TAKSing Data

In early October, I gave a benchmark test in my PreAP Precalculus classes to see what my students' strengths and weaknesses were in 7 of the 10 objectives they are required to master on a standardized test in April. Not surprisingly, my students did very well.

This is actually the first year I have ever taken an entire day of class instruction to give the test in class. Having motivated (for the most part), highly-intelligent, college-bound, academically competitive students, the math skills on the state-required TAKS test are far below what I have them doing in class. This year, giving the test in class, did allow me to get another quiz grade in, and give the students a "blast from the past" feeling as most of them breezed through one of the easiest tests they have seen in a long time. But notice I did say MOST.

Of my 70 students who took the benchmark, only one student earned below a 70% score. At a 66%, he confessed to me that he got off on his numbering on the Scantron when he bubbled in his answer choices. Of the remaining 69 students, there were only two other scores in the 70s, one of which was a 79. Only 12 scores were in the 80s, leaving the remaining 55 students earning an A, eight of which were perfect 100s. I'm such an awesome teacher!!

But TAKS is a minimum skills test, and since my students are doing math that is preparing them for calculus and eventual careers in math, science, and engineering, you'd expect ALL of them to make 100s, but they didn't!! I'm such a horrible teacher!!

But before I start "teaching to the test," I need to take a serious look at one objective in particular--Objective 9: Percents, Proportions, Probability, and Statistics. An alarming 26 students out of 70 (37%) missed at least one of the two questions covering these concepts, with three people missing BOTH questions. Why is that?

One question was a definitional question of central tendency, whereby students had to choose the correct statistic describing a pattern that occurred the MOST. Easy, the "MODE" is the "MOST." Mean, Median, and Range all describe different aspects of data. 23 of students not mastering this objective did not miss this one. But even then, this might be forgivable, since these terms do not come up in any class at the high school except Statistics itself, which is typically a senior-level class. The last time students were exposed to these terms was when they were initially exposed to them in 7th or 8th grade. Even then, many of these students went directly into pre-algebra in 7th grade and algebra in 8th grade, which means they perhaps never were officially taught it. But bright kids can pick these types of things up in the peripheral.

The culprit for the disastrous turnout was a question about percentage:

Janet is choosing between two brands of AAA batteries for her graphing calculator. A package or three Brand M batteries costs $5.50, and a package of three brand P batteries costs $3.85. What percent of the cost of Brand M batteries did Janet save by buying a package of Brand P batteries?

F. 17% G.30% H. 43% J. 70%

The correct answer is G. 30%

What made this question so difficult? Well, for starters, it combines English with Math, and anytime students have to READ to do a MATH problem, they panic because they must squeeze their own juice! Perhaps they don't know who Janet is as why she is so concerned with figuring out her savings, I mean, buy the cheap ones already!!! Or better yet, borrow a teacher's calculator and exchange the batteries out.

Some of the answer choices were results of common miscalculations, the most common being 3.85/5.50 x 100 =70%. This is a very important calculation that has relevance in the real world, and is one often encountered in students' science classes called "percent error." Students' inabilities to put themselves into the problem, to recognize the familiarity of the calculation, or their haste in just "punching numbers" and circling the first answer choice they have been able to generate are all possible explanations.

The key to this problems is realizing that she is only saving the DIFFERENCE of the two brands by buying the cheaper, or $5.50 - $3.85 = $1.65. Since she bought the cheaper, we must look at the ratio of the savings to the one she did NOT buy. Multiplying by 100 puts it back into a percent: $1.65/$5.50 x 100 = 30% savings.

Since the results were returned and all problems gone over, most students realized how to obtain the solution to this problem and admitted that they should have got that one correct. To be sure, I have had similar types of problems for warm ups, but I've exchanged Janet's name with teachers from our campus, and I've had them purchasing various items from silk pajamas to cheap costume jewelry, to crew-cab diesel trucks. I've used similar tactics for other problem types that were missed on the benchmark.

The next most-frequently missed objective was Objective 10: Mathematical Processes and Tools and Objective 7: 2-D and 3-D Representations where 6 out of 70 (about 8.6%) missed at least one. I think the trouble arises here from student's reluctance to read carefully, draw pictures, and map out a sequence in multiple-stepped problems, all of which have dire consequences on each of my precalculus exams. They are slowly learning that the days of "plug and chug" type problems are gone, and that many problems require several steps, if not several sheets of paper. Labeled diagrams are tantamount to helping them devise a plan and in defining the variables of interest. In effect, they are learning the new standards of a game with greater expectations.

As they progress throughout the year, staying diligent in their coursework, and earnestly participating in the "warm up" problems that target remote, isolated skills that have atrophied, their TAKS skills will take care of themselves. Anything less than a commended status on their tests in April is reproachable and an object of solicitude.

I think it has become a matter of pride among my preAP students to do well on things they are expected to ace. It's MY tests they should respectfully fear and prepare for, NOT the TAKS test. It's MY job to keep pushing them increasingly further as they are increasingly capable, reviewing, reassessing, and redoubling my efforts, emphasizing excellence, diligence, and persistence.