Education and demonstration – Mathematics – Arithmetic
Reexamination Certificate
2001-02-10
2003-06-10
Banks, Derris H. (Department: 3712)
Education and demonstration
Mathematics
Arithmetic
C434S195000
Reexamination Certificate
active
06575756
ABSTRACT:
BACKGROUND
1. Field of Invention
This invention relates to educational devices and more particularly to an apparatus in the form of blocks which can be arranged in various configurations to aid the teaching of mathematical concepts such as: pattern recognition, the Fibonacci series and Golden Ratio, and the inter relatedness of mathematics and other disciplines.
2. Description of Prior Art
In the field of mathematical teaching apparatus, currently referred to as math manipulatives, two and three-dimensional shapes and objects are used to model abstract concepts. It is accepted today in the field of elementary and secondary level teaching that modeling abstract concepts by tangible objects which can be arranged in a number of different configurations facilitates the understanding of concepts. The seeing, touching, and manipulation of these devices by the student acts to translate the abstract concept into a concrete form, thus rendering it from a perspective that is easier to visualize and comprehend.
Presently, there are many math manipulatives available for teachers to aid the learning of the base-ten system, multiplication and division, factorization of polynomials, linear equations, algebra, roots, ratios, patterns, and other concepts.
One concept in the field of secondary level teaching that has gained widespread acceptance recently, yet has few manipulatives to support it, concerns the importance of teaching how disciplines such as mathematics, biology, botany, music, art and architecture are interrelated. A manipulative that could aid the bridging of some or all of these disciplines would be of obvious value.
Another concept currently deemed of importance is the teaching of pattern recognition, a concept now generally thought to be a major element in aquiring problem-solving skills in all disciplines. However, there are few manipulatives presently available to aid the teaching and learning of this vital skill.
Another current trend is the increased attention given the Fibonacci series and the related Golden Ratio, witnessed by the increasing space allotted the subject in math textbooks. The Fibonacci series, named for its discoverer Leonardo “Fibonacci” da Pisa, is an infinite sequence of numbers that starts with 1 and builds by adding the current number to the prior number to produce the next number in the series. For example, the number prior to 1 is accepted to be 0, consequently 1 added to 0 produces the next number, another 1. This 1 is then added to the prior 1 to produce the next number in the series which is 2, and so on infinitely. The first part of the series progresses as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, . . . .
In the past eight centuries since its discovery, many connections between the Fibonacci series and nature have been identified as well as connections to disciplines such as art and architecture, music, technology, probabilities, and numerous others. The approximate ratio of 1:1.618 of any two adjacent numbers after the thirteenth in the Fibonacci series is also thought to be significantly related to the fields of study previously mentioned. This ratio is virtually the same ratio discovered by the Ancient Greeks, termed the Golden Ratio, and is designated by the Greek symbol &PHgr; (Phi), a tribute to Phidias, the Greek sculptor who most notably used the ratio in proportioning his work. Since that time, many artists, sculptors, architects, and composers have used the Golden Ratio as an aid in proportioning their work.
In the past the subject of the Fibonacci series and the related Golden Ratio has been treated mainly as an interesting curiosity. One possible reason this knowledge has not been used to better advantage is that no effective device was available to aid in the teaching of this concept. Another possible reason is that public awareness of the concept's importance, particularly regarding its applications in science and computer technology is very recent, consequently there has been little perceived need until now to develop relative teaching devices at the secondary level.
Some examples of teaching apparatus, games, toys, and devices employing blocks or shapes pertaining to mathematics in general or the Fibonacci series and Golden Ratio in particular are as follows:
W. H. Adams in U.S. Pat. No. 3,698,122 dated Oct. 17, 1972, discloses playing blocks for young children comprising squares, cubes and discs with dimensions related to one another by the Golden Ratio. While this invention may be suitable for toy building blocks, the scarcity of shapes provided limits its scope and effectiveness as an educational device.
G. B. Stone in U.S. Pat. No. 4,129,302 dated Dec. 12, 1978 discloses a game consisting of a set of playing pieces with lengths corresponding to consecutive numbers in the Fibonacci series. However, these pieces have little utility as teaching aids and there is no reference made to that regard.
M. E. Cohen in U.S. Pat. No. 4,078,342 dated Mar. 14, 1978 discloses a series of elements with sizes based on the Fibonacci series for use as a system to dimension architectural components for the purpose of economy. No mention is made concerning the use of this system as an eductional device.
P. S. Nogues in U.S. Pat. No. 4,332,567 dated Jun. 1, 1982 discloses a mathematical teaching apparatus comprising a cubic block array consisting of layers of various sized blocks with dimensions being multiples of a base unit cube. This device may be useful in teaching arithmetic, analytical and metric geometry, cubing and elementary algebra, however there is no mention of its use nor would it be suitable in teaching the Fibonacci series and the related Golden Ratio, pattern recognition, or the relationship of math to other disciplines. Also, the large number of blocks involved in the complete system makes it expensive to manufacture and difficult to manage in the classroom.
A. B. Jarvis in U.S. Pat. No. 4,504,234 dated Mar. 12, 1985 discloses a mathematical learning aid comprised of squares and cubes useful in learning mathematical operations. There is no mention of its use in teaching pattern formation, connections between mathematics and other disciplines, or the Fibonacci series and Golden Ratio.
W. A. Netsch, Jr. in U.S. Pat. No. 4,651,993 dated Mar. 24, 1987 discloses a design game using modules of the same shape at varying scales relative to a mathematical sequence such as the Fibonacci series useful in making designs for aesthetic purpose. The individual pieces of the game are restricted to being the same shape. Their is no reference of use as an educational device and the game would not be suitable as such.
C. Pollock in U.S. Pat. No. 5,137,452 dated Aug. 11, 1992 discloses interlocking blocks for teaching arithmetic to children. Although this block system may be suitable for teaching addition, subtraction, mutiplication, and division it is not suitable for teaching the Fibonacci series, pattern recognition, or the ways in which math is connected to other disciplines and makes no reference in that regard.
R. Dreyfous in U.S. Pat. No. 5,645,431 dated Jul. 8, 1997 discloses a teaching apparatus comprised of four-sided members useful for visualizing the rules of mathematical expressions. Again, there is no mention of the Fibonacci series and Golden Ratio, pattern recognition, or math connections, or any use thereof.
B. B. Aghevli in U.S. Pat. No. 5,868,577 dated Feb. 9, 1999 discloses a teaching device comprised of cubes, rectangular and triangular solids, and rectangular mats used for teaching factoring and other mathematical skills.
E. Kohlberg in U.S. Pat. No. 5,980,258 dated Nov. 9, 1999 discloses a mathematical teaching apparatus and method comprising block elements having related proportions for teaching counting and addition concepts.
All the devices described above are not suitable as aids in teaching pattern recognition, the ways in which mathematics is related to other disciplines, or for modeling the Fibonacci series and the Golden Section.
SUMMARY OF THE INVENTION
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Banks Derris H.
Fernstrom Kurt
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