**THE INFLUENCE OF STUDENTS’ KNOWLEDGE ON TERMINOLOGIES USED**

IN MATHEMATICS CURRICULUM ON THE ACADEMIC PERFORMANCE OF STUDENT IN MATHEMATICS

OF JUNIOR SECONDARY SCHOOLS.

IN MATHEMATICS CURRICULUM ON THE ACADEMIC PERFORMANCE OF STUDENT IN MATHEMATICS

OF JUNIOR SECONDARY SCHOOLS.

**Abstract**

*Vocabulary understanding is*

a major contributor to overall comprehension in many content areas, including

mathematics. Effective methods for teaching vocabulary in all content areas are

diverse and long standing. Teaching and learning the language of mathematics is

vital for the development of mathematical proficiency. Students’ mathematical

vocabulary learning is a very important part of their language development and

ultimately mathematical proficiency. This article draws on current

research-based evidence to (a) provide a rationale for teaching vocabulary, (b)

offer a review of research that supports the importance of teaching mathematics

vocabulary, and (c) describe specific strategies for teaching mathematics

vocabulary. It also addresses implications and the need for future research.

a major contributor to overall comprehension in many content areas, including

mathematics. Effective methods for teaching vocabulary in all content areas are

diverse and long standing. Teaching and learning the language of mathematics is

vital for the development of mathematical proficiency. Students’ mathematical

vocabulary learning is a very important part of their language development and

ultimately mathematical proficiency. This article draws on current

research-based evidence to (a) provide a rationale for teaching vocabulary, (b)

offer a review of research that supports the importance of teaching mathematics

vocabulary, and (c) describe specific strategies for teaching mathematics

vocabulary. It also addresses implications and the need for future research.

**CHAPTER ONE**

**INTRODUCTION**

**Background**

to the Study

to the Study

Vocabulary knowledge is

as essential to learning of mathematics as it is to learning how to read. In

language arts, mathematical words conjure up graphic representations of the

objects they label. But when it comes to abstract mathematical concepts, words

describe activities or relationships that often lack a visual counterpart. Yet

studies show that children grasp the idea of quantity, as well as other

relational concepts, from a very early age (Dehaene, 2007).

as essential to learning of mathematics as it is to learning how to read. In

language arts, mathematical words conjure up graphic representations of the

objects they label. But when it comes to abstract mathematical concepts, words

describe activities or relationships that often lack a visual counterpart. Yet

studies show that children grasp the idea of quantity, as well as other

relational concepts, from a very early age (Dehaene, 2007).

Mathematics is one of

the core subjects taught in contemporary human society. It is an indispensable

discipline in various field such as science, Engineering, Technology, social

sciences, Arts and others disciplines that are related. Many educators have

considered it as an indispensable to the educated man or woman. As a result of

its importance, it has been considered as a key subject in the school

curriculum. Nevertheless, Mathematics is the language of science.

the core subjects taught in contemporary human society. It is an indispensable

discipline in various field such as science, Engineering, Technology, social

sciences, Arts and others disciplines that are related. Many educators have

considered it as an indispensable to the educated man or woman. As a result of

its importance, it has been considered as a key subject in the school

curriculum. Nevertheless, Mathematics is the language of science.

Mathematics by

educational policy is made compulsory and it is among the core subjects that

have to be passed before any certificate can be issued or awarded to anyone.

educational policy is made compulsory and it is among the core subjects that

have to be passed before any certificate can be issued or awarded to anyone.

The relevance of

Mathematics to the society cannot be over- emphasized. As mathematics is a tool

in science, industry and commerce. It will enhance understanding of students

who have interest in mathematics. It will help the student to correct certain

ills of the society; one very important characteristic of child centered

approaches is play away method or activities. Method which they emphasized in

mathematics like other subject should be made practical where possible in the

classroom.

Mathematics to the society cannot be over- emphasized. As mathematics is a tool

in science, industry and commerce. It will enhance understanding of students

who have interest in mathematics. It will help the student to correct certain

ills of the society; one very important characteristic of child centered

approaches is play away method or activities. Method which they emphasized in

mathematics like other subject should be made practical where possible in the

classroom.

Mathematical vocabulary

refers to words that label mathematical concepts for example quotient, volume,

vertex, dividend, and hexagon (Sanders, 2007). According to Miller (2003)

students are likely to be handicapped in their effort to learn mathematics if

they do not understand the vocabulary that is used in mathematics classrooms,

textbooks and assessment tests. One of the obstacles that make mathematical

vocabulary difficult to learn is lack of opportunity (Paul and Sinha, 2010).

This is because much of the vocabulary used in mathematics classroom is rarely

encountered in everyday life. In addition, mathematics teachers often neglect

meaningful vocabulary instruction. Also, many terms have meanings in the realm

of mathematics that differ from their meanings in everyday usage (Njoroge,

2003).

refers to words that label mathematical concepts for example quotient, volume,

vertex, dividend, and hexagon (Sanders, 2007). According to Miller (2003)

students are likely to be handicapped in their effort to learn mathematics if

they do not understand the vocabulary that is used in mathematics classrooms,

textbooks and assessment tests. One of the obstacles that make mathematical

vocabulary difficult to learn is lack of opportunity (Paul and Sinha, 2010).

This is because much of the vocabulary used in mathematics classroom is rarely

encountered in everyday life. In addition, mathematics teachers often neglect

meaningful vocabulary instruction. Also, many terms have meanings in the realm

of mathematics that differ from their meanings in everyday usage (Njoroge,

2003).

Without appropriate

vocabulary instruction, students are likely to experience difficulties and

interference in the learning of concepts for which they have background

knowledge that appears unrelated to mathematics. Students need to know the

meaning of mathematics vocabulary words-whether written or spoken-in order to

understand and communicate mathematics ideas. According to Sanders (2007), terms,

phrases, and symbols are essential in communicating mathematical ideas; and

becoming fluent with them is vital for children’s mathematical learning.

vocabulary instruction, students are likely to experience difficulties and

interference in the learning of concepts for which they have background

knowledge that appears unrelated to mathematics. Students need to know the

meaning of mathematics vocabulary words-whether written or spoken-in order to

understand and communicate mathematics ideas. According to Sanders (2007), terms,

phrases, and symbols are essential in communicating mathematical ideas; and

becoming fluent with them is vital for children’s mathematical learning.

Research reveals that

the knowledge of mathematics vocabulary directly affects achievement in arithmetic,

particularly problem-solving (Staley, 2005). Riordain and O’Donoghue (2009)

indicated that vocabulary knowledge is strongly related to overall academic

achievement in school. Although students may excel in computation, their

ability to apply their mathematics skills will be hindered if they do not

understand the vocabulary required to master content and able to apply in

future situations. Thus teaching vocabulary in the mathematics content area is

a critical element of effective instruction.

the knowledge of mathematics vocabulary directly affects achievement in arithmetic,

particularly problem-solving (Staley, 2005). Riordain and O’Donoghue (2009)

indicated that vocabulary knowledge is strongly related to overall academic

achievement in school. Although students may excel in computation, their

ability to apply their mathematics skills will be hindered if they do not

understand the vocabulary required to master content and able to apply in

future situations. Thus teaching vocabulary in the mathematics content area is

a critical element of effective instruction.

Although Mathematics is

a visual language of symbols and numbers, it is expressed and explained through

written and spoken words. Thus, for students to excel in Mathematics, they must

recognize, comprehend and apply the requisite mathematical vocabulary. Teaching

mathematical vocabulary words solely as definitions as is the practice in most

Kenyan schools does not assist students in comprehending the word when found in

Mathematics textbooks and examination items. Students must be actively engaged

in building background knowledge using key content-specific vocabulary.

a visual language of symbols and numbers, it is expressed and explained through

written and spoken words. Thus, for students to excel in Mathematics, they must

recognize, comprehend and apply the requisite mathematical vocabulary. Teaching

mathematical vocabulary words solely as definitions as is the practice in most

Kenyan schools does not assist students in comprehending the word when found in

Mathematics textbooks and examination items. Students must be actively engaged

in building background knowledge using key content-specific vocabulary.

**The**

meanings of mathematics

meanings of mathematics

Mathematics is used to

communicate information about a wide range of different subjects. Here are

three broad categories:

communicate information about a wide range of different subjects. Here are

three broad categories:

• Mathematics

describes the real world: many areas of mathematics originated with attempts to

describe and solve real world phenomena – from measuring farms (geometry) to

falling apples (calculus) to gambling (probability). Mathematics is widely used

in modern physics and engineering, and has been hugely successful in helping us

to understand more about the universe around us from its largest scales

(physical cosmology) to its smallest (quantum mechanics).

describes the real world: many areas of mathematics originated with attempts to

describe and solve real world phenomena – from measuring farms (geometry) to

falling apples (calculus) to gambling (probability). Mathematics is widely used

in modern physics and engineering, and has been hugely successful in helping us

to understand more about the universe around us from its largest scales

(physical cosmology) to its smallest (quantum mechanics).

• Mathematics

describes abstract structures: on the other hand, there are areas of pure

mathematics which deal with abstract structures, which have no known physical

counterparts at all. However, it is difficult to give any categorical examples

here, as even the most abstract structures can be co-opted as models in some

branch of physics.

describes abstract structures: on the other hand, there are areas of pure

mathematics which deal with abstract structures, which have no known physical

counterparts at all. However, it is difficult to give any categorical examples

here, as even the most abstract structures can be co-opted as models in some

branch of physics.

• Mathematics

describes mathematics: mathematics can be used reflexively to describe

itself—this is an area of mathematics called meta-mathematics.

describes mathematics: mathematics can be used reflexively to describe

itself—this is an area of mathematics called meta-mathematics.

Mathematics can

communicate a range of meanings that is as wide as (although different from)

that of a natural language. (Staley, 2005).

communicate a range of meanings that is as wide as (although different from)

that of a natural language. (Staley, 2005).

Mathematics

by educational policy is made compulsory and it is among the core subjects that

have to be passed before any certificate can be issued or awarded to anyone.

by educational policy is made compulsory and it is among the core subjects that

have to be passed before any certificate can be issued or awarded to anyone.

The

relevance of Mathematics to the society cannot be over- emphasized. As

mathematics is a tool in science, industry and commerce. It will enhance

understanding of students who have interest in mathematics. It will help the

student to correct certain ills of the society; one very important

characteristic of child centered approaches is play away method or activities.

Method which they emphasized in mathematics like other subject should be made

practical where possible in the classroom.

relevance of Mathematics to the society cannot be over- emphasized. As

mathematics is a tool in science, industry and commerce. It will enhance

understanding of students who have interest in mathematics. It will help the

student to correct certain ills of the society; one very important

characteristic of child centered approaches is play away method or activities.

Method which they emphasized in mathematics like other subject should be made

practical where possible in the classroom.

The

problem of poor mathematical vocabulary has come into the spotlight again with

the concern being at the state, national, and global levels. The language of

mathematics is more difficult to read than any other subject area. The

mathematics material is so difficult to read, “with more concepts per word, per

sentence, and per paragraph than any other area”, it is particularly crucial to

emphasize vocabulary instruction in this content area (Monroe, 2007, p.4).

problem of poor mathematical vocabulary has come into the spotlight again with

the concern being at the state, national, and global levels. The language of

mathematics is more difficult to read than any other subject area. The

mathematics material is so difficult to read, “with more concepts per word, per

sentence, and per paragraph than any other area”, it is particularly crucial to

emphasize vocabulary instruction in this content area (Monroe, 2007, p.4).

Monroe’s

study investigated the effectiveness of graphic organizers in teaching the

vocabulary of mathematics. The results he found were that graphic organizers

can help develop conceptual understanding. Vocabulary research has been done at

all levels and social settings. Stahl’s and Fairbanks’ (2006) study looked at

the concerns with the effect of vocabulary instruction on the learning of word

meanings and on comprehension. They looked at the curriculum and teachers;

study investigated the effectiveness of graphic organizers in teaching the

vocabulary of mathematics. The results he found were that graphic organizers

can help develop conceptual understanding. Vocabulary research has been done at

all levels and social settings. Stahl’s and Fairbanks’ (2006) study looked at

the concerns with the effect of vocabulary instruction on the learning of word

meanings and on comprehension. They looked at the curriculum and teachers;

Stahl

and Fairbanks found two setting factors that have an effect on vocabulary

learning and comprehension. These factors are: a) whether instruction is

largely individual or done at least partly in a group setting and b) the amount

of time allocated to instruction.

and Fairbanks found two setting factors that have an effect on vocabulary

learning and comprehension. These factors are: a) whether instruction is

largely individual or done at least partly in a group setting and b) the amount

of time allocated to instruction.

As

for the curriculum, Schwarz (2009) states that mathematics curriculum needs to

focus more on content vocabulary and its usefulness to communicate

mathematically through both written and oral means. Schwarz targeted students,

who exhibited poor understanding of content vocabulary for mathematics. In her

study, some of the strategies that helped her target group increase their

mathematical vocabulary knowledge were: vocabulary journals, math journals, and

word walls.

for the curriculum, Schwarz (2009) states that mathematics curriculum needs to

focus more on content vocabulary and its usefulness to communicate

mathematically through both written and oral means. Schwarz targeted students,

who exhibited poor understanding of content vocabulary for mathematics. In her

study, some of the strategies that helped her target group increase their

mathematical vocabulary knowledge were: vocabulary journals, math journals, and

word walls.

**Student**

Knowledge/Attitude

Knowledge/Attitude

According

to Rubenstein (2007) students see mathematics as a foreign language because of

the vocabulary that is used solely in that content area. Another person who did

some research on this was Dresher (1934). He also found results that showed

mathematics, like other school subjects, have a technical vocabulary. According

to Dresher (1934), pupils cannot work problems if they cannot read and

understand them; they cannot understand the explanation of a problem if they do

not understand the terminology used. He made these claims almost seventy-five

years ago, and just six years ago Blessman and Myszczak (2001) had basically the same finding.

Students must understand the language of math in order to fully comprehend

concepts being learned. Also, Schwarz (1999) states in her research that if

students are unable to read and understand the directions to a mathematics

problem, they will be unable to answer the problem.

to Rubenstein (2007) students see mathematics as a foreign language because of

the vocabulary that is used solely in that content area. Another person who did

some research on this was Dresher (1934). He also found results that showed

mathematics, like other school subjects, have a technical vocabulary. According

to Dresher (1934), pupils cannot work problems if they cannot read and

understand them; they cannot understand the explanation of a problem if they do

not understand the terminology used. He made these claims almost seventy-five

years ago, and just six years ago Blessman and Myszczak (2001) had basically the same finding.

Students must understand the language of math in order to fully comprehend

concepts being learned. Also, Schwarz (1999) states in her research that if

students are unable to read and understand the directions to a mathematics

problem, they will be unable to answer the problem.

Reading

these articles shows that the research I am thinking about has been the focus

of some researchers for a long time with the findings coming up the same.

Students need to be aware that the mathematical vocabulary that their teacher

is teaching is something that will be important throughout their lives. Schwarz

came up with the conclusion that for students to better understand mathematical

vocabulary they must learn to recognize symbols, recognize vocabulary words

that name symbols, remember that symbols and words have the same meaning and

are pronounced the same, and they need to understand concepts expressed by the

symbols and words.

these articles shows that the research I am thinking about has been the focus

of some researchers for a long time with the findings coming up the same.

Students need to be aware that the mathematical vocabulary that their teacher

is teaching is something that will be important throughout their lives. Schwarz

came up with the conclusion that for students to better understand mathematical

vocabulary they must learn to recognize symbols, recognize vocabulary words

that name symbols, remember that symbols and words have the same meaning and

are pronounced the same, and they need to understand concepts expressed by the

symbols and words.

According

to Kotsopoulos (2007), students must continually and actively negotiate among

the mathematical meaning of a word, its everyday language meaning, and its new

meaning as well as its alternative meaning within the mathematical register. Blessman

and Myszczak (2001) along with Schwarz (1999) found results showing that

students need to understand the vocabulary before they can do the work.

Teachers and students alike need to realize that all students need to have a strong

understanding of mathematical vocabulary in order to be successful math

students.

to Kotsopoulos (2007), students must continually and actively negotiate among

the mathematical meaning of a word, its everyday language meaning, and its new

meaning as well as its alternative meaning within the mathematical register. Blessman

and Myszczak (2001) along with Schwarz (1999) found results showing that

students need to understand the vocabulary before they can do the work.

Teachers and students alike need to realize that all students need to have a strong

understanding of mathematical vocabulary in order to be successful math

students.

**Statement**

of the Problem

of the Problem

It has been observed

that many secondary school students finds mathematics as a difficult subject to

pass due to their inability to comprehend effectively the vocabularies of

Mathematics used in the curriculum. The final year academic output in

mathematics in West Africa Examination Council (WAEC) and other external examinations

signify the poor knowledge of students about the vocabularies used in the

teaching content. It is against this background that the researcher wishes to

critically examine the students’ knowledge on vocabularies (Mathematical

Language) used in curriculum of junior secondary school.

that many secondary school students finds mathematics as a difficult subject to

pass due to their inability to comprehend effectively the vocabularies of

Mathematics used in the curriculum. The final year academic output in

mathematics in West Africa Examination Council (WAEC) and other external examinations

signify the poor knowledge of students about the vocabularies used in the

teaching content. It is against this background that the researcher wishes to

critically examine the students’ knowledge on vocabularies (Mathematical

Language) used in curriculum of junior secondary school.

**Delimitation**

of the Study

of the Study

The study is specifically talking about the students’ knowledge on

vocabularies (Mathematical Language) used in curriculum of junior secondary

school. The study will concentrate on the mathematic vocabularies used in

teaching students and their consequence effects on the academic performance of

student in (5) Junior Secondary Schools in Ikere Local Government Area of Ekiti

State.

**Purpose of the Study**

The broad objective of the research project is to examine the

students’ knowledge of vocabularies used by their teachers in teaching

mathematics and subsequent impact on their academic output in Mathematics in

secondary schools in Ekiti State.

students’ knowledge of vocabularies used by their teachers in teaching

mathematics and subsequent impact on their academic output in Mathematics in

secondary schools in Ekiti State.

The specific

objectives are;

objectives are;

1. To examine what mathematical vocabularies

means to the junior secondary students in Ekiti State.

means to the junior secondary students in Ekiti State.

2 To determine the relationship between mathematical

language and academic achievement of Mathematics students in secondary schools

in Ekiti State.

language and academic achievement of Mathematics students in secondary schools

in Ekiti State.

**Significance of the Study**

The study will help the

school, ministry of education, government, teachers and curriculum planners to

provide solution for effective way of helping the students to comprehend the

vocabularies used in mathematics.

school, ministry of education, government, teachers and curriculum planners to

provide solution for effective way of helping the students to comprehend the

vocabularies used in mathematics.

It will enable the

government to employ adequate qualified teachers, to enhance effective learning

and teaching process. The findings will enable the teachers to make their

teaching more interesting by arousing and sustaining the interest of their

students. The study would go a long way to improve students’ ability in solving

problems with big vocabularies in Mathematics and also reduce teaching problems

in a greater measure.

government to employ adequate qualified teachers, to enhance effective learning

and teaching process. The findings will enable the teachers to make their

teaching more interesting by arousing and sustaining the interest of their

students. The study would go a long way to improve students’ ability in solving

problems with big vocabularies in Mathematics and also reduce teaching problems

in a greater measure.

**Research**

Questions

Questions

The following questions were of

interest in my research and helped drive this focus:

interest in my research and helped drive this focus:

1.

How did the integration of vocabulary strategies into the

mathematics curriculum increase low socio-economic students’ proficiency in

mathematics?

How did the integration of vocabulary strategies into the

mathematics curriculum increase low socio-economic students’ proficiency in

mathematics?

2.

Does the student’s prior knowledge of vocabularies have any

significant effect on their academic performance?

Does the student’s prior knowledge of vocabularies have any

significant effect on their academic performance?

3.

What were the attitudes and opinions of the adopted

curriculum strategies among learners?

What were the attitudes and opinions of the adopted

curriculum strategies among learners?

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