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JOURNAL OF RESEARCH IN NATIONAL DEVELOPMENT VOLUME 8 NO 2, DECEMBER, 2010


EFFECT    OF    WEBBING    INSTRUCTIONAL STRATEGY ON STUDENTS’ ACHIEVEMENT IN ALGEBRAIC WORD PROBLEMS

 

A. B. C. Orji and Uche Anaduaka

Department of Science and Environmental Education, University of Abuja, Abuja, Nigeria

E-mail:sanaduaka@yahoo.com

 

Abstract

This study investigated the effectiveness of webbing strategy on students’ achievement in algebraic word problems. It also sought to find out whether gender had any influence on the achievement of students exposed to webbing instructional strategy. A quasi –experimental non-equivalent control group design was used. The study was carried out in Gwagwalada Area Council, FCT, Abuja, Nigeria. The sample consisted of 118 Senior Secondary Two (SSII) students drawn from two randomly selected schools in the Area Council. The instrument used for data collection was an Algebraic Word Problem Achievement Test (AWPAT). A reliability index of 0.78 was obtained for the AWPAT. Data analysis was by mean, standard deviation and analysis of covariance (ANCOVA). Results revealed that webbing strategy significantly improved students (male and female) achievement in algebraic word problems. It was therefore recommended among others that the strategy be adopted for the teaching of mathematics word problems in primary and secondary schools.

 

Keywords: Problems, achievement, learning, webbing strategy.

 

Introduction


The place of mathematics in the life of any nation is closely linked with the place of development in that nation. Mathematics plays an indispensable role in realizing a nations’ dream of rapid scientific and technological development. In fact, no nation that wants to develop scientifically and technologically neglects the mathematical aspect of her school curriculum. Ihejieto (1989) considers mathematics as the ingredient for the effective articulation of the abstract elements of science that gives impetus to the development of technology. According to Ukeje (1997), without mathematics there is no science, without science there is no modern technology, and without modern technology, there is no modern society.

 

The advantages of acquiring mathematical knowledge are indeed so numerous. We are actually in a mathematical world. Mathematics cuts across every aspect of human life and opens up the mind to logical reasoning and analytical thinking. Harbor-Peters (2001) stated that the acquisition of mathematical skills is mandatory for proper intellectual development. This is why every student needs to be given opportunity to learn as much mathematics as he/she can in order to function effectively and intelligently in the society. However, it is common knowledge that many students dislike mathematics and the thought of the subject usually evokes phobia among students in primary, secondary and tertiary institutions. The scientific and technological revolution taking place in the world today makes it imperative that the schools give added emphasis to the development of a student’s understanding and appreciation of mathematical procedures and methods of reasoning to be carried along. Students, more than ever before need to be provided opportunities to acquire and utilize mathematical procedures in order to be able to properly analyze and comprehend the complex situations that are constantly arising in the affairs of our rapidly changing technological society.

 

Algebra is a branch of mathematics that uses mathematical statements to describe relationships between things that vary over time. It involves putting real life problems into equations and solving them. The most important outcomes in the study of algebra include the ability to think logically, to use principles, to see relationships, to pick out essentials, to analyze and to organize. Every student therefore needs the knowledge of algebra because it equips people with problem solving skills and much more because of the orderly way in which it enables individuals to think. However, many students find solving algebraic word problem extremely difficult. Clement (1982) and Fajemidagba (1986) found that students commit a lot of errors in word problem solving in mathematics. Consequently that aspect of mathematics is always poorly responded to in both internal and external examinations by students. Fajemidagba (1986) identified several factors as responsible for the poor achievement of students in mathematics word problems. According to him, such factors include misconception of mathematical statement which leads to errors.

 

Word problems consist of sentences. One therefore needs to understand what is being asked for and determine the key clues that can be used to find solution to the problem. The webbing instructional strategy is considered helpful in analyzing problems of this sort. Webbing is a method of visually representing relationships among ideas, concepts or events [Saskatoon Public Schools, 2009]. According to Harding and Terrell (2006), research in both educational theory and cognitive psychology reveal that visual learning techniques are among the very best methods for teaching students of all ages how to think and how to learn. With visual learning, they explained, students use manipulative, diagrams and plots to display large amounts of information in ways that are easy to understand and help reveal relationships and patterns.

 

Webbing as a visual learning technique involves relating available information about a topic or concept in a pictorial display. The technique helps to develop students’ ability to perceive relationships among ideas and concepts and to encourage students to recall prior knowledge. It can therefore be helpful in understanding and remembering the many ideas in mathematics word problems. With webbing, mathematical processes can be broken down into logical steps so that students can focus on one issue at a time. The structure of webbing starts from a central idea, concept, topic or question, gathering and linking thoughts until a woven network of ideas evolves.

 

Webbing therefore encourages a thoughtful approach to planning and organizing. According to Alaska Department of Education and Early Development (1996), webbing equips students with the skills of sequencing, comparing and classifying to create relationships of concepts and processes. It also facilitates understanding of key concepts by allowing students gradually drill down to the basic points and ideas needed in solving a problem. Webbing could be helpful in motivating, increasing recall, assisting understanding, combating boredom and organizing thoughts [Gardill and Jitendra, 1999; McCarthy-Tucker, 1992].

 

This study therefore set out to empirically ascertain the effectiveness of webbing strategy in improving students’ achievement in algebraic word problems.

 

Purpose of the study

The purpose of the study was to:

1.       Investigate the effectiveness of webbing strategy in improving students’ achievement in algebraic word problems.

2.       Determine the differential effect of webbing strategy on students’ achievement in algebraic word problems for male and female students.

 

Research questions

The following research questions guided the study

1.      What is the difference in the mean achievement scores of students taught algebraic word problems with webbing strategy and those taught with the conventional approach?

2.      What is the difference in the mean achievement scores of male and female students taught algebraic word problems with webbing strategy?

 

Hypothesis

The following null hypotheses were tested at 0.05 level of significance

Ho1: There is no significant difference in the mean achievement scores of students taught algebraic problems with webbing strategy and those taught with the conventional approach.

Ho2: There is no significant difference in the mean achievement scores of male and female students taught algebraic word problems with webbing strategy.

Ho3: The interaction effect of webbing strategy and gender on students’ mean achievement scores in algebraic word problems is not statistically significant.

 

 

Methodology

The study is a quasi-experimental factorial design with the variables in the study crossed in a 2×2 fashion. The design involved the non-equivalent pretest posttest control group as a result of the use of intact classes. The study was conducted in Gwagwalada Area Council of the Federal Capital Territory, Abuja, Nigeria. The population of the study comprised all Senior Secondary Two (SSII) students in secondary schools in the Area Council. Most of the secondary schools in the Area Council are private co-educational schools. Two of such schools were therefore through purposive sampling selected for this study. The sample consisted of 118 SSII students who were members of four intact classes drawn from the two selected schools. Two arms of SSII were drawn from each school and were randomly assigned experimental or control group. Each group therefore was based in one school. Altogether there were 62 students in the experimental group and 56 students in the control group. In terms of gender, there were 32 males and 30 females in the experimental group and 25 males and 31 females in the control group.

 

Teaching of both groups in their schools was done by their regular mathematics teachers using lesson plans prepared and validated by the researchers. This was to control experimenter’s bias and to reduce Hawthorne’s effect. All other extraneous variables were also adequately controlled. The job of the researchers during the experimental period was therefore supervisory to ensure that the lesson plans were adhered to strictly. Students in the experimental group were taught algebraic word problems using webbing strategy. Each topic or question to be discussed was charted or displayed. The teacher then guided a brainstorming session during which students were encouraged to come up with ideas and understanding related to the topic or question. The ideas were discussed and sieved and the relevant ones recorded in clusters or categorized around the displayed topic or question. This generally took a hierarchical or tree branch format with ideas branching into their subsection. Their counterparts in the control group were taught the same content using the conventional method of delivering lessons.

 

The instrument for data collection was an Algebraic Word Problem Achievement Test (AWPAT). The AWPAT was a 20 item multiple choice test with four options developed by the researchers from the content area taught to the students. A test blue print was used to put the items together. The ability process dimension of the test blue print was divided into lower cognitive and higher thinking processes. The 40:60 ratio for lower cognitive and higher thinking processes recommended for senior secondary classes by the National Policy on Education (Obodo, 2004) was adopted. Three experts in mathematics education and measurement and evaluation checked the AWPAT for face validity. A reliability index of 0.78 was obtained for the instrument using Kuder-Richardson Formula 20.

 

The AWPAT was first administered on the sample (experimental and control groups) before the commencement of the experiment to be able to ascertain both the effect of treatment and the homogeneity of the groups. Data from the administration were collected and kept and then the experiment began. The experiment lasted for four weeks excluding the days used in training the research assistants. All lessons stopped at the end of the fourth week and the AWPAT was re-administered to both groups. Data collected were analyzed using mean and standard deviation to answer the research questions and a 2 way (2×2) analysis of covariance (ANCOVA) was used to test the hypotheses.

 

Results

The results obtained are presented in the tables below in answer to the research questions asked and the hypotheses formulated.

Research question one

What is the difference in the mean achievement scores of students taught algebraic word problems with webbing strategy and those taught with the conventional approach?


 

Table 1: Mean and standard deviation of students’ scores in pre and post treatment AWPAT

 

Pre-treatment

Post-treatment

 

Group

N

Mean     SD

Mean      SD

Mean Diff

Exp

Control

62

56

24.54     6.31

24.58    6.19

63.  56   7.50

41.  39   6.53

39.02  

16.81

 Diff in Mean

 

0.04

22.17

 

 


  From the table above, it could be seen that the two groups were relatively equivalent at the initial stage with mean scores of 24.54 and 24.58 respectively. However, in the post test, the experimental group had a mean score of 63.52 while the mean score of the control group was 41.39. The difference in the mean scores of the two groups at that stage was found to be 22.17 as against 0.07 obtained in the pretest analysis. To ascertain whether this observed difference was significant, hypothesis one was tested. 

Ho1: There is no significant difference between the mean achievement scores of students taught algebraic word problems with webbing strategy and those taught with the conventional approach.


 

Table 2: Analysis of covariance (ANCOVA) of students’ scores in AWPAT (Teaching method x Gender).

Source of variance

Sum of squares

   DF

Mean squares

F

Significant 

Corrected model

Intercept

Pre-treatment

Teaching method

Gender

Teaching method*Gender

Error

Total

Corrected Total

9915.137

3949.749

 837.579

 5963.554

  44.134

 

2.329

1861.516

144873.000

11776.65

4

1

1

1

1

 

1

113

118

117

2478.784

3949.749

837.579

5963.554

   44.134

 

  2.329

 16.474

150.470

239.762

2.844

362.007

 2.679

 

 .141

.000

.000

.062

.000

.104

 

.708

 


Table 2 above shows that the computed F-ratio for the effect of the teaching strategy on achievement of students in algebraic word problems was 362.007 which is significant at P value of .00. Therefore at a higher P value of .05, the effect is also significant. This leads to the rejection of the null hypothesis of no significant difference in the mean achievement scores of students taught with webbing strategy and those taught with the conventional approach.

 

Research question two.

What is the difference in the mean achievement scores of male and female students taught algebraic word problems with webbing strategy?


 

 

 

Table 3: Mean and standard deviation of students’ scores in the pre and post treatment AWPAT by gender.

 

Pre-treatment

Post-treatment

 

Group

Gender 

N

Mean     SD

Mean     SD

Mean Diff

 

Exp

 

Male

Female

32

 

30

25.19     6.67

23.78     5.78

63.81    7.34

63.25    7.64

38.62  

39.47

 Diff in Mean

 

 

1.41

0.56

 

 


 From table 3 above, the male students of the experimental group had a mean score of 25.19 in the pre-treatment AWPAT while the female students of the same group had a mean score of 23.78 with a difference in mean of 1.41 between the two groups. When the AWPAT was re-administered after treatment, a high mean score of 63.81 was obtained for the male students and an equally high mean mark of 63.25 was got for the female students group with a difference in mean of only 0.56. For valid decision to be taken on the influence of gender on students’ achievement in algebraic word problems with webbing strategy, hypotheses two was tested.

Ho2: There is no significant difference in the mean achievement scores of male and female students taught algebraic word problems with webbing strategy.

 

Table 2 shows that the computed F-ratio for the effect of gender on students’ achievement was 2.679 which is not significant at P value of 0.5. Therefore, the null hypothesis stands accepted

Ho3: The interaction effect of webbing strategy and gender on students’ mean achievement scores in algebraic word problems is not statistically significant.

Table 2 shows that the computed F- ratio for the interaction effect of teaching strategy and gender on students’ achievement in algebraic word problems was 0.141 which is not significant at an alpha level of 0.05. The null hypothesis is therefore accepted. This means that there is no significant effect of the interaction between treatment and gender on students’ achievement in algebraic word problems.

 

Discussion of results

Results of data analysis presented in tables 1 and 2 show that students taught algebraic word problems using the conventional approach obtained a mean score of 41.39. However with the webbing strategy, students in the experimental group performed significantly better in the AWPAT with an average score of 63.56. This finding is consistent with the results of the researches conducted by Clement (1982) and Fajemidagba (1986) that found that students ordinarily do not do well in algebraic word problems especially when taught with the conventional approach. The result demonstrates the effectiveness of webbing strategy in bringing about significant improvement in the achievement scores of students in algebraic word problems. It therefore supports the report by Harding and Terrell (2006) that it has been found that visual learning technique is one of the best methods of teaching students how to learn and think and to be enthusiastic about learning. During the experiment, it was noticed that the experimental group’s morale and enthusiasm was high and they were seen showing great interest in the lessons. Creating a web of information relating to every question portrayed the need for students to be problem solvers and thinkers and not just memorizers of rules and the students found this very enjoyable.

 

It was observed in this study that for male and female students, there is no significant difference in their achievement in algebraic word problems when they are both taught with webbing strategy. Some other teaching strategies have been found to favor a particular sex more than the other when applied in the classroom (Harbor-Peters, 2001).  The result of this study, however, shows that webbing strategy is not one of such as it has proved to be quite suitable for any gender.

 

Conclusion

It is indeed clear from the findings of this study that students’ phobia for mathematics may not actually be that they do not understand its value and usefulness. Students fear for mathematics (especially word problems) and their consequent poor achievement in it, may be as a result of the method of teaching the subject/topic. It therefore behooves every mathematics teacher to tap the riches of webbing strategy so as to bring about improved performance of their students in mathematics and especially word problems.

 

Recommendations

          The following recommendations are therefore made:

1)      Webbing strategy should be adopted in the teaching of mathematics word problems in primary and secondary schools.

2)      Curriculum planners should incorporate the technique in the curriculum of teacher education so as to enable teacher trainees acquire the skills necessary for the use and application of the strategy.

3)      Seminars, Conferences and Workshops should be organized for mathematics teachers to expose them to the use and application of webbing strategy especially in teaching and learning of mathematics word problems.

 

References

Alaska Department of Education and Early Development(1996).A  collection of assessment strategies. Retrieved January 10, 2010         from www.      eed.state.ak.us/../mss-2asl.htm

 

Clement, J. (1982). Algebraic word problem solving: Thought process underlying a common misconception. Journal for Research in Mathematics Education. 13 (1) pp.16-30.

 

Fajemidagba, O. (1986). Mathematical word problem solving: An analysis of error committed by students. The Nigerian Journal of Guidance and Counseling. 2 (1) pp.23-30.

 

Gardill, M. C.and Jitendra, A. K. (1999). Advanced story map instruction: Effects on the reading comprehension of students with learning disabilities. The Journal of Special Education. 33 (1)pp.2-17.

 

 

Harbor-Peters V.F.A (2001). Unmasking some aversive aspects of school mathematics and strategies for averting them. Inaugural lecture, University of Nigeria, Nsukka. Enugu: Snaap Press Ltd.

 

Harding, G. and Terrell S. L. (2006). Strategies for alleviating math anxiety in the      visual learner. Retrieved February 2, 2010 from   www.coscc.cc.tn.us/baker/cartons2.htm

 

Ihejieto, D. O. (1989). Mathematics- An effective articulator of the abstract elements of the natural sciences for technological development. ABACUS,Journal of the Mathematical Association of Nigeria 19(1) pp 75-87.

 

McCarthy, T. (1992). Semantic webbing, semantic-pictorial webbing and standard basal teaching techniques: A comparison of three strategies to enhance       learning and memory of a reading comprehension task in the fourth grade classroom. Paper presented at the Annual Meeting of the Western         Psychological Association, April 30-May 3.

 

Obodo, G. C.  (2004). Principles and practice of mathematics education in Nigeria. Enugu: Floxtone Press.

 

Okereke, S. C. (2002). Impact of familiar quantities on pupils’ achievement in mathematics. In Matt. A. G. Akale [Ed.]. Proceedings of the 43rd Annual           Conference of STAN (pp. 358-362). Nigeria: Heinemann Educational Books Plc.

 

Saskatoon Public Schools (2009).Instructional strategies on line. Retrieved January 3, 2010. olc.spsd.sk.ca/DE/pd/instr/strats/webbing/index.html

 

Ukeje, B. O. (1997). The challenges of mathematics in Nigeria’s economic goals of vision 2010: Implication for secondary school mathematics. A lead Paper presented at the 34th Annual Conference of the Mathematical Association of Nigeria.