Students Learning Progression through Instrumental Decoding of Mathematical Ideas

Students Learning Progression through Instrumental Decoding of Mathematical Ideas

Stavroula Patsiomitou

Contact

University of Ioannina

Students Learning Progression through Instrumental Decoding of Mathematical Ideas

Article Fingerprint

ReserarchID

CSTSDE0RYT8

Students Learning Progression through Instrumental Decoding of Mathematical Ideas Banner

AI TAKEAWAY

Connecting with the Eternal Ground

Abstract

The current study aims to focus on mathematical tasks for students’ mathematical literacy and problem solving literacy. Excerpts are presented from dynamic hypothetical learning paths [DHLP] s and students’ learning progression. The excerpts center around activities aimed to develop the students’ geometrical thinking through the development of their ability to solve real-world problems. The students cooperated in class or worked individually to represent the images using their static or dynamic means and tools (e.g. compass and ruler, a computing environment, interactive boards, dynamic geometry software). My further aim was the students to utilize transformation processes for representations by instrumentally decoding their ideas on static and dynamic objects.

References

89 Cites in Article

Reference Format

Shaaron Ainsworth (1999). The functions of multiple representations.
S Ainsworth (2006). DeFT: A conceptual framework for learning with multiple representations.
F Almeqdadi (2000). The effect of using the geometer's sketchpad (GSP) on Jordanian students' understanding of geometrical concepts.
Bartolini Bussi,M (1996). Mathematical Discussion and Perspective Drawing in Primary School.
M Battista (2007). Second Handbook of Research on Mathematics Teaching and Learning.
M Battista (2011). Conceptualizations and issues related to learning progressions, learning trajectories, and levels of sophistication.
H Bauersfeld (1992). Integrating Theories for Mathematics Education.
J Bruner (1961). The act of discovery.
J Bruner (1966). Toward a theory of instruction.
J Bruner (1986). Actual Minds, Possible Worlds.
H Burkhardt (1981). The real world and mathematics.
Thomas Carpenter,Elizabeth Fennema,Penelope Peterson,Chi-Pang Chiang,Megan Loef (1989). Using Knowledge of Children’s Mathematics Thinking in Classroom Teaching: An Experimental Study.
T Carpenter,E Fennema,M Franke,L Levi,S Empson (1999). Children's mathematics: Cognitively Guided Instruction.
J Choppin (1994). Spiral through recursion.
D Clement,M Battista (1990). Research into practise: Constructivist learning and teaching.
(1995). Mathematical Learning and Small-Group Interaction: Four Case Studies: Paul Cobb.
P Cobb,E Yackel,T Wood (1992). A constructivist alternative to the representational view of mind in mathematics education.
A Coxford,Z Usiskin (1975). Geometry: A Transformation Approach.
E De Corte,L Verschaffel,B Greer (2000). Connecting mathematics problem solving to the real world.
Paul Drijvers,Juan Godino,Vicenç Font,Luc Trouche (2008). One episode, two lenses.
F Docq,A Daele (2001). Uses of ICT tools for CSCL: how do students make as their's own the designed environment.
M Dougiamas An exploration of the use of an Open Source software called Moodle to support a social constructionist epistemology of teaching and learning within Internet-based communities of reflective inquiry.
R Duval (1995). Sémiosis et pensée humaine.
F Ferrara,D Pratt,O Robutti (2006). The role and uses of technologies for the teaching of algebra and calculus: Ideas discussed at PME over the last 30 years.
H Freudenthal (1973). Mathematics as an Educational Task.
H Freudenthal (1983). Didactical phenomenology of mathematical structures.
Freudenthal (1991). Revisiting Mathematics Education: China Lectures.
Karen Fuson,William Caroll,Jane Drueck (2000). Achievement Results for Second and Third Graders Using the Standards-Based Curriculum Everyday Mathematics.
Van Hiele (1984). English translation of selected writings of Dina van Hiele-Geldof and Pierre M.
D Fuys,D Geddes,R Tischler (1988). The Van Hiele model of thinking in geometry among adolescents.
V Giraldo,E Belfort,L Carvalho (2004). Descriptions and conflicts in dynamic geometry.
E Glasersfeld (1995). Radical constructivism: A way of knowing and learning.
Gloriana González,Patricio Herbst (2009). Students’ Conceptions of Congruency Through the Use of Dynamic Geometry Software.
P Goldenberg (1999). Principles, Art, and Craft in Curriculum Design: The Case of Connected Geometry.
G Goldin,J Kilpatrick,W Martin,D Schifter (2003). National collaborative zones of proximal development in small group problem solving.
Merrilyn Goos,Peter Galbraith,Peter Renshaw,Vince Geiger (2003). Perspectives on technology mediated learning in secondary school mathematics classrooms.
Rajendran Govender,Michael De Villiers (2004). A dynamic approach to quadrilateral definitions.
R Govender,M De Villiers (2002). Constructive Evaluations of Definitions in a Sketchpad Context.
K Gravemeijer (2004). Creating Opportunities for Students to Reinvent Mathematics.
Angel Gutiérrez,Adela Jaime,José Fortuny,Angel Gutierrez,Jose Fortuny (1998). An Alternative Paradigm to Evaluate the Acquisition of the van Hiele Levels.
Nurit Hadas,Rina Hershkowitz,Baruch Schwarz (2000). The role of contradiction and uncertainty in promoting the need to prove in Dynamic Geometry environments.
J Hayes,L Flower (1980). Identifying the organization of writing processes.
R Hershkovitz (1990). Psychological aspects of learning geometry.
A Hoffer (1981). Geometry is more than proof.
K Hollebrands (2007). The role of a dynamic software program for geometry in the strategies high school mathematics students employ.
K Hollebrands,R Smith (2009). Using dynamic geometry software to teach secondary school geometry: Implications from research.
N Jackiw (1991). The Geometer's Sketchpad.
N Jackiw (2006). Mathematics and the Aesthetic: New Approaches to an Ancient Affinity. Mechanism and Magic in the Psychology of Dynamic Geometry.
N Jackiw,N Sinclair (2004). Iteration and Dynamic Geometry: Beyond Common Fractals with The Geometer's Sketchpad NCTM Philadelphia Session.
B Jaworski (2003). Inquiry as a pervasive pedagogic process in mathematics education development.
P Johnson-Laird (1983). Mental Models: Towards a Cognitive Science of Language, Inference, and Consciousness.
G Kadunz,R Sträßer (2004). Image -metaphordiagram: visualisation in learning mathematics.
I Kant (1929). Critique of Pure Reason.
J Kaput (1991). Notations and representations as mediators of constructive processes.
James Kaput (1999). Representations, inscriptions, descriptions and learning: A kaleidoscope of windows.
J Kaput (1992). Technology and Mathematics Education.
M Kline (1990). Mathematics in Western Culture.
J Krajcik,N Shin,S Stevens,H Short (2009). Using Learning Progressions to Inform the Design of Coherent Science Curriculum Materials.
S Patsiomitou (2012). A Linking Visual Representation DHLP for student's cognitive development.
Stavroula Patsiomitou (2013). STUDENTS LEARNING PATHS AS ˜'DYNAMIC ENCEPHALOGRAPHS' OF THEIR COGNITIVE DEVELOPMENT.
S Patsiomitou,E Koleza (2008). Developing students geometrical thinking through linking representations in a dynamic geometry environment.
S Patsiomitou,A Emvalotis (2009). Developing geometric thinking skills through dynamic diagram transformations.
S Patsiomitou,A Emvalotis (2009). Does the Building and transforming on LVAR modes impact students way of thinking?.
S Patsiomitou,A Emvalotis (2009). Economy' and 'Catachrèse' in the use of custom tools in a Dynamic geometry problem-solving process.
S Patsiomitou,A Emvalotis (2009). Composing and testing a DG research-based curriculum designed to develop students' geometrical thinking.
S Patsiomitou,E Koleza (2009). The development of students' geometrical thinking through Linking Visual Active Representations.
S Patsiomitou,A Emvalotis (2010). Students' movement through van Hiele levels in a dynamic geometry guided reinvention process.
S Patsiomitou,A Barkatsas,A Emvalotis (2010). Secondary students' "dynamic reinvention of geometric proof" through the utilization of linking visual active representations.
M Patton (1990). Qualitative evaluation methods.
(1937). Knowing What Students Know.
C Peirce (1903). The Essential Peirce, Volume 1.
R Pierce,K Stacey (2009). Using Dynamic Geometry to Bring the Real World into the Classroom.
H Schumann (2004). Reconstructive Modelling with Dynamic Geometry Systems.
H Schumann,D Green (1994). A review of “<i>Discovering Geometry with a Computer—Using Cabri-Géomètre</i>” Heinz Schumann & David Green, 1994 Lund (Sweden), Chartwell-Bratt, Student Literature ISBN 0 86238 373 0.
K Sedig,M Sumner (2006). Characterizing interaction with visual mathematical representations.
Anna Sfard (2001). Participationist Discourse on Mathematics Learning.
M Simon (1995). Reconstructing mathematics pedagogy from a constructivist perspective.
Martin Simon,Deborah Schifter (1991). Towards a constructivist perspective: An intervention study of mathematics teacher development.
Nathalie Sinclair,Nicholas Jackiw (2007). Modeling Practices with The Geometer’s Sketchpad.
M Sinclair (2001). Supporting and Understanding the Disruptive Student in the Classroom.
R Skemp (1986). The psychology of learning mathematics.
Carol Smith,Marianne Wiser,Charles Anderson,Joseph Krajcik (2006). FOCUS ARTICLE: Implications of Research on Children's Learning for Standards and Assessment: A Proposed Learning Progression for Matter and the Atomic-Molecular Theory.
P Smith,J Wedman (1988). Read-thinkaloud protocols: A new data-source for formative evaluation.
Kaye Stacey (2012). The International Assessment of Mathematical Literacy: PISA 2012 Framework and Items.
L Steffe,J Gale (1995). Constructivism in education.
S Stevens,N Shin,J Krajcik (2009). Towards a model for the development of an empirically tested learning progression.
P Thompson (1987). Mathematical microworlds and intelligent computer-assisted instruction.
S Toulmin (1958). The uses of argument.
Luc Trouche (2004). Managing the Complexity of Human/Machine Interactions in Computerized Learning Environments: Guiding Students’ Command Process through Instrumental Orchestrations.

Download References

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

Stavroula Patsiomitou. 2014. \u201cStudents Learning Progression through Instrumental Decoding of Mathematical Ideas\u201d. Global Journal of Computer Science and Technology - C: Software & Data Engineering GJCST-C Volume 14 (GJCST Volume 14 Issue C1).

More Citation Formats

Select Citation Style:

Download Citation

GJCST Volume 14 Issue C1

Explore Journals Explore Volume Read This Issue

Journal Specifications

Crossref Journal DOI 10.17406/gjcst

Print ISSN 0975-4350

e-ISSN 0975-4172

Keywords

‘dynamic’ hypothetical learning path learning progression linking visual active representations teaching cycle

Submission ReceivedDecember 11, 2013
Peer Review Double Blind
Handling Editor
Accepted January 5, 2014
Published January 15, 2014

Version of record

v1.2

Issue date

May 14, 2014

Language

Experiance in AR

Explore published articles in an immersive Augmented Reality environment. Our platform converts research papers into interactive 3D books, allowing readers to view and interact with content using AR and VR compatible devices.

View in VR

Read in 3D

Your published article is automatically converted into a realistic 3D book. Flip through pages and read research papers in a more engaging and interactive format.

View in 3D

Article Matrices

Total Score: 101

Country: Greece

Subject: Global Journal of Computer Science and Technology - C: Software & Data Engineering

Authors: Stavroula Patsiomitou (PhD/Dr. count: 0)

View Count (all-time): 315

Total Views (Real + Logic): 9067

Total Downloads (simulated): 2261

Publish Date: 2014 05, Wed

Monthly Totals (Real + Logic):

Month 1: 37 views
Month 2: 62 views
Month 3: 33 views
Month 4: 38 views
Month 5: 64 views
Month 6: 30 views
Month 7: 52 views
Month 8: 25 views
Month 9: 24 views
Month 10: 32 views
Month 11: 36 views
Month 12: 34 views
Month 13: 36 views
Month 14: 40 views
Month 15: 28 views
Month 16: 24 views
Month 17: 35 views
Month 18: 34 views
Month 19: 32 views
Month 20: 35 views
Month 21: 41 views
Month 22: 42 views
Month 23: 30 views
Month 24: 30 views
Month 25: 45 views
Month 26: 14 views
Month 27: 40 views
Month 28: 23 views
Month 29: 33 views
Month 30: 28 views
Month 31: 24 views
Month 32: 35 views
Month 33: 42 views
Month 34: 33 views
Month 35: 36 views
Month 36: 46 views
Month 37: 27 views
Month 38: 26 views
Month 39: 30 views
Month 40: 42 views
Month 41: 31 views
Month 42: 38 views
Month 43: 44 views
Month 44: 25 views
Month 45: 40 views
Month 46: 46 views
Month 47: 46 views
Month 48: 25 views
Month 49: 15 views
Month 50: 29 views
Month 51: 32 views
Month 52: 44 views
Month 53: 28 views
Month 54: 21 views
Month 55: 38 views
Month 56: 28 views
Month 57: 23 views
Month 58: 21 views
Month 59: 47 views
Month 60: 41 views
Month 61: 42 views
Month 62: 32 views
Month 63: 26 views
Month 64: 18 views
Month 65: 27 views
Month 66: 11 views
Month 67: 28 views
Month 68: 32 views
Month 69: 28 views
Month 70: 26 views
Month 71: 32 views
Month 72: 33 views
Month 73: 33 views
Month 74: 20 views
Month 75: 28 views
Month 76: 39 views
Month 77: 28 views
Month 78: 29 views
Month 79: 33 views
Month 80: 21 views
Month 81: 41 views
Month 82: 38 views
Month 83: 32 views
Month 84: 21 views
Month 85: 19 views
Month 86: 31 views
Month 87: 31 views
Month 88: 26 views
Month 89: 29 views
Month 90: 31 views
Month 91: 35 views
Month 92: 29 views
Month 93: 28 views
Month 94: 45 views
Month 95: 27 views
Month 96: 34 views
Month 97: 28 views
Month 98: 24 views
Month 99: 32 views
Month 100: 21 views
Month 101: 40 views
Month 102: 36 views
Month 103: 16 views
Month 104: 28 views
Month 105: 28 views
Month 106: 21 views
Month 107: 13 views
Month 108: 25 views
Month 109: 45 views
Month 110: 28 views
Month 111: 47 views
Month 112: 35 views
Month 113: 15 views
Month 114: 37 views
Month 115: 29 views
Month 116: 23 views
Month 117: 38 views
Month 118: 30 views
Month 119: 25 views
Month 120: 35 views
Month 121: 25 views
Month 122: 34 views
Month 123: 27 views
Month 124: 17 views
Month 125: 16 views
Month 126: 46 views
Month 127: 18 views
Month 128: 28 views
Month 129: 26 views
Month 130: 15 views
Month 131: 29 views
Month 132: 43 views
Month 133: 37 views
Month 134: 16 views
Month 135: 35 views
Month 136: 47 views
Month 137: 41 views
Month 138: 21 views
Month 139: 36 views
Month 140: 46 views
Month 141: 24 views
Month 142: 51 views
Month 143: 54 views
Month 144: 46 views
Month 145: 29 views

Total Views: 9067

Total Downloads: 2261

2026 Trends

Our website is actively being updated, and changes may occur frequently. Please clear your browser cache if needed. For feedback or error reporting, please email [email protected]