Posted at 11.30.2018

Content

- Effectiveness of teaching mathematics using Real-life context on spatial ability and problem-solving capability at supplementary level
- Need and need for the study
- Objectives of the study
- Hypotheses developed for the study

- Methodology of the study
- Design of the study
- Sampling procedure
- Sample for the study
- Selection of content
- Procedural information on the study
- Development of lesson plans
- Tools developed/used for the study
- Implementation phase
- Analysis of the data
- Effectiveness of educating mathematics using Real life-context (TMRLC) on spatial potential in Mathematics.
- Table 1: Frequencies and percentage of students' responses on spatial capacity test
- Table 2: Descriptive statistics of pre spatial capability in mathematics
- Table 3: Descriptive information of post spatial capability in mathematics.
- Table 4: Results of descriptive information regarding spatial
- Ability and gender.
- Effectiveness of teaching mathematics using Real Life-Context on problem-solving capacity in mathematics:
- Table 5: Descriptive reports of post problem-solving potential in mathematics
- Table 6: Results of descriptive information regarding problem
- solving potential and gender.
- Major results of the study
- Discussion
- Educational implications of the study

Effectiveness of teaching mathematics using Real-life context on spatial capacity and problem-solving capacity at extra level

Abstract

In the present study an effort was made to study the effectiveness of teaching mathematics using True to life framework on spatial potential and problem fixing ability at extra level. This area of research has been of extensive interest to teachers who have realize that the best goal of education is program of what is learnt at institution in life. It had been expected that students learn better when given autonomy and when their ideas are respected. This plan provides all the expected features including hands-on-experience, experiential & significant learning in a real life setting up (framework). The analysis utilized pre -test post-test control group experimental design corresponding the communities on intelligence. Test consists of 32 students with equal number of boys and girls in both experiment and control categories. The studies of the study are: 1. Coaching of mathematics using real life-context was found to be a highly effective strategy in increasing the spatial ability and problem-solving capability in mathematics of students. 2. There is absolutely no factor in the spatial potential and problem-solving potential in mathematics of students with respect to gender as an effect of coaching of mathematics using real life-context.

"One of the chief triumphs of modern mathematics is having found out what mathematics is really".

-Bertrand Russell.

Mathematics is the topic around which the rest of the subjects move. "The subject of mathematics has been attaining importance and playing significant role in school curriculum". Furthermore it is the fact that subject matter which is most readily useful for an illiterate, as its knowledge is utilized in all day to day activities. Earlier were the times when the classes studied mathematics for disciplining their imagination, the public depended after mathematics because of its utility in everyday activities. The quantity system was developed to enable the individuals deal with large numbers. The origin of geometry itself lies in the practical issue of demarcation of areas after floods almost annually in Egypt.

Mathematics has performed a decisive role in accumulating our civilization. But in doing so, it has additionally made itself essential for the life and progress of modern world. In the modern world, we must be more and more exact, make larger use of quantitative terms, and have to be appropriate to a split second. All of this requires large computations and minute mathematical understandings. Whenever a farmer throws a stone to operate a vehicle away the birds eating his super fruit, he is implementing a 'reach or miss' method. If one rock misses he can simply try another. But the throwing of 'Apollo' in space to attain the moon could not be such a very simple hit or neglect. The multimillion dollar project is much less easy to lose as a stone. In cases like this right amount of thrust in rockets, accuracy and reliability with time and angle of launching, shape to provide bare minimum friction etc. , were required. How to get these values lies in the site of higher mathematics.

In today's social setup, mathematics is very much important for the common man. In this get older of rates, taxes, insurance, premium, cost savings and interest, rents and propaganda, only a person with good mathematical backdrop can be sensibly sure that he is getting his credited.

Mathematics hasn't only been useful in its own right but it has also enriched this world by assisting in the development of other domains of knowledge such as physical sciences, anatomist, social sciences, economics, psychology, logic, viewpoint and fine arts. Mathematics offers a contribution in the field of aesthetic appreciation. Experience with rhythm, percentage, balance, symmetry and so forth are essentially numerical and are basic to certain areas of appreciation, which can be of course immediately linked with our daily life activities.

The Country wide Curriculum Framework (NCF)(2005) speaks about the reorientation of the curriculum towards addressing the 'higher goals', which will make better use of that time period that children spend in school in conditions of the situation resolving and analytical skills it develops, and in preparing children to better meet a wide variety of problems in life.

National Council of Mathematics Instructor says that the target is "for everyone students to become ever more able and prepared to engage with and solve problems". The challenge for professors is to find ways during mathematics teaching for students to activate in thinking critically and creatively.

The NCF highlights that part of mathematics such as spatial thinking aren't developed enough in the curriculum. In addition, it questions 'what can mathematical education do to activate the mind of each student, and how do it strengthen the student's resources?

Spatial ability identifies skill in perceiving the visible World, transferring and modifying first perceptions, and emotionally recreating spatial areas of one's visual experience minus the relevant stimuli. Several categories of spatial abilities may be recognized. Spatial orientation is the capability to keep track of objects or locations in space even after a rotation or movements to a new location; spatial conception involves identifying spatial relationships regarding gravity or one's own body in spite of distracting information; and spatial manipulation entails the ability to mentally turn two or three-dimensional results rapidly and accurately.

Spatial abilities develop, partly when children manipulate and explore objects and environments. Generally, there is commonly a strong romantic relationship between how well one functions on verbal responsibilities and non-verbal jobs. However, many people are more skilled in a single area than another, and some researchers argue for recognizing and valuing people's strengths with different ability. Spatial understanding is very important to achievements in many areas, including mathematics, spelling, punctuation and capitalization, mapping, understanding time, sketching, copying, buying, changing point of view, and handwriting. These skills require spatial knowledge of quantity, direction, period, condition, location, and size, way of movement, collection and size. Thus school skills rely significantly on root spatial understanding.

Mathematics also takes a great deal of spatial skill coping with principles like place value, signs or symptoms (x & +), borrowing and department. Fractions are realized as a visual part of a complete. Algebra required a tight adherence to sequential guidelines while working through multiple-step problems, the effective math's student keeps the spatial image of an formula like a controlling scale, carefully treating each aspect of the formula during problem fixing. Geometry requires spatial understanding of angles, certifications, diagrams and the logical order of proofs time is spatial; it requires understanding ordered sequences such as times of the week, months of the entire year and conditions.

Keeping all the above concerns in mind if we go to your regular school room, we find that almost all of the above factors are not by any means practiced. As well as the NCF is directing out that children should learn in their own style i. e. , they have to build their own knowledge, which is in fact not happening since there is absolutely no such provision in the school. A proposed solution is teaching mathematics using real life-context strategy. Thus an effort was made to study the effectiveness of this innovative strategy with the factors test anxiousness, spatial ability and problem-solving potential, which includes been mainly emphasized by NCF (2005).

Traditional teachers are concerned only with the demonstration skills neglecting the student's degree of understanding and involvement even though various methods like laboratory method, project method, breakthrough method, heuristic method and various models like concept attainment model etc. were launched. Mathematics is actually trained monotonously and children are unaggressive listeners in the context.

Michael (1997) has discovered that emphasis should be given on the use of activities to teach which has the to activate student's curiosity triggering them question. Jeffery and Linda (2003) conducted a study of science and mathematics students, which revealed dissatisfaction over learner-centered instruction. The analysis was geared to improve the use of learner-centered education. The real reason for it was the setting of teaching this content only as a theory rather than in practical viewpoint, even though the key purpose of getting educated is to use whatever is learnt through formal education in resolving their problems.

For case, if we have a strategy in mathematics, like areas, how many children are able to find the area of their house where they you live? Whether it's a 30 x 40 site, how many of these are in a position to say that its area is 1200 sq. feet. Though they solve problems related to finding the area of your square or a rectangle etc. nonetheless they are not in a position to relate it to their daily life.

Because of these reason i. e. the method employed by the professor, mathematics is regarded as a difficult subject by the students. In mathematics, understanding is essential instead of other themes where rote learning or 'general prattle' is enough. Nonetheless it is regrettable that students are today learning mathematics through rote memorization. Pupil considers mathematics as theoretical and abstract but still it is very tightly related to to the "real world".

The National Council Teachers of Mathematics (NCTM) in 1989 came out with a comprehensive statement of objectives for pupils to attain. Five broadly stated objectives will be the pursuing, pupils need to:

Learn to value Mathematics.

Become confident in their capability to do Mathematics.

Become mathematics problem solvers.

Learn to speak mathematically.

Learn to reason mathematically.

Each of the aforementioned named objectives is pertinent for pupils in kindergarten through level twelve, and beyond, through one's life-time. To value mathematics methods to leave pupils feel it is important in school and in society in an ongoing way. The use of mathematics and functional in the each day situations, individuals face problems involving number.

Any mathematics curriculum and its own transaction become important and fruitful only once students are able to apply at least some of the mathematics principles in their lifestyle. Quite simply, they should be able to analyze and solve such problems.

In this way, framework based teaching and learning of mathematics helps it be more important and creates a concrete idea about the subject. Context based teaching and learning is a brain-compatible system of instructions that generates meaning by linking academic content with this content of students' daily life to bolster students understanding of mathematics and broaden their perspectives. Context teaching and learning is an instructional system, which is dependant on the idea that interpretation emerges from the partnership between content and its own context. Context offers indicating to content. The broader the contexts with in which students have the ability to make connections, the greater meaning content will carry for them. An excellent part of the instructors' job then is to provide context. A lot more students are able to connect their educational lessons to this context, the greater meaning they will are based on these lessons.

Contextual coaching and learning engages students in significant activities that help them connect academic studies with their framework in real-life situation. By making these relationships, students see indicating in schoolwork. When students formulate assignments or identify interesting problems, when they make options and agree to responsibility, search out information and reach conclusion. When they positively choose, order, coordinate, touch, plan, investigate, question and make decision to attain objectives, they connect educational content to the context of life's situations and in this way the students discover meaning of the ideas. The breakthrough of meaning is the central feature of CTL. Asked to learn something that seems meaningless, students seen invariably to ask, "Why do we have to learn this?" Rightly they look for so this means for significant and goal, in their schoolwork. Their quest for interpretation is natural. Based on the distinguished Psychologist Viktor. E. Frankl (1984), "Man's main concern is never to gain pleasure or to avoid pain but rather to see a interpretation in his life". Neuroscience confirms the brain's need to find so this means. Whenever we are asked to do something we have not done before, immediately we try to recall whether we've experienced anything similar. The mind tries to hook up the new activity with activity it recognizes. After the brain finds the meaning, its physical framework changes as it creates neurological contacts (Gem and Hopson, 1998; Greenfield, 1997).

Because the mind constantly seeks interpretation and retains the meaning, teaching should participate students as a visitor for finding meanings. Coaching should lead scholar grasp the non-public significance of the lessons they are really studying. As the renowned philosopher Alfred North whitehead said. "The kid should make them (ideas) his OWN, and should understand their program here and today in the circumstances of his actual life". Contextual coaching and learning (CTL) asks students to do just that. Since it invites students to make interconnection that reveal so this means, CTL gets the potential to interest all students in learning. The important characteristics of contextual teaching learning strategies are problem established, use of multiple contexts, pulling up on college student diversity, helping self regulating learning and utilizing genuine assessments.

Effective education must give clear emphasis to connecting true to life framework with subject-matter content for the college student, and this requires a more "linked" mathematics program. In many of today's class rooms, especially in secondary school and college or university coaching is a subject of putting students in class rooms designated "mathematics", and then attempting to fill their minds with facts through lectures, words books and the like. Aside from an occasional lab, work booklet, or "story problem", the component of CTL is absent, and little look at was created to hook up what students are learning with the entire world in which they'll be expected to work and spend their lives.

With this theoretical background, a study is planned to study the potency of educating mathematics using real life-context.

To study the effectiveness of educating mathematics using real life framework on spatial ability at secondary level.

To study the difference in spatial potential at supplementary level between children as an effect of teaching mathematics using real-life framework.

To study the effectiveness of instructing mathematics using real life framework on problem dealing with ability at supplementary level.

To review the difference in problem-solving capability at supplementary level between children as an impact of instructing mathematics using true to life context.

The coaching of mathematics using true to life context does have a positive result in the spatial ability at secondary level.

There is not a factor in the spatial ability at supplementary level between boys and girls as an impact of instructing mathematics using true to life context.

The teaching of mathematics using real life context does have positive influence on the problem fixing ability at secondary level.

There is not a significant difference on the condition solving potential at supplementary level between boys and girls as an effect of educating mathematics using true to life - context.

The present study is experimental in mother nature. The pre -test post-test control group experimental design was employed for the study. In such a design, subjects are allocated to the experimental and control group by complementing instances. This design is also called as "randomized control-group pre-test-post-test design". With this design, content are designated to experimental and control organizations by random methods and given spatial ability test and problem solving capability test in mathematics before and after the treatment.

The investigator conducted this review in Mysore city of Mysore area in Karnataka talk about. The Mysore city contains four zones particularly the North, South, East and Western zone. And out of these four areas only the western zone was considered for the study. In this area four private universities were picked by the investigator through purposive sampling. And RPM was administered for complementing the groups. Among the four classes, two schools matched exactly in terms of intellect of the students. Out of which Mysore west Sevanikethan Institution was designated as the experimental group and Manasarowar Pushkarani Vidyashram was given as the control group randomly.

The two preferred schools are similar with respect to the following reasons.

The educational standard and infrastructure facilities available in both academic institutions are moderate, so the influence of the procedure can be determined easily.

Both the institutions are following same syllabus (CBSE) and the medium of training (English).

The power of the class is similar in both schools.

Both the classes are situated in the residential area.

The teaching personnel is equally trained in both schools.

The investigator observed the classes of control group taken by the original teacher, so the traditional instructor is equally effective in educating with the investigator.

The sample consists of 64 students of 2 academic institutions i. e. , Lions Sevanikethan College and Manasarowar Pushkarni vidyashram in which the former was regarded as the experimental group and the later was considered as the control group.

Only one section was there in both institutions. Both these universities were matched up on brains test i. e. , RPM. 32 students each from both the groups were considered as the test for the study. Out of 32 students in both the groups, there have been 16 males and 16 young ladies.

For the goal of the study the investigator has gone through the entire text publication and picked the matters which gave scope for instructing mathematics using real-life framework. About 8 subject areas were chosen from 4 items namely profit and reduction, special types of quadrilaterals, area and quantities. The topics selected were Income and damage, Trapezium, Parallelogram, Rectangle, Square, Section of parallelogram, Level of a right circular cylinder and Level of a right round cone.

Lesson programs were made by taking into account of 4 E's- Exploration, Description, Expansion and Evaluation, where complete contribution of students was ensured. This lesson planning model meticulously follows the initial format of the science curriculum improvement review (1992), which is acknowledged with the best student achievement increases in major clinical tests and significant improvements in student knowledge attitudes and inquiry skills.

In the exploration stage instructors provide opportunities' for the students to explore through all appropriate senses and be fully involved. In the reason phase the instructor interacts with children to discover their ideas. Here the teacher's approach is to question skillfully so that students use the experiences of the explorations to construct scientific meaning. Inside the expansion phase professor helps the students to arrange their thinking by applying what they have just discovered to other ides or experience that relate with the lessons. Inside the evaluation phase professor evaluates the conception by examining changes in children's ideas and by their mastery of relating science and real life- contexts.

Raven's standard intensifying matrices

Problem-solving ability test in mathematics

Spatial ability test (a sub test of differential aptitude test)

The students of both experiment and control group were pre-tested on test anxiety problem solving capability test and spatial capability test.

The investigator has systematically educated 8 matters using real life context to the experimental group preceded by systematically planned and formatted daily lessons based on real life framework. The investigator got taken classes based on the ready instructional materials, using 4E's procedure. Students were given opportunities to take part in different type of activities. They were left absolve to ask questions & discuss things with one another and also with Investigator. The investigator used the ideas and remarks distributed by students as a topic for discussions. Through the experimental period the Investigator acted as a facilitator of learning, enjoyed an important role inside the classrooms. And in addition maintained a dairy where the daily observations of class room interactions were recorded. The classes were used regular math's periods of the school. Within the control group regular professor taught the students and covered the selected units about in the same number of periods.

After a difference of four weeks, students were post analyzed again on a single tools viz. , problem dealing with capability test, test nervousness scale, special capability test.

Total raw ratings obtained on Spatial capacity test were changed into percentiles and then to marks. Rate of recurrence of students, grades were computed and also 't' for both pretest and posttest were calculated and tabulated below.

From the desk 1 it is clear that in the pre test the number of students who obtained B & C marks was similar in amount in both groupings and also there have been no students which has a grade. While, in the posttest, a great improvement was within the experimental group. Two students of experiment group achieved A level where as none in the control group. Also the amount of students who acquired B grade in experimental was 10(32. 4%) and 3 participants (9. 7%) in the control group. Hence we can say that improvement was because of the context used by the investigator. To be able to learn if the difference is significant on pre spatial capability between experimental and control groupings suggest, standard deviation and't' ideals were determined and provided in the next table.

From the above mentioned desk 't' value obtained regarding pre problem-solving ability was found to be significant at 0. 05 level.

In other words it was discovered that there is a significant difference one of the students between the experimental and the control group. Because of this, pretest results were regarded as covariate to be able to nullify the difference. So to learn the effectiveness of TMRLC on spatial potential, the next hypotheses were created.

From the stand 3, it is clear that the F value for spatial ability is found to be 192. 870 which is highly significant. In other words, the test group achieved better than the control group on spatial capability test. Using real life-context an attempt has been created by the investigator to build up the spatial potential, which was found to work through the result obtained.

In order to check the hypothesis 4 the mean, S. D and 't' value is computed and tabulated below.

From the desk 4, it is clear that the 't' value for spatial potential with respect to gender is found to be 0. 030 which is not significant at 0. 05 level.

Thus regardless of the gender all the students have equally improved upon in the spatial capability. In other words this process is equally effective for both boys and girls. Similar results were found in the studies conducted by Christopher Edwards (2000) and parry (1999).

From the research of data gathered on pre lab tests it was discovered that there is no factor in the mean ratings obtained by the test and control groups which demonstrated their equivalence. For example the t value obtained on pre problem handling ability by the categories is 0. 224 which is not significant at 0. 05 level.

In pursuance of the target 1 of the analysis, and to test the hypothesis 1, indicate, S. D and 't' value were calculated and tabulated below.

From these table it is clear that the mean score obtained on problem-solving ability by experimental group (11. 21) is higher than that of control group (8. 13). It really is recognized by 't' value (3. 066) as found to be significant at 0. 05 level. This indicates a greater improvement among the list of students of experimental group in problem-solving capacity. Hence hypothesis 1 is accepted. That is contributed to the procedure distributed by the investigator.

This finding is concordance with the results obtained by Whitelegg & Parry (1999), Rennie & Parker (1998), and Abdul Samad. P. K (2005).

The above improvement may be contributed to the method utilized by the investigator. Where in the students were designed to relate the concepts with their daily life activities. While educating the idea of volume of a cylinder the students were made to list out its request in their day-to-day activities. In the end students started finding relevance in their studies and participated enthusiastically in the act of learning.

As the sample comprises of both children, the potency of teaching mathematics using real life-context with respect to gender was also discovered which is tabulated as follows.

From the desk 6, it is clear that 't' value for problem-solving ability regarding gender is found to be 0. 432 which is not significant at 0. 05 level. In other words, there is absolutely no significant difference in the problem-solving ability in mathematics between children as an effect of TMRLC. Irrespective of the gender all the students in experimental group have upgraded in their problem-solving abilities at alike.

1. Coaching of mathematics using real life-context was found to be a highly effective strategy in increasing the spatial potential and problem-solving ability in mathematics of high school students.

2. There is no significant difference in the spatial potential and problem-solving ability in mathematics of students regarding gender as an impact of coaching of mathematics using real life-context.

3. Teaching of mathematics using real life-context is equally effective for both boys and girls.

It is inferred from the above observations that teaching mathematics using real life-context at high school level is available to be very effective compared to that of standard method of instructing. Rennie & Parker (1996) have looked into the effective framework in math's problems by looking at the performance of math's college student on two sets of matched up problems, one set in place included problems inlayed in real life framework & other set included abstract problems regardless of real life event. They found that the student's performance better on the context wealthy problem & they found these problems more interesting. Similar finding was also found by the investigator in the present study. In the present research the experimental group was taught through real life-context and were examined for problem-solving potential and it was discovered that this group demonstrated a greater improvement in their performance as compared to the control group where they were taught through conventional method. The real reason for this may be the usage of various techniques, experiments and student initiative activities and complete involvement from the university student side.

Apart out of this students started out perceiving mathematics as a component and parcel with their life and even they experienced that they are deploying it in their day-to-day life. A number of the students portrayed that the technique utilized by the investigator was "Innovative, attractive, interesting wherein we're able to understand the application of mathematics in our day-to-day life". Most of them portrayed that after affecting themselves in this technique they have found mathematics as very interesting.

The analysis also unveiled that instructing mathematics using real life-context has better spatial ability one of the students. Spatial capability identifies skill in perceiving the visible world. Fennema and Sherman (1977) discovered that there is a significant relationship between spatial visualization and mathematics accomplishments and a noticable difference of spatial test performance through training of geometric skills. The results of this research go along with the result of the present analysis. Because the students were educated through various activities and firsthand experience like while instructing the idea of areas the students were made to measure the region of their playground, the school room area etcinevitably all these led to the introduction of spatial ability on the list of students.

From the above talk we can conclude that real life-context coaching is an efficient method of instructing mathematics.

1. It had been discovered that the coaching of mathematics using real life-context works well in improving problem-solving ability and spatial ability in mathematics. In this method learner learns the concepts or concepts by using contextual learning method where in the students perceive mathematics as a part and parcel of life. So this method can be virtually feasible to utilization in the institution to facilitate important learning one of the students.

2. This analysis also gives a picture of your innovative classroom where in the concern is given to students autonomy and real life-context teaching. This research paved a pathway for a wholesome classroom which contributes to healthy relationship among students and with instructors.

3. This method involves the contextual learning strategy unlike the traditional or activity methods. It does not require highly prepared apparatus, expensive laboratories, and huge infrastructure. This method is very much indeed suitable for the rural create combined with the cities.

4. The teaching of mathematics using real life-context will foster the creativeness amongst the pupils.

5. Training programs on real life-context teaching could be organized for pre-service and in-service instructors so as to develop an understanding and to equip them with the necessary skills for the successful implementation of this method in the classroom.

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