As a third grade Lead Teacher in P.S. 64 in the Bronx I am responsible for the math instruction within my own classroom.My teaching goal for the school year 2005-2006 was to be more effective in differentiating instruction and meeting the individual needs of each student. The plan I developed was to use the summative unit math assessments that were a school requirement, as well as the Princeton Review tests required by the Region formatively to help me determine student progress as well as what students needed. As I compiled the data from these sources in November 2005, I realized that the students were failing and little was being learned. I decided to shift my focus.
P.S. 64, on Walton Avenue in the Highbridge section of the Bronx, has 994 students: 80.6% are Hispanic, 17.9% are African American, 1.5% are Asian and others. Of the 80.6% Hispanic students, 37%
have been identified as English Language Learners. Even though 50% of the students went home each day to Spanish language dominant homes where 25% of the parents did not speak English. My class of 20 students was considered a monolingual class and, therefore, did not qualify for any supportive language services.
Lev Vygotsky developed a social development theory of learning.
He believed that the life-long process of development is dependent on social interaction and that social learning actually leads to cognitive development.
Black and William show that formative assessment practices can be used to improve performance or practices. Formative assessments include any activities undertaken by teachers that provide feedback to both students and teachers.
The National Council of Teachers of Mathematics suggest that assessment and instruction must be integrated so that assessment becomes a routine part of classroom activity rather than an interruption.
Sociograms: Sociograms were done to determine children’s social status as well as perceptions of their mathematical knowledge and skill. I asked about whom students would like to have lunch with, whom they would like to work with in Math, and whom they would like as friends.
Questionnaire: The questionnaire was about being a Math Explorer In an effort to create excitement about solving math problems, the daily Math period became the “Math Explorers”
Assessments of Student Achievement: Summative: 3 Math Unit Tests as well as the Princeton Review test. Formative: Mid-year assessment; oral/slate assessments.
Conversation Notes: Teacher’s notes of comments and conversations among the students.
The sociograms were done over a three month period, from October through December. The class composition was evenly divided between students who spoke English consistently at home and in school, and those who primarily spoke English only in school. The collected responses showed me that with the exception of three students, the class was able to work together. The answers to the questionnaire told me that the students enjoyed math and liked solving problems. The three Unit Math Tests and the Princeton Review test results showed that half the class had a failing score. In contrast to this data, when the mid-year assessment was given in a “formative
manner”, 80% of the students were successful. Oral/slate assessments, as well as partner problem solving, showed the same success.
The data that I collected suggests that particularly for low-level readers and students who are English language learners, assessments of content should be done within a collaborative social
framework. This data supports the research done by Lara Goldstone and Carol Tureski which showed that second language learners are not confident users of English when working in academic subjects. The oral/slate assessments indicated to me that this was a time to build capacity and confidence in the students. Assessment cannot be perceived by the students to be an extraneous part of learning: it is learning. Formative assessments must be consistent and well thought out, because it is through them that lasting and fundamental improvements in teaching and learning will happen.
Whenever possible, administer summative assessments in a
formative way. This knowledge is especially important for new and beginning teachers, because they lack their own classroom experiences that would validate their deviation from following the exact instructions in the teachers’ manuals.
Elementary schools must adopt a promotional policy that evaluates students 50% high stakes paper and pencil tests and
50% portfolio work. There can be no one test at any level in
the educational life of a child that will determine success or
failure. This research shows that any promotional policy must include multiple forms of assessment. There should not be a time in a child’s educational life where one test determines the child’s future.
Irrespective of their language skills as determined by the New York State English Second Language Achievement Test, language enrichment for second language learners should be available on a weekly schedule