| Learners in algebra reform secondary classrooms use structures of metaphor in understanding mathematics. The Experientialist theory of embodied cognition holds that reason arises from the nature of bodily experience, reason is largely metaphorical and imaginative, has emotional engagement, and is mostly unconscious. reasoning. This study situates the mathematics learning by individuals between the general study of reason in embodied cognition and study of historical development of mathematics through conceptual metaphor.; Data are from 50 existing classroom observations done in 1989–1990 by Pennsylvania State University researchers and graduate students with teaching experience. Participants field tested a technology-intensive first year algebra reform curriculum. Verbatim transcripts were created using audiotaped recordings, annotated with field notes and computer screen images. This researcher developed criteria to select 5 transcripts for study, then scrutinized, coded, analyzed, and interpreted the selected data. What are the observable metaphors learners use? How do learners shift attention among elements of metaphor during the process of coming to understand? It is posited that learners use metaphors to explain, highlight, compare, form, and remember ideas.; Novel and conventional metaphors used in learning mathematics were identified. Metaphors originated with teachers, curriculum, and students. In the majority of cases, learners' attention shifts from source to target of the metaphor, an Explanatory use. In some cases, grounds or tensions are observable. Highlighting use occurs when focusing on one common aspect. Comparison use occurs when attention switches back and forth between source and target, usually following several Explanatory uses. No Forming or Mnemonic uses were identifiable, possibly due to studying introductory rather than later chapters.; Metaphors grouped in patterns operated as hinges, nests, and fans, to harvest and carry meanings and structures from specific embedded-in-the-world latter meanings and structures are displayed in general conventional form. This study forms an “existence proof” that K–12 classroom mathematics may be experienced through metaphor, offering a perspective of learners using metaphor in understanding mathematics. |
