Gordon, S. P. (2006) Placement Tests: The Shaky Bridge Connecting School and College Mathematics. Mathematics Teacher, 100, 174-178.
The main point of this article concerns the transition between high school and college mathematics. Most incoming freshman are placed in a class determined by their results on placement tests. Gordon argues that this approach is extremely unsuccessful and contributes to the unpopularity of .He believes that since the changes implemented by NCTM’s Curriculum and Evaluation Standards for School Mathematics, Colleges no longer understand what students have been taught in their schools. With the increased emphasis on conceptual understanding, the greater use of technology, and the reduced emphasis on algebraic manipulation and procedural proficiency, freshmen are equipped with a very different set of skill, skills that many would argue to be preferable in a college setting. However, these Placement tests – used at almost every college for more than 20 years- test the degree to which students have mastered basic algebraic manipulation, and little else. Students are often placed far below where they are conceptually, and the colleges complain about how students are placing lower and thus how unprepared freshman are. On the other hand, some students from more traditional high schools do very well on the tests and are surprised to find that the course requires much higher levels of thinking and reasoning then they are able. Gordon suggests combining placement tests with other indicators of ability, such as ACT or SAT scores, portfolios of work, and semesters of math taken.
The more I look at this article, the more I feel that the author is making a big deal out of a small issue. There are no clear statistics to show that so many students are being misplaced. Gordon uses only anecdotal evidence and the vague data collected by angry high school teachers who would have liked to see their students placed higher. I would like to see, at the very least, quotes from the students themselves showing their negative feelings about their placement, preferably some statistics about the portion of students who feel misplaced. The students should be the judges based on their own knowledge of their own skills.
Secondly, from my own experience, I do not feel that students will be able to succeed in college mathematics without the algebraic manipulation skill that Gordon so casually dismisses. If students cannot, for example, quickly factor polynomials then they will have a tough road ahead in college mathematics. If students do not have these skills, perhaps it is better for them to take remedial or other math classes so that they are more prepared.
Gordon also claims that students perform poorly on the test because their understanding is more conceptual than procedural. From our reading in class, particularly the comparison between the 2 schools Amber Hill and Phoenix Park, I am convinced that if students have a solid conceptual understanding of mathematical concepts, then they should not have problems with these questions, in fact, they should score just as high or higher on the tests.
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I thought the way you organized your paragraph was really great and flowed nicely. I think you did a good job of paraphrasing the author's thoughts and refraining from inserting your own thoughts. You also summarized key points so that your paragraph was interesting and made sense.
ReplyDeleteI was confused at first about what changes the NCTM had caused and thus was a little lost as to why colleges don't understand what students have been taught in their schools. But as you continued to write I understood. Overall I thought you did a great job!
From my experience, the issue in this article wasn't a problem because my college advisor recommended that I take a combined Calc. 1/2 course to get a feel for college math even though I had already taken Calc. 1/2 in high school. I think I can see this being an issue though, just because even within the transition of one math class to another within the same college, I have experienced teachers who expect me to know lots of symbols and concepts that I don't.
Emily,
ReplyDeleteI really liked how clear and detailed your first paragraph was. I am interested in reading the article, but I honestly feel like you covered everything so clearly that I don't have any need to read the article. I do find it interesting though that the author thinks we should combine placement tests with other factors, such as ACT scores, because I would argue that standardized tests would have the same problems as placement tests. But maybe that's just me.
My only question on what could have been clearer is what did NCTM change. I have no idea about that. Also, I don't know anyone at BYU who has taken a math placement test, so I don't really understand the importance of this article at our particular college. But, again, maybe that's just me.
Thanks for your post!
You did a great job organizing your thoughts into a cohesive, flowing paragraph. I believe that this is an important issue: are students prepared for the challenges of college level math. You have a very good summary of thoughts from the author.
ReplyDeleteHowever, I would like more information on the changes implemented by NCTM and how those changes affected the understanding of college professors understanding.
Very good summary. You hit all the main points and were clear and concise. It is a very interesting dilema most colleges face.
ReplyDeleteI disagree with the above comments regarding mentioning of the changes of NCTM. I don't think it was necessary to include since the article is more about the affect on college enrollments of students into math classes. So, nice job sticking to the main points.
I did get lost sometimes within your sentences. So I suggest shortening sentences or adding more punctuation. This will clarify and add more understanding to your summary. But, overall you did a great job. I enjoyed the ideas presented.
I would summarize what Gordon's thoughts are in your opening topic sentence.
ReplyDeleteYou did a great job in the analysis of the article. I could tell you put thought into it. You brought up good points and supported them.
By the way, I agree with your points.