DMC Newsletter September 2007
The Developmental Mathematics Committee of
AMATYC!
Chair’s Welcome by
Jack Rotman
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 the subcommittee reports and some items from me. Thanks for contributing!
Quick
Links to contents
Faculty Development Subcommittee
Instruction & Technology Subcommittee Report
Tips and Tricks; Information Needed:
Being Really Specific by Sonia Mihok
Exit
Problems in a Math Class by Geoff
Akst
Jeopardy by Jeff Morford
A
Sabbatical Report by Ted Panitz
Introducing Radical Equations by Ana Vamadeva
Faculty Development Subcommittee
Gail Burkett, chair of the subcommittee
The prep math department at
We have a web page for ‘abuse of technology’ on the DMC website; try it http://devmath.amatyc.org/AbuseTechnology.htm and then contribute your tip or story.
Please send your short articles to Gail Burkett at burkettg@pbcc.edu
Instruction and Technology
Subcommittee Report
by Judy Giffin, chair
The State of Ohio is strongly proposing increased ACT scores and is planning to require an “intermediate” Algebra requirement before any college-level math courses may be taken (again depending on ACT placement). We are already seeing great increase in the number of Developmental Mathematics students we need to serve here at Rhodes State College. We will want to discuss any observations our committee members have made during the last year.
On our campus, all Developmental Algebra students are now
required to use TI-83 Plus or TI-84.
Even Pre-Algebra classes are beginning to use more technology after
fundamentals are mastered. Our students
observe they need to review basics mentally before they are able to use
technology intelligently. (Note:
Two of our evening instructors are using TI-83 and TI-84 calculators and some of our special class projects in their high school math classes. We are keeping lines of communication open hoping to encourage more students to plan for college. I will bring other ideas to share at our AMATYC meetings in November. Hopefully, we will discuss the new TI-Nspire and other technologies you are using on your campuses. Please feel free to express any concerns by e-mail now or at the meetings in November.
Submitted by Sonia Mihok,
I find it helpful to write down every step in solving math problems both in calculations and description in words of what is being done. This helps student better understand their notes when they get home.
For example, compare the two sets of steps for the same problem.
Solve for x given
x² - 3x = 4
Brief
x² - 3x – 4 = 0
(x – 4)(x + 1) = 0
x =
4 x = -1
Specific
x²
- 3x – 4 = 4 – 4
Set equation equal to zero by adding the opposite to both sides
x²
- 3x – 4 =
0 Next:
Factor the trinomial into two binomials
What factors of -4 add up to -3
(-4)(1)
(-4) + 1
(x-4) and
(x+1)
Note: This method of factoring only works when the coefficients
of x are 1
(x – 4)(x + 1) =
0
x – 4 =
0 x + 1 = 0
Set each
factor with a variable equal to zero
x – 4 +4 =
0+4 x + 1-1 = 0-1 Solve each equation for x
by adding the opposite to both sides
x = 4
x = -1”
x² - 3x =
4
Check your
answer by replacing x with your solution
4² - 3(4) =
4 (-1)² - 3(-1) = 4
16-12 = 4 1 + 3 =
4
4 = 4 ü 4 =4
ü
Submitted by Geoff Akst, Borough of
One of my favorite classroom techniques is what I call "exit problems". I picked up this technique when observing a part-time faculty member teach a developmental math class some 30 years ago, and it became a part of my pedagogical bag of tricks.. Here's how it works: the instructor stops talking in class about 10 minutes before the scheduled end, and puts a few problems on the board. The problems reflect what the instructor has covered that day, and they vary in difficulty. Students at their seats work the problems, and then bring them up to present to the instructor, who is seated at the front of the room.
The instructor silently indicates whether each answer is right or wrong, but does not explain any mistakes made to lead to wrong answers. If all answers are correct, the student can leave. If even one answer is wrong, the student returns to his/her seat to rework the problem, checking class notes, the text, etc. and then brings up the new answer. In this way, the class shrinks to students who didn't get it, and the instructor can speak to each one to develop a strategy for catching up.
It's a way of introducing individualization into what is after all a system of mass education. A variation on "exit problems" is to invite the first student who gets all the problems correct to serve as the official grader, sitting in the instructor's seat and reacting to other students. Every student I've ever asked to be a grader (a great honor, I explain) has seemed eager, if only to socialize with classmates. Meanwhile, the instructor can go for coffee or read the morning newspaper (just kidding!) The strategy of "exit problems" particularly lends itself to double classes which meet for more than an hour-and-a-half, in which everyone needs a break.
by Jeff Morford,
I never thought I'd like to use a Jeopardy-style review in my classroom. I always worried about what other students would do while one student answered a question. Recently I've been teaching a small learning community section of pre-algebra and decided I was willing to give it a try.
To keep everyone active I divided the students into two teams and crossed Jeopardy with Family Feud. One person on the first team picked a category and value and tried to answer the posted question. The role of being the first person to try a question rotated on the team. Meanwhile the other team got ready to steal. If the first person missed it the other team could give an answer to steal. If that team missed the question then the other team got a chance to answer as a team. For the next question the roles reversed- no one team could control the board by repeated right answers. Students explained answers when the other group asked how they found the answer and a couple problems that stumped the whole class lead to good discussions.
I may try this in a larger class by having all the groups write down their answer for an attempt to steal. Groups with the right answer will split the points if the original team misses.
The Template: see Sept07 Morford jeopardy_template.ppt
I found the template I used at the technology site for the
Grant County
A Specific Example (activity): Sept07 Morford test1 review 074.ppt
I have also provided the activity I put together for my class's review so you can see what a completed activity might look like. After revealing an answer click on the house to return to the main board. Pressing next just reveals the next question instead. I've changed the template so it just requires moving the cursor over the house to return to the main board.
Finally, my students were disappointed I did not have a Final Jeopardy question for them. I had to scramble and use one of the Mindstretchers in the textbook we use. I'd recommend you have a Final Jeopardy question ready in case your class also gets into the game as much as mine!
A Sabbatical Report: Lots of Information (something for everybody) by Ted Panitz
An
excellent report from a sabbatical, with general and specific information.
http://www.capecod.edu/faculty/tpanitz/sabbat.pdf
Introducing Radical
equations in a Developmental Math classroom
by Ana Vamadeva,
When teaching solving with
radical equations, how many of us still use algebraic skills to introduce the
topic? Whether your curriculum is reform based or traditional, chances are in many text
books that are in use today, solving radical equations would mimic the
following steps: Isolate the radical
term, square both sides, solve for x, and check for extraneous solutions.
Following this, some texts
would have a graphing calculator shot of the equation, and read off the
solution as the point of intersection.
What I have tried to do in my
Elementary Algebra class is a shift of philosophy. Here is an example of a lesson introducing
solving with radicals. The lesson begins with an important exercise.
Exercise: Draw the basic square root function by hand, with the aid of an
input/output table.
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Having
students draw the graph of 
by hand, we are
helping them refresh some ideas that has been discussed
before.
One of the important
realizations would be the
concept of domain.
Upon creating the graph of ,
we can now ask students to draw the graphs
of 
all on the same axes.
Students could now be asked to
provide the solutions
for the equations with the aid of the graphs they see
This way of introducing the
graph and making the students see the intersections being the solutions
visually help make sense of the entire situation. Having done these graphs
prior would help them have a better perspective when the algebraic skills are
introduced. Observing there is no point of intersection for
,
helps the student understand extraneous solutions very well when explained
algebraically.
Once these basics have been
communicated, I feel students are better equipped to handle the algebra. The
relevance of basic graphs makes a lasting impression for the study of any
equation or function. Radical equations would be a great place to try this
technique.
Once this is done, students
may proceed to working problems algebraically, you might want to even talk
about inside/outside changes and the effects on the graphs in proceeding
further to tie the graphs to the algebraic equations.
For example, consider showing
solving of 
using graphs & tables with translations. (prompt students with questions like, Give the basic function in 
, What are the translations in words? Draw a
graph of f labeling all important points.
As Developmental math faculty
we need to realize the different learning styles each student possess. Tying the algebra to graphs and tables could only
help more students learn and appreciate mathematics.
The Special Interest Group (SIG) on Research in Research in
Undergraduate Mathematics Education (an MAA committee) is holding the annual
Conference on Research in Undergraduate Mathematics Education, February 28 –
March 2, 2008,
NADE (National Association for Developmental education) supports a conference directed at research in developmental education: 4th International Conference on Research in Access and Developmental Education, and they have a web site at http://www.ncde.appstate.edu/researchconf3.htm . Also, we hope to create better connections with the NADE ‘Math-SPIN’ group; if you are a member of that group, and would be willing to facilitate this work, please let me know. rotmanj@lcc.edu
Update on Committee
Business: AMATYC’s New Committees to Start November
2007
On November 4, the new AMATYC committee structure takes effect. These are the new committees:
Innovative Pedagogy Strategies
Division/Department Issues
Placement/Assessment
Teacher Preparation
Mathematics for AAS programs
Developmental Mathematics
Mathematics Intensive/College Mathematics
This new structure is the result of work over a 2 year period, with approval by both AMATYC’s Executive Board and the Delegate Assembly. As you can see, Developmental Mathematics will continue as a committee. Some existing committees will see their work distributed across all committees (such as Equal Opportunity and, to some extent, Distance Learning).
For the DMC, the primary changes will be operational. As part of the new committee structure, each committee will have some Regional Representatives; these Regional Representatives will form an Executive Committee, and the Executive Committee will meet at least once during the conferences (starting in 2008). No other changes to membership are involved; most DMC members will not notice any differences in the way we function.
For THIS conference (2007,
Chair’s Wanderings: What’s
Right, What’s Wrong
By
Note: This is part 1 of a 3 part
series on Developmental Mathematics; parts 2 and 3 will appear in our next two
Newsletters.
Textbooks:
Who is driving the bus? (Or, which comes first … )
The first note in
this series on “What’s Right, What’s Wrong” dealt with mathematical robustness. Next, it might help to examine the
relationships between publishing and our profession.
What’s Right … Well, right up there on this list would
be the fact that new authors (including some members of our committee) have
written and published books; in some cases, these texts provide a fresh
alternative to the rest of the market.
In terms of helping students, the presence of the digital resources for
most books is great (DVD, tutorials, web sites, complete online support, etc).
As for What’s Wrong
… There is a tendency, I think, for publishers to put a lot of emphasis on
those digital resources, with perhaps less attention given to the actual
mathematics in textbooks. I realize that
my conclusion here may not be shared, but I think that many “textbooks” are
really just “annotated example manuals” – a long series of organized examples
with steps annotated, followed by opportunities for students to practice.
So, what’s wrong
with that … doesn’t it help students when the book shows lots of
examples with commentary?
Certainly! However, the question
is this – where is the mathematics? Is
the mathematics the sequence of steps (procedures)? Is the mathematics a series of “how to”
chapters? Or, is mathematics a set of
related sets of concepts, some of which are demonstrated in a variety of
procedures? And, is mathematics the
tools we use … or is mathematics based on understanding objects and
relationships, with a variety of tools used to carry out needed activity?
I hope that you agree
that this is not a trivial issue. Do our
textbooks encourage the memorizing of procedures and allow people to confuse
this with meaningful mathematics? Do our
textbooks focus so much on the tools of the trade (technological or other) that
our students think that the tools are the mathematics?
How does
this concern relate to publishing? Here it is … a company will
generally only try to publish a book when there is a known ‘market’ for
it. I think almost all current
developmental books are way too procedure-centered, and could benefit from
including larger concepts and relationships.
However, book companies may not see a market for this – I think the
companies are mostly looking to publish a new book with one more color than the
competition, or one more digital resource.
If you agree that
this issue is important, consider whether there are textbooks on the market
that deal with mathematics in the way you think it should. Now, no textbook does it perfect … they don’t
know your favorite trick for teaching linear inequalities! However, when you are searching for
textbooks, do you see books that are mathematical textbooks – and not just
annotated example manuals?
“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 work with the publishers. First,
we need to convince them that there is a market for developmental mathematics
textbooks with meaningful mathematics. Second,
we need to be willing to back this up when it comes time to select
textbooks. Third, some of us need to be
willing to do the writing of these textbooks.
You might see the
connection between this note and the first one on mathematical robustness – it
is hard to include mathematics that is not covered in our textbooks.
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 Syllabus project has a page there … 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 September 2007; submissions are welcome!!
Official Leadership of the Developmental Mathematics Committee of AMATYC:
Subcommittee Chairs:
Eric Aurand Gail
Burkett
Research in Classroom Faculty
Development
EricAurand@dcccd.edu burkettg@pbcc.edu
Judy Giffin Joseph
Steever
Instruction &
Technology Issues Content,
Assessment, Retention
giffin.j@RhodesState.edu wcsteej@wcc.vccs.edu
Chair of the DMC Liaison to AMATYC Executive Board