
reading by 2 to 1."
How well are we doing at the college level to remediate the thousands of our
students that enter our Intermediate Algebra development program? The answer,
unfortunately, is not very well. "Nationwide, as at CUNY, fewer than half of
the students directed to take one or more remedial classes (`developmental
education') complete them." Dr. Bailey, Director of the Community College
Research Center at Teachers College at Columbia University said: `Many, many
community college presidents will say that math developmental education is the
most difficult problem they're facing."
We at the college level, whether teaching developmental programs or not, need
to initiate or join the debate on refocusing Intermediate Algebra. In
particular, we need to consider the efficacy of our present programs by asking
and answering questions such as the following:
* What is the policy for selecting students
to enter developmental courses?
* What are the goals of our develop-
mental program? (What does it mean
to prepare a student for College Algebra?)
* How is mathematical reasoning
* How are reading, writing, and pre-
sentation skills incorporated, if at all?
* How much emphasis is placed on
students learning to translate a written
description of a problem into a math-
* What is the primary pedagogical
approach? (teacher centered or
* What is the principal instructional
method (e.g., lecture, small group)?
* How heavy is the emphasis on skill and
drill? How effective is it?
* What types of testing are employed (e.g.,
multiple choice, fill-in the blanks)?
* Does class size matter?
* What college career paths do students
follow who pass the developmental
* Is the course content suitable?
* How important is it to create positive
attitudes in the students? How is this
The ensuing debate over the answers to these questions will lay the groundwork
for refocusing Intermediate Algebra, as it did for College Algebra twelve
years ago. The philosophy to "educate students for the future rather than
train them for the past" is as applicable to Intermediate Algebra as it is to
(Everyone is encouraged to join in the debate on Intermediate Algebra and to submit articles on it to the Vision-Potential Newsletter.)
 Online Discussion of Questions/Postings
Kansas City Kansas Community College
This is a continuation of Don Haussler's article "The Marriage of Writing and
College Algebra" that appeared in the February 2011 issue of this Newsletter.
These Postings are writing assignments that Don has given his
Posting #1: At this point in your academic career, you have had experiences
(good and bad) with mathematics and mathematics instructors. Select either one
of the good or one of the bad experiences and "talk" about it.
Posting #2: Pick 2 "strategies" that you use when you study material in your
favorite class. How could you use these strategies to be more successful as a
mathematics student? If you do not feel either of them would work in a
mathematics class, select 2 other strategies you would try.
Posting #3: You have just come from math class. The instructor has talked
about a topic that is totally new to you. What are your feelings at this time?
How will you work with this new concept between now and the next class session
to gain a better grasp of it?
Posting #4: You have just taken a look at your course outline in algebra class
and notice that a unit test is scheduled for 2 weeks from today. What will be
your plan in preparing for the test? Also, select 1 thing that you have never
tried to do in getting ready for a test and tell how you will work with it in
preparing for this test.
Posting #5: Technology (computer, graphing calculator, software packages,
etc.) has become a part of many math classes the past few years. Knowing that,
what is your comfort level in making use of it? For you, personally, what is
the greatest challenge you will face in working with this new
Posting #6: Bill, Jane and you have just formed a study group to work on your
math class. Of the 3, you are the "expert." It seems to you that Bill and Jane
do not contribute much to the group --i.e. you do all the work and they
benefit. How do you feel about this? How will you handle this situation
Posting #7: Midterm of this semester is quickly approaching. Evaluate your performance in this particular math class. Include both the positive and negative things about YOU so far. Then, discuss how you will maintain the positive things about this semester and how you will try to change the negative items.
Are there four consecutive integers such that the sum of the first two times the sum of the last two is a power of two (i.e., 2)? First determine if the smallest of the integers is even or odd and then either give an example answering the Query in the affirmative or show that no solution is possible.
 Basketball's 3-Point Shot
The 3-point shot was first adopted by the National Basketball Association in
the 1979-80 season. For the first five years, the number of 3-point attempts
per game averaged 2.8 per game. However this changed starting with the 1984-85
season when both the number of attempts per game (3Pt Att/g) and the
percentage of successful attempts (3Pt%) began to increase as shown in the
following Table. (Source: Basketball-Reference.com.)
a. Plot the 3-point attempts (3Pt%) starting
with the 1985-86 season. Number the
seasons, letting 1 denote the 1985-86
season, 2 the 1986-87 season, 3 the
1987-88 season, etc. Develop a reason-
able model and use it to predict the num-
ber of 3-point attempts in the 2007-8
b. Plot the percentage of successful 3-point
attempts (3Pt%) starting with the
1985-86 season. Number the seasons,
letting 1 denote the 1985-86 be season,
2 the 1986-87 season, 3 the 1987-88
c. What is the general shape of the scatter
plot (power, exponential, logarithmic)?
d. Which of the two functions:
gives a better fit to your scatter plot
and provides a more accurate pre-
diction to the 32.6% success rate in
the 2007-8 season? Explain your
 Unemployment by Education Levels
"The Labor Picture for February" (2011) underscores the importance of having a
college degree when entering the job market as reported in The New York
Time in the following table.
 Eight Good Behaviors
Google recently published (The New York Times, March 13, 2011) the
results of its study on "Making a Better Boss," an effort to improve
management. The results contain the following list of Eight Good Behaviors.
Could these behaviors be modified (e.g., replace the word "employees" by
"students," "team" by "class") to Make a Better Teacher?
1. Be a good coach
* Provide specific, constructive feedback,
balancing the negative and positive.
* Have regular one-on-ones, presenting so-
lutions to problems tailored to your
employees' specific strengths.
2. Empower your team and don't
* Balance giving freedom to your employ-
ees, while still being available for advice.
Make "stretch" assignments to help the
team tackle big problems.
3. Express interest in team members' success
and personal well-being.
* Get to know your employees as people,
with lives outside of work.
4. Don't be a sissy: Be productive and results
* Focus on what employees want the team
to achieve and how they can help achieve
* Help the team prioritize work and use
seniority to remove roadblocks.
5. Be a good communicator and listen to your
* Communication is two-way: you both
listen and share information.
* Hold all-hands meetings and be
straightforward about the messages
and goals of the team. Help the team
connect the dots.
* Encourage open dialogue and listen to
the issues and concerns of your
6. Help your employees with career
7. Have a clear vision and strategy for the
* Even in the midst of turmoil, keep the
team focused on goals and strategy.
* Involve the team in setting and evolving
the team's vision and making progress
8. Have the key technical skills so you can
help advise the team
* Roll up your sleeves and conduct work
side by side with the team when needed.
* Understand the specific challenges of the
* Supported by the National Science Foundation and the U.S. Military Academy.
|Home | Textbook | Newsletter | Discussion Forum | Contact