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IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 6 Issue 10, October 2019

ISSN (Online) 2348 – 7968 | Impact Factor (2019) – 6.248

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Mathematics Teachers’ Level of Knowledge in Mathematics Content and Students’ Achievement in Mathematics in

Secondary Schools in Kakamega County, Kenya Mr. Polycarp Muchesia Ishenyi P

1P and Dr. Martin Sibweche WanjalaP

2P

P

1 PPh.D Candidate, Masinde Muliro University of Science and Technology,

Kakamega, Kenya

P

2 PDepartment of Mathematics Education, Masinde Muliro University of Science and Technology,

Kakamega, Kenya Abstract

The paper reports findings of a study that sought to assess the effects of Mathematics teachers’ content knowledge on achievement in Mathematics among secondary school students in Kakamega County, Kenya. Specific objective was to investigate the relationship between Mathematics teachers’ level of knowledge in Mathematics content used in Mathematics instruction and students’ achievement in Mathematics. The study was guided by the TPACK theory, and was implemented using descriptive survey research design, via mixed methods approach. Multi-stage sampling was done to sample 80 Mathematics teachers from 801 teachers in public secondary schools in Kakamega County. The researcher used questionnaire, interview schedule, and document analysis guide. Data collected were analyzed using descriptive and inferential statistics. Results revealed no significant relationship between Mathematics teachers’ content knowledge and student achievement in Mathematics. These findings will provide useful facts and figures that may be used to formulate better policies on Mathematics education. Key Words: Mathematics, Content, Knowledge, Achievement

1. Introduction Mathematics is a very important subject and plays several roles in the society. According to Hughes (2005), Mathematics forms an essential prerequisite for joining tertiary colleges and universities as well as for self-employment. Friendland (1985) further affirms that many professionals such as engineers and accountants use it. It therefore plays a very important utilitarian role in the society. Besides, it has communication role. Communication of messages, ideas and research findings are done by use of Mathematics. Communication of research findings is done both in numerical and graphical forms then analyzed and decisions made based on the findings (Macau 2000). Mathematics has aesthetic role in the society. Beauties generated from architectural and engineering designs, for instance, the beautiful houses, cars and other models are as a result of Mathematics (Ishenyi, 2015). Ishenyi further asserts that Mathematics has a social role too. Thus, it teaches intervals, sequences and series which are applied in social life, for instance, rhythms in the music world and entertainments. Concepts such as diagonals, course and tracks are well applied in games such as soccer, basketball, hockey and swimming among many other games (Ishenyi, 2015). Besides the aforementioned roles of Mathematics, many countries of the world have lamented on weaknesses in ways Mathematics is taught and learned in schools (European Mathematical Society, 2012). A lot of research evidence is accumulating regarding teachers’ impact on children’s learning experiences in Mathematics. Several of such research evidences are highlighted in this study. The teachers’ content knowledge affects their instruction delivery. According to Ball et al., (2008), a broad range of mathematical content understanding enables teachers to make connection between Mathematics topics in a curriculum. Furthermore, Pedagogical Content Knowledge is the unique understanding of subject matter that allows a teacher to design, apply, and evaluate the appropriate instructional strategies and representations for particular topics that meet students’ needs (Grossman, 1991; Shulman, 1987). This makes a teacher to deliver instruction using appropriate techniques. The benefit of effective teaching techniques in supporting teachers to assist students become good problem solvers cannot be overemphasized (CCSSO, 2010). A teacher with Technology Pedagogy Knowledge understands the reciprocal relationship between technology and pedagogy (teaching and learning) in matter of affordances, and constraints (Harris et al., 2009). For example, some teaching methods (e.g., collaborative teaching and learning as well as Mathematics discourse) are enhanced by the integration of digital technologies including Wiki, WebQuest, Skype, and other communication and social networking programs. However, one of them can be better than the others based on its affordances and constraints toward the selected teaching

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strategy. Effective teaching therefore calls for teacher’s technological, pedagogical and content knowledge to be sufficiently used in the classroom. The teacher has a central role in orchestrating the oral and written discourse in ways that contribute to students’ understanding of Mathematics (National Council of Teachers of Mathematics [NCTM], 2000). Teachers must also decide on how to organize and orchestrate the work of students, what questions to ask to challenge those with varied levels of expertise, and how to support students without taking over the process of thinking for them and thus eliminating the challenge (NCTM, 2000). NCTM advocates for the development of an inquiry-based Mathematics tradition. In an inquiry-based environment, learning is viewed as an active, constructive activity in which students are encouraged to explore, develop conjectures, and solve problems. Students are also encouraged to discuss and communicate their ideas and results, often within small, cooperative groups as well as with their teachers. NCTM (2000) authenticates the value of inquiry-based Mathematics instruction by calling for efforts aimed at creating collaborative and student-centered environments, where students have opportunities to reason and construct their understanding as part of a community of learners (NCTM, 2000). Several studies show that classroom instruction in Mathematics at the high school level remains overwhelmingly teacher-centered, with greater emphasis placed on lecturing rather than helping students to think critically and apply their learnt knowledge to real life situations (Cobb, Wood, Yackel, & McNeal, 1992). Most high school Mathematics teachers view Mathematics as a rigid and fixed body of knowledge, and think that their responsibility is to transmit this knowledge to their students (Staples, 2007). In Kenya, the concern on making students better problem solvers by the Ministry of Education (MOE) through Strengthening Mathematics and Science Education (SMASE) workshops is on high gear. The message preached to teachers in these workshops is that teachers must embrace ‘hands on’ approach to teaching Mathematics. This approach encourages classroom discourse that sees learners actively involved in the learning process. However, the Kenyan national examinations help teachers to define what content is important and therefore have a role to play in influencing teachers’ classroom practices (Wanjala et al., 2016; Pedulla et al., 2003). The Kenya National Examinations Council (KNEC) examines secondary school learners’ Mathematics content recall, comprehension, application as well as general reasoning. Some students perform well though majority fail (KNEC, 2019). According to the KNEC (2019), Kenya Certificate of Secondary Education (KCSE) mathematics means scores for 2012 to 2018 were as summarized in table 1.

Table 1: Performance in KCSE from 2012 to 2018 in Mathematics Nationally

Year Candidature Mean Scores (%) Std Deviation

2012 433,014 28.66 18.83

2013 444,792 27.58 20.01

2014 483,630 24.79 22.15

2015 522,870 28.66 23.10

2016 577,079 27.58 23.36

2017 615,773 23.1 20.41

2018 660,204 24.23 21.11

From the performance displayed in Table 1, the performance in KCSE Mathematics on average is below 30%. This shows low achievement in concepts in the subject. This low achievement was the basis of this study. Mathematics is an essential prerequisite for joining colleges, for communicating ideas and research findings, and for industrialization as well as for employment (Friendland, 1985; Hughes, 2005; Ishenyi, 2015; Macau, 2000). Unfortunately, in Kenya, Mathematics as taught at secondary school level is performed poorly, going by the KCSE results of the last seven years as shown in table 1.




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Kakamega County is one of the most affected in this regard, as students in public secondary schools continue to perform dismally in mathematics, which has been the case for the last five years as asserted by Kakamega County Director of Education (2019). The cited KCSE Mathematics performance in Kakamega County and the Country is by all standards poor. This poses a very worrying scenario for the fact that should the poor performance in Mathematics persist, Kakamega County and the Country at large may face a shortage of professionals such as engineers, doctors, accountants, architects, scientists and better teachers of Mathematics among many others. This threatens the realization of Kenya’s vision 2030 whose main aims are to transform Kenya into an industrializing and middle-income country by providing high quality of life to all its citizens by 2030. One of the main reasons behind the dismal performance in Mathematics is teachers lack of sufficient content knowledge (Lyublinskaya & Tournaki, 2012; Polly, 2011; McCray & Chen, 2012). Teachers’ content knowledge needs to be investigated with a view of reversing this trend through revisiting policies of teacher engagement. However, current research on assessment of teachers’ content knowledge and learner’s achievement in Mathematics in Kakamega County is scanty, which makes policy action a toll order. It is on these premises that the present study was carried out.

1.1 Purpose and Objective of the Study

The purpose of this study was to assess the effects of Mathematics teachers’ content knowledge on achievement in Mathematics. Specific objective of the study was to investigate the relationship between Mathematics teachers’ level of knowledge in Mathematics content used in Mathematics instruction and student achievement in Mathematics.

1.2 Research Hypothesis

The following null research hypothesis was formulated from the specific objective and tested at 95% confidence level. Ho1: There is no significant relationship between Mathematics teachers’ level of knowledge in Mathematics content

used in Mathematics instruction and student achievement in Mathematics

2. Literature Review The literature reviewed comprises: theoretical framework; mathematics teachers’ content knowledge and achievement in mathematics; and measurement of teacher effectiveness and achievement in mathematics.

2.1 Theoretical Framework This study based its research on the Technological Pedagogical and Content Knowledge (TPACK) theory which was developed by Mishra and Koehler (2006). They explained that they came up with this model after their 5 year experimental studies on the way teachers of varied cadres operated in their classroom. Their studies were based on Shulman’s (1986) work. Initially, Shulman banked on the notion that every teacher has a set of knowledge which is knowledge of some specification regarding the subject taught and a set of knowledge regarding the way teaching is done thus pedagogy. Shulman also said that a teacher needs to blend the two sets of knowledge to come up with an amalgamated knowledge that effectively serve to teach. He referred this to as PCK meaning Pedagogical Content Knowledge. In a span of 20 years later on, Mishra & Koehler (2006) realized a big revolution with regards to the emergency of technology use in the teaching process. At that juncture, technological knowledge was taken as another set of knowledge not connected to content and pedagogy sets of knowledge. Within the 5 years of their study, Mishra & Koehler (2006) came up with a fresh model which they referred to as TPACK representing combined Technology knowledge, Pedagogy knowledge and Content Knowledge. This model included technology in the first PCK model. The new outfit blended the three domains of knowledge which stressed on their interactions and connections as the knowledge regions which the teachers work with as illustrated in figure 1.




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Figure 1: The TPACK Model of Mathematics Instruction

Figure 1 shows that Mathematics instruction ought to encompass every fraction of the TPACK model. The model gives us room to construct and come up with blends of knowledge that creates the most desirable atmosphere for learners. Therefore the model in figure 1 illustrates teachers’ Knowledge in technology, Pedagogy and content required for teaching learners a subject and teaching it effectively. Harris, Hofer, et al, (2010) asserts that the TPACK model simply explains why a much known teacher in the world may not be the best teacher in the subject for a simple justification that he does not make the subject easily learnt. They reiterate that to be a wonderful teacher, you should blend content knowledge with pedagogy knowledge. The current study therefore assesses the teachers’ Content Knowledge and its effects on the learners’ achievement in Mathematics at secondary schools in Kakamega County, Kenya, with a view of encouraging effective teaching that would improve student academic achievement in Mathematics.

2.2 Mathematics Teachers’ Content Knowledge and Achievement in Mathematics

There are a several areas of knowledge that Mathematics teachers need to have such as Content Knowledge or knowledge of subject matter (CK). Knowledge of the subject matter and Pedagogy Knowledge (PK) are taken to be a basis of sound teaching (Grossman, 1991; Shulman, 1987). Content knowledge of Mathematics (CK) is suggested to have three sub categories namely: Specialized Content Knowledge (SCK), Common Content Knowledge (CCK) as well as Horizon Content Knowledge (HCK) (Ball et al., 2008). According to Ball et al. (2008), CCK is defined as the general knowledge in mathematics that is required in all over the professions related to mathematics. They also described the SCK as the Specific Mathematical Knowledge that is needed for teaching Mathematics. Additionally, HCK was described as a wide range of knowledge that a teacher is expected to have to help him connect between the topics of a given curriculum. There are other categories of knowledge namely; Knowledge of Content and Students (KCS) which is a combination of mathematics content and learners’ process of learning and the Knowledge of Content and Teaching (KCT) which is a combination of teaching knowledge and mathematics content knowledge (Ball et al., 2008).

There also exists 21st Century Learning Skills notion which is a model of skills, knowledge (Foundational Knowledge, Meta Knowledge and Humanistic Knowledge) and expertise. The model is considered as very important by teachers since




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they are equally useful to pupils in order for them to be successful in work and their general wellbeing, though on the other hand has drawn a lot of attention as well as disapproval with the growth of technology use in education cycles (Boling & Beatty, 2012). The definition of the Twenty-first century learning is done in varied ways and in other common ways, though Mishra and Kereluik (2011) suggested 10 basic conceptual frameworks in 3 groups as follows: 1) Foundational Knowledge that comprises of information literacy, content, and knowledge across disciplines, 2) Meta Knowledge that comprises Critical Thinking, Collaboration, and innovativeness, and 3) Humanistic Knowledge that is composed of Job Skills, Culture Competencies, and Ethical Awareness. Figure 2 below shows the skills in the three categories of knowledge.

Figure22: Categories of 21st Century Skills Relevant to Mathematics

Based on the 21 P

stP century learning skills shown in Figure 2, Churches (2009) considered collaboration more important skill

and so listed it as the fourth element in his Bloom's Digital Taxonomy. Another argument that Information Literacy, Cultural Competence, and awareness constitute the sole skills that fit to be referred to as 21 P

stP century learning skills (Mishra

and Kereluik, 2011). With regard to measuring knowledge, Hunt (2003) asserts that getting to know the level of knowledge one has is difficult because it is invisible and that tools to be used to measure TPACK must be to standard in order to manage gauging the teachers’ instruction design, lesson plans, classroom activities, assessment tasks and thereafter compare them with effectiveness in the teaching of an educator. On the other hand, knowledge can be measured using a fitness assessment using observations that find required information regarding teacher’s knowledge, their abilities, as well as their cognitive skills (Hill et al., 2008; Stronge, 2007). To investigate the teacher’s knowledge and its impact on teacher quality, various measures are used. Strong (2011) avers that mathematics knowledge can be investigated using several methods such as tests or even observations in the classroom. This study investigated mathematics teachers’ knowledge in Mathematics content using interviews with standardized test items well designed to establish the teacher’s knowledge in content used in Mathematics instruction. Hill and Rowan (2005) mounted a study to find out if teacher’s knowledge in mathematics used for mathematics instruction had a positive influence on the students’ mathematics performance. The researchers employed mixed methods approach where grade one participants (n=1190) as well as grade three participants (n=1773) were used to study their performance improvements. The study lasted one year. The performance improvements for that period of one year were nested within teachers (n=334 and n=365), and the teachers again were nested within schools (n=115). The findings of the study showed




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that the teachers’ knowledge in mathematics significantly related to performance improvements for both the third graders and the first graders. In their longitudinal survey research, Marshall and Sorto (2006) asked themselves, “why are some teachers more effective than others?” Their enthusiasm to understand the relationship that exists between preparation of the teacher, his pedagogy and learners performance raised the morale of the researchers to proceed with their research and therefore, they focused on Mathematics teachers’ knowledge. The study analyzed the effects of teacher’s knowledge on student’s performance. Information collected from the sampled Guatemalan schools was used. A conceptual framework was presented which linked the teacher’s work to student learning. While this was done along with a general idea of the existence of varied domains of knowledge, their research focused on the Guatemalan context, whose overall results made available scientific backing for a widely held conviction in mathematics education, “effective teachers have different kinds of mathematical knowledge”. Guimaraes, R., Sitaram, A., Lucia, J., Shimpei, T., and Lenora, R. (2013) investigated the effect of teacher’s knowledge in content on mathematics performance of 4th grade Brazilian pupils. The study used test performance as a measure. Information collected yielded longitudinal data from the participating 6 states in Brazil that took part in the year 1999 in the FUNDESCOLA program. The analysis was done by use of value added framework which controlled for the teacher as well as the student distinctiveness, structure of the class, and the schools fixed effects. Their results showed that teachers who had higher knowledge in content had a higher direct influence on the students’ test scores. These findings are also similar to those of Campbell et al., (2014), who investigated whether there was a significant association between teachers’ content knowledge in mathematics and performance of their students. Their study of the newly employed teachers revealed a significant association between upper elementary teachers’ content knowledge in mathematics and their students’ performance in the subject. The results were arrived at after all the characteristics of the teacher level and students were controlled. The fact that Campbell et al, (2014) controlled for intervening variables of their study could be the reason that explains their research findings and those of the present study.

2.3. Measurement of Teacher Effectiveness and Achievement in Mathematics

Learners Achievement as used in this study refers to the correct leaner responses to questions on content taught during a Mathematics lesson as well as their scores in tests and examinations. A lot has been documented regarding measurement of learners’ achievement as reviewed below. Student achievement (rather than examining teachers’ knowledge or measuring their teaching performance) is the most commonly used measure for evaluating teacher effectiveness (McCaffrey et al., 2003). Among many measurements of learners achievement in Mathematics is observation protocols. Observation protocols can be used to measure the teacher’s TPACK though they vary in their objectives, procedures, subject matter, grade level, complexity, observer requirements (knowledge, training), durations, frequency, and validity and reliability level (Little et al., 2009; Strong, 2011). Quantitative ways of measuring effectiveness of the teacher for instance value-added modeling (VAM), teaching artifacts, teacher portfolios, as well as teacher aptitude tests have less validity and reliability threats (McCaffrey et al., 2003). A statistical process for measuring teacher effectiveness by comparing student achievement scores in more than one year (value-added models), came as a result of the emerging public call for educational accountability after the technical report of Sanders and Rivers of 1996 (McCaffrey et al., 2003). The state of Tennessee adopted the first version of value-added models of assessment namely the Tennessee Value-Added Assessment System (TVAAS). This was a statistical system of analysis Williams Sanders and Robert McLean developed while at the Tennessee University (Sanders & Horn, 1994), as part of its education reform package of 1992. This came before other states like Iowa, Ohio, Colorado, and Pennsylvania started to utilize their accountability systems (Tucker & Stronge, 2005). Also, the Dallas Independent public school system was a pioneer in adopting another form of a statistical process for measuring teacher effectiveness by comparing student achievement scores in more than one year with more considerations to student and school characteristics (Goe, 2008). The main purpose for this mixed-model methodology educational assessment was to assess the effects of the entire school system (principals, teachers and school board of management members) on learners’ achievement. However, the model was eventually used to examine teacher effectiveness most of all. All value-added models were employed to support the claim that student achievement is an indicator of teacher effectiveness (Bracey, 2004; Nye et al., 2004). However, this claim is short of an articulated definition for teacher effectiveness and how it causes the change in learner achievement (Ding & Sherman, 2006), although there is an attempt to consider all teacher, student, and school variables in a hierarchical linear model study (Odden et al., 2004). This tool of




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educational measurement was expected to provide valuable information about students’ learning growth and identify what factors affect student achievement (McCaffrey et al., 2003). As a research based assessment model (Fallon, 2004), the value-added models are deployed to tackle the effectiveness of teaching by measuring the growth of student achievement over a wide range of trajectories rather than evaluating the difference in student achievement scores between a sequence of two years (e.g., cohort-to-cohort change models) (Koretz, 2008; Sanders, 2006). Value-added models were claimed to be more objective and valid measures of teacher quality (Sanders & Rivers, 1996) than other traditional teacher quality measures. However, evidence of their validity and reliability is not strong enough to allow them to be taken as the only basis for sensitive decisions for instance employing or dismissing a teacher (National Research Council and National Academy of Education, 2010). Value-added models employ the Univariate Response Model to analyze a longitudinal data of student scores in multiple cohorts (Sanders, 2006). Value-added models are supported as a robust model of measurement when the effect of student characteristics is controlled (McCaffrey et al., 2004). Despite these strengths, some shortcomings are associated with the value-added models. Such models’ validity and reliability are questionable since these models are limited to include differences between and among teachers, bias measurement, and measurement error, and unstable and nonrandom assignment of student and teacher is also a major threat to the validity of such measurement (National Research Council and National Academy of Education., 2010; Newton et al., 2010). Also, the value-added models narrow curriculum and focus on the achievement trajectories of students instead of the learning trajectories (Newton et al, 2010). The learning trajectories have broader objectives than the achievement trajectories, which only represent student score growth for limited number of standardized test questions that are not necessarily reflect all learning objectives. Therefore, the VAM should not be taken as the only source of teaching quality evidence; instead, assessment should include other sources of evidence such as classroom observations and lesson artifacts. (Koretz, 2008; Kupermintz, 2002; Strong, 2011; Tucker & Stronge, 2005). Lyublinskaya and Tournaki (2012) examined how professional development of content authoring influences Mathematics teachers TPACK development and in turn affects their students’ algebra achievement scores. After a one-year professional training spent creating curriculum that integrates TI-Nspire technology, four Algebra teachers from a New York City public high school were evaluated for their TPACK developmental levels. Researchers utilized their developed TPACK Levels to measure teachers’ artifacts and their teaching practices. Their results indicated the importance of lesson plan preparation in teacher effectiveness and the impact of teachers’ TPACK levels on student achievement. Students as the recipients of instructions are qualified to judge the performance of their teachers at least in terms of their characteristics and teaching ethics (Little et al., 2009; Strong, 2011). In this form of teacher evaluation, students are asked to rate their teachers’ general teaching practices and behavior on a 4 or 5-point Likert scale, but the scale has to be well designed to increase its validity and reliability (Little et al., 2009). Students’ personality factors affect their rating bias; especially given students’ lack of knowledge of content, pedagogy, classroom management, and other teacher quality areas. Student evaluation is still low cost and non-time consuming and is found to provide valuable information about teacher behavior and practices, especially when feedback is from secondary and college students (Follman, 1995). Other than student evaluation, principal evaluation can be done. Teacher evaluation that is conducted by principals and vice principals through classroom observations is commonly done for high-stake decisions (Brandt et al., 2007), although such evaluation type, whether formal or informal, can be used also for formative purposes (Downey et al., 2004; Heneman et al., 2006). School administrators, in positions that give them opportunities to observe and interact with teachers on a daily basis and access much information about their teachers, are very good candidates to provide a valid and reliable evaluation (Little et al., 2009; Strong, 2011). However, principals usually do not receive appropriate training on how to implement a valid and reliable teacher evaluation (Brandt et al., 2007). In addition, their evaluation can be biased by their personal interpretation of teaching behavior (Little et al., 2009; Strong, 2011). In research, principal evaluation is not strongly supported to be a predicator of teacher effectiveness. The relationship between teacher effectiveness and principal evaluation measured from the learners achievement ranged from not significant (Wilkerson et al., 2000) to weak (Bommer et al., 1995; Harris & Sass, 2009; Jacob & Lefgren, 2008).




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Principal ratings of teachers were compared to other methods of teacher effectiveness evaluation and were found more valid and reliable in predicating teacher effectiveness than proxy measures (e.g., certification, experience, major) and as accurate as value-added models (Harris & Sass, 2009), whereas other researchers found it less valid and reliable than value-added models (Jacob & Lefgren, 2008) and student ratings of teachers (Wilkerson et al., 2000). Threats of validity and reliability in principal evaluation came from low level of training, low observation frequency, and infrequent use of protocols or rubric for evaluations (Little et al., 2009; Strong, 2011). The principal evaluation is more practical and reliable as compared to traditional ways of measuring the quality of a teacher. Measuring teacher’s knowledge is hard because of its invisibility. The teacher’s TPACK can therefore be measured by measuring the students’ achievement (Hunt, 2003). Other major types of assessing the TPACK and its impact on teacher quality include self-evaluation measures such as open-ended and close-ended questionnaires as well as interviews, classroom observation and the evaluation of teaching artifacts (lesson plans, student work, classroom activities and teaching materials) (Koehler et al., 2012). This study sought to find out the association between Mathematics teachers’ content knowledge and achievement of students in Mathematics. Interviews and document analysis were used to collect data for this objective. Student note books as well as their progress records were analyzed to establish their academic achievement. According to Kothari, (2010), analysis of secondary data can yield more detailed and new information.

3. Methodology A descriptive survey research design was adopted in this study. Creswell (2003) suggests that explanatory studies are advantageous when not much has been written about the topic or the population being studied, and that the design also allows the use of mixed research methodology that combines elements of qualitative and quantitative methods. This study combined both elements of qualitative and quantitative methods in data analysis. Kothari (2010) supports descriptive research design and notes that the surveys are concerned with describing, recording, analyzing and interpreting conditions that exists or without the researcher having any control of the variables studied. The design was therefore appropriately used to; describe record, analyze and interpret information about Mathematics teachers’ content knowledge, and learners’ achievement in Mathematics without the researcher having any control of these variables. The study was conducted in Kakamega County in Kenya which is located in western part of Kenya with its headquarters in Kakamega town. According to the Kenya National Examinations Council (KNEC, 2019), Kakamega County is one of the counties that perform poorly in Mathematics. This prompted the researcher to carry out a study in this location with a view of coming up with recommendations that may improve on Kenya Certificate of Secondary Education (KCSE) performance in Mathematics in the County and in Kenya as a whole. The target population of this study was the 801 Mathematics teachers in public secondary schools within Kakamega County. The study sample comprised of 80 teachers of Mathematics, who were selected from the target population of 801. This formed 10% of the targeted respondents, which was deemed sufficient to represent the entire population (Mugenda & Mugenda, 2003). This sample was arrived at by use of multi-stage sampling technique as shown in table 2.

Table 2: Sampling Frame Sampling Procedure Population Sample Purposive sampling of sub county schools 429 276 Simple random sampling of schools to participate. 276 80 Purposive sampling of form one teachers 801 174 Simple random sampling teachers to participate 174 80 Purposive sampling of students to participate 32012 334 Data was collected using the teacher questionnaire, teacher interview schedule, and document analysis guide. The questionnaire was used to collect background information of the respondents while document analysis was used to collect information about students’ achievement in Mathematics. The interview was conducted to collect information on the teacher’s knowledge in Mathematics content used in Mathematics instruction. The interview schedule had both closed and open-ended questions, which aimed at providing in-depth information on content knowledge of the teacher. The collected raw data was sorted, edited, classified and tabulated ready for analysis. Data analysis involved the use of descriptive and inferential statistics computed by aid of SPSS version 23. Descriptive statistics involved computation of frequencies and percentages to analyze data of the demographic information of respondents and respondents’ content




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knowledge. Inferential statistics used involved Pearson’s correlation to test the null hypotheses (HR01R). The correlation was brought on board to establish the strength and direction of association between the two variables. The demographic data was collected on school type, age of participants and gender distributions. The county comprises of 429 secondary schools. Of the 276 out of 429 schools sampled, 216 were co-educational, 24 boys’ schools, and 36 girls’ schools. Of the 80 teachers sampled in the study, 49 were male while 31 were female. Of the sampled 334 students, 156 were male while 178 were female. This comprised 10.43% of the total form one students’ population in the County.

4. Results The objective of this study was to investigate the relationship between Mathematics teachers’ level of knowledge in Mathematics content used in Mathematics instruction and Students’ Mathematics Achievement (SMA). Data concerning teachers’ level of knowledge in Mathematics content and their students’ achievement in Mathematics were collected using the instruments that were administered to the sampled respondents as per the research design. The null hypothesis, Ho1, stated as: Ho1: There is no significant relationship between Mathematics teachers’ level of knowledge in Mathematics content

used in Mathematics instruction and student achievement in Mathematics This hypothesis was tested inferentially using bivariate Pearson’s correlation in order to determine the direction and strength of association between the two variables in question. Results were as presented in Table 3.

Table 3: Correlation of Teachers’ Content Knowledge and Students’ Achievement

Variable Students’ achievement Teachers’ content knowledge level

Descriptives Mean S.D

Teachers’ content knowledge level 0.125 - 92.06 9.04

Students’ achievement - 0.125P

* 56.85 5.75 * p = 0.062, α = 0.05 As noted from Table 3, there was a weak positive association between teachers’ level of Mathematics content knowledge and their students’ Mathematics achievement [r=.125, p=.062 at α=.05]. This is because the Pearson’s correlation coefficient obtained is closer to zero than to 1, hence the description of the association as ‘weak’. Furthermore, it can be observed from the Table that the sign of the correlation coefficient (r) is positive, which implies that Teachers with high level of Mathematics content knowledge are likely to produce higher Mathematics achievement mean scores from their students as compared to teachers with lower levels of Mathematics content knowledge score and vice-versa. The association between the two variables was deemed to be non-significant because the p-value associated with the Pearson’s correlation was greater than 0.05, the stipulated alpha level of significance. All these inferential test results imply that there was no significant association between teachers’ Mathematics content knowledge and students’ Mathematics achievement, which is in tandem with the assertion of the null hypothesis, Ho1. The null hypothesis was therefore not rejected because of empirical evidence arising from data collected by the Students’ Mathematics Achievement Document Analysis Guide and Mathematics Teacher Content Knowledge Interview Guide.

5. Discussion of Findings It was established that there was no significant relationship between Mathematics teachers’ level of knowledge in Mathematics content used in Mathematics instruction and student achievement in Mathematics. This association was not statistically significant at the 0.05 alpha levels, which was in tandem with the assertion of the null hypothesis of the study. The positive value of the correlation coefficient implies that a teachers’ high level of Mathematics content knowledge would also lead to a high students’ Mathematics achievement mean score and vice-versa. This association, though weak, is statistically non-significant because the p-value associated with the calculated correlation coefficient is greater than the stipulated alpha value. These findings are similar to those of Strong, (2011), whose mixed methods study revealed that there was weak positive association between students’ achievement and teachers’ content knowledge. However, unlike the present study Strong, (2011) found out that the association between the two research variables was strong. Findings of this study are however in disagreement with those of Odumosu and Areelu, (2018). Their Nigerian study, which focused on teachers’ content knowledge and students’ achievement in algebra was done using a test re-test quasi- experimental design and used a sample of 421 senior secondary school II students and 12 mathematics teachers from eight




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public and four private schools in Education District 5 of Lagos State. Their results revealed that all categories of the subjects were equally affected by content knowledge in algebraic achievement after exposure to teachers’ content knowledge.

6. Conclusions From the objective of the study reported in this paper, it was found out that there was no significant relationship between Mathematics teachers’ level of knowledge in Mathematics content used in Mathematics instruction and student achievement in Mathematics. Based on empirical evidence arising from data that were collected by this study’s research instruments and the subsequent statistical data analysis, the conclusion arrived at was that students’ achievement scores in Mathematics do not depend on the level of content knowledge in the subject. Students’ may obtain low achievement scores in Mathematics even if their Mathematics teacher has a high level of content knowledge and vice-versa. The study found that there is no significant association between Mathematics teachers’ level of content knowledge and students’ academic achievement in Mathematics. This is a very important milestone that has several implications for instructional practice. For instance, a teacher may not require very high level of content knowledge to be an effective teacher.

7. Recommendations from the Study It is on the basis of such an effect size, that several recommendations are hereby made to key stakeholders in the education sector, for purposes of policy action. Recommendations for the Teachers’ Service Commission (TSC) The current employment criteria used by the TSC to hire new teachers at secondary school level are made such that teachers with higher level of content knowledge stand a high chance of being employed first, as compared to those with lower content knowledge. However, as this study found out with respect to the objective, a teachers’ content knowledge in Mathematics has no association with their students’ Mathematics achievement mean score. If we are to improve students’ achievement in the subject therefore, the current employment criterion by TSC needs to be revised, at least for the sake of attainment of national goals of Mathematics education. Recommendations to Ministry of Education (MoE) Findings from this study have implications for the MoE, specifically the Kenya Institute of Curriculum Development (KICD). Curriculum planners need to develop a greater awareness and understanding of the various variables that significantly predict Mathematics achievement among secondary school students, and thus integrate them into the existing curriculum. References Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. doi: 10.1177/0022487108324554 Boling, E. C., & Beatty, J. (2012). Overcoming the tensions and challenges of technology integration: How can we best

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First Author Biographies Mr. Polycarp Muchesia Ishenyi holds a BEd degree (Mathematics and Economics, Moi University-1995), a Master of Science degree in Science Education (Mathematics option-2012) from Masinde Muliro University of Science and Technology (MMUST), Kenya. He works as a part time lecturer of mathematics education in Kenyan Universities. Currently he is a PhD student at MMUST. He has published several articles in refereed Journals and one text book with Lap lambert, Germany. He is a member of Kenya Association of Educational Administration and Management (KAEAM) and has presented scholarly papers in KAEAM symposia, and participated in National and international conferences such as Strathmore Mathematics International Conferences. Second Author: Dr. Wanjala Martin is a Senior Lecturer in the Department of Science and Mathematics Education, a specialist in mathematics education with a PhD from Moi University, Kenya and postdoctoral research experience from the University of Witwatersrand South Africa. He engages in teaching, research and supervision of students.


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