MATHEMATICS REFORM

A clear vision for learning mathematics is one where students engage in meaningful mathematics experiences through the use of concretematerials andmanipulatives, visuals, technology, and other resources . It is important for students to build on their prior learning and knowledge of keymath concepts and tomake connections to their ownworld. Inquiry, problem solving, discussion, and question posing are all important parts of mathematics learning. Teachers need to use a variety of learning and assessment strategies to accommodate the different learning styles of their students.Mathematics investigations are important for students to engage in, as they can providemultiple opportunities for students to learn and apply mathematics in creative and purposeful ways. It is important for teachers to provide meaningful feedback (formative assessment or assessment for learning) to their students throughout the mathematics learning process. This is important for student improvement and for teacher reflection on the effectiveness of the mathematics opportunities they are providing for their students. It is important for teachers and administrators to engage in

ongoing professional growth opportunities and for them to reflect continuously on the mathematics teaching and learning that is happening in their classrooms and schools. This can be done most effectively through job-embedded learning techniques, such as professional learning communities or teams (PLCs or PLTs); peer coaching; group lesson study; and collaborative planning, scoring, and marking. All members of the school community, including educators, students, and parents, should be actively involved in meaningful mathematics (see Resource 1: Ontario Association for  Mathematics EducationVisionStatement).

In the early 1980s, educators were faced with a cry for a “back to basics”mathematics curriculum, which was a reaction to the “new math” of the 1960s and 1970s. At the same time, there was increasing interest in problem solving as a focus of mathematics education. As a result of the research of Piaget and other developmental psychologists, mathematics educators were shifting the focus from content to how children can best learn mathematics. Mathematics curriculum, pedagogy, and epistemology have undergone intense rethinking in the past decade and a half. A great responsibility for the success of reformhas been placed on the classroom teacher, according to recent mathematics education documents (NCTM, 1991;NRC, 1989;Romberg&Carpenter, 1986).

The role of the teacher has shifted from expert “information/ answer giver” to guide, facilitator, listener, and observer. The emphasis in the classroom has moved from traditional, skill-based procedural tasks to problem solving and reasoning. There is now cross-strand, cross-category, and cross-subject integration of mathematics tasks. There is communication and discourse about mathematics topics and increased use of technology, manipulatives, and group work. Students are involved with contextual, real-life problems that focus on developing problem-solving strategies rather than finding one single correct answer. Teaching for meaning and understanding is the goal, with the use of a variety of strategies to help students visualize abstract ideas (e.g., pictures, graphs, models, technology, language). The mathematics program also includes authentic, complex, multidimensional assessments. To some classroom teachers, many of these ideas may be new and, therefore, may require changes in practice to make them a reality.

Implementing educational reforms for teaching and learning places profound demands on teachers. If teachers are to move toward these reform visions, all teachers (novices and experts)will need to make major changes in their knowledge and beliefs about mathematics learning and teaching, as well as in their teaching practices. The changes teachers are expected to make require large amounts of time and professional development support. Many teachers’ images and beliefs about mathematics and what mathematics learning involves may still be incompatible with current research and reform efforts in the field. Several factors have influenced mathematics reform. The National Council of Teachers of Mathematics has been the main driving force in the current mathematics reform movement in North America. Other factors include national and international assessments that compare student performance, whose results appear regularly in the news media. For example, in many states, the state test results are published in local newspapers with rankings from lowest to highest. This creates a huge stigma for schools, particularly if the contextual data about mobility and socioeconomic and demographic information are not published along with the test scores. As well, curriculum documents and commercial textbooks are major factors in the reform movement.

Unfortunately, many teachers have not been given the appropriate professional development to understand the philosophy and pedagogy behind the reform-based textbooks. As a result, many teachers may be using these textbooks in a more traditional manner (for example, open the text book to the next page, teach the lesson, assign the questions, assign homework, take up the homework at the beginning of the next day’smath class),which is a less effective way of teaching. This approach also renders the new textbooks a poor investment, as they are not being used for their intended purpose (for example, the new textbooks aremeant

to enhance problem-solving skills and promote deep conceptual understanding through the three-part lesson model: explore the problem in a group or with a partner using a student-generated strategy, connect via a teacher lesson related to the problem and what was observed while students were solving the problem, and a reflection or math debrief/congress where the group discusses effective strategies and understanding of the concepts).