DMC Newsletter January 2007
The Developmental Mathematics Committee of
AMATYC!
This newsletter offers you some “tips and tricks” from
colleagues, as well as an update on Committee business. Included also is a brief report from the
committee meetings in
What does the committee need? Well, we need some subcommittee leadership
(see the report from committee meetings in
Quick Links to contents
An Alternative Method of Simplifying Radicals John Close & Celestina Punzalan
Fraction Method for Factoring Darla Aguilar
Calculator JavaScript Jeff Morford
Report from Committee Meetings in Cincinnati
The Newsletter and Website; Syllabus Project
An Alternative Method of Simplifying Radicals
Many Elementary Algebra texts simplify radicals using the “Multiplication Property”, as shown in the following example:
Our students have struggled with this method partly because it requires them to ‘see’ perfect squares. Over the last decade or so, we have had a great deal of success using an alternative method that uses the prime factorization of the radicand. A typical example follows:
When teaching this alternative method, we give the following instructions: “Get the prime factorization of the radicand. Circle (or underline) pairs of like factors. One factor from each circle (or pair) goes outside the radical sign and factors that aren’t circled ( or underlined) remain inside. Multiply the factors outside. Multiply the factors remaining inside.” That verbiage sounds a bit strange at first, but usually a few examples are all it takes for the students to ‘get it’.
This method extends easily to radicals of higher indices. For instance, to find third roots, circle (or underline) sets of three like factors; to find fourth roots, circle (or underline) sets of four like factors, and so on.
Negative radicands under odd indices can be handled by using repeated factors of -1, as in the following example:
Sometimes this explanation doesn’t mesh well with the problem sets in a traditional text. However, that issue can be resolved by carefully rearranging the order of the various subsections of each problem set.
Submitted by John F. Close,
Here is an example: 9x2 + 6x – 35
To begin: multiply the first and last numbers together (9 x 35= 315) and find the factors of the product that subtract (because the last sign is a subtraction) to make the middle term (21 x 15 =315 and 21-15=6 so we want to use 21 and 15)
put in with the factors on top of the first number
Reduce the fractions
Then rewrite with the denominator in front of the x term: (3x + 7)(3x – 5)
Example number 2: 5x2 – x – 18
5 x 18=90 so we need factors of 90 that subtract to make 1. Those factors would be 10 and 9 (10-9=1)
we would make the 10
negative because we want to get a negative one answer in the middle
Reduce to get 
Rewrite as (5x + 9)(x
– 2)
Submitted by Darla Aguilar,
"Over the last few years I have put together a few
simple calculators using Java
First I thought that as students come to me asking for extra practice on a specific type of problem I could create a new calculator for them to use. While it would not show the intermediate steps it is easy to create a large number of random problems and the students can get immediate feedback if they are right.
Then I thought about how I can use these scripts to give students a better sense of variables and algebra and how to use them. I thought I could give Beginning Algebra students print outs of the html source code (View Menu . . .Source on Internet Explorer). Students could then describe the kind of calculator they are going to make and create it. For instance a student could make a calculator where other students will practice solving equations of the form ax + b = c. The HTML basics would all be in the template and they would just have to rearrange the input boxes, adjust the text and make the Submit and Give the Answer buttons return the value of ( c - b )/a.
So, let me offer the following. Feel free to view the source of my web pages and copy to your own web site. Invite students to create similar calculators. I'll post them and give the students credit if you and they want. Also feel free to view other scripts I've created at:
http://msumorfords.com/jeff/presentations/michmatyc_summer_2000.htm , or
http://hfcclab.info/materials11.htm
View, use and modify the source code as you desire.”
Submitted by Jeff Morford,
Report from Committee Meetings in
The DMC had two business meetings during the conference (November 2006), with a total of about 50 different people attending a meeting. The group had some outstanding conversations, and began making some plans for work of interest. The first order of business was the new subcommittee structure, shown in the table below:
|
Subcommittee |
Purpose |
External Links |
|
Instructional and
Technology Issues |
What classroom
methods produce better learning or keep students motivated? What technology
should be used in face-to-face or on-line? Focus on current
issues in pedagogy Resources for
faculty |
Distance
Learning. |
|
Content,
Assessment and Retention Issues |
What should be
emphasized? How should ‘math’
be assessed? How do we support
under-represented students in our curriculum? Focus on current
issues in content & retention |
Program/Curricular
Issues; Tech Math/AAS; Placement & Assessment. |
|
Faculty
Development |
What ‘training’
would help new faculty in the profession? What resources
exist for continuing development? |
Faculty
Development. |
|
Research |
What does classroom research show? Is there evidence that a pedagogy ‘works’? |
Placement & Assessment |
Each of these 4 subcommittees needs at least one leader (as
a subcommittee chair); two people at the meeting indicated that they would be
willing to provide this type of leadership … so two more people are
needed. The DMC chair will continue to
“collect names” of those interested until the end of February 2007; if you are
interested, just send me (
The groups considered two existing AMATYC position statements that originated from our Committee; in each case, some minor wording was suggested. These modifications will be submitted to AMATYC for approval at the Spring 2007 Executive Board meeting.
The chart below gives the possible project(s) for each subcommittee
|
Instructional and Technology Issues |
Examine calculator usage – both policies and results (connects to research subcommittee work). |
|
|
Content,
Assessment and Retention Issues |
Collect data on placement test cutoffs in use. Collect information on placement systems, by developing a form to collect data from local colleges and/or affiliates. |
Note: Coordinate
our work with the AMATYC “Placement and Assessment Committee” |
|
Faculty Development |
Add a page to the committee web site, with links to local faculty development resources. |
|
|
Research |
Develop a database on “what works” using informal research. As a start, contact project ACCCESS fellows concerning their projects. |
|
These tasks came from the committee meetings in November; they will be defined more fully when the subcommittee leadership has been identified. At this point, my top priority is to establish the leadership so the work will get done … if you are interested in leading a subcommittee, let me know.
The Newsletter and Website;
Syllabus Project
This newsletter has the honor of showing the first contributions from our members (for a long time) … and there are three of them! The Newsletter Editor couldn’t be happier -- at this point, that editor is the DMC chair.
“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. Like the Newsletter, you can send contributions to me!
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 April 2007; submissions are welcome!!