DMC Newsletter February 2008
The Developmental Mathematics Committee of
AMATYC!
Chair’s Welcome by
Thanks for your participation in the Developmental Mathematics Committee (DMC). We are doing important work together!
This Newsletter has 5 items submitted by members, as well as some reports and other items from me. Thanks for contributing!
Quick
Links to contents
Tips and Tricks; Information Needed:
Quizzes
in a Different Way by John Boncek
Zero
in Division: Images … Concrete by Dan, Sheldon
Free
(online) Math Texts by Alain
Using
Pattern Building to Generate Symbolic Form by Ed Laughbaum
Arithmetic
& Number Sense Course by Jeff
Morford
DMC
Subcommittees: 2
Traveling Workshop in Developmental Mathematics
Network and Sharing Session 2008 Conference
Themed
Session for Developmental Mathematics 2009 Conference
Developmental Mathematics “Focus Conference”
Submitted by John Boncek,
Several of my teaching colleagues have remarked that I have an unusual way of administering quizzes to my developmental mathematics students.
Once a week, I ask my students to solve one or two problems based on material we've covered in class. In order to receive full credit, they must show all their work. They are permitted to use a calculator, ask me questions, and refer to their class notes and textbooks. On occasion, I permit them to work on the problems in two-person teams.
Each quiz lasts about 15 minutes. While they are working, I wander the room, observing and commenting on their work. I often stop and ask questions, make suggestions, or give praise.
I grade their work on a scale of 5 (F) - 10 (A), and count it as 10-20% of their final grade in the course. Any student who arrives on-time and spends the allotted time working on the problems knows that they'll receive a grade of at least 6 (D). (Note: Although a grade of 'D' is considered passing, developmental studies students must earn a 'C' to progress on to the next course.)
Why do I quiz this way?
1. Many of our students will not do
homework. This type of quiz guarantees that
everyone in class will spend at least 15 minutes per week solving
problems. Occasionally, success on the
quiz is sufficient incentive for a student to attempt more of the homework
problems on their own outside of class.
2. It decreases tension in the classroom. Many of our students have not been in a
mathematics classroom for many years and are afraid of being tested. This type of assessment makes them feel more
comfortable and often results in higher quality work. I also get an opportunity to get to know each
student by name and to interact with them on a face-to-face basis.
3. I get to see how my students are approaching
the material we've studied. I gain
immediate insight into what they're thinking and where they're confused. It also gives me an opportunity to correct
their errors before they've become bad mathematical habits.
4. It gives me a pool of questions that the
class can use for review for major tests.
Zero in Division: Images … Concrete
Submitted by Dan, Sheldon,
Dividing zero by a nonzero number is like dividing no money on the table among 5 people (each will get nothing)
Dividing a number by zero is like having $5 on the table and no one to divide it among (will not do that)
by Alain
The first outcome of
Using
by
Ed Laughbaum, The
<
The brain uses a
considerable amount of time generalizing patterns. As such, it is quite
proficient at its work. In creating the symbolic representation of a function from
a contextual situation, we find that many of us ask students to translate the
English to algebra using key words. This can end in failure because of the
various meanings of words and sentence structure. If our students display weak
English skills, then we exacerbate the translation process.
For good or bad, on
average, the brain will generalize a pattern after being exposed to it three
times. Nobel Laureate Gerald Edelman describes the brain this way, “… the
brain’s capacity to generalize is astonishing.” It makes sense that a big part
of the teacher’s work should involve pattern building to a generalization.
An example of
converting a “linear” situation to symbolic form is available on the DMC
website … here is the link
Using
Pattern Building to Generate Symbolic Form. The process also works well for
exponential, rational, and quadratic functions. Because the brain tries to
generalize on its own, we typically want to embed the pattern building in a
guided discovery activity to avoid incorrect generalizations – as best we can.
[Editor note: Sometimes, it seems like one
repetition is enough to generate a pattern … seems to especially work when the
process results in the WRONG pattern being generated (like ‘reducing rational
expressions’). J and L]
Arithmetic & Number
Sense Course
by Jeff Morford,
by Jane Tanner, DMC Liaison to the AMATYC Executive Board
Jane Tanner, Northeast Vice President, is our new liaison from the Executive Board. She has 25 years experience of teaching developmental math, including the past 6 years of online instruction. Her role is to bring any concerns that the DMC Committee has to the board, as well as assisting with any motions that the committee wants the board to consider.
by
The new AMATYC Academic Committee process involves the appointment of 8 Regional Representatives to each committee. For the DMC, these people have volunteered and have been appointed by AMATYC:
|
Akst |
Geoffrey |
NY |
North
East |
|
|
Ellis |
Wade |
CA |
|
West
|
|
Feenstra |
Jennifer |
GA |
|
South
East |
|
Love |
Marilyn |
WV |
|
Mid
|
|
Mansky |
Cheryl |
OH |
|
|
|
|
Pat |
OR |
|
|
|
Shotwell |
Jeanette |
TX |
|
South
West |
|
Storey |
Eleanor |
CO |
|
Central
|
These Regional
Representatives are providing valuable assistance to the DMC; I have conferred
with them on the direction for the DMC and on specific projects … and I
appreciate their help!
From
Change is a process, right? At the 2006 AMATYC conference, we started a “4 subcommittee structure”; immediately prior to that, we did not have any functioning subcommittees (though we had others in the past). We even had people volunteer to lead these 4 groups, and some general ideas for what they would do.
During the next year, however, it became clear that we did not need 4 subcommittees at this time. Our major work is being accomplished by ‘ad-hoc groups’ (see other notes in this newsletter). After conferring with our regional representatives and DMC leaders, we have developed a new plan.
Therefore, I am announcing that the DMC will now have two subcommittees.
Content, Assessment, & Research Subcommittee:
Basically, ‘what we do’.
Chair: Judy Giffin
Instruction and Faculty Development:
Basically, ‘how we do it’.
Chair: Gail Burkett
I am confident that this structure will meet our current needs; we will remain flexible so that we can respond to future needs of our members and the profession.
Traveling Workshop in Developmental Mathematics
By
At the 2007 Conference, the AMATYC Coordinator for Traveling Workshops (Pat Averbeck) presented basic information to the DMC at one of our meetings. Those in attendance were excited by the possibility of bringing this type of training to some of the faculty who are not able to attend conferences.
A team of people volunteered to get the Developmental Mathematics Traveling Workshop started (DM TW). Since the conference, these people have contributed ideas for the topics that should be included in the DM TW. So far, these ideas have been suggested:
1. the students themselves, where the disconnect that got them into our developmental math courses occurred and why,
2. about how persons acquire math concepts and skills anyway,
3. other persons' answers to "when am I ever going to use this?",
4. maybe some other views on assessment---continuous or discrete?
5. how others handle specific topics (ie, fractions; (mis)use of calculators; etc)
6. How about a work shop on using technology in developmental courses, successes and failures…or pros and cons
7. How about Study Skills for Developmental Math Students
These are the current volunteers for the DM TW:
Cheryl Mansky,
Gail Burkett has agreed to lead the project. We can still use help with this project (we need lots of input, ideas, and expertise). If you are interested, contact either Gail or Jack.
Network and Sharing Session … Returns to
AMATYC Conference 2008
We have submitted a proposal to host a “Developmental
Mathematics Network & Sharing” session at the conference this November (
The structure is like this … we identify a few ‘hot topics’ in the profession, and a label discussion table for each one. Those attending start with one topic, and stay with it as long as they like. There is no agenda or program; this is direct professional-to-professional networking focused on getting answers and sharing information.
We (Judy Giffin, Gail Burkett, and
Themed
Session for Developmental Mathematics
For the
At this point, the process starts with people indicated if they are interested in working on the themed session planning – picking the topic (theme) and eventually identifying presenters. If you are interested, just let Jack know!
Developmental Mathematics “Focus
Conference”
By
The DMC is developing a concept for a national focus conference on developmental mathematics. Although this is in the very early stages of exploration, we are developing a concept for a national focus conference on developmental mathematics. The need here is due to the tendency for college mathematics efforts (like grant funding) to focus on “math intensive” courses and for high school mathematics efforts (like NCTM) to focus on K-12. Most developmental mathematics efforts at creating a new vision or systematic course redesign have been state- or locally-based; those efforts – often valuable – have not translated into basic changes in our curriculum or instruction.
The current work is being based on issues identified by the ‘leaders’ of the DMC (regional representatives, subcommittee chairs); I am working to transform that input in to a concept paper for a focused conference. This effort would likely require AMATYC getting a grant to cover partial costs of the conference.
Highlights of the current draft include:
Ø Rationale (developmental mathematics, nationally, remains relatively unchanged.
Ø Prior Attempts (local or state efforts, limited impact; no recognized ‘models that work’)
Ø Why Old Approach Did Not Work (faculty isolation, lack of a shared vision, administrative issues)
Ø Focus Conference (two days, specific outcomes, plan for dissemination)
If you have any suggestions for this activity or comments to
the highlights listed above, contact
Even though we do not know much at this point about where this will end up, I wanted to keep the DMC membership informed.
Chair’s Wanderings: What’s
Right, What’s Wrong
By
Note: This is part 3 of a 3 part
series on Developmental Mathematics; parts 1 and 2 appeared in our last two
Newsletters.
Professionalism?
What does that mean?
The first note in
this series on “What’s Right, What’s Wrong” dealt with mathematical
robustness. The second note examined the
relationships between publishing and our profession. This last note presents a challenge to us as
professionals
What’s Right … Among the members of this Committee are many committed faculty who answer the call for
assistance. For example, in early December
2007, an email was sent asking for volunteers to help AMATYC Project ACCCESS
fellows; within 24 hours, we had over 20 people offer to help. We have about 10 people who have volunteered
to help with the “DM TW” (Developmental Mathematics Traveling Workshop). Outside of the formal membership of the DMC,
many people attend our committee meetings – when they could chose to attend a
session at the conference.
As for What’s Wrong … I think the two largest problems (especially true in developmental
mathematics) are isolation and no shared professional standards.
First, many faculty
are isolated
from others who share the same profession outside of their home institution. Unlike the classic professions (medicine and
law), we have fairly low rates of participation in our professional
societies. This is not a matter of fault
– it’s clear that faculty compensation is not at the level of medicine and law,
and lower compensation makes it much more difficult to participate
professionally.
However, there are
some professional activities that only involve expenditure of time and energy
(as opposed to $$), or a modest amount of money. Certainly, a professional conference (like
AMATYC or NADE) is a significant cost; how about the membership cost? AMATYC membership is currently $75 per year,
with half-price membership available for adjunct faculty.
Everybody who is a
member of the DMC is probably a member of AMATYC (that’s the way it’s supposed
to work), so am I preaching to the choir?
Well, here’s another question – how often do each of us remind our ‘non-member
colleagues’ that they really ought to join AMATYC? Do all of our departments report with pride
that “70% of our math faculty are members of AMATYC”?
Nationally, our
AMATYC membership is roughly 10% of the practicing professionals. Although it is impossible to get good data on
this, I suspect that this participation rate is a bit lower within
developmental mathematics.
Second, a lack of shared
professional standards results in a lowered rate of achieving
positive results. Now, we don’t need
professional standards of public behavior (though other professions could
benefit!) – no, what we are missing is a collection of
standards that identifies outcomes that we see as desirable and accepted means
of achieving those outcomes. Therefore,
we spend our professional discussions generally sharing little tricks and hints
– which can be shared because they don’t depend on common outcomes or means.
Should we have one
and only one accepted standard for outcomes and methods? Absolutely not. Within medicine, there are several accepted
standards (roughly called “MD”, “DO”, and “PC”). We could have 3 sets of standards to meet the
varying demands placed on our programs, and our professional discussions would
rise to a higher level.
“Don’t find fault …
find a remedy; anybody can complain.”
Henry Ford
To fix this problem (if we agree that it is a problem), we need
to take on the work – and not wait for others to fix our problem. First, we are (each and every one) the best
ambassadors for professional participation with AMATYC … make it a part of your
routine conversations with colleagues. Second,
many of us are involved with affiliates of AMATYC – membership in an affiliate
is a great thing, but is no substitute for involvement with a national
organization … at your affiliate meetings and in email discussions, encourage
AMATYC membership as well. Third,
within AMATYC, we should begin the process of identifying sets of professional
standards (you might call them “models”).
As a related
concept, think about this … the DMC will need a ‘new chair’ in 2009. I will be finishing these two 2-year terms in
‘office’, and we will need a person willing to take on the job of being
chair. It is not too early to begin
considering this role; if you are interested, or just want to explore the idea,
just send me an email.
My goal with this
essay is to challenge your thinking and provide some possible direction. I’m not trying to convince you that I am
right (could happen, though J),
only that there might be some ideas worth pondering.
Consider what you could contribute to a future Newsletter.
“Contributions” does not mean “hours of work”. A contribution might be 25 words describing a cool website you’ve found. A contribution might be 50 words recommended a book you’ve read recently (related to math education). A contribution might be 100 words outlining something that seems to “work” for your students in the classroom or online. Just send your contribution to rotmanj@lcc.edu.
The website is doing well. The “Links” page is updated … the Newsletters are posted … and there is an electronic DMC membership form.
DMC Membership Form
If you know of anybody who might be interested in joining our committee (and if they belong to AMATYC), they can go to our web page to complete a membership form: Link to Online DMC Membership Form
Future Newsletters
The chair (
The next DMC newsletter is likely to be sent during May 2008; submissions are welcome!!
Official Leadership of the Developmental Mathematics Committee of AMATYC:
Subcommittee Chairs:
Gail Burkett Judy
Giffin
Instruction &
Faculty Development Content,
Assessment, & Research
burkettg@pbcc.edu giffin.j@RhodesState.edu
Chair of the DMC Liaison to AMATYC Executive Board