Changes in approach towards Mathematics teaching and learning

CHANGES IN HOW TEACHERS TEACH MATHEMATICS AND HOW STUDENTS LEARN MATHEMATICS

Students in reform-oriented mathematics curricula (compared to traditional programs) perform better in assessments of mathematics understanding of concepts but poorer on assessments of computational ability (Dessert, 1981). Mathematics content decisions at the secondary level are impacted primarily by seven different factors (Cooney, Davis, and Henderson, 1975):

1. Requirements or regulations from governing bodies (e.g., OSPI or the Legislature).

2. Objectives developed by a teacher, a department, or a district committee.

3. The students’ expected use of the content to be taught.

4. The students’ interest shown in learning the content.

5. The teachers’ interest in teaching the content.

6. The predicted difficulty of the content.

7. Authoritative standards expressed by professional groups (e.g., National Council of Teachers of Mathematics or Washington State Mathematics Council).

Teachers’ content-decisions differ and are impacted by their mathematical knowledge, their interest and enjoyment in teaching mathematics, their beliefs in the importance of mathematics, and their expectations of what students can achieve (Porter et al., 1988). A distinct minority of teachers make content decisions based on their strong convictions about mathematics (and these teachers often are not the ones with the greatest mathematical knowledge) (Freeman, 1986). Teachers’ prior experiences as students learning mathematics in school settings have a strong impact on their subsequent practice and beliefs as professional teachers of mathematics. In this regard, Ball (1987) described the need of teachers to “unlearn to teach mathematics.” The responsibilities of the teacher as a professional have been redefined by the reform movement: A mathematics teacher today is responsible for understanding how each student constructs a personal understanding of mathematics within the complex environment of the ongoing mathematics classroom (Steffe, 1988). Three elements are basic requirements if positive reform is to occur in how mathematics as it is both taught and learned (Lovitt et al., 1990):

1. Mathematics teachers must reflect on their current practices and then be encouraged to develop, in very practical terms, a clear vision of what the suggested changes in mathematics education imply for their own personal behavior and role as a mathematics teacher.

2. Mathematics teachers need access to exemplary curriculum materials that help them reflect on their current roles as teachers, try out new roles, and modify their actions as teachers in line with the “accumulated experience” of the many teachers involved in the development and testing of the materials.

3. Mathematics teachers need access to a motivating and well-structured in-service program that focuses on supporting their professional growth as they try to reshape how students learn mathematics in their classrooms.

“The goal of many research and implementation efforts in mathematics education has been to promote learning with understanding. But achieving this goal has been like searching for the Holy Grail. There is a persistent belief in the merits of the goal, but designing school learning environments that successfully promote

understanding has been difficult” (p. 65) (Hiebert and Carpenter, 1992). The words “slow and difficult to achieve” best describe the classroom changes suggested by professional guidelines for improving mathematics education (Cooney, 1985; 1987). The primary hindrances are teachers’ beliefs regarding the nature of mathematics (e.g., as a formal., external structure of knowledge rather than a human activity). These beliefs subsequently impact the teachers’ view on how mathematics needs to be taught (even though they often do not believe that this is the best way to teach mathematics) (Dossey, 1992). Clarke (1997) identified 12 factors that influence teachers as they try to change their role and actions in mathematics classrooms (listed in random order):

1. The educational reform movement in general.

2. The principal and school community supporting the teacher.

3. Access to internal support personnel in the teacher’s building.

4. A spirit of collegiality, collaboration, and experimentation on a teaching staff.

5. The building of grade-level teams of teachers.

6. Access to innovative curriculum materials.

7. Access to an extended and varied inservice program.

8. The availability and input of external support personnel.

9. Access to an educational researcher as an audience and a critical friend.

10. Establishment of outcomes (goals and assessments) valued by the teacher.

11. The day-to-day conditions under which the teacher works.

12. The teacher’s knowledge or understanding of mathematics.