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Virginia Journal of Education


No Jumping Through Hoops

A Floyd County teacher describes how he reached his students without teaching to the SOL test.

by Andrew G. Givens

Can your students succeed on the Standards of Learning End-of-Course tests if you don’t “teach to the test?” You know about the increasing pressure for high test scores and about discussions of using those numbers to judge teacher effectiveness. As the pressure builds, more teaching to the test inevitably happens. Some of my colleagues readily admit this. I don’t think this is a positive development, nor do most educators: Teaching to the test can compromise the quality of education or, at the least, degrade the experience for students. It also degrades the experience for teachers.
Like all teachers, I want my students to succeed—which means, among other things, passing the EOC test. But I want my students to do more than that. I’m a math teacher, and I want them to experience a quality math education. I want students to come away feeling like they learned something worthwhile, something that can be applied in useful and meaningful ways. I want them to see that math has real power and significance, that it is relevant in their daily lives, and that it can even be fun. This is my hope.  
I think some of that hope became reality last spring in my geometry class, where I explicitly avoided attention to and focus on the EOC test, SOL lingo, SOL test items, SOL test pressure—and testing altogether. Yet the class ended up with a 95 percent pass rate on the geometry EOC test.
I know that many teachers can and do hit their SOL goals without teaching to the test, and I don’t presume to have found all the answers. I just want to add my perspective to a dialogue that often seems somewhat one-sided, that teaching to the test is becoming necessary to ensure high pass rates 

The Challenge
Many American students, of all ages, identify math as their least favorite subject. Certainly, most students I encounter aggressively admit that math is their least-liked course, as shown on the interest survey I’ve given the nearly 850 students I’ve taught in my seven years of teaching.
Math has a bad reputation; students think it’s boring, difficult, or at best a “necessary evil” on the road to graduation. Yes, some love it, but in general students seem to just tolerate math.
So, a math teacher faces the daunting challenge of motivating students to work hard at something they don’t enjoy, often find difficult, and may have struggled with or failed in the past. At the end of this challenge these same students must pass a high-stakes test that can affect the teacher’s job security. No wonder teaching to the test has become so prevalent.
Like many teachers, I found myself tempted by more narrowly-focused instruction, with an eye on SOL test preparation, rather than enriching the curriculum and enhancing the math experience. But if I didn’t enjoy teaching math because it was being bogged down by SOL test concerns, then how in the world could my students enjoy themselves? So I decided to focus completely on enriching the classroom experience for my students and myself without explicit regard for the SOL test. Making class time worthwhile for students became my top priority.

A Radical Idea
I started by asking students what they disliked about math classes, and you can probably guess what they said. They don’t like homework. They don’t like tests, particularly on Fridays, which seemed to be a common practice. They don’t like busy work, which they recognize as just filling time. They don’t like a seemingly endless flow of lectures and worksheets. They don’t like doing problems out of the textbook. They don’t like reading.

So, for the most part, except when time constraints made it impossible, I threw out these modes of instruction.
My students want to believe that what they’re studying is significant, not a waste of their time or energy. They like digital gadgets, the Internet and computers. They like seeing how math can be used in cool ways, such as saving lives, making money, creating spectacular effects in movies, or making their favorite games work. In short, they like knowing that what they are studying serves a greater purpose than just passing a test.

Their feedback focused my strategy, and pointed to the more advanced cognitive abilities in Bloom’s Taxonomy, specifically analysis, application, evaluation and synthesis. I planned all our learning activities so they would involve these four forms of higher-order thinking, using more active and hands-on methods. Additionally, I wanted to integrate auditory, tactile, visual and kinesthetic modes of interaction. I discovered that carefully crafted learning activities using a balanced mix of all of these forms of thinking and modes of interacting creates an environment of rich variety and cognitive stimulation. I believe that when students fully participate in good faith within this framework they’ll develop real math acumen, a kind that allows them to truly appreciate its significance and application. The EOC test was the only test my students took during the semester. I did not give a single test. Really, no tests! I assessed student progress and knowledge by other means.
The most critical factor in this approach is effort. My primary concern was that all students participate completely, openly and honestly in every learning activity. If they did, according to my hypothesis, they would develop enough math proficiency to apply it and pass an EOC test. So everything I planned and did had to be designed to ensure authentic effort by all students. I made sure they experienced rigor, relevancy and reward (the joy of successfully completing something significant or difficult or both). They assumed ownership of their own learning largely because they found that what they were doing was interesting, occasionally fun, enjoyable, significant, and less pressure-packed because grades were not dependent on tests. I labeled my newly developed approach, designed from student feedback, E4 or “the power of E.”

Exposure, Experience, Enrichment, Expertise—E4
E4: exposure, experience, enrichment and expertise, begins with exposing students to a topic and addressing its origin, derivation and relevancy, answering the question “Why should we care about it?” I steer clear of saying anything about the SOLs or the test. The course is about geometry, and naturally the SOLs must be satisfied, but the course is not about standards. It’s about what you can do with geometry.
During the exposure phase, I keep it “short and sweet,” conveying information in a variety of ways, minimizing (or eliminating) lecture, notes and textbook. Instead, I use physical and interactive demonstrations or videos to show the topic’s significance. Sometimes a game like Battleship or billiards or a kinesthetic activity like a tour around campus works well. Often I’ll guide students in a tactile activity like constructing a 3-D model. This is a real joy in geometry, the mathematics of spatial relationships of shapes: Try constructing a bridge without using triangles, for example. Such efforts show students different ways of thinking about math, invoking new interest. 

The next phase is experience. Once students have a basis for pursuing a topic, other than that the teacher says so, they make their first attempts at using the theory to understand how it works. They gain experience by drawing, measuring or resolving and applying formulas or algebra to geometrical shapes. This does involve basic practice with the theory, but I will not overdo “drill and practice.” That just teaches students to memorize formulas without understanding why they work the way they do. For example, students should understand where the value of pi comes from and its effects before they mindlessly use it simply as another button on the calculator. I like to show where in nature pi is found and demonstrate how it shows up in different and seemingly unrelated mathematical phenomena. 

I award credit in the experience phase for honest, good-faith effort rather than accuracy.  It’s all about trying freely, without anxiety, and learning by mistakes. I make sure every student succeeds in their practice efforts and products before we move to the next phase.

This geometry class taught me that students will learn effectively when the topic is interesting and relevant, which is much more appealing than forcing themselves to learn under the pressure of a test. They’re learning because of the intrinsic value and joy of geometry. They want to pursue it; they don’t have to do so. Students often entered the classroom with an eager question: “What are we doing today, Mr. Givens?”

Enrichment involves analysis and application. Here, we perform empirical proofs and experiments, using observation, measurement and data collection. Students evaluate their proofs by comparing formulas to measurements, observations and data, which helps them master formulas more readily. They’ve analyzed and applied formulas, sometimes using a compass and ruler, sometimes online with an interactive drawing application, not simply exercised them in problems. 

Finally, students show their expertise. I have them evaluate their work, not by testing, but by a vehicle I call a “qualitative evaluation.” I write open-ended, Bloom-style questions including a mix of descriptive, analytic and numeric problems about a specific concept. Because QEs are so difficult, students may collaborate, or use their notes, portfolios, textbooks or other resources, even the Internet. (Students are given different versions of the instrument and so they realize that copying their partner’s answers is fruitless. However, comparing effort and answers can be a useful learning experience.) These QEs easily reveal who has mastered the content, which concepts have not been successfully assimilated, and where the knowledge gaps still remain. 

Other significant expertise activities include projects or other special assignments, such as an essay, PowerPoint presentation, animation or game, which allow students to demonstrate their proficiency. I prefer these kinds of projects because they let students fully synthesize or apply their knowledge. However, this does create a time management issue that must be overseen carefully.
Here again, there are no tests, no unending stream of worksheets, and no homework, although students do often choose to work on projects at home.

This E4 structure supports differentiation as well, particularly in the expertise phase. Students may choose which product they want or I may make specific assignments based on learning styles or needs.

Assess without Testing 
Why is testing such a huge part of academic life? Sure, there are good reasons and appropriate situations for it, but it shouldn’t be the “motivation” for learning. Earlier in my career, I followed the traditional practice of testing frequently—after all, it was what I remembered of my own experience in high school. That regimen included textbook chapter tests, unit tests, quizzes, midterm exams, and a final exam but, thank goodness, no state-mandated standards test.

Assessment can be done well without using traditional testing methods. I use monitoring and dialogue, visiting each student every class period, while they are working, regardless of phase. Direct, focused and individual conversation with students about their work is most telling, and lets me quickly assess how well they understand the topic by their use of terminology and the clarity of their answers. If their explanations aren’t clear, detailed, complete, and logically ordered or connected, I can focus my re-teaching efforts or individual assistance as necessary.

For basic practice with mathematical expressions and formulas (in the experience phase), we score worksheets in class, immediately. This gives me a quick assessment of global and individual accuracy on vital skills, which informs my instruction for the next activity. Again, it’s the honest, diligent effort that counts; accuracy will become a natural byproduct of the learning process. 
Accuracy, comprehension, completeness and rigor do count in the expertise phase.  Students know by then that they must demonstrate in concrete ways the quality of their knowledge. However, rather than a test, they must apply, evaluate or synthesize their knowledge, which is also a learning activity. Learning continues. I accept their work when they believe it’s ready for submission and evaluation. I award a grade based on a previously delivered rubric, and offer specific feedback for improvement without providing the correct answers. Then they can work on their projects further. Often, I allow students to submit their work to classmates for a peer review. Learning continues. Keep in mind that these products are much more than worksheets or simple numeric answers to word problems. 

SOL Test Readiness
Although we avoided explicitly discussing the SOLs and the EOC test in class, I did familiarize students with the electronic testing application they would use on exam day. We have access to the ePAT testing program, created by the state for test-item practice and training with the testing environment. I took a period, using our school’s mobile laptop computer lab, to show students how the testing program works. They practiced using it to answer test questions, but the focus was on how to use the application, not the math content of the questions. We did check answers for correctness, however, since the students were naturally eager to see their results.

Success without Teaching to the Test
I believe my pedagogical approach strengthened students’ critical thinking and problem-solving abilities, as well as their logical mathematical reasoning. Even when students encountered a test item on a concept or formula they might not have encountered explicitly in class, they were equipped to think their way through it and try varied approaches.

For this particular class, my nontraditional approach worked: 21 of 22 students passed the EOC geometry test (95.45 percent), and the mean score was 446 (600 is maximum), which correlates to a 78.1on a traditional grade scale. Every student in the class passed the course.

I asked for honest feedback from my students, using a satisfaction survey with four simple questions: 1. How much did you enjoy this course? 2. How much did you learn in this course? 3. Did this course meet your expectations? 4. Did the teacher do a good job helping you learn? Each question allowed students to answer anonymously on a 5-point scale, 5 being the most positive answer. Overall, students reported a 3.825/5 (77 percent) satisfaction rate with the course. Question 1scored at 3.9 (78 percent) for how much students enjoyed the class and question 4 averaged 4 (80 percent) satisfaction with the teacher. While these numbers are significantly positive, there is also room for improvement. I’d like all of my performance metrics to move closer to 100 percent. However, it does appear that both my students and I succeeded in this geometry course without teaching to the test.

Givens (, a member of the Floyd County Education Association, teaches at Floyd County High School.



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