effects of advance organiser strategy during instruction on secondary school students’ mathematics...

BERNARD N. GITHUAj and RACHEL ANGELA NYABWA

EFFECTS OF ADVANCE ORGANISER STRATEGY DURING

INSTRUCTION ON SECONDARY SCHOOL STUDENTS’

MATHEMATICS ACHIEVEMENT IN KENYA’S

NAKURU DISTRICT

ABSTRACT. Students have continued to perform poorly in KCSE examinations in

certain mathematics topics taught in secondary schools in Kenya. One such topic is

commercial arithmetic. Successful teaching of mathematics depends partly on correct use

of teaching methods in classroom settings. This study sought to examine how the use of

advance organisers during instruction affect students achievement in commercial

arithmetic. There is however inadequate documented information in research conducted

in Kenya on the effects of the use of advance organisers on students’ achievement in

mathematics. The purpose of this study was therefore to develop and use advance

organisers to augment the teaching of commercial arithmetic and then investigate its

effects on student achievement in the topic. A simple random sample of four provincial

mixed-sex secondary schools in Nakuru district was obtained. The study was carried out in

a mathematics classroom setting. Solomon four-group design was employed. The

experimental groups received the advance organisers as treatment and two control groups

were taught in the conventional way. The sample size was 142 students. A mathematics

achievement test (MAT) was used. The instrument was pilot tested to ascertain its

reliability. The validity of the instrument was checked by experts from the Department of

Curriculum and Instruction. The MAT was administered to two groups before the teaching

of the topic and then to all four groups after learning the topic of commercial arithmetic.

Statistical package for social sciences (SPSS) was used for data analysis. Descriptive

statistics (mean, standard deviation, percentages) and Inferential statistics (ANOVA,

ANCOVA and t-test) were used for data analysis. The level of significance for acceptance

or rejection of hypothesis was set at 0.05 a-level. The results indicated that students taughtusing advance organisers had significantly higher scores in MAT than those taught in the

conventional way. Gender did not affect achievement. Major recommendations from the

study are that teaching using advance organisers should be included in the syllabus during

training and in-servicing of teachers, and teachers should be encouraged to use advance

organisers when teaching mathematics where applicable.

KEY WORDS: advance organiser strategy, mathematics achievement

j

Author for correspondence.

International Journal of Science and Mathematics Education (2008) 6: 439Y457# National Science Council, Taiwan (2007)

INTRODUCTION

Though teachers’ possession of high academic qualifications, enthusiasm

in teaching, mastery of both procedural and declarative knowledge, and

capacity to facilitate learning in classrooms is important, the effective use

of an appropriate teaching method or strategy is critical to the successful

learning and teaching of mathematics. Knowledge of how a specific

teaching method or strategy impacts students’ learning may help

mathematics teachers in selecting teaching methods that enhance the

effectiveness, efficiency and quality of learning and teaching the subject in

classroom settings.

During the last ten years students’ achievement in mathematics at the

Kenya Certificate of Secondary Education (KCSE) has been and continues

to be dismal (KIE, 2000, 2001). For instance, the KCSE mathematics

examination results for 2001 and 2002 revealed that students had low

national mean scores of 18.51% and 19.49%, respectively.

Several factors have been cited as causes of this poor performance in

mathematics including language and symbolism used in mathematics

instruction; nature and organization of the syllabus; teaching methods and

availability of teaching materials (Akala, 2000). Even with such a dismal

performance, female students had a lower achievement as compared to

males. For example, in 2001 girls obtained an average of 15.83% while

boys had 21.19% (Aduda, Thuku &Wangugi, 2000; KNEC, 2002). In the

following year, girls obtained an average of 16.44% while boys had

22.53% (KNEC, 2003). Such an underachievement among girls has been

attributed to cultural view of mathematics as a male domain, competitive

modes of assessment in favour of boys, gender biased textbooks, lack of

positive female role models in mathematics and modes of teaching that

are individualistic or competitive as opposed to being cooperative.

Gender differences in mathematics at Kenya Certificate of Secondary

Education national examinations are, therefore, highly significant

(Aduda et al., 2000; Eshiwani, 1974; Makau, 1994; Obura, 1991; KNEC,

2002, 2003). Gender differences in mathematics performance has,

however, not been significant at the Kenya Certificate of Primary

Education (KCPE) national examinations (Eshiwani, 1985; Kirea, 1989).

Such situation calls for the need for a continuous search for effective

methods or strategies of teaching mathematics. One such teaching/

learning strategy is the use of advance organisers during instruction.

An advance organiser is a small amount of verbal, visual graphic or

written information that is presented to learners in advance of new

material that is to be learned within an instructional session (Lefrancois,

BERNARD N. GITHUA AND RACHEL ANGELA NYABWA440

1997). It is an organisational framework that teachers present to students

prior to teaching new content to prepare them for what they are about to

learn. Advance organisers are usually given at the beginning of a lesson

to unfold and reinforce or direct students thinking (Eggen, Kauchak &

Harder, 1979).

According to Eggen et al. (1979), there are two types of advance

organisers, namely, the expository advance organisers and the compar-

ative advance organisers. Advance organisers come in many formats,

some of which commonly used are: (i) expository advance organisers

that describe new content to which students are to be exposed; (ii)

narrative format in which information is presented to students in story

format; (iii) an analogy; (iv) skimming, in which a teacher previews

important information quickly by noting main points in a text; and (v)

graphic organisers which are non-linguistic and which visually represent

what students will learn. Advance organisers are super ordinate concepts

within which learners can subsume the new material and relate it to what

they already know (Lefrancois, 1997). The use of advance organisers as a

teaching strategy may be used to activate prior knowledge, which provides

a conceptual framework for integrating new information. The advance

organisers are meant to provide cognitive structures to which the learning

can be anchored. A teacher prior to presenting a lesson may give an

advance organiser by either stating clearly the objectives of topic, its

relevance and use in daily lives, explain his/her expectations of the

students after learning a topic, make generalisations of the specific topic or

give an analogy that compares closely to the content of the topic that is to

be learned.

Ausubel (1967) advocated the use of advance organisers during

instruction and indicated that it leads to meaningful learning as opposed

to rote learning. To learn meaningfully learners must relate new knowl-

edge to what they already know. According to Ausubel (1967) an

organising statement called advance organiser presented at the beginning

of a lesson acts as a connection between material to be learned and the

learner’s cognitive structure. An advance organiser acts as a roadmap that

guides a student over the new content to be learned (Eggen et al., 1979). In

this teaching model, a teacher helps a learner break major concepts into

smaller related concepts and to determine the relationships between new

ideas and old among the new ideas themselves (Eggen et al., 1979).

According to Good & Brophy (1995), this is integrative reconciliation of

concepts. During the presentation of advance organisers, lessons are

interactive and learners develop their own ideas and process their own

information.

EFFECTS OF ADVANCE ORGANISER STRATEGY 441

According to Mayer (1979), effective advance organisers are those

that present key terms, principles, models or illustrations rather than

characterising the new material with reference to previous knowledge or

expository explanations. Generally concrete models, analogies or exam-

ples, sets of higher order rules or discussions of main themes are more

effective organisers than specific factual pre-questions, outlines and

summaries. Grippins & Peters (1997) indicated that the use of advance

organisers makes a significant difference in recall and comprehension of

subject matter. Mayer (1979) suggested that the most effective advance

organisers are those that: (i) allow the learners to generate all or most of

the logical relationships in the material to be learnt, (ii) point out rela-

tionships between familiar and less familiar material, (iii) are relatively

simple to learn, and (iv) are used in situations in which the learner would

not spontaneously use an advance organiser.

The use of advance organisers is one method which could enhance

students understanding of difficult topics in mathematics. The instruction

model that has been widely used with advance organisers for organising

instruction is the Ausubel model. It is designed to teach interrelated bodies

of content. It is an information processing model in which the broader or

more inclusive ideas are presented first followed by less inclusive ideas.

The comparative advance organiser, usually an analogy, is a very

effective type of advance organiser (Eggen et al., 1979). It can be adapted

to fit the background of a particular student population. The value of

an analogy advance organiser is dependent upon two factors: the famil-

iarity of the analogy to students and the degree of overlap between the

ideas taught and the analogy used. The more familiar the analogy, the

easier it will be to use in order to retrieve information (Eggen et al.,

1979). Analogies help link the new to the familiar concepts (Good &

Brophy, 1995).

The advance organisers also enhance the students’ motivation to

learn. It reinforces and directs students’ thinking. The advance organiser

is an efficient instructional strategy since the learner is able to know

beforehand what is going to be learned (Eggen et al., 1979). Advance

organisers are especially useful when the material is not well organised

and the learners lack knowledge needed to be able to organise it well for

themselves (Ausubel, 1968).

The topic Fcommercial arithmetic,_ which is a major topic in the

secondary school mathematics curriculum, has consistently been one of

the difficult areas for pupils to learn in the secondary school mathematics


syllabus in Kenya. The topic Fcommercial arithmetic_ is taught at formthree level and also at form one level (KIE, 2000). It is divided into

commercial arithmetic I taught at form one and commercial arithmetic II

taught in form three (KIE, 1992). The strategy of dividing the topic into

two has not succeeded in making the topic easier. According to KIE

(2000) commercial arithmetic was one of the areas that students per-

formed dismally in the national examinations in 1997 and 1998 where

more than 65% scored a 0 mark. KIE (2001) also indicated that this was

an area in which students had a lot of difficulties.

There are well documented strengths of advance organisers as an

instructional strategy (Anderton & Steiner, 2003; Ausubel, 1960, 1978;

Bills, 1997; Coffey & Canas, 2003; English, 1993; Grippins & Peters,

1997; Huitt, 2000; Kirkland, 1981).

Advance organisers are associated with increased learning and

retention of subject matter (Stone, 1983), improved reading comprehen-

sion (Kirkland, 1981), and meaningful learning of intellectual skills such

as mathematics (Lai & Repman, 1996). Stone’s meta-analysis studies

indicated a significant difference in recall and comprehension of learned

material. A study by English (1993) indicated that the use of analogies

increased students_ success in solving mathematical problems and

enhanced the learning of mathematics. Some studies, however, indicate

that advance organisers have some weaknesses. For instance English

indicated that analogies may posses structures that distract students from

learning the subject matter accurately. McAdaragh (1981) indicated that

students background experience and type of advance organiser may

hinder the attainment of certain science concepts. Anderton & Steiner

(2003), however, argued that the contradictory findings on the role of

advance organisers in improving learners_ achievement were due to

varying contexts in which they were used. Such contexts include content,

quality and type of advance organiser, and age of participants, hence

making it difficult for studies done in different contexts to be compared.

In this study, the weaknesses of the use of advance organisers, par-

ticularly analogies during instruction, were considered and improved

upon. Analogies were, therefore, presented explicitly and involved real

life situations of business transactions that obtain in Kenya’s Nakuru

district. Appropriate orienting strategies were used during mathematics

lessons. The analogies were, therefore, well adapted to suit the form three

students_ in secondary schools and the social context in Kenya.


Purpose of the Study

The purpose of this study was to develop and use advance organisers to

augment the teaching of commercial arithmetic and then measure its

effects on students_ achievement in the mathematics topic.

The objectives of the study were:

i. To find out whether there is any statistically significant difference in

mathematics achievement between students who have been taught

using advance organisers and those who have been taught in the

conventional teaching methods.

ii. To find out whether gender affects achievement when advance

organisers are used.

Hypotheses of the Study

The following null hypotheses were tested at the 0.05 a-level.

HO1 There is no statistically significant difference in students_mathematics achievement between students taught using

advance organisers and those taught in the conventional

teaching methods.

HO2 There is no statistically significant gender difference in

achievement among secondary school students when taught

commercial arithmetic using advance organisers.

Conceptual Framework

The conceptual framework of the study was based on the Ausubel’s

model of meaningful reception learning and systems theory developed

by Ayot & Patel (1987) and Gerlach & Ely (1980). The framework

shows an advance organiser as an intervention in the teaching and

learning process of a mathematics topic, which was proposed to aid in

improvement of students_ achievement in the subject. The teaching

learning process in this model is portrayed as being dynamic with inputs

and outcomes.

The dependent variable in this study was the student’s achievement in

commercial arithmetic. The researchers investigated whether the use of

advance organisers as a teaching strategy influenced the student’s

achievement in mathematics as compared to the use of Bconventional^or traditional teaching methods. The independent variables were the


advance organisers presented to students and the conventional or

traditional teaching methods. Conventional or traditional teaching

methods in this study refer to all the regular methods of teaching

mathematics as opposed to the use of planned advance organisers for all

mathematics lessons as was the case in this study.

In addition to these variables, and noting that the outcome of the study

was likely to be influenced by the students_ and teachers_ characteristics,the researchers introduced two extraneous variables in the study. One of

these, which was studied in this research, was the gender variable. The

other extraneous variable was the teacher’s training and experience. To

account for this variable, the study proposed using teachers who have a

minimum qualification of a diploma in education and have taught form

three class for a minimum of 2 years.

It was proposed that these two sets of variables were interrelated in

that the extraneous variables would have an influence on the teaching

learning process which ultimately influenced the student’s performance.

Figure 1 shows the representation of the relationships among variables

within the conceptual framework.

RESEARCH METHODOLOGY

This study used the Solomon’s 4-group, non-equivalent control group

design which is appropriate for experimental and quasi-experimental

studies (Ogunniyi, 1992). The design overcomes external validity weak-

nesses found in other designs and also provides more rigorous control by

having two control groups as compared to other experimental designs

(Koul, 1984). This design involves a random assignment of intact classes

to four groups. The study adopted a quasi-experimental design, as the

subjects were already constituted and school authorities don_t allow

reconstitution for research purposes (Borg & Gall, 1989). Figure 2 shows

(i) Learner characteristics • Gender

(ii) Teacher characteristics • Training • Experience

Teaching/Learning Process • Advance Organizers

expository method • Conventional teaching

methods

Students’ Achievement in mathematics

Extraneous Variables Independent Variables Dependent Variables

Figure 1. Conceptual framework of the study.


the non-randomised Solomon’s 4-group, non-equivalent control group

design.

In Figure 2, the variables are defined such that: O1 and O3 are pre-

test; O2, O4, O5 and O6 are post-test; and X is treatment.

Group E1 received the pre-test, X and post-test; group C1 received a

pre-test and a post-test; group E2 was not given the pre-test but received

X and post-test and group C received the post-test only. Groups C1 and

C2 were taught using conventional teaching methods. This design

enabled the experimenter to control and measure the main effects of

testing. The main effects of maturation and history were controlled in

this design by having two groups taking pre- and post-tests. This design

actually involved conducting the experiment twice, once with the pre-

tests and once without pre-tests. If the results of the two experiments

were in agreement, the experimenter had considerable confidence in his/

her findings (Koul, 1984). To avoid contamination, the treatment and

control groups were from different schools. The regression effects were

taken care of by two groups not taking the pre-test. The same teachers

who had been teaching them taught the students in the classroom, and

the lessons were conducted at the same time as previously taught so that

the students were unaware of the experimentation process.

The treatment was administered to the whole form three class (where

more than one stream exists) in order to avoid the Hawthorne effect.

Furthermore, the form three students in the two experimental schools did

not know the topic commercial arithmetic was taught as an experiment.

This topic was among the four mathematics topics that were scheduled

for teaching in one school tern of twelve weeks. The pre-test was treated

as a normal classroom test that students regularly take in the course of

instruction while the post-test was also taken as a normal test that is

administered after a topic has been covered. The mathematics teachers in

the two experimental schools were trained on the use of advance orga-

nisers when their students were on recess. The Hawthorne effect was,

GROUP NOTATION

E1 (N=32) 01 X O2 (Experimental group)

C1 (N=36) 03 O4 (Control group)

E2 (N=46) - X 05 (Experimental group)

C2 (N=28) - - O6 (Control group)

Figure 2. The non-randomised Solomon 4-group, non-equivalent control group design.


therefore, adequately controlled. However, only results from one stream in

each school was used for analysis of data and for the acceptance or

rejection of the hypotheses of the study.

Population

The schools that participated in the study were from Nakuru district.

Nakuru district was chosen as it has a varied population and also the

highest number of schools in Rift Valley Province. The target population

was form three mathematics secondary school students in the provincial

mixed-sex schools within Nakuru district because the topic of commercial

arithmetic is taught at this level (KIE, 2000). It is a mature group of stu-

dents and not an examination class. The study concentrated on the

provincial mixed-sex secondary schools that are disadvantaged in KCSE

mathematics examinations as compared to the single-sex schools. There

were only eleven provincial mixed-sex secondary schools in Nakuru

district.

Sampling Procedure and Sample Size

Simple random sampling was employed to select four schools out of the

possible eleven. Four schools were chosen because the Solomon 4-group

design required four groups. Each school formed a group in the Solomon

4-group design so that the interaction was minimised during the exercise.

The assignment of groups to either experimental or control groups was

done by simple random sampling. According to Mugenda & Mugenda

(1999) the required size is at least 30 cases per group. The classes used

for the exercise were found to have between 30 and 45 students. Therefore,

the actual sample size obtained was 142 students. All mathematics

teachers in the two experimental schools were trained for five days on the

creation and use of advance organisers. The advance organisers that were

used in this study were all exhaustively discussed with the mathematics

teachers before using them. The mathematics teachers in the two control

schools were not trained on the creation and use of advance organisers and

were, therefore, expected to use conventional or traditional methods in

their instruction.

Instrumentation

The mathematics achievement test (MAT) was used to collect the required

data. It was an eight item instrument that tested students_ knowledge,


comprehension, application and mathematical skills on working out short

answer questions that were set on simple and compound interest,

appreciation and depreciation, higher purchase and income tax. The

maximum score for the test was 34 marks. Its reliability was 0.7564 from

the K-R-20 formula. The pilot test was conducted in Koibatek district that

neighbours Nakuru district. Three mathematics experts from the Educa-

tion Department of Egerton University and two mathematics teachers

checked the validity of the instruments.

Two schools, one experimental (E1) and the other control (C1),

received a pre-test to enable the researchers to have knowledge of the

entry level of the students before the experiment began. Students in one

of the schools were taught using the advance organisers while those in

the other were taught in the conventional way. The other two schools

involved in the study, one experimental (E2) and one control (C2), did

not receive a pre-test.

How Advance Organisers were Built and Taught

The mathematics topic that was taught to form three students in ex-

perimental schools by use of advance organisers (analogies) was

commercial arithmetic whose subtopics included: simple and compound

interest; appreciation and depreciation; hire purchase and income tax.

Appropriate analogies for each of these subtopics were constructed and

used during instruction at the beginning of each mathematics lesson. The

analogies were constructed in such a way that they reflected the business

transactions that take place in Kenya’s society. They were closely related

to the daily economic activities and culture of the people in Kenya’s

Nakuru district.

For each of the subtopics that were taught, the six steps for creating

and using advance organisers as recommended by NETnet (2002) were

followed. Analogies that were used in the teaching of the various sub-

topics therefore had the following sequence of steps: statement of the

TABLE I

Independent sample t-test of pre-test scores on MAT based on groups E1 and C1

Variable Group N Mean SD t-value P-value

MAT E1 32 10.41 4.01

C1 36 9.19 5.85 1.003 0.320 ns


objective of the lesson; oral presentation of subject matter from general

to specific; integrative reconciliation, in which students were expected to

relate new ideas to the old, and critically discuss new ideas and

definitions; promotion of active reception learning, in which students

were expected to give their own examples that were similar to the ones

given by the teacher; encouragement of learners to adopt a critical

approach to the subject matter; and application of the subject matter to

solution of problems using derived formulae.

RESULTS

The independent sample t-test for MAT pre-test mean scores for groups E1

and C1 were not significantly different (Table I) implying that the groups

had similar characteristics and were therefore suitable for the study.

The independent sample t-test of pre-test scores on MAT based on

gender showed that the mean scores for male and female students were

not significantly different (Table II).

Effect of Advance Organiser on Students_ Performance in Mathematics

To establish the effect of advance organiser on students_ performance in

mathematics, the post-test scores of the MAT were analysed. Hypothesis

TABLE II

Independent sample t-test of pre-test scores on MAT based on gender

Variable Gender N Mean SD t-value P-value

MAT Male 41 10.24 5.72

Female 27 9.04 3.91 1.034 0.305 ns

TABLE III

Post-test MAT mean scores obtained by students in the study groups

Group E1 E2 C1 C2 Total

N 32 46 36 28 142

Mean score 17.41 18.39 12.03 16.61 16.20

E1 = experimental group 1, C1 = control group 1

E2 = experimental group 2, C2 = control group 2


HO1 sought to establish whether there was a significant difference in

performance between students_ taught using advance organiser and those

taught in the conventional way. Table III shows the MAT mean scores

obtained by the students.

Table III shows a higher mean score for the experimental groups with

advance organisers compared to the control groups. The mean scores for

the experimental groups E1 and E2 were 17.41 and 18.39, respectively. A

one-way ANOVA procedure was used to establish whether there was a

statistically significant difference in mean scores among the four groups.

The results indicated that differences in mean scores among the four

groups were statistically significant at the a = 0.05 level (Table IV).

TABLE IV

One-way ANOVA of the post-test scores on the MAT

Sum of squares Df Mean square F P-value

Between groups 898.751 3 299.584 6.572 0.000

Within groups 6,290.326 138 45.582

Total 7,189.077 141

TABLE V

Scheffe’s post hoc comparison of the post-test MAT means for the study groups

Dependent variable

(I ) Learning

program

(J ) Learning

program

Mean

difference I-J Significance

Sum of post-test

achievement

E1 E2 j0.99 0.939

C1 5.38* 0.014

C2 0.80 0.572

E2 E1 0.99 0.939

C1 6.36* 0.001

C2 1.78 0.177

C1 E1 j5.38* 0.014

E2 j6.36* 0.001

C2 j4.58 0.255

C2 E1 j0.80 0.572

E2 j1.78 0.177

C1 4.58 0.255

* Mean difference is significant at p e 0.05


To show which groups had significant mean differences in mathe-

matics, achievement a post hoc test of multiple comparisons using

Scheffe’s method were used. Scheffe’s method was preferred since the

sizes of the samples selected from the different populations were not

equal; moreover, comparisons other than simple pair-wise between two

means were not of interest (Kleinbaum & Kupper, 1978). Table V shows

the results of the Scheffe’s post hoc comparisons.

From Table V the results indicated that experimental group 1 (E1) and

control group 1 (C1), and experimental group 2 (E2) and control group 1

(C1) are significantly different at the 0.05 a-level. However, the mean

score of experimental group 1 (E1) and control group 2 (C2), experimental

group 2 (E2) and control group 2 (C2) were not significantly different at

the 0.05 a-level.ANCOVA procedure was used to confirm if the experimental group 1

(E1) and control group 1 (C1) scores were significantly different. The

results are shown in Table VI. The adjusted mean scores in the

ANCOVA are shown in Table VII.

The results from Tables VI and VII confirmed that the differences in

mean scores in the experimental group 1 (E1) and control group 1 (C1)

are statistically significant.

A further comparison was needed to check the mean gain of the

students in the pre-test and post-test for the experimental group 1 and the

control group 1 (See Table VIII).

TABLE VI

ANCOVA of the post-test MAT scores with pre-test scores as covariate

Sum of squares Df Mean square F P-value

Pre-test for MAT 1,669.857 1 1,669.857 50.986 0.000

Use of advance organisers 291.553 1 291.553 8.902 0.004

Error 2,128.834 65 32.751

TABLE VII

Adjusted MAT mean scores obtained by students

Group N Mean Standard error

E1 32 16.771 1.016

C1 36 12.592 0.957


Table VIII shows that experimental group 1 (E1) had a higher mean

gain score than control group 1 (C1). The experimental group gained

more than the control group (C1). A paired sample t-test between mean

gain scores of E1 and C1 indicated significant difference in mean gains,

t =j6.574, P G 0.05. Thus the group that was taught using advance

organiser had a higher mean gain score than the control group. The

hypothesis that there is no statistically significant difference in mathe-

matics achievement between students taught using advance organisers and

those taught through the conventional teaching methods was rejected at

the 0.05 a-level. Therefore, using the advance organiser method improves

students_ performance in mathematics more than when the students are

taught in the conventional teaching methods.

Isolated and Combined Effects of Advance Organisers and Gender on

Mathematics Achievement

An independent sample-t-test on the post-test MAT scores of male and

female students who were exposed to advance organisers revealed no

statistically significant gender differences in their mathematics achieve-

ment (Table IX).

Both male and female students performed relatively the same. There

was no significant difference between the 83 boys and 59 girls exposed

TABLE VIII

Comparison of the mean scores and mean gain obtained by students in the MAT

Overall (N= 68) Experimental group 1 (E1) Control group 1 (C1)

Pre-test mean 9.80 10.41 9.10

Post-test mean 14.72 17.41 12.03

Mean gain 4.92 7.00 2.81

TABLE IX

Independent sample t-test of the post-test MAT scores of male and female

students exposed to advance organisers

Gender N Mean SD T P-value

Male 83 16.34 7.08

Female 59 16.02 7.28 0.261 0.794


to the advance organisers though the boys had a slightly higher MAT

mean gain score (Table X).

Table X indicates that boys and girls performed equally well when

exposed to advance organisers. A paired sample t-test between the mean

gain scores in MAT by gender indicates no significant differences with

t = 1.32, p = 0.19.

Hypothesis HO2 which stated that there are no statistically significant

gender differences in achievement among secondary school students

when taught mathematics using advance organiser was therefore ac-

cepted at a 0.05 a-level.

DISCUSSION

This study was not a replication but rather tried to improve upon the

weaknesses of the use of advance organisers in the previous studies.

Therefore, stimulating discussions were used during mathematics lessons

to enhance the understanding of the subject matter embedded in the ad-

vance organisers. The finding that advance organisers improved students

achievement in commercial arithmetic makes a contribution to knowledge

in this area. The other finding that the use of advance organisers in in-

struction was attributable to no significant gender differences in

mathematics achievement is quite significant in Kenya and the world at

large.

Students taught mathematics through advance organisers performed

significantly better than those who were taught through the conventional

or traditional teaching methods. This means that the use of advance or-

ganisers enhanced learners_ mathematics achievement more than conven-

tional teachingmethods.White (1997) argued that learners who lack prior

knowledge are most likely to benefit from the use of advance organisers.

Half of the research reviewed on the effect of advance organisers

TABLE X

Comparison of mean gain of students’ pre- and post-test scores in MAT

by gender

Test Male Female

Pre-test 10.24 9.04

Post-test 16.34 16.02

Mean gain 6.10 5.98


(Grippins & Peters, 1997) on learners_ achievement indicated that the use

of advance organisers makes a significant difference on recall and com-

prehension of new material that is learned. Furthermore, other research

(Good & Brophy, 1995; Mayer, 1975) indicated that advance organisers

have a positive influence on learning outcomes. These research studies

therefore support the findings of this study.

It can, therefore, be argued that advance organisers are meta-cognitive

tools that in this study allowed meaningful reception of mathematical

content hence leading to higher achievement. Therefore, if this strategy is

effectively used it would lead to improvement in achievement in mathe-

matics in national examinations.

The use of advance organisers and specifically the analogies have

been found to be more appealing and motivating to learners than

definitions and generalisations (Eggen et al., 1979). They further argued

that when carefully planned, analogies trigger learner’s interest and add a

measure of humour to a learning activity. Advance organisers provide

learners with a framework to link previous knowledge to the new material

that is being learned (Ausubel, 1967). Advance organisers, if well se-

lected, enhance the explanation and integration of new material to

learners_ schema of knowledge. The advance organisers used in this

study had similar qualities and therefore resulted in learner’s higher

achievement than conventional teaching methods.

Effect of Advance Organisers on Girls_ and Boys_ Achievement

The findings of this study showed that there was no significant difference

in mathematics achievement between girls and boys taught by the use of

advance organisers. It was further found that both girls and boys

performed significantly better when exposed to advance organisers than

those who were taught through conventional teaching methods.

Though there are recorded gender differences in mathematics

achievement at KCSE (KIE, 2001; KNEC, 2002), studies conducted by

Mondoh (1998) indicated that girls can perform as well as boys if they

are given the chance to interact and discuss mathematics concepts freely

in mathematics classrooms. In this study advance organisers in general

and analogies that were used in this study in particular, provided a

conducive learning environment in which neither sex was disadvantaged

in learning mathematics. The use of advance organisers in teaching

secondary school mathematics could be used to reduce gender disparity

in KCSE mathematics examinations.


CONCLUSIONS

Based on the results of the study, the following conclusions were

reached.

1. Students who are taught mathematics using advance organisers

perform better than those taught with conventional teaching methods.

2. Gender does not affect students_ achievement in mathematics when

students are taught using advance organisers.

Implications of the Study

The use of advance organisers in teaching results in better students_performance in mathematics and the students_ gender does not affect theirmathematics achievement. The use of advance organisers is therefore a

suitable method for teaching. Curriculum developers should encourage

teachers to use this method in teaching mathematics especially applied

mathematics so that the students can be able to see the relevance of the

topic and also enjoy lessons. The teacher training colleges and universities

should emphasize advance organisers as an effective method of teaching

mathematics.

Recommendations

1. Recommendations for educators

a. Mathematics curriculum developers should include the teaching

of mathematics using advance organisers as part of the teacher

education syllabus during the training of mathematics teachers.

b. Teachers should be encouraged by education stakeholders to use

advance organisers in teaching mathematics topics where it is

applicable.

c. During in-service training of teachers the use of advance

organisers in teaching mathematics should be included.

2. Recommendations for further research

a. A study on other types of advance organisers and their effects on

achievement and motivation to learn mathematics should be

carried out.

b. A comparative study should be conducted on the students_attitudes towards teaching using advance organisers versus when

taught by the conventional teaching methods.


c. Research on the topics that can be taught effectively using ad-

vance organisers should be identified from mathematics curricula.

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Department of Curriculum and Instruction,

Egerton University,

P.O. Box 536, Njoro 536, Kenya

E-mail: [email protected]


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