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Mathematical Analysis

Lecture 1: Math. Analysis

A Survey of Instructional Strategies used by Primary School Teachers for the attainment of Millennium Development Goals in Basic Mathematics

Introduction

The purpose of general education is to provide rich and significant experiences in the major aspects of living. This is directed so as to promote the fullest possible realization of personal potentialities and the most effective participation in a democratic society. The contributory role of basic mathematics curriculum in achieving these laudable goals cannot be over emphasized especially in the primary school. This is why there is much emphasis on mathematics as a core subject in the primary and secondary school levels of education in Nigeria (FGN 2004). Mathematics as a bedrock of science and technology and as a school subject is recognized as the foundation without which a nation cannot become prosperous and economically dependent (Umonyang, 1997).This underscores the significance of the mathematical competence of all the learners at basic level of education, at the same time the need for teachers to make learning of mathematics more interesting to the learner  is imperative. In order words, good teaching should begin with the teacher having a clear, mental way of the exact changes he has to bring about in the learner.

Mathematics is a tool used in the daily lives of the individual. Every daily activity of man requires the knowledge and use of mathematics inquiry needed for action learning to take place which will help learners to develop essential 21st century skills through relevant and authentic content and contexts in the MDG. Agwagah, (1996) stressed the important role of mathematics and mathematics teachers in national development in actualising the needs of the learner and society in MDG programmes. Teachers' method of instruction has not been effective in meeting the needs of this national development in Nigeria. Teacher instructional strategies especially at the foundation level of teaching and learning is a vital aspect of the nation's productively independent (Okolo, 2000).

Research reports (Bruner, 1996, Darling-Hammond & Snyder, 1992) have indicated that changes are necessary in the way mathematics is been handled. The traditional method of instruction does not relate mathematical problems to the real world, help students think about realistic situations, or help students to generate and pose their own solutions. As a result, students may become unmotivated to learn and unconnected with what the teacher is doing in the classroom, developing an overall negative attitude towards mathematics.

At the primary school level, there is need for teachers to make learning of mathematics more interesting to the learner (pupils) by using good and varied instructional strategies which the teacher adopt and use to facilitate learning of abstract concepts, by helping to conceptualize ideas and stimulate the learners' imagination; they are known to increase the learners' active participation in the learning of mathematics. The use of varying instruction strategies in mathematics helps both the teacher and students in understanding each other. Since instructional strategies are so important, it becomes necessary that teachers learn to make use of effective and appropriate instructional method for the success of the Millennium Development Goal (MDG) programme. Some MDG scope and objective are extension of Universal Basic Education (UBE) to respond to World global reforms. Nigeria adopted a National Economic Empowerment and Development Strategy (NEEDs) in 2004, seeking to implement the UBE law in order to provide better schools and trained teachers and trainers (Okebukola, 2005). MDG was initiated by Federal Government of Nigeria, to achieve its laudable goals as follows:

• Eradicate extreme poverty and hunger,
• Achieve universal primary education,
• Promote gender equality and empower women
• Reduce child mortality
• Improve maternal health
• Combat HIV and AIDS, malaria, and other diseases
• Ensure environmental sustainability
• Develop a global partnership for development

Hence good instructional method of teachers is needed in our basic mathematics. The country need to make this a priority to make MDG goals come to reality. The purpose of this paper is to evaluate instructional strategies used by primary school teachers for the attainment of MDG in basic mathematics

 

The results of findings are as stated in tables:

Question1: What are the characteristics of teachers who participated in the basic mathematics of MDG?

The demographic variables of teachers in Ekiti State public and private primary schools are as stated in table 1.

Table 1: Teachers characteristic used for the basic mathematics in public and private primary school

Characteristics

Gender

Male

Female

 

Public: (n=300)

 

50(30)

250(150)

% attendance

 

60

60

Private:(n=100)

 

14(6)

86(28)

% attendance

 

42.86

32.56

 

Total:(N=400)

 

64(36)

336(178)

% attendance

 

56.25

52.98

 

Total

300(180)

60

100(34)

34%

400(214)

52.5

Experience

 

0-5

6-10

>10

 

 

90(40)

80(30)

130(70)

 

 

 

 

80(20)

20(12)

-

 

 

 

 

 

170(60)

100(42)

130(70)

 

35.29

42

53.85

Total

300(140)

46.67

100(32)

32

400(172)

43.00

Qualification

 

TC11

NCE

BSc Ed/BEd

Others

 

 

40(15)

70(40)

120(60)

70(32)

 

 

 

 

 

20(6)

50(20)

25(5)

5(0)

 

 

 

 

 

 

60(21)

120(60)

145(65)

75(32)

 

 

 

35

 

50

 

44.83

 

42.67

Total

300(147)

49.00

100(31)

31.00

400(178)

44.50

Marital Status

 

Single

Married

 

 

65(32)

235(76)

 

 

49.23

32.34

 

 

69(24)

31(7)

 

 

34.78

 

22.58

 

 

 

134(56)

266(83)

 

 

 

41.79

 

31.20

Total

300(108)

36

100(31)

31.00

400(139)

34.95

No of teachers who participated in the MDG programme are shown in the parentheses

Table 1 shows the number of teachers who had attended the MDG programme in Ekiti State public and private schools. Male and female teachers in public schools have the same chance of attendance of 60% each. In the private primary schools, only 42.86% of male have attended with 32.56% female teachers in attendance. The overall attendance of teachers in public schools was found to be 60%, while that of private schools was 34%. On the whole, 56.25% of male teachers have attended so far with 52.98% of female teachers in both public and private primary schools.

The highest percentage of the experience of teachers who have been on service for more than 10 years was found to be 53.85% in public schools. This is closely followed by those who have been on service between the last 5 years of 44.44%. While the list of teachers who have their experience between 6-10 years was found to be 37.50% in  private schools, teachers who have been on service between 6-10% had the highest percentage. This is closely followed by teachers have the experience between 0-5 years of 44.44%. It was found that there was no teacher of 10 years and above teaching experience. In overall, teachers who have been on service for more than 10 years had the majority of attendance with 53.85%. This is closely followed by those between 6-10 years of teaching service. Teachers with 5 years teaching experience had the least percentage of attendance of 35.29%.In all, public teachers had the majority of attendance in the MDG programme of 46.67%,while private school teachers had 32%

Majority of teachers who hold National Certificate in Education (NCE) (57.14%) in public primary schools have attended the MDG programme, followed closely by those with bachelors in education degree (45.71%). Teacher grade11 had the least percentage of attendance of 37.50%. This shows that majority of teachers in private schools who have attended the programme had NCE of 40%. Follow by grade 11 teachers of 30%. Teachers who have bachelors in education had the least percentage of attendance of 20%. In overall, NCE teachers of both public and private schools have the highest attendance of 50%, this is followed by those with bachelors of education degree 44.83% This is followed closely by those who have other qualifications (42.67%). Teacher grade11 had the least percentage of attendance of 35%. In all, public school teachers had the highest percentage of attendance of 49% and only 31% of the teachers in public schools have attended the programme with 49.23%.

Only 32.34% of married teachers have attended the programme with 34.78% of single teachers in private schools. This is closely followed by married teachers of 22.58%. Overall, single teachers had the highest percentage of attendance of 41.79%, while only 31.20% married teachers have attended so far. The overall teachers who have attended was found to be 36% in public schools. The study also shows that only 31% of teachers in private schools have attended the MDG programme. Table 2 shows teachers' awareness, understanding and usage of basic mathematics curriculum in primary schools.

Question 2: Are teachers aware of the usage of basic mathematics curriculum of MDG programme?

Table 2: Awareness, understanding and usage of basic mathematics curriculum of MDG programme

Categories %

Public(n=300)

%

Private(n=100)

%

Have the MDG curriculum in mathematics

300(185)

61.67

100(31)

31

Understand curriculum

300(144)

48

100(51)

55

Use the curriculum

300(109)

36.33

100(64)

64

Understand the purpose of MDG

300(123)

41

100(47)

47

 

Table 2 shows that more than half (185) 61.67% of the teachers in public schools have the MDG curriculum in mathematics, while only 31% of teachers in private schools used the basic mathematics curriculum in primary schools. Private school teachers understand the purpose of using the curriculum better (54.6%) than public schools (47%). Both public (41%) and private (47%) schools teachers could understand the purpose of MDG curriculum as shown in table 2.Table 3 shows the structure of instructional strategies used by teachers

 

Question3: Is there any difference in the structure of instructional strategies used in basic mathematics curriculum for MDG programme?

Table 3: Frequency of the structure of instructional strategies used by teachers in both

Public and private primary schools

Structure

Zones

 

A

B

C

D

E

TOTAL

%

Group work

20

25

21

19

23

108

27

Drill

24

18

20

23

20

105

26.2

Participatory

6

9

10

9

6

40

10

Demonstration

6

7

5

8

8

34

8.5

Conversation

3

4

3

7

6

23

5.8

Inquiry modelling

4

5

7

5

7

28

7.0

Class audience

7

4

5

6

6

28

7

Independent study

10

8

 

9

3

4

34

8.5

Table 3 shows the structure of instructional strategies used by teachers in teaching the students in the basic mathematics curriculum of MDG programme. The frequencies of each of the instruction as used by teachers in teaching the pupils are as shown according to LGAs (zones). The total frequencies of occurrence of each instruction are as shown in the last column. These frequencies show that group work and drill methods had the highest number of occurrence for teaching the students with 108(27%) and 105(26.2%) respectively. This is followed by participatory approach with a total frequency of 40(10%). The next is the demonstration and independent study strategies with the frequency of 34(8.5%) each. Inquiry and class audience strategies have the least frequencies of occurrence of 28(7%) each. Table 4 shows the analysis of instructional strategies used for teaching basic mathematics in primary schools.

 

Hypothesis 1: There is no significant difference between the instructional strategies used by teachers of public and private primary schools in basic mathematics

Table 4: Chi-Square analysis of the Instructional strategies used in Public and Private Primary Schools

Methods

Public

Private

Total

df

cal

tab

Rmk

Group work

168(56)

81

137

 

 

 

 

 

7

 

 

 

 

 

138.7

 

 

 

 

 

14.01

 

 

 

 

 

Significant

Drill

165(55)

73

128

Participatory

120(40)

64

104

Demonstration

114(38)

53

91

Conversation

76(25)

39

64

Inquiry

96(32)

47

79

Class audience

99(33)

49

82

Independent study

105(35)

55

90

Total

314

461

775

 

Table 4 shows the chi-square c (138.7) > table (14.07). Hence the hypothesis is rejected. Therefore, there is significant difference between the instructional strategies used by teachers in public and private primary schools in the MDG programme.

Hypothesis2: There is no significant difference between public and private schools teachers in the awareness, understanding and usage of the MDG Curriculum.

Table 5 shows the difference in the awareness, understanding and the usage of MDG curriculum.

Table 5: Awareness, understanding and the usage of MDG curriculum in Public and Private Schools

Categories %

Public(n=300)

Private(n=100)

Df

 

 

Rmk

Have the MDG curriculum in mathematics

61.5

31.3

 

 

3

 

 

18.32

 

 

7.82

 

 

Sig

Understand curriculum

48.4

54.6

Use the curriculum

35.36

63.67

Understand the purpose of MDG

41.16

46.74

Table 5 shows the chi-square X2c (18.32) > X2t(7.82). Hence the hypothesis is rejected. Therefore there is significant difference between the public and private school teachers in the awareness, understanding and usage of the basic mathematics curriculum. By implication the private schools teachers has more understanding and use the curriculum of the MDG better than the public schools, though the public teachers have more copies of the curriculum more than the private schools teachers.

 

Hypothesis3: There is no significant influence of teacher's instructional strategies on the achievement of basic mathematics curriculum for MDG programme.

Table 6: Influence of teachers' instructional strategies on achievement of basic Mathematics curriculum

Categories

Public n=300

Private n=100

Total

 

 

25.7

 

 

3.84

 

Influenced

195

63

258

Do not influence

105

37

142

Total

300

100

400

 

Table 6 shows that cal 25.7 was greater than  table3.84 at α=0.05 level of significance. Therefore the hypothesis is rejected. This implies that there is significant difference in the influence of teacher's instructional strategies and the achievement of basic mathematics curriculum for MDG programme

 

Discussion

The study revealed some differences in the characteristics of teachers of public and private schools in terms of experience, qualification and marital status. High proportion of teachers in private schools had lower educational qualification. This calls for proper monitoring of standard in the employment of teachers in the private schools since most of the Nigerian children will spend there basic years in these schools. This finding was corroborated by Meremikwu& Enukoha (2006) &NCTM (2000) who reiterated a good standard for school maths at basic level.

Further findings of this study showed that MDG curriculum is not well wildly used in public schools, but are used in private schools. Since, they do not understand the purpose of MDG programme. The MDG programme stressed the need to develop national curriculum modules for primary and junior secondary education in line with MDG programme. The reason why during the long vacation, teachers are organised and trained in the use and adaptation of the modules from the national curriculum through workshop, seminars and meeting on curriculum delivery. This in effect will improve student's achievement with a functional basic educational curriculum. The study also showed that many teachers of both public and private schools do not use some of instructional methods needed for the basic needs of the learners in mathematics. It was also found that only few methods were used for the teaching of basic mathematics. The findings of the study also revealed significant influence of instructional strategies in the advancement of basic mathematics. Hence, researchers (Kolawole, 2004; Darling-Hammond, 1996; UNESCO&ISESCO, 2001) have discovered major problems facing mathematics teaching in terms of teachers methods and called for teachers training and re-training as a way of consolidate and enlarge concepts and skills of teachers in the teaching process. When teachers do not use appropriate instructional strategies, they are less likely to achieve the desire learning outcomes. Hence, instructional strategies are an important of achieving the basic mathematics curriculum meant for MDG programmes.

Conclusion and Recommendations

There is need to widely spread the use of MDG curriculum through proper monitoring in both public and private primary schools to build capacity for the MDG at the foundation and basic level in core subjects such as mathematics and science. Modules for teaching mathematics are not always readily available for primary schools despite the emphasis of the MDG plan. Availability of these in both public and private schools will help to build good foundation for Nigerian pupils in the important subjects like mathematics.

 

 

 

 

 

References

Agwagah, U.N.V. (1996). Instructional deficiency in some secondary school maths topics; challenge of maths educators for future maths education. A paper presented at the 33rd annual conference of mathematical association of Nigeria.(MAN).

Burner, J(1966). Toward a theory of instruction. New York; Norton

Darling – Hammond, L & Snyder, J (1992) Conclusion study and the traditions of inquiry; the scientific tradition. In P.W Jackson (Ed), Handbook of research and curriculum. P. 41-78. New York; Macmillan

Darling-Hammond,I(1996) what matters most; a competent teacher for every child ; Quality Teaching for the 21st Century. Kappan Phi Dilta 78(3); 173-200.

 

Dugdale ,S(1990). Beyond the evident contnt goals pant111. An undercurrent- enhanced approach to trigonometric identities. Journal of Mathematical Behaviour. 9; 233-287

 

Federal Republic of Nigeria (2004) National Policy on Education

Jaworski, B (1994). Investigating Mathematics Teaching. London; Falmer

Meremikwu, A,N& Enukoha, I.O(2006). Primary mathematics instructional aids and universal basic education in Nigeria. Mathematical association of Nigeria (MAN) proceed of annual national conference

Mousley, J, Lambdin, D & Koc,Y(2003). Mathematics teachers education and technology, in Bishop,N. A et.al (edu) second International Handbook of Mathematics Education; Dordrecht; Kluwer.

National Council of Teachers of Mathematics (2000) Principle and standards for school mathematics (NCTM).Reston.V.A

Okebukola, P (2005). Enhancing the relevance of STAN to national development. Memorial lecture NOTE of STAN at the 46th National Conference

Okolo, U.P (2006). The challenges of Universal Basic Education (UBE). The role of secondary mathematics. Paper presented at the 43rd Annual Conference of Mathematical Association of Nigeria (MAN) Bauchi; Nigeria. P1-13

Okoye F.N (2000). Strategies for improving the teaching of mathematics in secondary school in E.C Iloputaife (ed) effective science and computer education in the new millennium. Enugu; science and computer education department, Enugu state university of technology

 

Thompson, A (1984). The relationship of teachers conception of mathematics and mathematics teaching instructional practice. Educational study in mathematics.15 (2); 105-127 Dordrecht: Reidel.

Umonyang, IE (1997) Maximizing student's achievement in mathematics thought multi- grade classroom teaching approach; paper presented at the 40th national conference of Science Teacher Association of Nigeria (STAN) p.25

About the Author

Dr. Mrs Abiodun A.Popoola

University of Ado-Ekiti

Ado-Ekiti

Mathematical Analysis with limits of sequences?

I need a little help getting started with this mathematical proof:

For any b ∈ R [the set of real numbers], prove that lim(b / n) = 0.

To simplify take b = 1. You want to show that 1/n ---> 0 as n ---> infinity.

1st thing to do: check out the def. of limit. It's very important that you understand
this. In the definition "epsilon" occurs. Try a *specific* epsilon -- say 1/1000.
How large must n be for !1/n -- 0| to be < 1/1000?

What about b/n? For example, 300/n?

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