This study focused on preservice teachers at early childhood and elementary levels to identify prior beliefs they bring to their mathematics methods classes, how these beliefs affect their understandings about mathematics teaching and learning, and how these beliefs are reconstructed while engaged in a contructivist designed mathematics methods course. Data collected included in-depth student journal entries, personal histories of preservice teachers' prior mathematics experiences, and small group interviews. An interpretive analysis of the data identified emergent themes related to preservice teachers' beliefs about themselves as learners and teachers of mathematics and how these beliefs were reconstructed during the course. Five major themes were identified: preservice teachers prior beliefs and experiences; increased understandings about themselves as learners of mathematics; new learning about mathematical pedagogy; new or different ways of learning mathematics; and anger about their previous mathematics experiences.

The research and the study focus on the problem of dissociated learning. Why do students fail to connect with knowledge? The purposes of the study are: to summarize research pertaining to brain growth; to describe educational approaches and tactics consistent with this research; to test a brain research-based program designed to connect children to knowledge. The study rests on two research-based assumptions: strategies that connect dysfunctional or developmentally delayed students with thinking and learning will connect children in general with thinking and learning; educational activities integrating spatial information processing with linguistic processing will develop thinking skills more effectively than programs that do not. The apparent reason for the success of a spatial/linguistic program is that cross-modal activities mirror, or model, the integrated processes of the brain, impacting attention, emotion and logical operations. Increasing numbers of students fail to connect with writing. Many of these students can draw. Can drawing be used to connect these students to writing as thinking? The hypothesis is that a cross-modal activity combining drawing (a spatial activity) with writing (a linguistic activity) will develop descriptive, analytical and inferential thinking skills more effectively than a writing program that does not. The study targets children who receive special services, including those with language- and attention-related problems. To test the hypothesis, a quasi-experimental/control study was designed, involving 200 students in grades K, 3, 4, 5 and 6 in intact classrooms in two elementary schools. Approximately 2,000 pieces of data revealed a significant effect for the treatment, Drawing/Writing, on writing and thinking skills in the experimental group, including students who receive special services. The conclusions of the research are that brain research has relevance for education and that cross-modal activities provide antidotes to dissociated learning. The conclusion of the study is that, as a writing program, Drawing/Writing has broad usefulness and appeal.