Kin-Keung Poon

Pilot study on algebra learning among junior secondary students

The purpose of the study reported herein was to identify the common mistakes made by junior secondary students in Hong Kong when learning algebra and to compare teachers’ perceptions of students’ ability with the results of an algebra test. An algebra test was developed and administered to a sample of students (aged between 13 and 14 years). From the responses of the participating students (N = 815), it was found that students in schools with a higher level of academic achievement had better algebra test results than did those in schools with a lower level of such achievement. Moreover, it was found that a teachers perception of a students ability has a correlation with that students level of achievement. Based on this finding, an instrument that measures teaching effectiveness is discussed. Last but not least, typical errors in algebra are identified, and some ideas for an instructional design based on these findings are discussed.

A New Approach to the

The frequency assignment problem is to assign a frequency which is a nonnegative integer to each radio transmitter so that interfering transmitters are assigned frequencies whose separation is not in a set of disallowed separations. This frequency assignment problem can be modelled with vertex labelings of graphs. An L(2, 1)-labeling of a graph G is a function f from the vertex set V(G) to the set of all nonnegative integers such that |f(x)-f(y)|ges2 if d(x, y)=1 and |f(x)-f(y)|ges1 if d(x, y)=2, where d(x, y) denotes the distance between x and y in G. The L(2, 1)-labeling number lambda(G) of G is the smallest number k such that G has an L(2, 1)-labeling with max{f(v):visinV(G)}=k. In this paper, we develop a dramatically new approach on the analysis of the adjacency matrices of the graphs to estimate the upper bounds of lambda-numbers of the four standard graph products. By the new approach, we can achieve more accurate results and with significant improvement of the previous bounds.

L(2,1)

The Wiener number of a connected graph is equal to the sum of distances between all pairs of its vertices. In this paper, we shall generalize the elementary cuts method to homogeneous n-gonal nets and give a formula to calculate the Wiener numbers of irregular convex triangular hexagons.

-Labeling of Some Products of Graphs

Abstract An L ( 2 , 1 ) -labeling of a graph G is a function f from the vertex set V ( G ) into the set of nonnegative integers such that | f ( x ) − f ( y ) | ≥ 2 if d ( x , y ) = 1 and | f ( x ) − f ( y ) | ≥ 1 if d ( x , y ) = 2 , where d ( x , y ) denotes the distance between x and y in G . The L ( 2 , 1 ) -labeling number, λ ( G ) , of G is the minimum k where G has an L ( 2 , 1 ) -labeling f with k being the absolute difference between the largest and smallest image points of f . In this work, we will study the L ( 2 , 1 ) -labeling on K 1 , n -free graphs where n ≥ 3 and apply the result to unit sphere graphs which are of particular interest in the channel assignment problem.

On Wiener numbers of polygonal nets

This article focuses on a simple trigonometric problem that generates a strange phenomenon when different methods are applied to tackling it. A series of problem-solving activities are discussed, so that students can be alerted that the precision of diagrams is important when solving geometric problems. In addition, the problem-solving plan was implemented in a high school and the results indicated that students are relatively weak in problem-solving abilities but they understand and appreciate the thinking process in different stages and steps of the activities.

The L ( 2 , 1 ) -labeling of K 1 , n -free graphs and its applications

ABSTRACT The use of dynamic geometry software (DGS) is becoming increasingly familiar among teachers, but letting students conduct inquiries using computers is still not a welcome idea. In addition to logistics and discipline concerns, many teachers believe that mathematics at the lower secondary level can be learned efficiently through practice alone. Thus, the application of DGS remains limited to demonstration and explanation. This article discusses how a set of pre-constructed dynamic geometry (DG) materials was designed to teach the ‘similar triangles’ concept. The reactions and behaviour of students with relatively low levels of mathematic achievement are also analysed. Finally, the potential value of pre-constructed DG materials, with lab sheets and teacher intervention, in inquiry activities for junior-level students is discussed.

Tour of a simple trigonometry problem

In this paper, we report a pilot study on engaging a group of undergraduate students to explore the limits of sin(x)/x and tan(x)/x as x approaches to 0, with the use of non-graphic scientific calculators. By comparing the results in the pretest and the post-test, we found that the students had improvements in the tested items, which involved the basic concepts of limits, but had room for further improvement in those that required them to explain their answers. An analysis of the students’ performances in the tests by using the APOS (i.e. action-process-object-schema) theory framework is reported. Reflections and suggestions on how to teach the topic more effectively are provided.

Pre-constructed dynamic geometry materials in the classroom – how do they facilitate the learning of ‘Similar Triangles’?

ABSTRACT GeoGebra is a mathematics software system that can serve as a tool for inquiry-based learning. This paper deals with the application of a fraction comparison software, which is constructed by GeoGebra, for use in a dynamic mathematics environment. The corresponding teaching and learning issues have also been discussed.

Exploring the Limits of Trigonometric Functions: Results and Reflections from a Pilot Study.

In this note, we will focus on several applications on the Dirichlets box principle in Discrete Mathematics lesson and number theory lesson. In addition, the main result is an innovative game on a triangular board developed by the authors. The game has been used in teaching and learning mathematics in Discrete Mathematics and some high schools in Hong Kong.

Learning fraction comparison by using a dynamic mathematics software – GeoGebra

This paper focuses on the representation of a proper fraction a/b by a decimal number base n where n is any integer greater than 1. The scope is narrowed to look at only fractions where a, b are positive integers with a<b and b not equal to 0 nor equal to 1. Some relationships were found between b and n, which determine whether the representation will become either finite decimal, pure recurring decimal or mixed decimal base n. Three theorems have been proven to indicate the deciding factors and the relationships. In addition, the length of the finite decimal numbers base n was further explored.