America believes that education is the best, most lasting gift that a free society can bestow on its children. Billions of dollars and untold human resources are expended in the public arena in the attempt to give our children the best education possible. Then the question arises: How do we know what they know? Systemically we struggle with that question. The pendulum swings from anecdotal teacher reports to portfolios to standardized tests. None of these completely satisfies or answers our basic question of how do we know what they know.
At present under the No Child Left Behind Act (NCLB), all students in the eleventh grade are required to take a test representing learning in math, reading, writing and science. All students who have complete 10th grade in Vermont are expected to show proficiency in these areas.
Mathematics is a cumulative discipline. In every course at the high school, our goal is to expose the students to the new content while reinforcing and improving their knowledge from previous courses. We regularly review material through Graded Reviews, Warm-ups, Remember & Reviews, and incorporating different perspectives of the material in SAT, problem solving, and NECAP style questions.
When NCLB was enacted, each state was required to define standards. The Vermont Department’s goal was to: “To provide a structure from which standards-based district, school, and classroom curriculum can be developed, organized, implemented, and assessed.” They organized mathematical topics into four content strands: Number and Operation, Geometry and Measurement, Functions and Algebra and Data, Statistics and Probability, defining Grade Level Equivalents in each strand. (See http://education.vermont.gov/new/html/pgm_curriculum/mathematics/gle.html)
When a student is enrolled in a class, the four content strands are inter-related. For example, a student in Geometry will need to incorporate both Algebraic and Number and Operation skills and concepts, in addition to Geometry and Measurement skills, to successfully complete a problem. Students are expected to retain knowledge as they progress through the grades. A truly educated student will have a well-balanced knowledge base in all four content strands.
As a department, we are perplexed as to why our students can successfully test on material when it is covered in class, but as juniors only 24% are showing proficiency on our NCLB assessment, the New England Common Assessment Program (NECAP). In an attempt to raise the students comfort level with the NECAP test we are going to use a model similar to the one we have used with the SATs. To prepare students for the SATs, we have used released SAT questions to expose the students to the test and the style of questions. This process has been very successful and students have said the process was very helpful in preparing them for the SAT experience.
We recently created four practice tests to help us identify what students have retained from the four content strands. These will be administered to freshmen and sophomores. These mini-NECAP tests are thirty-minute eight-question tests with four multiple choice and four short answer problems. Two are designed for the freshman level and two for the sophomore level. The material tested is culled from three years of NECAP released materials and is carefully selected to be of an appropriate skill level to the group being tested (example freshman test A does not include more than the most basic of middle school geometry questions).
In an attempt to create an authentic assessment we will count these mini-NECAPs as a test grade. As stated earlier the students have been exposed to the content being assessed and it is a fair judge of their abilities.
As a department, we will collect data from the four mini tests to help us to evaluate our programs and make changes that will strengthen our students for the standardized testing that can be important to their future beyond the walls of Hartford High School. Keep a look out for future news bulletins from the math department as we strive to better prepare our students to show what they know and know what they need to know in an ever increasingly complex world.