Assessment Report for MAT 152B SLO: Factor a polynomial
On Exam 1, students were given a problem with 7 factoring questions. Here are some observations. There were 18 students that took this exam. 100% of them knew to first factor out the GCF, but 61% did not know how to continue and factor a difference of cubes. 89% successfully applied the factoring by grouping method and the same percent were successful in factoring a trinomial where the first coefficient is a “1”. 61% were successful in applying the AC method for factoring trinomials, and 11% were successful with some of the steps but made at least one mistake along the way, the rest had no clue on applying the AC method. 72% were able to factor out the GCF from an expression that involved higher powers, 17% had the right idea but made at least one error, and the rest were clueless. All but one student (94%) successfully recognized that a polynomial was prime. Only 56% of the students were able to factor a perfect square trinomial. They had difficulty knowing where to start. Once they recognized that it was a perfect square trinomial, they were successful.
Closing the gap It is recommended that students receive additional reinforcement on memorizing the sum of cubes and difference of cubes formula. It is also recommended that additional review time be spent on techniques of factoring. The perfect square trinomial technique was the first topic learned. By the time the exam was taken, the students had forgotten this technique. It is likely that students will be able to retain the information if older topics are continually reinforced.
Below is the exam question that was analyzed:
Problem 1 Factor the following completely
A.
B. 
C.
D. 
E.
F.
G. 
This seems very through. A couple of comments:
On the sum and difference of two cubes. I always approach this as a skill in following a formula and do not have them memorize these two formulas as they are generally available inside the cover of high level texts. As a result, I would be recommending further practice in pattern recognition and formula application.
With the perfect square trinomial, when I first teach this I explain that it is a handy shortcut but if it is not sticking during their first exposure to factoring, there is the tried and true AC method as a fall back position. At the mat 152B level, if they can factor the problem with the AC method I am good with that. They need to decide if they want to focus a fewer techniques in order to master them or if they are ready to also take on the shortcut in additon to the key techniques. For some, too many techniques of the first go around is over whelming and they can still get the job done (theorically) without this short cut.
Just some thoughts.
________________________________________
From: Green,Larry - Math Instructor
Sent: Tuesday, February 05, 2008 4:04 PM
To: Marinelli-Laster,Beth - Learning Disability Specialist; Tomolillo, Christina - Psychology Instructor; Green,Kurt - Instructor
Cc: Armbrust,Bruce - Instructor; Ellis,Jane - Math Instructor; McDonough, Colleen - Math Instructor; Richardson,Steve - Instructor; Shen, Helen - Math Instructor
Subject: Initial MAT152B Assessment report
Dear Assessment Committee,
Attached is my initial report of my assessment of the MAT 152B class that I am teaching. Please give me feedback on this.
Thanks,
Larry
Larry Green
Instructor, Department of Mathematics
Lake Tahoe Community College
1 College Dr
South Lake Tahoe, CA 96150
(530) 541- 4660 x 341
GreenL@LTCC.edu