Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experience
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Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experience
Coming to Our Senses: Reconnecting Mathematics Understanding to Sensory ExperienceAna Pasztor School of Computer Science Florida International Univers Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experiencesity University Paik, Miami, FL 33199 pasztora@cs.fiu.eduMary Hale-Haniff School of Social and Systemic Studies Nova Southeastern University 3301 College AvenueFort Lauderdale, FL 33314hale-haniff@email.msn.comandDai ia M. Valle Claude Pepper Elementary School 14550 S.W. 96 St.Miami, FL 33186The chi Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experienceld cannot conceive of tasks, the way to solve them and the solutions in terms other than those that are available at the particular moment in his or hComing to Our Senses Reconnecting Mathematics Understanding to Sensory Experience
er conceptual development. The child must make meaning of the task and try to construct a solution by using material she already has. That material caComing to Our Senses: Reconnecting Mathematics Understanding to Sensory ExperienceAna Pasztor School of Computer Science Florida International Univers Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experience87, p. 12)IntroductionAt this time, we are experiencing a global shift from a positivist (rationalist) paradigm toward a constructivist (naturalistic) paradigm. This shift is emerging in a wide range of academic areas such as philosophy, the arts, education, politics, religion, medicine, physics, ch Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experienceemistry, ecology, evolution, psychology, linguistics (Lincoln 8c Guba. 1985: Schwartz 8c Ogilvy. 1979). and mathematics—mathematics education in partiComing to Our Senses Reconnecting Mathematics Understanding to Sensory Experience
cular.The term “paradigm” refers to a systematic set of assumptions or beliefs that comprise our philosophy and world view. Beginning with fundamentalComing to Our Senses: Reconnecting Mathematics Understanding to Sensory ExperienceAna Pasztor School of Computer Science Florida International Univers Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experiencepartially supported by the following grants: NSF-CISE-EIA-9812636 with the DSP Center, NSF-MII-EIA-9906600 with the CATE Center, and ONR-NOOO 14-99-1-0952 at Florida International University.1https://khothuvien.cori!the world, including the actions we take as inquirers, cannot occur without referenc Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experiencee to those paradigms (Lincoln & Guba, 1985). In mathematics education the paradigm shift has been a top-down shift beginning with the theoretical founComing to Our Senses Reconnecting Mathematics Understanding to Sensory Experience
dations of mathematics education and then moving to the level of professional organizations which have been leading extensive efforts to reform schoolComing to Our Senses: Reconnecting Mathematics Understanding to Sensory ExperienceAna Pasztor School of Computer Science Florida International Univers Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experiencee new 2000 Principles and Standards for School Mathematics of the National Council of Teachers of Mathematics (NCTM, 2000) may be the most significant effort up to this time. So far. however, the paradigm shift is not yet emanent at the grass roots level of the classroom in terms of actual changes i Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experiencen mathematics classroom practices. One of the reasons for this may be that the constructivist theories espoused by the researchers are as yet too abstComing to Our Senses Reconnecting Mathematics Understanding to Sensory Experience
ract to readily lend themselves to implementation. Even NCTM's (2000) new guidelines, which were designed to provide "focused, sustained efforts to imComing to Our Senses: Reconnecting Mathematics Understanding to Sensory ExperienceAna Pasztor School of Computer Science Florida International Univers Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experience, given that the very same communities whose members started the constructivist reform movement often lack an awareness for the need to translate the new principles even to their own behavior, let alone to embody them. “This is not altogether surprising because leading practitioners at all levels te Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experiencend to be so busy with day-to-day problems that they seldom have adequate time for metalevel considerations. As the folk saying states: ’When you are uComing to Our Senses Reconnecting Mathematics Understanding to Sensory Experience
p to your neck in alligators, it's difficult to find time to think about draining the swamp"' (Lesh. Lovitts. & Kelly. 1999. p. 32).In this paper we wComing to Our Senses: Reconnecting Mathematics Understanding to Sensory ExperienceAna Pasztor School of Computer Science Florida International Univers Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experiencechool mathematics:Teaching. Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well.Learning. Students must learn mathematics with understanding, actively building new knowledge from experience and prior kno Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experiencewledge. (NCTM. 2000. chapter 2).Careful reading of these two standards raises a number of questions: What is mathematics knowledge? What constitutes uComing to Our Senses Reconnecting Mathematics Understanding to Sensory Experience
nderstanding? What is learning with understanding? How do we gain access to students’ experience and prior knowledge? What kind of experience and prioComing to Our Senses: Reconnecting Mathematics Understanding to Sensory ExperienceAna Pasztor School of Computer Science Florida International Univers Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experience own experience, rather than from what happens to be the teacher's experience?These and related questions drive our pilot research project. The pilot project, in turn, is part of a larger, ongoing project that we have come to call the Linguistic Action Inquiry Project. The goal of the Linguistic Act Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experienceion Inquiry Project has been to facilitate change in a variety of domains of human communication. Its primary tool has been the utilization and refineComing to Our Senses Reconnecting Mathematics Understanding to Sensory Experience
ment of a shared experiential language (SEL) and the enhancement of the person of the facilitator, be that a teacher, a therapist, or a researcher, asComing to Our Senses: Reconnecting Mathematics Understanding to Sensory ExperienceAna Pasztor School of Computer Science Florida International Univers Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experiencemethodology of linguistic action inquiry can help successfully root mathematical understanding in students' prior sensory experiences, and2.to learn, utilizing SEL. how students naturally organize their experiences when they try to understand mathematics.In all action-research cycles of the pilot pr Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experienceoject we utilize SEL to model, help adjust fit of and reflect upon students' experiences linked to mathematics understanding. This represents a uniqueComing to Our Senses Reconnecting Mathematics Understanding to Sensory Experience
2opportunity to document such experiences lor the purpose of relining mathematics teaching methodologies and curricula in ways that allow consistent uComing to Our Senses: Reconnecting Mathematics Understanding to Sensory ExperienceAna Pasztor School of Computer Science Florida International Univers Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experienceist, we will lay the groundwork of our guiding theoretical flamework by contrasting positivist and constructivist paradigms and their methodological implications both for teaching and learning in general, and for mathematics education in specific. We will then present existing efforts to demystify m Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experienceathematics and reconnect it to students' everyday experiences, and we will argue for the need to root consistent mathematics understanding in studentsComing to Our Senses Reconnecting Mathematics Understanding to Sensory Experience
’ sensory experiences. We conclude the fiist pan of the paper by defining basic components of SLL. the shared experiential language, which is the prerComing to Our Senses: Reconnecting Mathematics Understanding to Sensory ExperienceAna Pasztor School of Computer Science Florida International Univers Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experienceuistic action inquiry methodology, where the poison of the educator.■researcher is the primary teaching, research instrument, and which we have been developing in the context of our Linguistic Action inquiry Project. In the third pan of the paper wo then illustrate our pilot project where we are ada Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experiencepting this approach to teaching mathematical thinking to a group of fourth-grade students in a manner that effectively implements the intent of the NCComing to Our Senses Reconnecting Mathematics Understanding to Sensory Experience
IM 2000 guidelines. Lastly, we offer some concluding thoughts and suggestions.The Guiding Theoretical Framework1.1Contrasting Positivist and ConstrucComing to Our Senses: Reconnecting Mathematics Understanding to Sensory ExperienceAna Pasztor School of Computer Science Florida International Univers Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experiencenature of reality), epistemology (assumptions about how we know what we know), and methodology (Denzin & Lincoln. 1994; Lincoln & Guba. 1985). Table 1 summarizes some key distinctions between the two thought systems as they relate to our subsequent discussions on mathematics education. It also paral Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experiencelels table 2.1 of (Kelly & Lesh. 1999. pp. 37-38), particularly from the point of view of methodology.Positivist ViewConstructivist ViewNature OÍ RealComing to Our Senses Reconnecting Mathematics Understanding to Sensory Experience
ity and KnowledgeReality is a single and fixed set of knowable, objective facts to be discovered.Reality is not accessible. Multiple and dynamic subjeComing to Our Senses: Reconnecting Mathematics Understanding to Sensory ExperienceAna Pasztor School of Computer Science Florida International Univers Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experience an only be understood in relationship Io the larger context.Knowledge is matching realityKnowledge is finding fir with observations..Nature of the Learning'leaching ProcessTeaching is one-way transmission of fixed knowledge Io the passive Student.Teacher and student bulb ac lively participate to co Coming to Our Senses Reconnecting Mathematics Understanding to Sensory Experience-create nowlearnings.Gọi ngay
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