Earlier in the week, each student had to prepare a work-in-progress for today’s Learning Theories class.\u00a0 Here is the text I prepared during the week:<\/p>\n
Learning Theories Module \u2013 Paper 1 (Work-in-Progress Presentation)<\/span><\/p>\n Van Hiele Model \u2013 A theory that describes how students learn geometry<\/strong><\/p>\n by Gerard Kilkenny<\/p>\n 00 \u2013 Introduction (300 Words)<\/strong><\/p>\n The purpose of this paper is to examine how the van Hiele model can be used as a framework in the teaching and learning of geometry to Junior Cycle Maths students.\u00a0 It goes on to explore how elements of the classical learning theories of cognitivism and constructivism are embedded in the van Hiele theory. \u00a0In particular, it provides a comparative analysis of the Van Hiele model wih the theoretical learning frameworks of Gagne, Piaget, Bruner and Vygotsky. \u00a0The concluding section discusses possible implications of the Van Hiele model for eLearning design.<\/p>\n 10 \u2013 Van Hiele Model (The 5 Levels) (480 Words)<\/strong><\/p>\n Level 1 (Visualisation), Level 2 (Analysis) Level 3 (Abstraction), Level 4 (Deduction), Level 5 (Rigour).<\/p>\n 20 \u2013 Van Hiele Model (The 4 Properties) (110 Words)<\/strong><\/p>\n Property 1 (Fixed Sequence), Property 2 (Adjacency), Property 3 (Distinction), Property 4 (Separation).<\/p>\n 30 \u2013 Van Hiele Model (The 5 Phases) (180 Words)<\/strong><\/p>\n Phase 1 (Inquiry), Phase 2 (Directed Orientation), Phase 3 (Explanation), Phase 4 (Free Orientation), Phase 5 (Integration)<\/p>\n 40 \u2013 The Gagne Van Hiele Connection<\/strong><\/p>\n Gagn\u00e9 et al (1992, p.44) list “verbal information” as one of the \u201cfive kinds of learned capabilities\u201d (R-40, p.44) and this can perhaps be mapped to van Hiele\u2019s Level 0 where “the student can learn names of figures\u2026\u201d (Usiskin, 1982, p.4). \u00a0Similarly, the capability of identifying the diagonal of a rectangle is provided as an example of the capability \u201cintellectual skill\u201d by Gagn\u00e9 et al (1992, p.44) (R-40, p.44) which appears to have it\u2019s equivalent in van Hiele\u2019s Level 1 where students can understand that “rectangles have four right angles” (Hoffer, 1979, 1981) or that a rectangle “has\u00a0two equal diagonals\u201d (The Project Maths Development Team, 2014, p.32).<\/p>\n 50 \u2013 Van Hiele and Piaget<\/strong><\/p>\n Piaget (1953) (R-50) argues that children do not enter the formal operational stage until they are 14 years of age and that they cannot learn formal proofs before this period. Van Hiele (1985) (R-51) describes similar properties in his penultimate geometric level deduction although he does not specify which age pupils reach this level. \u00a0In Irish secondary schools, students generally don\u2019t study formal proofs in geometry until second or third year when they are approximately 14 years old. \u00a0(R-04)<\/p>\n 60 \u2013 Van Hiele, Vygotsky and Bruner<\/strong><\/p>\n Van Hiele questioned the notions of growth being linked with biological maturation. Instead, in ways that have much in common with Vygotsky (1978), he saw development in terms of students\u2019 confrontation with the cultural environment, their own exploration, and their reaction to a guided learning process. (p.112)<\/p>\n 70 \u2013 Neuroscience and Teaching<\/strong><\/p>\n What can neuroscience teach us about teaching? (Dr. William O\u2019Connor)<\/p>\n http:\/\/icep.ie\/wp-content\/uploads\/2011\/02\/What-can-neuroscience-teach-us-about-teaching.pdf<\/p>\n 80 \u2013 Implications for ICT and Instructional Design<\/strong><\/p>\n Book (Principles of Instructional Design), Book (Michael Allen\u2019s Guide to e-Learning) Software (GeoGebra).<\/p>\n Key References<\/strong><\/p>\n Curran, S. (2014).\u00a0Is The Van Hiele Model Useful in Determining How Children Learn Geometry?<\/em> Munich:\u00a0GRIN.<\/p>\n Gagn\u00e9, R. M., Briggs, L. J., & Wager, W. W. (1992). Principles of Instructional Design<\/em>. Fort Worth: Harcourt.<\/p>\n Piaget, J. (1953). The Origin of Intelligence in the Child<\/em>. London: Routledge and Kegan Paul.<\/p>\n Project Maths Development Team (2015). Teacher Handbook First Year. Retrieved September 25, 2016, from\u00a0 http:\/\/www.projectmaths.ie\/documents\/handbooks\/firstyearhandbook2015.pdf<\/p>\n Usiskin, Z (1982). Van Hiele Levels and Achievement in Secondary School Geometry<\/em>. \u00a0University of Chicago<\/p>\n Yazdani, M. A. (2008). \u00a0The Gagne \u2013 van Hieles Connection: A Comparative Analysis of Two Theoretical Learning Frameworks. \u00a0Journal of Mathematical Sciences & Mathematics Education<\/em>, 3(1), 58-63.<\/p>\n","protected":false},"excerpt":{"rendered":" Earlier in the week, each student had to prepare a work-in-progress for today’s Learning Theories class.\u00a0 Here is the text I prepared during the week: Learning Theories Module \u2013 Paper 1 (Work-in-Progress Presentation) Van Hiele Model \u2013 A theory that describes how students learn geometry by Gerard Kilkenny 00 \u2013 Introduction (300 Words) The purpose … Continue reading M1-Week 5-Class<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,9],"tags":[],"class_list":["post-401","post","type-post","status-publish","format-standard","hentry","category-learning-theories","category-week-5"],"_links":{"self":[{"href":"http:\/\/gerardkilkenny.ie\/index.php\/wp-json\/wp\/v2\/posts\/401","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/gerardkilkenny.ie\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/gerardkilkenny.ie\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/gerardkilkenny.ie\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/gerardkilkenny.ie\/index.php\/wp-json\/wp\/v2\/comments?post=401"}],"version-history":[{"count":5,"href":"http:\/\/gerardkilkenny.ie\/index.php\/wp-json\/wp\/v2\/posts\/401\/revisions"}],"predecessor-version":[{"id":2493,"href":"http:\/\/gerardkilkenny.ie\/index.php\/wp-json\/wp\/v2\/posts\/401\/revisions\/2493"}],"wp:attachment":[{"href":"http:\/\/gerardkilkenny.ie\/index.php\/wp-json\/wp\/v2\/media?parent=401"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/gerardkilkenny.ie\/index.php\/wp-json\/wp\/v2\/categories?post=401"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/gerardkilkenny.ie\/index.php\/wp-json\/wp\/v2\/tags?post=401"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}