This study sheds light on the various strategies to teach mathematics and whether they are employed or not. The study investigates the employed mathematics-teaching strategies in Arab schools in northern Israel, and the hindrances that prevent teachers from applying diverse effective strategies in their classrooms. The researcher follows the qualitative approach based on in-depth interviews and recommendations of previous studies and observation to obtain the maximum benefits and give accurate qualitative results based on interviews, from Arab schools in northern Israel who study in six different schools. Teachers assert that employing the different innovative strategies are vital and efficient in teaching mathematics, but there are many handicaps that prevent teachers from exploiting them including, amongst others, the imposed duties to complete the entire amount of loaded study material during the semester, as well as the lack of available tools to computerize classes and teaching process in general, the lack of building tangible tools, and the low proficiency level of some teachers. The results of the interviews showed that technology is rarely employed in teaching mathematics – if ever, as well as innovative and modern strategies. The study concludes that the heavy burden of teaching mathematics should be lightened to allow space for creativity in teaching strategies, as they need more time to be employed. In addition, for mathematics to be understood properly, the teaching process should be interesting to attract students. Besides this, the suggested strategies are advantageous to be applied in the teaching process.

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Research Article

Innovative Ways to Teach Mathematics: Are they Employed in

Schools?

Yousef Methkal Abd ALGANI*1

Sakhnin College, Department of Mathematics, Israel, yosefabdalgani@gmail.com

* Corresponding Author: yosefabdalgani@gmail.com

This study sheds light on the various strategies to teach mathematics

and whether they are employed or not. The study investigates the

employed mathematics-teaching strategies in Arab schools in northern

Israel, and the hindrances that prevent teachers from applying diverse

effective strategies in their classrooms. The researcher follows the

qualitative approach based on in-depth interviews and

recommendations of previous studies and observation to obtain the

maximum benefits and give accurate qualitative results based on

interviews, from Arab schools in northern Israel who study in six

different schools. Teachers assert that employing the different

innovative strategies are vital and efficient in teaching mathematics, but

there are many handicaps that prevent teachers from exploiting them

including, amongst others, the imposed duties to complete the entire

amount of loaded study material during the semester, as well as the

lack of available tools to computerize classes and teaching process in

general, the lack of building tangible tools, and the low proficiency

level of some teachers. The results of the interviews showed that

technology is rarely employed in teaching mathematics – if ever, as

well as innovative and modern strategies. The study concludes that the

heavy burden of teaching mathematics should be lightened to allow

space for creativity in teaching strategies, as they need more time to be

employed. In addition, for mathematics to be understood properly, the

teaching process should be interesting to attract students. Besides this,

the suggested strategies are advantageous to be applied in the teaching

process.

Accepted: 16 October 2019

Keywords: Teaching mathematics,

Conceptual method, Innovative

method.

DOI: 10.18009/jcer.612199

Publication Language: English

Introduction

The role of education nowadays is undeniable. It is the driving force that moves

society from the state of inertia and slow growth to the rapid movement of progress and

development in economic and human resources. Education is an issue of national security

and the first line of defense against the dangers and disadvantages of globalization. It is also

the basic tool for the investment of human resources, which is now the main basis for

economic progress and globalization (Algani, 2018).

To cite this article: Algani, Y.M.A. (2019). Innovative ways to teach

mathematics: are they employed in schools?.

Journal of Computer and

Education Research, 7 (14), 496-514 . DOI: 10.18009/jcer.612199

Journal of Computer and Education Research Year 2019 Volume 7 Issue 14 496 -514

Science and knowledge are the main basis for any development, so they should be a

priority for all countries in order to cope with the massive technological development that

the globe currently witnesses. Mathematics is an integral part of science; in fact, it is the core

component of science. If we understand its importance and the critical role of its applications

in life, we can use it in the right ways that will contribute to the scientific and technical

progress of our nation. However, the fact that the vast majority of students consider it a

difficult subject to learn makes it urgent for schools to exploit all resources and strategies to

help students understand it (Algani, 2018).

Unfortunately, the findings of the latest Meitzav tests

in the schools in which the

research will be held, indicate low achievements in mathematics and in the sciences (around

40%) both in comparison with the results at the level of the Arab sector as a minority

population and at the national level. In addition, the findings show that in the questionnaire

which examined the position of school pupils towards the two subjects, about 80% of the

pupils in Grade 8 gave higher importance to the study of the two subjects, although only an

average of 55% reported that they enjoyed learning sciences and mathematics. It should be

remembered that only a small percentage of the pupils who continued their studies in high

schools are studying in the science track, and most of them study mathematics at the 3-unit

level (National authority for measurement and evaluation in education in Israel-RAMA,

2018).

Thus, all available means should be employed to improve teaching all materials,

especially mathematics. Furthermore, some important obstacles stand in the face of

employing effective strategies in teaching mathematics in schools, which are manifested

mainly in the burden of completing the entire loaded study material of the textbook. This

way, the ultimate objective would be to manage teaching the entire textbook in one semester

at the expense of employing various strategies while teaching. Moreover, teachers would

have to build upon the material taught by the previous teachers because mathematics is a

Meitav (Measure of Efficiency and School Growth) is a system of tests and surveys conducted in elementary

and intermediate schools in Israel. The tests are held in the subjects of Science and Technology, the native

language (Hebrew or Arabic), Mathematics and English. The surveys are conducted among the pupils, teachers,

and principals, and deal with a long list of subjects that reflect the social and pedagogical climate in the school.

The tests and surveys are held annually in a third of the schools, so that every school participates in Meitav once

every three years. The tests and surveys are conducted by RAMA (National Authority for Measurement and

Evaluation in Education).

Journal of Computer and Education Research Year 2019 Volume 7 Issue 14 496 -514

cumulative science. Nonetheless, if the previous teacher was not good enough, a critical

problem arises; the current teacher would have to explain the material that the student did

not understand in order to be able to explain the new material, which would be time

consuming amongst other things.

Teachers should pay careful attention to the strategies applied in teaching

mathematics after taking into consideration the existing obstacles, the needs of students, and

the objectives that have to be to fulfilled, since "teaching strategies are tools that the teacher

uses to achieve the objectives, mainly the intellectual development of the student (Enríquez

et al., 2018, p.115). By the same token, the statement of Entwistl (2005) which is cited in

Enríquez et al., (2018: 115), is that: It is essential, for the teacher, to pay attention not only to

the topics that must be included in the programs and that should be addressed in class, but

also, and simultaneously, in the manner in which it can be considered more convenient for

those topics to be worked on by the students. The relationship between themes and the way

to approach them is so strong that it can be argued that both themes and didactic treatment

strategies are inseparable. It is evident that the way the material is presented and explained

affects the students' understanding and their attraction to mathematics. This urges teachers

to employ various strategies that have proved to be efficient and to employ technological

innovation and creativity while teaching mathematics.

Penina Kamina and Nithya Iyer (2009) approve this fact: The way in which it is

taught in the classrooms of basic education makes abstract contents prevail, without support

in resources that allow building knowledge, going from concrete and semi-concrete

representations of mathematical ideas and concepts, to synthesis activities that facilitate the

abstraction and generalization of the mathematical contents of the level. The way

Mathematics is taught is as important as the content. However, in order for the innovative

strategies to be effective, the relationship between the teacher and student should be good, as

it helps to "improve academic success" (Coe, 2018, p.29) because "students try harder,

knowing someone cares about the outcomes. Students feel more comfortable seeking help

when the relationship is positive and supportive" (ibid). In this way, teachers influence

student's attitudes and outcomes. Students will be "willing to exert more energy learning the

lesson and helping their peers" (ibid).

Journal of Computer and Education Research Year 2019 Volume 7 Issue 14 496 -514

All nations should keep up with the massive continuous development in all fields,

and "*a+n alternative process or method of teaching has to be adopted in this fast developing

world, where knowledge explosion has been taking place every day in every sphere of life. It

is unreasonable to expect that spoken or written words alone can convey the volume of

relevant information to the learner" (Rajkumar & Hema, 2016, p.1), especially in teaching

mathematics. It is vital to note to the fact that there are plenty of modern teaching methods

that employ technology such as Smart Classrooms, Flipped Classrooms, Virtual Classrooms,

Blended Learning, and mobile learning (Rajkumar & Hema, 2016). However, the current

situation of the schools that imposes various restrictions, especially in terms of resources,

makes it difficult to employ them in schools. Thus, in this study, only the applicable methods

and strategies are to be discussed, and the question here is: What are the innovative ways to

teach mathematics that teachers have employed in Arab Israeli schools? However, teachers

should be familiar in the first place with the objectives of teaching mathematics in general

prior to deciding how to teach it, because setting up the objectives determines the way

mathematics is to be taught.

General Objectives of Teaching Mathematics

It is generally agreed that the basic objective of teaching mathematics is, on the one

hand, to prepare students for public life regardless of their work or future aspirations, and

on the other hand, to give students the ability to understand mathematics itself in school or

after graduation. However, there are additional objectives that should be borne in mind such

as to provide students with the ability to use proper thinking methods, to apply inductive

and deductive reasoning, to be contemplative and reflective, and to acquire problem solving

skills.

Teachers should emphasize the importance of mathematics in public life by teaching

students about the impact of mathematics on cultural development. Moreover, it is vital to

provide students with the necessary skills to understand what they are studying and to

discover new relationships, as well as to help them in shaping positive trends and attitudes

towards mathematics. Helping students to rely on themselves in studying mathematics is

also necessary, alongside with developing good habits such as accuracy, order, cooperation,

mutual respect and constructive criticism, and improving mental skills and scientific

innovations (Algani, 2018).

Journal of Computer and Education Research Year 2019 Volume 7 Issue 14 496 -514

How to achieve these goals?

Teaching mathematics is an enjoyable profession, but it is not an easy task, and it

derives both its pleasure and its difficulty from the nature of mathematics and the nature of

the learner and his\her perception of it. Like any profession, teaching requires knowledge

and art. Teachers must develop themselves professionally by constantly researching the

developments in mathematics and attending events such as conferences, seminars, meetings

and professional training sessions in mathematics to be familiar with the appropriate

knowledge as well as learning methods and strategies that make the learning environment

effective. Teachers would then be able to connect mathematics with daily life and to provide

students with examples and applications that are tangible so that they can interact with the

teacher and interact with the material and with the learning environment, and can recognize

the importance of mathematics (Algani, 2019).

Teachers should be creative in choosing examples close to the living experience of

students. They should also connect mathematics with abstract thought as well as the real

things in life for students to understand and love mathematics. Teaching mathematics this

way facilitates students' integration into society and helps them to learn the art of thinking. If

mathematics is not related to the individual in any way, learning it will be useless and

merely involve memorizing for the exams. Students have many talents, and teachers should

help them to use them and provide them with all the available means of illustration,

especially modern ones (Algani, 2019)

Einat Heyd-Metzuyanim (2015; 2016), in her articles about the impact of procedural

method and conceptual method on learning mathematics and its relationship with learning

patterns and the fear of mathematics, concluded that the conceptual method leads to the

development of learning mathematics among students and increases their motivation to

study mathematics. She also pointed to the strong relationship between difficulties in

mathematics and the traditional method of learning, which leads to a fear of mathematics

and math tests which she sees as a vicious cycle: Ritual Learning Difficulties in

Mathematics Math Anxiety Ritual Learning.

Journal of Computer and Education Research Year 2019 Volume 7 Issue 14 496 -514

How Do We Teach Mathematics?

We have to teach our students to study mathematics as a practical subject, not as

purely theoretical material. They have to memorize mathematical laws and rules only, and

we should guide them to the way they apply them to be familiar with them and get used to

them at an early age. Ernest (1988) suggests specifying a practical class to introduce students

to some rules of mathematics in the surrounding environment through a number of activities

and methods, including presenting live examples.

Kristi Coe (2018) pointed out in her article Strengthening Student Educational

Outcomes: Mathematics Menu of Best Practices and Strategies that mathematics should be

taught together with strategies such as magic squares and crossword games and decoding,

entertainment with numbers, where students use several calculations and mathematical

rules sequentially to reach a relationship between them, and make use of the maze and

knowledge maps. Mathematics can be taught by playing games, as "some research has found

that game-based learning is an effective way to enhance motivation and performance" (Coe,

2018, p.73). However, "Choosing which game to play depends on the instructional goal and

the learning target. Games can be used both for instruction and practice. Games may also

give students the opportunity to apply new learning" (ibid). The teacher must develop

strategies for cooperative action and teamwork among students, because of their positive

effects. By the same token, practical application of mathematical rules, and the connection of

mathematics to our life, will increase motivation to learn mathematics and allow the student

to understand its basic principles and applications.

Through exploring assignments and demonstration in mathematics the student

understands mathematical theories in depth, overcomes the difficulties and common

mistakes in mathematics, and sees the beauty of mathematics. Also. It is a good idea to

exploit technology and mobile phones in the search for mathematical laws or to practice

mathematical problems through games, which also develop the intellectual abilities of

students and complements the educational materials. Moreover, the application of modern

teaching methods is vital. The aim of using modern technological tools in education is to

raise the level of the educational process as a whole, and thus to create a generation that

would keep up with scientific and technological developments. Such a generation will then

be capable of excelling and taking a leading role in building the nation and its various

Journal of Computer and Education Research Year 2019 Volume 7 Issue 14 496 -514

scientific institutions through new educational methods dependent upon modern innovative

curricula with a primary focus on the student learner. Masa'adeh argues that teaching

mathematics to students at different educational stages may seem difficult for teachers,

students, and even parents at home.

The disparity between the educational abilities of the students and individual

differences between the students, the lack of educational qualifications among the teachers,

and the differences in the educational levels of the parents, causes a critical gap in teaching

mathematics. All this requires reconsidering the nature of the curriculum for mathematics

itself, the quality of the methods used in its explanation, and finally, the extent to which the

students accept their content and achieve good results at the end of each semester (Algani,

2018). Teachers should employ technology in teaching mathematics because students love

technology, and they will be more than happy to study mathematics through technological

tools. There are various ideas that can be exploited, and teachers can use innovative and

creative ideas to encourage students to study mathematics and most importantly understand

it. Besides, "when used strategically, technology can provide students with greater access to

conceptual understanding and procedural fluency" (Coe, 2018, p.37). However, it is not

enough to use technology alone, as it "cannot replace effective teaching or intervention

activities" (ibid). Coe also asserts that technology can provide students with additional

representations of mathematical ideas, allow inquiry-based exploration, reinforce procedural

learning and fluency, and provide efficient screening and diagnostic assessment data (ibid. p.

38). According to the Ministry of Education (2013; 2014; 2018) significant learning

occurs

when students learn beyond the facts, interpret information, create connections between

facts, think about the processes of their comprehension, and apply new concepts to new

situations. They must think, solve problems, change their positions and opinions, develop

skills and build knowledge. The Ministry of Education in Israel defined a few pedagogical

In his book, Freedom to Learn , Carl Rogers (1973) placed significant learning in opposition to learning by rote.

In his opinion, significant learning is defined as experiential learning, the opposite of rote learning which focuses

on the repetition and memorization of facts that are easy to forget and easily to cram into the mind, and to which

the student does not attribute any meaning. According to Rogers, significant learning occurs when the student

sees what is relevant in the study material, the connection between the material to his own aims, needs and

interests, and its contribution to his development. The components of significant learning, in the words of

Rogers, are: personal involvement and giving the student the opportunity to innovate; the learner himself

evaluates his own achievements. David Ausubel (1963) defines significant learning as the non-arbitrary and non-

verbal integration of new ideas into the cognitive structure of the learner.

Journal of Computer and Education Research Year 2019 Volume 7 Issue 14 496 -514

principles, the application of which is liable to lead to significant learning. These principles

are based on a constructivist paradigm. Constructivism is a theory of learning or of

significant creation that proposes an explanation on the nature of knowledge and how

people learn. It claims that people create or build up their understanding and new

knowledge on the basis of interaction between what they already know and believe and the

ideas, events and activities with which they come into contact (Richardson, 1997). The

constructivist approach is based on the following premises:

Learning as an active process: In the process of learning, every student is active

cognitively, physically, socially and emotionally in the construction of personal significance.

Learning as a constructivist process (building up of knowledge): In the process of learning,

the student builds up personal knowledge through the use of previous knowledge. The

combination of earlier and new knowledge contributes to the construction of new

understanding. In this process, knowledge is built up actively by the learner through an

internal cognitive process at a high level that acts on stimuli from the environment (Michael,

2003), Learning as a social process: Learning occurs in the social interaction between students

and their classmates and arouses internal processes of significant creation.

Authentic learning: This type of learning is based on experience in the real world. In

this type of learning, materials and activities are arranged around connections "in real life" in

which they are used.

Feedback from continuous evaluation: This is information that is provided by an

agent (e.g. teacher, colleague, book, parent, self, experience) in relation to the aspects of

performance or understanding (Hattie & Timperley, 2007). It reflects a continuous process

that provides teachers and learners with information about the development of the learning

process and allows for significant feedback for the evaluation of learning during the process

and after its completion in order to make decisions about teaching improvement.

Application of the constructivist teaching methods: Experiential learning (practical activity)

is one of the foundation stones of science and technology studies, and is essentially the

interaction between physical and cognitive activity. Experiential learning is important for the

buildup of knowledge, understanding and skills, for the demonstration of events and

processes, for the clarification of scientific terms, and for the discoveries of learning and

research.

Journal of Computer and Education Research Year 2019 Volume 7 Issue 14 496 -514

Coping with learners in heterogenic classes: People differ in their cognitive

structures. They are differentiated by many qualities such as personality, learning style,

needs and desires, cognitive abilities, ways of thinking, tendencies, habits of thought, and

other variables. As a result, the role of the teacher is to expose their minds (previous

knowledge, perceptions, attitudes, behavior, beliefs and positions) to a variety of experiences

suitable for the construction of active knowledge.

Promoting motivation to study science and technology: An important condition for the

occurrence of significant learning is interesting study and internal motivation. Among the

activities that strengthen internal motivation is the cooperation of students in choosing the

aims of study and the methods of evaluation; initiating experiences that arouse interest in the

subject under study; clarification of the benefit value of the material studied. Another

important factor in creating internal motivation is self-efficacy, thus teachers should provide

challenging tasks that suit the abilities of the students and give them constructive feedback

that expresses trust in their abilities. These pedagogical principles are the core components,

and their significant application in the class will improve the process of teaching and

learning.

Prior Conditions for the Application of Learning

In order to allow for effective learning in the classroom, a number of conditions are

required relating to the perceptions and positions of those involved in the process, the

educational environment, the study program, the learning-teaching process, and its

evaluation. According to the document "Policy for the Advancement of Significant Learning

in the Education System" (2013), the conditions that allow for the learning and advancement

of students are as follows:

Perceptions and Positions: Regarding learning as a process that occurs among a group

of people, teachers and students, who establish a system of relationships characterized by

mutual respect, by reception and inclusion, through holding a discourse based on dialogue

within the group and between groups.

Educational Environment: An emotional and positive atmosphere and a learning

environment that allows for initiative and personal interpretation, autonomy in the adaption

of processes for the needs of the learners. Appreciation for personal and group investment,

attribution of importance to the processes as well as to the results.

Journal of Computer and Education Research Year 2019 Volume 7 Issue 14 496 -514

Learning: Learning is the outcome of internal motivation, interest, and curiosity, and

not by external motivation such as expecting a prize or fear of punishment. The student is

active in the learning process, derives significance from it, and feels that his aims are

achieved. Learning builds a sense of capability, encourages achievement, and motivates new

learning.

Study Program: State study programs that allow for flexibility and adaptability for the

aims of the individual and society, engagement with local values and general human aspects,

with problems relating to life, authentic and relevant. It is necessary to reduce the required

range of material in the study programs in order to provide place for the processes of

significant learning and expected achievements in relation to the individual learner, besides

achievements in the sphere of knowledge. Teaching and evaluation promotes in-depth

learning of the students through personal significance, interest and curiosity, through the

inclusion of all the students with their various talents and abilities, the use of a variety of

teaching and evaluating methods, in order to give response to their differences.

Evaluation processes are established for the sake of learning at all levels, beginning

with policy evaluation and its continuous updating to the evaluation of student

achievements and feedback on their learning experience for the sake of continual

improvement. Appreciation of initiatives in which expression is given to qualitative

processes of teaching-learning-evaluation at the level of the teacher and of the school.

Organized school environment makes it possible, through a policy of pedagogic

flexibility and the empowerment of the teaching and management staff, to encourage

learning at all stages, both adults and students.

Harpaz (2014) defines two types of conditions so that significant learning can occur:

internal conditions and external conditions. The internal conditions are the states of

consciousness that allow for significant learning; the external conditions are the

characteristics of the environment that allow for and encourage internal conditions to

achieve significant learning. The internal conditions are related firstly to the "inner

motivation" and secondly to the "understanding of the student", to the material defined as

the product of significant learning. According to Harpaz, regarding the first condition, the

inner motivation for dealing with the learning activity occurs when a person performs an

action that causes pleasure to him or her or because it is considered to be of value. This

condition is not sufficient alone; it also requires understanding. When a person is involved in

Journal of Computer and Education Research Year 2019 Volume 7 Issue 14 496 -514

some assignment but does not receive some understanding of it, the learning is not

significant (Harpaz, 2014b). For the external conditions, Harpaz suggests that advancement

in significant learning is related to the educational environment which increases the situation

of "involvement in the process of learning which creates understanding". These external

conditions include a study program, a teacher, teaching methods, evaluation systems,

organization of student learning, and the physical structure and equipment of the schools.

Harpaz explains these conditions as follows:

The Study Program: The study program must be devoted to the authentic interests of

the students. The fundamental principle of the study program which allows for significant

learning is to teach meaningful subjects (Harpaz, 2012).

Teaching Methods: The fundamental principle of teaching which allows for significant

learning is indirect teaching that strengthens inner motivation to be involved in active

learning, the building up of knowledge and the creation of understanding.

Evaluation Systems: The fundamental principle of evaluation which allows for

significant learning is rich feedback that is continuous and mediating. Rich feedback means

to give the student detailed information about his achievements and failures. Continuous

feedback means giving it throughout the learning process (not only after examinations).

Mediating feedback means also on the product (academic research, art creation, film

production, etc.) that the student creates (not only through the direct evaluation of the

teacher).

Organization of Student Learning: The fundamental principle that guides learning

towards becoming significant learning is giving students a choice. The school must allow for

a wide range of choice for students, based on the realization that people give significance to

knowledge and creativity through choosing it. The choice itself is significant, and the school

should offer a variety of subjects to enable a wide choice.

Physical Structure and Equipment: Schools are physical environments that do not invite

the students to remain in them, and certainly not for significant learning. New standards

should be created for educational institutions and their equipment.

Ma'abrah (2018) suggests other innovative teaching methods to be applied in

teaching mathematics. Starting with a computerized class, the use of explanatory methods

that rely on direct teaching and information transfer should be used. The role of the teacher

is to create educational situations that enable students to solve problems and to discover

Journal of Computer and Education Research Year 2019 Volume 7 Issue 14 496 -514

mathematical relationships. A computerized class enhances creative thinking because it

requires advanced thinking abilities and capabilities such as classification, comparison,

organization, and analysis. Students resort to inventing unusual methods, and prefer to use

scientific thinking during computer learning through the application of the students'

intellectual model, and the technological tools used in the computerized programs such as

the dictionary, the calculator, the plotter, the graphic, etc. The media employed in the

educational process, including audio, visual and text techniques, have a significant and

effective role in the better comprehension of the material by the students through the use of

different senses at the same time.

Moreover, mental calculation is an advantageous method to apply. It is manifested in

the solving of mathematical problems accurately, correctly, and quickly without the need for

the student to use pen, paper, or calculator. Mental calculation is one of the most important

mathematical skills that are useful to students, especially in the elementary stages. It

increases students' confidence and prepares them to complete their course without obstacles

or difficulties. Several countries, including the United States of America and Jordan, have

promoted this skill by recommending that it be provided to students in schools.

Ma'abrah also recommends that teachers should consider presenting the study

material in sophisticated and innovative ways, for example in using cameras, data projectors

or video films as tools to explain the lesson in a simple way by audio and visual means at the

same time; children are the most responsive to this method. The verbal method alone is not

enough to convey the information in the desired form; when synchronizing the verbal

method with the visual one, it will reach the students in a simpler way, leading to a deeper

entrenchment in their minds. In addition, teachers should consider employing the

connecting method, as memory is a network of cells that helps students understand terms

and concepts. Thus, when presenting any information, it must be linked to something real, or

concepts already explained before, and the teacher should be aware of the extent of

interaction of students, and choose the appropriate method for each of them.

Concentration should be on teaching the strategies, skills, and methods of thinking

that are needed to solve any equation correctly, which creates independent students who

rely on themselves. Likewise, classroom discussion and dialogue are of vital importance; that

is achieved via open questions, interviewing students until the right answer is reached and

the desired ideas are discovered, whether through critical thinking or yes/no questions.

Journal of Computer and Education Research Year 2019 Volume 7 Issue 14 496 -514

Thus, "consistently engaging students in these routines can change student's dispositions

about mathematics" (Coe, 2018, p.34). In addition, Ma'abrah claims that providing swift

corrections for classwork is essential; when students are asked to solve a worksheet or an

assignment in mathematics, it must be corrected within a short period of time with the

proper answers and comments. Collective learning is also important, which is manifested in

the students' interaction with each other, such as asking a question in class, with each

student writing down his/her answer, and then discussing these answers with each other.

Besides, offering moral support to students is critical, which is achieved by encouraging

phrases which raises their morale at the same time. Classroom conversation and discussion

is an essential means through which students' difficulties and common mistakes can be

discovered.

Method

Life stories expose the significance and subjective interpretation given to his life by

an individual, and to certain events that occur during the course of his life (Plummer,

1995). In this research work I am trying to expose the teaching methods used by teachers of

mathematics in Arab schools in Israel, and to describe the emotional state of 48 pupils of

the Arab sector in Israel. Raising their personal stories is intended as information that can

be used as a parameter for the effective improvement of their experience in the school.

Location of the participants was carried out through personal acquaintance with their

teachers and parents who helped in finding additional research participants.

The collection of research data was done through semi-structured interviews

conducted with each of the participants alone in a study room in the school. Each interview

extended from half an hour to fifty minutes. The appointed time of the interview was fixed

in advance, and at the beginning of the meeting each pupil received brief information

about the subject of the interview and was asked to agree to its recording, with the

explanation that the research was anonymous and confidential. Agreement was given

verbally by the pupils, parents and teachers. The personal questions made use of the

narrative interview technique that allowed for the presentation of stories and film scripts

of a mathematics lesson that can explain the experience of pupils in the transition from the

intermediate to the high school level.

Journal of Computer and Education Research Year 2019 Volume 7 Issue 14 496 -514

Participants in the research included 48 Arab pupils during their first term in

different school stages (primary stage, middle stage, and high stage). All of them are of the

different socio-economic background. According to the report of their teachers, their

achievement in mathematics ranged in level from low to high (all the names of the

interviewees are fictitious).

Findings

In this section the findings of the interviews are presented in an attempt to

understand the methods the teachers applied in their mathematics lessons. The research

findings indicate five categories: application of constructive learning principles, use of a

variety of teaching and evaluating methods, differential teaching, use of digital tools and

applications, and evaluation for the sake of learning. In order to identify the teaching

practices that promote learning, the interviews in this research contained a central

question: What, in your opinion, are the types of teaching practices that promote

significant learning which the teacher has applied in teaching the subject you are studying?

Analysis of the students' answers to the above question was made according to a

previously described qualitative analysis. The categories were constructed from an analysis

of the content of the interviews with the students according to key words. The content

analysis which was collected from the interviews and classified into categories was based

on the professional literature. The findings of the question were compared to the literature

background and to other research studies.

Findings of the Interview Question

The content was received in answers to the question: What in your opinion are the

types of teaching practices that promote significant learning that the teacher applies in

teaching mathematics? This was based on a number of guiding questions. The categories that

were received after the content analysis present the teaching practices that promote

significant learning accompanied by examples.

Application of Constructive Learning Principles

Most of the students reported the non-application of the teaching practices based on

the principles of constructive learning. The students gave examples that showed the non-use

of the constructivist principles as described below:

Journal of Computer and Education Research Year 2019 Volume 7 Issue 14 496 -514

When Sam was asked, he replied that: "The teacher did not co-opt the students in the

independent construction of knowledge through investigation". Yusuf says that: " She does not give

the student an opportunity to take a significant part in the learning process in an active manner such

as participating in projects". Dani says that: "The teacher does not explain to the students why they

are learning a certain subject, for example, how is it connected to other subjects in daily life or in

future professions, and give examples from our real world". Tom says that: "The students are not

working on assignments in groups".

This finding was not supported by the document of the Ministry of Education (2018)

in which a number of pedagogical principles were defined for the promotion of significant

learning. One of these principles was the constructivist approach in which the learner builds

up his knowledge by himself through the use of active learning, group work, and relating to

relevant components. In addition, while he is learning, the student reflects upon his own

process of learning.

Use of a Variety of Teaching and Evaluating Methods

Some of the students noted the non-use of various teaching methods in order to

promote learning. The students answered as follows:

When Avi was asked, he replied that: "The teacher does not bring examples to the

classroom and only draws on the board or solves problems". Sara says that: "There are no concrete

mathematical presentations in the lessons". Sami says that: "The teacher does not mark homework

assignments". Hadi says that: "The teachers do not mark homework assignments in a thorough

manner".

This finding was not supported by Harpaz (2014) who claimed that the fundamental

principles of teaching which allows for learning is the use of indirect teaching methods such

as mentioned above which increase active involvement in the building up of knowledge and

the creation of understanding by the student himself.

Differential Teaching

Differential teaching is teaching that is adapted to the personal characteristics and

unique abilities of the student. It is also one of the procedures on which the students

reported. The lack of concern for differential teaching was expressed in the following

sentences:

Journal of Computer and Education Research Year 2019 Volume 7 Issue 14 496 -514

When Tome was asked, he replied that: "I feel that the lessons on mathematics do not

make sense to me, I do not understand mathematics, and the teacher does not pay attention to me".

Amer says that: "Lessons in mathematics are difficult; the teacher begins the lesson by solving

examples and no one understands what he is doing". One of the students noted that (Badre): "I am

trying to understand the study material at home, and my parents help me to understand it".

According to Keller (1983), the approach of adapting teaching to the characteristics

and abilities of the students is one of the ways that makes learning more relevant to the

student. Relevance in learning is one of the three main principles of significant learning that

was declared in the document of the Ministry of Education (2018).

Use of Digital Tools and Applications:

A number of students emphasized that the teachers do not use digital tools in

mathematics lessons. One of the students said:

When Omar was asked, he replied that: "The teacher does not even activate the computer

in the classroom even though there is a computer and a screen in it during the lesson". Another

student Taha stated that: "The teacher sometimes uses the computerized display but she reads the

formulas from it and we do not understand anything".

This finding was not supported by the professional literature which stresses the need

for using technological tools for promoting significant learning. Ashburn and Floden (2006),

in their book Meaningful Learning Using Technology, emphasize that technology acts for the

learners like an intellectual partner who helps them to advance in thinking, learning and

understanding the world in which we live. Learning with the help of technology will

promote significant learning if it is based on the involvement of the learners in the

construction of knowledge; on dialogue; on self-expression of the knowledge acquired; on

the use of reflective thought. All this is achieved through the processes of learning that

include, among other things, visualization.

Evaluation for the Sake of Learning:

Some of the students emphasized that the teachers use evaluation only in the

examinations at the end of the semester. Examples from the answers of students who stress

this importance are as follows:

When Alex was asked, he replied that: "The teacher always gives homework and does not

mark our answers, and if he marks them he does not say why they are not correct. He does not give

us examinations to know if we know the material or not". Another student Ana stated that:

Journal of Computer and Education Research Year 2019 Volume 7 Issue 14 496 -514

"The teacher always asks questions during the lesson, but if we do not answer correctly he becomes

angry and does not like insults".

This finding is not supported by Harpaz (2014) who claims that the fundamental

principle of evaluation allows for significant learning through rich feedback, which is

continuous and mediating. It is rich because it gives the student detailed information about

his achievements and failures; it is continuous because it is done throughout the learning

process (not only in examinations); it is mediating because it is also derived from the product

that the student creates (not only from the direct evaluation of the teacher). The document of

the Ministry of Education (2018) also emphasizes the importance of continuous evaluation

which gives teachers and learners information about the development of the learning process

and allows for significant feedback in evaluating learning during its process and afterwards

in order to make decisions on the improvement of teaching.

Conclusions

This study highlights the strategies that are used in schools to teach mathematics. It

stresses some innovative strategies to teach mathematics and examines whether they are

applied in schools or not. The strategies are divided into five subcategories. The results of the

interview revealed the low applicability of the included strategies in classrooms. The study

concluded that more attention should be paid to the strategies employed in teaching

mathematics, and technology. Also, innovative and modern strategies should be considered

in schools because they proved advantageous in teaching mathematics. Moreover, this study

concludes that the load of mathematics curricula is to be reconsidered, and the priority

should be students understanding of mathematics via exploiting various means and

employing modern technological innovative strategies in teaching mathematics.

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... There are many articles (1)(2)(3)(4)(5) which focus on innovative ways to teach mathematics in schools. The main focus of these studies is on finding shortcomings in ongoing practices and use of technology to make them more effective. ...

... However, these studies lack in suggesting alternate ways of teaching specifically topic wise. In the article (1) ,it is recommended that the teaching process should be interesting to attract students by adopting creativity in teaching strategies, but they do not provide examples from daily life taking into account the surroundings of the learner. The studies (2)(3)(4)(5) recommend different innovative methods and approaches for learning, like building students' hard and soft skills through innovative teaching approaches to mathematics, employing pretest and post-test experimental designs to analyze the contribution of innovative teaching, use of smart gadgets for different tasks like teaching, designing question papers, assessment of student, feedback and research methodology. ...

... Using technology for achieving educational goals, making learning more effective, efficient or enjoyable (Algani, 2019;Goodyear & Retalis, 2010), has become understood as Technology-Enhanced Learning (TEL) -an approach that is based on integrated knowledge about technological applications (how a certain technology works), subject matter knowledge (concepts that could and should be taught with this technology), and teaching strategies (how to teach with this technology). According to Goodyear and Retalis (2010) TEL technologies can be categorized as follows: ...

  • Janika Leoste Janika Leoste

Technology-Enhanced Learning (TEL) innovations are sometimes difficult to be sustainably implemented. Based on the TEL innovation of Robomath (enhancing math learning with educational robots) I suggest that a TEL innovation process passes on the teachers' level through three distinct stages (Awareness, Acceptance and Adoption) where the odds of the innovation becoming sustained in teachers' practices are influenced by various sustainability factors. I propose the TELIP (Technology-Enhanced Learning Innovation Process) model and suggest that by following the TELIP model it is possible to improve the chances for a TEL innovation to become permanently implemented in teachers' classroom practices.

... Every class of plants looks like the same but each grows differently and gives different products (Abenti, 2020). For this reason, individuals who are successful in a field of education can be successful in all fields, and should be replaced by the opinion that individuals can be successful in different fields (Abenti, 2020;Algani, 2019;Al-Zoubi & Al-Adawi;Doğan, 2019). Multiple intelligence theory, which advocates that multiple intelligence fields can be used for individuals to develop different strategies for teaching and learning, helps teachers to learn by using the active learning model in their lessons and to make students learn by doing (Estrella, 2016;Shearer, 2004). ...

In this research, it is aimed to introduce the teaching process related to the mathematics course designed according to multiple intelligence theory and to evaluate the students' opinions about the teaching process. Action research design was used in the research. Purposeful sampling method was used in the research group. The research group consisted of 18 students attending a high school. As a result of the evaluation of the observation forms applied, the students developed materials and activities related to their own intelligence areas related to trigonometry. The interview form was analyzed with descriptive analysis method. As a result of the research, it was determined that the students stated that the lessons were more fun and they learned the subject more easily with the activities designed according to multiple intelligence theory. It was concluded that the students learned by doing by themselves because they prepared the materials themselves, they participated in the classes more actively but the application process took too much time and the learning environment was noisier.

... The teacher makes a very big contribution to enrich the thinking style of his students. Yousef Methkal Abd Algani (2018;2019a;2019b), in his articles speaks about the impact of teacher on learning mathematics and its relationship with learning patterns and thinking styles and the fear of mathematics among students and about increasing their motivation to study mathematics. He pointed to the strong relationship between difficulties in mathematics and the thinking style, which leads to a fear of mathematics and math tests which he sees as a cycle: Ritual Learning Difficulties in Mathematics Math Anxiety Ritual Learning. ...

  • Rajadurai Rajkumar Rajadurai Rajkumar

Technologies for Mathematics education and help learning become more social and engaging for students. So that the Internet and other technologies have transformed nearly every aspect of our society, particularly in the scientific and commercial sectors, yet classrooms of today appear largely. This contrasts with students' experience outside of the classroom, as evidenced by the explosion of the innovative teaching methods and learning strategies, where interactions and learning have increasingly become collective products rather than individual efforts."Smart classroom, Flipped Classrooms, Virtual Classrooms, Blended Learning, Mobile Learning, Personalised learning" in the technology infrastructure to facilitate cooperative learning that leverages physical and semantic spaces to achieve innovative mathematical pedagogical formats. Keywords: Smart Classroom, Flipped Classrooms, Virtual Classrooms, Blended Learning, Mobile Learning, and Personalised learning.

The reported research attempts to trace possible reasons for third grade learners' limited progress in numeracy in a low socioeconomic status (SES) South African context. This is done through two lenses, both stemming from Sfard's commognitive (The term "commognition" has been offered by Sfard (2008) as an amalgam of "cognition" and "communication," thus expressing the unity of these concepts. Since its original appearance, some authors (including Sfard herself) have preferred using the word "communicational" to describe Sfard's framework. We chose to stick with "commognitive" because we believe it clearly points to the specific theoretical stance presented in Sfard (2008), whereas "communicational" might point to many other theories or frameworks that have something to do with human communication.) framework. One lens aims to analyze two learners' (Mina and Ronaldo (all names are pseudonyms)) mathematical and identity discourse both in one-on-one interviews and in a small group "math club" lesson led by the second author. The other examines the mathematical milieu in which these learners have participated through the analysis of a school mathematics lesson which exemplifies prevalent instructional practices in this milieu. Relying on the distinction between ritual and explorative participation, we show that while Mina was acting in an extremely ritualized manner, Ronaldo was more explorative in his actions. However, the milieu, as seen in the school lesson, encouraged almost exclusively ritual participation. Thus, while Mina was identified as a good student, Ronaldo was identified as an outcast or "troublemaker." We conclude by drawing implications to the tenacious nature of rituals in the mathematics classroom and the effects that these rituals may have on students' identities.

  • Einat Heyd-Metzuyanim Einat Heyd-Metzuyanim

This study uses a new "communicational lens," which conceptualizes the activity of learning mathematics as interplay between "mathematizing" and "identifying," in order to study how the emotional, social, and cognitive aspects of learning mathematics interact with one another. The proposed framework is used to analyze the case of Idit, a girl who started out as a high achiever in 7th grade math and ended up failing that same subject in 9th grade, complaining of severe "mathematics anxiety." This paper traces the narratives endorsed by Idit's parents and teacher, which form the background for the development of her ritual participation in mathematical discourse. Next, it attempts to link Idit's ritual participation in a course taught by the author with Idit's eventual failure in mathematics. The mechanism behind this failure is conceptualized as a vicious cycle that thrives upon the basis of a ritualistic discourse motivated mainly by grades and other instrumental motives for learning mathematics. The analysis of this case gives rise to a model of how mathematical identities of failure may develop hand-in-hand with the failure to learn new mathematical skills.

One of the most important uses of manipulatives in a classroom is to aid a learner to make connection from tangible concrete object to its abstraction. In this paper we discuss how teacher educators can foster deeper understanding of how manipulatives facilitate student learning of math concepts by emphasizing the connection between concrete objects and math symbolization with, preservice elementary teachers, the future implementers of knowledge. We provide an example and a model, with specific steps of how teacher educators can effectively demonstrate connections between concrete objects and abstract math concepts.

  • J.A. Michael
  • Harold Modell

The working model for "helping the learner to learn" presented in this book is relevant to any teaching context, but the focus here is on teaching in secondary and college science classrooms. Specifically, the goals of the text are to: * help secondary- and college-level science faculty examine and redefine their roles in the classroom; * define for science teachers a framework for thinking about active learning and the creation of an active learning environment; and * provide them with the assistance they need to begin building successful active learning environments in their classrooms. Active Learning in Secondary and College Science Classrooms: A Working Model for Helping the Learner to Learn is motivated by fundamental changes in education in response to perceptions that students are not adequately acquiring the knowledge and skills necessary to meet current educational and economic goals. The premise of this book is that active learning offers a highly effective approach to meeting the mandate for increased student knowledge, skills, and performance. It is a valuable resource for all teacher trainers in science education and high school and college science teachers. © 2003 by Lawrence Erlbaum Associates, Inc. All rights reserved.

Feedback is one of the most powerful influences on learning and achievement, but this impact can be either positive or negative. Its power is frequently mentioned in articles about learning and teaching, but surprisingly few recent studies have systematically investigated its meaning. This article provides a conceptual analysis of feedback and reviews the evidence related to its impact on learning and achievement. This evidence shows that although feedback is among the major influences, the type of feedback and the way it is given can be differentially effective. A model of feedback is then proposed that identifies the particular properties and circumstances that make it effective, and some typically thorny issues are discussed, including the timing of feedback and the effects of positive and negative feedback. Finally, this analysis is used to suggest ways in which feedback can be used to enhance its effectiveness in classrooms.

Applying creative skills in teaching math at the primary school stage

  • Y Algani

Algani, Y. (2018). Applying creative skills in teaching math at the primary school stage. Journal of International Economy and Business, 6, 26-33.