Abstract:
This study describes the attributes of a highly accomplished mathematics teacher as
reported by the students in their class, and also determines whether high school students
can differentiate between highly accomplished mathematics teachers and others.
The 51-item instrument, Students Evaluating Accomplished Teaching – Mathematics,
was developed to map the construct of highly accomplished teaching as articulated by
the National Board for Professional Teaching Standards in their Adolescent and Young
Adulthood Mathematics Standards. Two focus groups of New Zealand high school
mathematics teachers reviewed these Standards, and found that there were more
similarities than differences between the Standards and what they would expect of a
highly accomplished teacher in New Zealand. Questionnaire items were drafted relating
to each of 470 statements in the Standards. These items were trialled in New Zealand
high schools, and analysed using factor analysis and item response theory, to select
items that completely mapped the Standards. The questionnaire was then administered
to 1611 students in the classes of thirty-two National Board Certified Teachers and
twenty-six non-Board colleagues in 13 states of the USA.
Multivariate analysis of variance and discriminant function analysis were used to
establish that students can record and report the difference between NBCTs and their
non-Board certified colleagues, and describe what students believe are the attributes of
a good teacher. Highly accomplished teachers build a relationship between their
students and the mathematics curriculum, as well as with the language and processes of
mathematics, by engaging their minds with challenging material and rich tasks. These
results provide further validation of the NBPTS certification process, and indicate that
students provide dependable evaluations of their teachers. The student evaluation
questionnaire could be used with confidence in both the USA and New Zealand to
identify highly accomplished mathematics teachers.