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Can you get all the numbers in the first row of the grid highlighted? (Hint: you can change the grid width
Number Worlds: visualisation and experimentation 32
(2000)
Factors, divisors and multiples: Exploring the web of students' connections
Stephen Brown (1979)
Some Prime Comparisons
T. Eisenberg, T. Dreyfus (1991)
On the reluctance to visualize in mathematics
(2002)
Conceptions of divisibility: Success and understanding
R. Stavy, D. Tirosh (2000)
How Students (Mis-)Understand Science and Mathematics: Ntuitive Rules
Consider each picture. Is it a picture of factors, multiples, primes or squares? How do you decide?
M. Artigue (2002)
Learning Mathematics in a CAS Environment: The Genesis of a Reflection about Instrumentation and the Dialectics between Technical and Conceptual WorkInternational Journal of Computers for Mathematical Learning, 7
MAA Notes Series
Walter Zimmermann, S. Cunningham (1991)
Visualization in teaching and learning mathematicsCollege Mathematics Journal, 23
L. Edwards (1995)
Microworlds as Representations
R. Noss, L. Healy, C. Hoyles (1997)
The Construction of Mathematical Meanings: Connecting the Visual with the SymbolicEducational Studies in Mathematics, 33
L. Burton (1998)
The Practices of Mathematicians: What do They Tell us About Coming to Know Mathematics?Educational Studies in Mathematics, 37
C. Hirsch (1988)
Curriculum and Evaluation Standards for School Mathematics
Rina Zazkis (1999)
Intuitive rules in number theory: Example of ‘The more of A, the more of B’ rule implementationEducational Studies in Mathematics, 40
Rina Zazkis, Peter Liljedahl (2002)
Arithmetic Sequence as a Bridge between Conceptual FieldsCanadian Journal of Science, Mathematics and Technology Education, 2
S. Campbell, Rina Zazkis, C. Maher, R. Speiser (2002)
Learning and teaching number theory : research in cognition and instruction
Tasks to explore in Number Worlds
Can you highlight the even numbers without using the Show Evens button? Can you highlight the odd numbers
R. Noss, C. Hoyles (1996)
Windows on Mathematical Meanings
J. Wimp, K. Devlin (2002)
The math gene: How mathematical thinking evolved and why numbers are like gossipThe Mathematical Intelligencer, 24
L. Edwards (1995)
Computers and Exploratory Learning
R. Zazkis, P. Liljedahl (2002)
Arithmetic sequence as a bridge among conceptual fieldsCanadian Journal of Science, Mathematics and Technology Education, 2
(2002)
Prime Decomposition : Understanding Uniqueness
What could you do to highlight the number 169 (without clicking it directly!)? How about the number 320? Use the Increase by one row button to check your answer
Experimental Mathematics: Computational Paths to Discovery
E. Goldenberg (1991)
Seeing beauty in mathematics: using fractal geometry to build a spirit of mathematical inquiry
R. Stavy, D. Tirosh (2000)
How Students Mis/Understand Science and Mathematics: Intuitive Rules (Ways of Knowing in Science Series)
Rina Zazkis, S. Campbell (1996)
Divisibility and Multiplicative Structure of Natural Numbers: Preservice Teachers' Understanding.Journal for Research in Mathematics Education, 27
Angie Su (2000)
National Council of Teachers of Mathematics
General invitation for reflection: What have you found surprising or helpful or interesting in your experience with Number Worlds? REFERENCES
Recent research demonstrates that many issues related to the structure of natural numbers and the relationship among numbers are not well grasped by students. In this article, we describe a computer-based learning environment called Number Worlds that was designed to support the exploration of elementary number theory concepts by making the essential relationships and patterns more accessible to learners. Based on our research with pre-service elementary school teachers, we show how both the visual representations embedded in the microworld, and the possibilities afforded for experimentation affect learners' understanding and appreciation of basic concepts in elementary number theory. We also discuss the aesthetic and affective dimensions of the research participants' engagement with the learning environment.
"Technology, Knowledge and Learning" – Springer Journals
Published: Oct 11, 2004
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