ABSTRACT
This study was aimed at establishing the pedagogic strategies influencing pupils’ learning of algebraic concepts in upper primary school classes in Laikipia West sub-County, Kenya. The three objectives of the study were to establish; (i) the widely used pedagogic strategies in teaching algebra; (ii) the factors influencing the teachers’ choice of pedagogic strategies in learning of algebra; and (iii) the pedagogic strategy that contributes most to pupils’ learning of algebra in upper primary classes. In Kenya, researchers in the past have addressed the cause of poor performance in Mathematics at national level in Kenya Certificate of Primary Education but have not addressed the pedagogic strategies applied in teaching and learning of algebra in upper primary classes in Kenya with particular focus on Laikipia West sub-County. The researcher used a descriptive survey design. Descriptive survey included both qualitative and quantitative in data collection to obtain responses from both Mathematics teachers and pupils in the upper primary school classes where algebra is mostly taught. The target population was 85 primary schools and 581 trained teachers in Laikipia West sub-County. First stage sampling included a simple random sample to select 17 schools representing 20% of target population to ensure all categories in the population is represented. Two trained Mathematics teachers from each school teaching standard seven class were purposively selected. Moreover, simple random sampling was used in selecting two hundred and sixty
(260) class seven pupils following their class registers. Data was collected through questionnaires for both teachers and pupils; achievement test for pupils, observation schedule and interview schedule were administered to Mathematics teachers. The research instrument was piloted to enhance the validity and reliability. The achievement test was used to test pupils’ competence in algebra guided by the syllabus approved by the Ministry of Education. Data obtained was analyzed using statistical package for social science (SPSS version 22.0). The study revealed that there was significant difference in the pedagogical strategy used by teachers (F = 427.53, P = 0.0001). Cooperative learning was the most used strategy. The most effective pedagogical strategies that contributes to pupils’ learning of algebra, was similarly found to be cooperative strategy, (χ2 = 29.001, P = 0.031). The study, therefore, concluded that poor performance in algebra by students can be attributed to lack of active participation in the Mathematics classroom.
CHAPTER ONE
INTRODUCTION AND BACKGROUND OF THE STUDY
Introduction
This chapter contains the background to the study, statement of the problem, purpose of the study, the study’s objectives, research objectives and significance of the study, the study’s scope, and limitation of the study, assumptions, conceptual and theoretical frameworks and operational definitions of terms.
Background to the Study
Mathematics is considered one of the fundamental subjects for any school curriculum and for the future of any nation (Cockcroft, 1982). Algebra is one of the branches of Mathematics that uses mathematical statements to explain relationships between variables and time. It solves mathematical problems that are in form of symbols which can be built by students due to their experience with numbers (Cockcroft, 1982).
According to the NCTM (1989), algebra is used in most mathematical problems. Students apply algebraic functions in Mathematics in their daily life due to the need to have a highly-sophisticated knowledge of the representations as used in algebra. Quantitative methods are often used in other social disciplines such as sociology, psychology, economics and natural sciences. Due to this, algebraic knowledge is often needed not only in Mathematics but also in the above-named disciplines (NCTM, 1989).
Blanton and Kaput (2005), state that learners develop their early algebraic reasoning in the primary schooling. Warren and Cooper (2008) further note that algebraic reasoning in
the lower primary classes is not only about thinking about algebra but also having a structural perspective in regard to looking at the Mathematics numbers. The integration of algebra in the primary schools is important as it increases power, depth and coherence to the Mathematics taught in schools and also prepares the students to advanced algebra taught in later stages of future a student’s life (Kaput, 2007). According to Cockcroft (1982), primary school algebra is more accepted by students and more emphasis has been made on early algebraic reasoning and patterning in both lower classes and pre-primary schools. Further, Carraher, Schliemann, Brizuela & Earnest (2006) states that, despite being introduced in early stages of learning, algebraic concepts taught in the upper primary school classes have influenced their learning of algebra. The awareness of structural relationships of patterns helps learners to develop algebraic thinking early in their lives and later helps them grasp the complex structures of arithmetic (Carraher, Schliemann, Brizuela & Earnest, 2006). School students can be engaged in algebraic activities such as; simplifying algebraic expressions, substitution and writing expression that provide them with the opportunity to practice other advanced thinking skills for instance the generalization skills (Kaput, Carraher, & Blanton, 2007).
Kaput (2008) on longitudinal view of algebra, sees algebra as problem solving and thinking skills that are developed in lower primary schooling and later improved further in the upper primary school. When students seek out and connect the generalities in measurements, geometry, numbers and algebraic thinking, pedagogic strategies used in the teaching of algebra such as expository and heuristic can be the unifying factor for both the primary and secondary school level Mathematics curricula. Van Amerom (2003)
argued that students can acquire algebraic concepts before studying formal algebra through solving nonstandard problems.
Algebra is an important link of the basic algebra content learnt in primary school curriculum to the more advanced secondary school Mathematics which include; quadratic equations, calculus and trigonometry. Arcavi (2008) observes that algebra as a branch of Mathematics is often intimidating to middle level students and affects their attitude negatively in regard to Mathematics. A US Department of Education (2008) report entitled, Foundations for Success, shows that most of the drops in Mathematics grades were observed during middle school when algebra was introduced to students. Furthe,r the inclusion of algebra in primary school does not imply adding traditional algebra to the school curriculum; rather, it means providing entry points for algebra through treating existing topics in a deeper and more connected way (Kaput, Carraher, & Blanton, 2007). NCTM (2000) report shows that patterning activities can help students move towards understanding functional relations. Rich problem contexts can play an indispensable role, as experience and reasoning in some situations may support students in generating abstract knowledge (Carraher & Schliemann, 2007).
Cockcroft report (1982) suggested that efforts should be made to discuss some algebraic ideas with all the students. It is important for students in primary schools to learn Mathematics from well trained teachers. Enrolling for more advanced Mathematics classes is not the solution to understanding the teaching of Mathematics for the students (Reys and Fenell, 2003). It is important for the teachers to understand how their students learn the Mathematics content; they must also be able to make use of instructional tools
to teach Mathematics to the students (Hill, Rowan, and Ball, 2005). Cockcroft (1982) concluded that for those of average attainment only some simple algebraic work on formulae and equations which involves symbolization is desirable and that formal algebra is not appropriate for lower attaining pupils.
Algebra helps prepare students for the job market and also prepare them for the advanced inadequate time given for the learners to study on their own and concepts used in post- secondary learning (NCTM, 2000). Research conducted on algebra to investigate the pedagogical practices led to better student results in Mathematics (Anthony and Walshaw, 2008). Subsequent research study in Kenya by Eshiwani (2001) and Miheso (2002) identified factors that are believed to cause poor performance in Mathematics such as: poor methods of teaching, lack of modeling activities, use of advanced mathematical language and inadequate time given for the learners to study on their own. These studies have shown that the success of any educational reform lies in its ability to come up with new pedagogical identities, which is inclusive of setting up new educational trends and the imparting of new knowledge to both the students and the teachers. Despite these studies having focused largely in secondary school level, the determination of the teaching of algebra in primary schools in Kenyan context is imperative but lacking opportunities to express algebraic ideas to construct knowledge.
In Kenya, Mathematics is among the compulsory subjects in primary schools. The performance at national level has been generally poor in the recent years, but worst performed in algebra which is taught early in primary schools, (KNEC, 2010). Algebra is
particularly challenging to students owing to the poor teaching skills. Report from Kenya National Examinations Council 2010 shows that, KCPE performance in Mathematics has been very poor for the last nine years from (2006-2014), (KNEC Report 2014).
Table 1.1: Candidates’ Mathematics performance in KCPE in selected years.
| Types of questions | No. of questions | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 |
| Arithmetic (a)mechanical (b)applied | 9 24 | 54.04 52.66 | 55.57 29.39 | 21.51 41.71 | 59.24 45.99 | 67.37 50.31 | 38.59 42.62 | 76.10 42.36 | 68.34 45.19 | 58.15 42.56 |
| Data from table | 3 | 56.00 | 43.38 | 43.25 | 39.21 | 64.33 | 63.09 | 44.82 | 58.90 | 52.84 |
| Geometry | 8 | 45.96 | 46.19 | 40.64 | 46.28 | 54.75 | 49.82 | 67.84 | 47.22 | 56.79 |
| Graphs | 2 | 55.31 | 37.44 | 52.41 | 52.53 | 32.26 | 47.96 | 33.47 | 47.48 | 48.92 |
| Algebra | 4 | 42.64 | 37.77 | 42.49 | 41.18 | 53.05 | 44.41 | 50.51 | 47.93 | 47.50 |
Source: KNEC 2014.
Learners’ performance on algebra in the 9 years
Figure 1.1: Student K.C.P.E Performance in Algebra 2006 – 2014
Based on the secondary data on the students’ K.C.P.E performance 2006 – 2014, there has been overall increase in the performance in Algebra at a regression R2 value of 42.3%. The above table also indicates that candidates might have experienced problems with questions item from topic on Algebra scoring below an average mean mark of 50% from year 2006 to 2014. Algebraic concepts are also applied in geometry and its poor performance for nine consecutive years from the year 2006 to 2014 has been absurd. Performance in geometry was slightly above that in algebra. One of the reasons cited by KNEC (2014) was poor interpretation of the problem, poor teaching strategies showing no innovativeness which does not involve pupils’. In the year 2010 there was an improved performance in algebra where candidates scored a mean score of about 53.05. This showed an improvement on the average scores. This means that teachers might have
involved varied teaching strategies and more practice on algebra. This poor performance from national level is not different from K.C.P.E Mathematics performance in Laikipia West sub-County.
