Learning strategies

Learning strategies are behaviours and thoughts affecting the learners' motivation or affective state, or the way in which the learner selects, acquires, organises and integrates new knowledge (Weinstein & Mayer, 1986). The use of learning strategies has emerged as a critical variable in the learning process (Wang, Haertel, & Walberg, 1993). Research findings (Anthony, 1994a; Campione, Brown, & Connell, 1989; Herrington, 1992; Schoenfeld, 1987; Swing, Stoiber, & Peterson, 1988) have prompted a number of mathematics educators to promote the teaching of specific strategic behaviours as one way to improve learning outcomes (see Herrington, Wong & Kershaw, 1994).

Recent curriculum documents such as Mathematics in the New Zealand Curriculum (Ministry of Education, 1992), and A National Statement on Mathematics for Australian Schools (Australian Education Council, 1991) promote a range of cognitive and metacognitive learning strategies including elaboration, orgcmisation, planning, monitoring, checking and reflection. New curriculum documents also reflect current debate on how mathematics is learnt: "the purpose ofstudying procedures and algorithms shifts from proficient execution to reflective analysis of mathematical patterns and relationships" (Hiebert, 1992, p. 448).

For many mathematics educators constructivism captures the essence of the proposed learning changes (Leder & Gunstone, 1990). The automation of skills and passive learning should be replaced by active learning processes in which learning is understood as a self-regulated process of resolving inner conflicts that often become apparent thorough concrete experience, collaborative discourse and reflection: "As new experiences cause students to refine their existing knowledge and ideas, so they construct new knowledge" (Ministry of Education, 1992, p. 12). Although constructivism clearly promotes appropriate learning strategies as a significant factor in successful learning, Noddings (1993) warns that "turning students loose 'to construct' will not in itself ensure progress toward genuinely mathematical results" (p. 38). Although all students inevitably perform constructions the mathematics that they produce may not necessarily be adequate, accurate or powerful: "weak acts of construction" described by Noddings (1990) are flimsy and often indistinguishable from rote learning.

Hennessy (1993) commented that too few of today's classrooms encourage students to perceive what they are doing as the construction of knowledge. Likewise, Bereiter (1992) claimed that "the constructivist view of learning, although widely shared by educators, is kept hidden from the students" (p. 354). Without the knowledge and application of appropriate st~ategic learning behaviours students will be ill-equipped to cope with the high cognitive demands of a constructivist learning environment (Perkins, 1991). It is of concern that

research findings (Anthony, 1994b; Baird & Northfield, 1992; Peterson, 1988; Schoenfeld, 1987) indicate that many students exhibit passive learning behaviours. Those strategies that students reported using most often were not those that are frequently proposed as facilitative of learning, such as elaboration, summarising,

and metacognitive strategies to direct and control mathematics learning.

In order to ensure that instructional demands and practices in the mathematics classroom do in fact provide students with the opportunity and the stimulation to construct powerful mathematical ideas for themselves and come to know their own power as mathematical thinkers and learners, it is timely that we learn more about learning strategies and their relation to knowledge construction and performance. To provide an alternative viewpoint from research studies which focus on explicit strategic identification, or on instructional intervention, this paper identifies five possible reasons for students' failure to use appropriate learning strategies.