Foundational Experiences as a Curriculum Design Principle for Secondary Mathematics

2019 ◽  
pp. 358-363
Author(s):  
Ralph Mason
Keyword(s):  
Curriculum Design ◽  
Design Principle ◽  
Power Laws ◽  
Secondary Mathematics ◽  
Exponential Functions ◽  
Instructional Activities

Students must make sense of the mathematics they are learning, if they are to understand it. When students are encountering a mathematics topic primarily through that topic’s mathematical forms—its symbols, terminology, definitions, operations, and algorithms—the richness, potency, and completeness of their understanding will depend on their prior, pre-formal experiences with that topic. Foundational experiences activities enable students to construct images, patterns, and ideas—in a word, memories—that will enable them to see the sensibility of the topic’s mathematical forms when they learn them. We invite participants to explore some examples of instructional activities designed to provide foundational experiences for the mathematics of powers, from power laws through geometric sequences to exponential functions. With these examples, participants will consider these questions: How can foundational experiences contribute to students’ understandings of the math behind the topic’s formal content? What are the qualities that we should invest when designing foundational experience activities?

Foundational Experiences as a Design Principle for Mathematics Curriculum for Children

2019 ◽  
pp. 42-47
Author(s):  
Paul Betts
Keyword(s):  
Curriculum Design ◽  
Design Principle ◽  
Mathematics Curriculum ◽  
Success For All ◽  
Instructional Activities

Students must make sense of the mathematics they are learning, if they are to understand it. When students are encountering a mathematics topic primarily through that topic’s mathematical forms—its symbols, terminology, definitions, operations, and algorithms—the richness, potency, and completeness of their understanding will depend on their prior, pre-formal experiences with that topic. Foundational experiences activities enable students to construct images, patterns, and ideas—in a word, memories—that will enable them to see the sensibility of the topic’s mathematical forms when they learn them. We invite participants to explore some examples of instructional activities designed to provide foundational experiences for multiplication. What are the qualities that we should invest in foundational experience activities? How can such activities be positioned within curriculum design, with the goal of increasing the quality of students’ understandings of mathematics topics, in pursuit of success for all participants in school math?

Beyond the principle of similitude: renormalization in the bronchial tree

1986 ◽  
Vol 60 (3) ◽  
pp. 1089-1097 ◽  
Author(s):  
B. J. West ◽  
V. Bhargava ◽  
A. L. Goldberger
Keyword(s):  
Renormalization Group ◽  
Power Laws ◽  
Bronchial Tree ◽  
Group Property ◽  
Scaling Relation ◽  
Exponential Functions ◽  
Generation Number ◽  
Harmonic Variation ◽  
Successive Generations ◽  
Stable Structures

The average dimensions (diameter, length, and volume) of the airways in the mammalian bronchial tree, long thought to be exponential functions of the generation number, are shown to be power laws in generation number modulated by a harmonic variation. These data are satisfactorily described by means of a functional scaling relation--renormalization group property--between successive generations for the average variable of interest. This type of scaling may provide a mechanism for the morphogenesis of complex but highly stable structures.

Activities: Iterating Linear Functions—An Introduction to Dynamical Systems

1997 ◽  
Vol 90 (2) ◽  
pp. 122-136
Author(s):  
Jonathan Choate
Keyword(s):  
Mathematics Education ◽  
Dynamical Systems ◽  
Numerical Methods ◽  
Mathematics Curriculum ◽  
Secondary Mathematics ◽  
Linear Functions ◽  
Exponential Functions ◽  
Numerical Iteration ◽  
Symbolic Methods ◽  
And Mathematics

The arrival of computers has caused some major changes in both mathematics and mathematics education. One of the biggest shifts has been from an emphasis on symbolic methods to one on numerical methods. One field of mathematics, dynamical systems, requires considerable number crunching and is just coming into its own because we currently have the ability to perform extensive calculations easily. This article introduces students to this new field. The study of sequences created by using numerical iteration provides interesting new ways to approach many of the concepts central to the secondary mathematics curriculum, such as functions in general and linear and exponential functions in particular.

scholarly journals A CURRICULUM DESIGN FOR EDUCATING CONSERVATORS OF ISLAMIC MANUSCRIPTS

2017 ◽  
Vol 15 (3) ◽  
Author(s):  
Paul Hepworth ◽  
Karin Scheper ◽  
Mandana Barkeshli
Keyword(s):  
Developing Countries ◽  
Curriculum Design ◽  
Instructional Activities ◽  
Total Program ◽  
Assessment Strategies

To meet the pressing need for more training for conservators in developing countries dealing with Islamic manuscripts, a curriculum design was prepared. This details the skills and information needed and organizes instruction into modules that can be taught as a total program or semiindependently with adaptation to many different circumstances in different settings. The modules are augmented by specified objectives, possible instructional activities and assessment strategies.

Experiential Learning Based Engineering Curriculum to Develop Meta-Competencies

2011 ◽  
Author(s):  
Zahed Siddique ◽  
Amy Bradshaw ◽  
Patricia Hardre´ ◽  
Farrokh Mistree
Keyword(s):  
Experiential Learning ◽  
Curriculum Design ◽  
Engineering Students ◽  
Standard Of Living ◽  
University Of Oklahoma ◽  
Instructional Activities ◽  
Multiple Levels ◽  
Course Sequence ◽  
Development Of Competencies ◽  
Systemic Development

The competitiveness of the U.S., which is linked to our standard of living, is dependent on our ability to produce a large number of sufficiently innovative engineers prepared to address issues related to complex systems. Hence, our focus is on research and the associated development of curriculum and instructional activities that address the engineering competencies related to innovation. In this paper, we present a hierarchical curriculum design model, grounded in experiential learning. The model addresses curriculum design from multiple levels: design of experiential activities to provide targeted scaffolding and support for engineering students to develop competencies, then mapping the competencies at course, course sequence, and curriculum levels, for systemic development of competencies at higher order cognition. We illustrate the hierarchical approach for the design of a three-course sequence around the Formula Society of Automotive Engineers (FSAE) Racing team at University of Oklahoma, Norman, to foster meaningful learning, innovation, systems-level thinking, and the attainment of career-sustaining skills through authentic experiences. With a view to stimulating discussion, in this paper we highlight some of the salient features of our plan and some issues that warrant further investigation.

scholarly journals Putting transition at the centre of whole-of-curriculum transformation

2015 ◽  
Vol 6 (2) ◽  
pp. 73-79
Author(s):  
Marcus O'Donnell ◽  
Margaret Wallace ◽  
Anne Melano ◽  
Romy Lawson ◽  
Eeva Leinonen
Keyword(s):  
Higher Education ◽  
Curriculum Design ◽  
Design Principle ◽  
Integrated Approach ◽  
The Other ◽  
Curriculum Model ◽  
The World ◽  
Curriculum Transformation ◽  
Curriculum Renewal ◽  
The University

This paper describes the development of a model for institution-wide curriculum transformation at the University of Wollongong (UOW). Transition – a curriculum-integrated approach that enables a smooth, supported shift into and through higher education and a successful transition from the university to the world of work and lifelong learning – is one of three key principles at the heart of the UOW Curriculum Model. This paper focuses on transition as a whole-of-curriculum design principle and the way this principle informs the other elements of the UOW Curriculum Model. It aims to extend the concept of “transition pedagogy” developed by Kift and colleagues  and to show how it has been used to inform our larger project of curriculum renewal.  

The Relation Between Teachers' Diagnostic Sensitivity, their Instructional Activities, and their Students' Achievement Gains in Reading*

2013 ◽  
Vol 27 (4) ◽  
pp. 283-293 ◽  
Author(s):  
Lars Behrmann ◽  
Elmar Souvignier
Keyword(s):  
Reading Comprehension ◽  
Classroom Management ◽  
Reading Program ◽  
Multilevel Analyses ◽  
Moderating Effects ◽  
Management Skills ◽  
Judgment Accuracy ◽  
Achievement Gains ◽  
Instructional Activities ◽  
Main Effects

Single studies suggest that the effectiveness of certain instructional activities depends on teachers' judgment accuracy. However, sufficient empirical data is still lacking. In this longitudinal study (N = 75 teachers and 1,865 students), we assessed if the effectiveness of teacher feedback was moderated by judgment accuracy in a standardized reading program. For the purpose of a discriminant validation, moderating effects of teachers' judgment accuracy on their classroom management skills were examined. As expected, multilevel analyses revealed larger reading comprehension gains when teachers provided students with a high number of feedbacks and simultaneously demonstrated high judgment accuracy. Neither interactions nor main effects were found for classroom management skills on reading comprehension. Moreover, no significant interactions with judgment accuracy but main effects were found for both feedback and classroom management skills concerning reading strategy knowledge gains. The implications of the results are discussed.

Power-laws

2011 ◽  
Author(s):  
Bruce J. West
Keyword(s):  
Power Laws
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