Critical Analysis Of Realistic Mathematics Education Essay

This essay is a critical analysis of Realistic Mathematicss Education ( RM untraditional manner utilizing existent life context to do a proper construct in pupils ‘ head for our subject. Coincident additive equation is besides a portion of National Curriculum of England for mathematics at cardinal phase 3 ( KS3 ) but usually schools start this subject in twelvemonth 8 and more formal use of coincident equation in twelvemonth 9. But I have decided to get down it in twelvemonth 7, so that pupils have adequate clip to develop algebraic believing decently. Our purpose is to familiarise this subject in such a manner that pupils feel comfort during work outing the system of additive equations.So I have decided to use unit Comparing measures examples from MiC text edition

Gender of the participant:

I have targeted my 15 pupils in the category of assorted gender and bulk of them are boys and there are merely 5 misss in the category. As Forgasz ( 2006 ) argues that misss are better academically over male childs in mathematics and Arnold ( 1997 ) states that “ there may be differences in the development of the map of encephalon hemispheres, and that linguistic communication development follows a biological ripening ‘timetable ‘ , where misss have a faster rate of advancement than male childs. ” ( Library, 2001, p.1 ) The same instance is here in our mathematics category, in all formative and summational appraisals the achieved consequences of misss are ever better than male childs. Since the figure of pupils is few in my category therefore I can easy concentrate on every pupil to accomplish my marks.

Social background of the participant:

All pupils are belonging to wholly different cultural backgrounds, acclaiming from Somalia, India, Pakistan, China, Morocco and Great Britain. So I can state that my category represents multicultural group. Half of the Somalian pupils have merely migrated from their state so they have terrible linguistic communication job and largely remainder of the pupils besides face the same job because English is non their place linguistic communication. Most of my pupils belong to the working category households and some of them are populating in councils ‘ houses. So their societal background is non strong. Huge chances of larning are non available to them. They ca n’t entree the installations like tutoring.

Algebra and its background

aˆ? Mason ( 1996 ) defines algebra and provinces that

“ The word algebra is derived from the jobs of al-jabr ( literally, adding or multiplying both sides of an equation by the same thing in order to extinguish negative/fractional footings ) , which were paralleled by jobs of al-muqabala ( deducting the same thing from or spliting the same thing into both sides ) . ” ( Wessels, 2009, p.16 )

Teaching algebra seems to hold been a coaching job since Ancient Times ( Radford, 2000 ) . Many researches are in procedure to do the algebra easy to understand for the students but still algebra is considered a difficult topic among the pupils

Traditional manner of instruction and larning algebra has been a large factor in death of its popularity. Lack of engagement of pupils during the category is a common image. It has been observed that it has reached such highs that pupils dislike algebra. In worst scenario they even are scared of it. Bertrand Russell writes in his autobiography

“ The beginning of Algebra I found far more hard, possibly as a consequence of bad instruction. I was made to larn by bosom: The square of the amount of two Numberss is equal to the amount of the squares increased by twice their merchandise. I had non the vaguest thought what this meant, and when I could non retrieve the words, my coach threw the book at my caput, which did non excite my mind in any manner ” . ( Kooij, 2001, p.1 )

At present the state of affairs is non different, still the pupils are go throughing out their General certificate of secondary education without proper apprehension of algebraic tools. In the consequence they have wholly incorrect perceptual experience of algebraic tools in the remainder of their lives and they are become the portion of formal traditional system. Algebra, which is a representative mathematical linguistic communication, must be apprehensible for pupils as it is of critical importance. Bing capable of work outing algebra can take the pupils to pull off acquisition advanced. Thinking logically and analysing accurately is a accomplishment that a good mathematician can develop easy. Mathematicss learning should advance students ‘ ability to work out jobs in many domains.The algebra comprises of following chief divisions that are variables, dealingss, map, equations and in equations ( inequalities ) , and graphs

The debut of system of equations?

“ Equations are mathematical statements that indicate equality between two looks. ” ( Wessels, 2009, p.18 ) .System of additive equations means more than one additive equations holding more than one variable. But here our mark is non work outing the equations ; our mark is merely to develop system of equations through comparing measures and associate them through existent life context. So that pupils can experience comfort while pull stringsing system of equation. It has been observed by the researches that bulk of the in-between schools pupils face jobs in understanding and work outing the algebraic additive equations ( Eric J. Knuth & A ; Ana C. Stephens ‘s et al. , 2006 ) .

Misconception of Equal mark:

Before presenting the coincident equations there are some issues and jobs which need to be discussed. The first and really serious job in twelvemonth 7 pupils in misconception of equal mark ‘=’.Since in National Curriculum of Mathematics algebra starts at twelvemonth 7 and at this phase pupils have no proper construct of algebraic symbols and the common job which are found in the probe is the incorrect perceptual experience of equal mark ‘= ‘ , As Stephens et Al. ( 2006 ) besides argues that “ many of the troubles that pupils have when working with symbolic look and equations may be attributed to their misconceptions about the significance of the equal mark. ” ( p.299 ) . Mexicia ( 2008 ) besides states that a common error among pupil is misconstruing the equal mark as a signal for making something, alternatively of taking that mark as an operator. Generally for pupils, the equal mark flashes a button in their heads to get down working on something instead than its ain entity as a “ symbol of equality ” or “ measure sameness ” .

Alibali et Al. ( 1999 ) argue that “ many simple and in-between school pupils demonstrate unequal apprehension of the significance of the equal mark, often sing the symbols as an proclamation of the consequence of an arithmetic operation instead than as a symbol of mathematical equality. ” ( Stephens et al. , 2006, p.298 ) . He farther explains by give an illustration from six grade pupils ‘ i.e. 8 + 4 = ? +5 ( Falkner et al. 1999 ) and says that it was found by Falkner et Al. that “ many pupils provided replies of 12, 17, or 12 and 17 – replies that are consistent with an apprehension of equal mark as denoting a consequence, pupils added all the Numberss in the equation or added all the figure before the equal mark, once more bespeaking an operational position of the equal mark ” ( Stephens et al.,2006, p.298 ) .

Use in day-to-day life

The existent intent of algebra instruction is to ease the pupils to utilize algebraic symbols or tools to assist in work outing the existent life jobs ( Wessels, 2009 ) . So it is necessary for the pupils that they have pilot cognition of all algebraic operations before pull stringsing the system of additive equations. Majority of the pupils at this degree have jobs to pull strings the system of additive equations. “ Graeber & A ; Tanenhaus ( 1993 ) says that “ It has been found from the legion surveies that when pupils are working on doing the algebraic equation they do non recognize the state of affairs modeled in the job when finding which operation to use, so they select the operation by thinking, by seeking all operation and taking one that gives what seems to them a sensible reply, or by analyzing such belongingss as the size of the Numberss involved. ” ( Schifter, 1999, p.63 )

Realistic Mathematics Education:

The development of the RME ( Realistic mathematics instruction ) evolved after 30 old ages of developmental research in instruction and larning mathematics in the Netherlands and is chiefly based on Freudenthal ‘s reading of mathematics as a human activity ( Freudenthal, 1973 )

Past Review

Realistic Mathematicss Education ( RME ) was the Dutch attempt to alter and reform the instruction of Mathematics all around the universe in 1970s. It was developed by utilizing extended research and chiefly applies the thoughts of three mathematicians Freudenthal, Treffers and Gravemeijer ( Autumn, 2003 ) .This theory was developed by Wiskos undertaking in Netherlands. The modern-day construction of RME is largely determined by Freudenthals positions on mathematics.

Two of its major points are

Mathematicss must be connected to world

Mathematicss should be perceived as a human activity. ( Zulkardi, 2002 ) .

Freudenthal positions on the method of mathematization were that students should be involved in guided reinvention of mathematics which in other words means that the students should develop their mathematical thought themselves same as mathematicians did before them, get downing with informal schemes and so bit by bit traveling to more formal schemes, so RME context is used to assist pupils to understand Mathematics which is in maintaining with Freudenthals theory about mathematics that it must be near to the existent life, furthermore the intent of doing it valuable for kids, mathematics should be related to the kids and finally be reflecting the society ( Carol Marshall, 2003 ) . Later on, Treffers ( 1978, 1987 ) gave the thought of two types of mathematization in an educational context and differentiated “ horizontal ” and “ perpendicular ” mathematization ( Zulkardi, 2002 ) Freudenthal ( 1991 ) divides the horizontal and perpendicular mathematization and depict them as

“ Horizontal mathematization leads from the universe of life to the universe of symbols. In the universe of life one lives, Acts of the Apostless ( and suffers ) ; in other one symbols are shaped, reshaped, and manipulated, automatically, comprehendingly, reflectingly: this is perpendicular mathematization. The universe of life is what is experienced as world ( in the sense I used the word before ) , as is symbol universe with respect to abstraction ” . ( Fauzan, 2002, p.39 )

Principles and Features of RME

The features of RME are historically related to three Van Hiele ‘s degrees for of acquisition

Mathematicss ( de Lange, 1996 ) . Here it is assumed that the procedure of larning returns

through three degrees:

A student reaches the first degree of thought every bit shortly as he can pull strings the known

features of a form that is familiar to him/her ;

Equally shortly as he/she learns to pull strings the interrelation of the features he/she will hold reached the 2nd degree ;

He/she will make the 3rd degree of believing when he/she starts pull stringsing the intrinsic features of dealingss.

Traditional direction is inclined to get down at the 2nd or 3rd degree, while realistic attack starts from first degree. Furthermore, by the guided reinvention rule and progressive mathematization pupils are guided pedagogically and expeditiously from one degree to another degree of believing through mathematization. These two rules and the construct of ego developed theoretical accounts ( Gravemeijer, 1994 ) can be used as design rules in the sphere specific direction theory of mathematics instruction.

Features or Dogmas of RME

By sum uping three Van Hiele ‘s degrees and Treffer ‘s modern mathematization and Freudenthal ‘s didactical phenomenology, Zulkardi ( 2002 ) describes five cardinal characteristics of Realistic Mathematics Education.

a ) The usage of contexts.

B ) The usage of theoretical accounts.

degree Celsius ) The usage of pupils ‘ ain productions and buildings.

vitamin D ) The synergistic character of the instruction procedure

vitamin E ) The intertwinement of assorted larning strands. ( Zulkardi 1999 )


Harmonizing to Gravemeijer ( 1994 ) for instructional design there are three cardinal rules of RME viz.

aˆ? guided reinvention through progressive mathematization,

aˆ? Didactical phenomenology

aˆ? Self developed theoretical accounts or emergent theoretical accounts.

Guided reinvention through progressive mathematization:

Harmonizing to the first principal of RME, students should be given the opportunity to pattern the same procedure by which mathematics was invented and a acquisition path has to be mapped out that help the students to happen the intended mathematics by themselves and the reinvention of mathematical construction creates when the pupils start to utilize the day-to-day everyday linguistic communication to do contextual jobs into good organized and formal mathematics form. ( Armanto, 2002 )

‘Mathematizing ‘ is a chief motion in RME and this activity chiefly involves generalising and formalising ( Gravemeijer, 1994 ) . Treffers ( 1987 ) defines the procedure of mathematization and provinces that formalising includes modeling, typifying, schematizing and specifying, and generalizing is to understand in a brooding sense and by work outing the contextual jobs in realistic attack pupils learn to mathematize contextual jobs. ( Fauzan, 2002 )

De Lange ( 1996 ) described the procedure of conceptual mathematization in RME and provinces that the procedure of developing mathematical constructs and thoughts starts from the existent universe, and at the terminal we need to reflect the solution back to the existent universe and in other words in mathematics education things are taken from existent universe, are methamitised and so brought back to existent universe. ( Fauzan,2002 )

Didactic phenomenology:

Freudenthal ( 1983 ) present the idea of didactical phenomenology which means that larning mathematics should be start from the existent life contexts which are meaningful for the students and it will actuate the pupils in larning procedures. ( Fauzan, 2002 ) .But existent life does non intend that merely context through world ;

Self developed theoretical accounts:

The 3rd cardinal rule by Gravemeijer ( 1994 ) for instructional design in RME is self developed models.This rule plays an of import function in doing a connexion between informal cognition and formal cognition. Harmonizing to it we have to give the chance to the pupils to utilize and develop their ain theoretical accounts when they are work outing the jobs. To get down with the pupils will develop a theoretical account which is familiar to them. After the procedure of generalising and formalizing, the theoretical account bit by bit becomes an entity on its ain ( Armanto, 2002 ) .

Gravemeijer ( 1994 ) describes “ this procedure a passage from model-of to model-for. After the passage, the theoretical account may be used as a theoretical account for mathematical logical thinking ” ( Fauzan, 2002, p.42 )

Misconception of ‘realistic ‘

There is a misconception about RME that its context are ever from existent life, it is non necessary ever ; it might be some fanciful narratives and thoughts to pull the concentration of the pupils towards the contextual job. Hadi, ( 2002 ) defines that existent universe is the universe which is outside the mathematics, it may be your school, your category or house or anything outside the mathematics. Gravemeijer ( 1999 ) explains the significances of world and provinces that

‘The usage of the label ‘realistic ‘ refers to a foundation of mathematical cognition in

state of affairss that are experientially existent to the pupils. Context jobs in RME do

non needfully hold to cover with reliable every-day life state of affairss. What is cardinal, is

that the context in which a job is situated is experientially existent to pupils in that

they can instantly move intelligently within this context. Of class the end is that

finally mathematics itself can represent experientially existent context for the pupils. ‘ ( Fauzan, 2002, p.42 )

Realistic mathematics instruction is non merely associate mathematics with existent life, it has proper regulations and rules under which we have to learn pupils.

Harmonizing to Feudenthal ( 1973 ) pupils should non be inactive receiving system ; they should be a portion of larning through contextualizing procedure for their cognitive development. “ In RME ‘real universe ‘ is the get downing point for the development of mathematics constructs and thoughts ” ( Hadi, 2002, p.32 ) . Learning mathematics means making mathematics, of which work outing mundane life jobs ( contextual jobs ) is an indispensable portion ( Armanto, 2002 ) . Freudenthal ( 1971 ) explicate this activity which is performed in RME is:

An activity of work outing jobs, of looking for jobs, and besides an activity of forming a capable affair. This can be a affair from world, which has to be organized harmonizing to mathematical forms if they have to be solved. It can besides be a mathematical affair, new or old consequences, of your ain or others, which have to be organized harmonizing to new thoughts, to be better understood, in a broader context, or by an self-evident attack. ( Fauzan, 2002, p.34 )

The construct of equal mark in RME:

As we have discussed that one of the issue related to algebraic system of additive equations is the misinterpretation of equal mark. Nicole M. McNeil ( 2006 ) besides argues that clear construct of equal mark is necessary for understanding the algebraic additive equation moreover it has been proved by the researches that if pupils have proper apprehension of equal mark so they have more possibility to work out system of additive equations right. The misinterpretation of the pupils can be resolved by utilizing RME, because as Zulkardi ( 2002 ) states that the first feature of RME is the usage of context so it can be possible that pupils can unclutter the construct of equal mark through context from existent life, Besides Alibali et Al. ( 2005 ) accent on the pedagogue to give more “ attending to the contexts and formats in which they are showing jobs because little differences in how jobs are presented can act upon what pupils come to understand about the associated constructs. “ ( NICOLE M. MCNEIL et Al. , 2006, p.383 ) . Furthermore Nicole M. ( 2006 ) put more emphasis on the instructors ‘ professional development and alteration in mathematical course of study and bettering the learning methods to convey the proper construct of equality mark in algebraic equations from contexts.

To get the better of this job some course of studies “ seek to offer pupils some aid to develop the algebraic thoughts and to get and do sense of marks. For illustration, in the new Ontario Curriculum of Mathematics ( Ministry of Education and Training 1997 ) , pupils are introduced to a sort of ‘transitional ‘ linguistic communication prior to the standard alphanumeric- based algebraic linguistic communication and are asked to happen the value of ‘ * ‘ in equations like: * + * + 2 = 8 or the value of ‘ a-? ‘ in equations like 32 +a-? + a-? = 54. This ‘transitional linguistic communication ‘ attack, as any pedagogical attack for learning algebra, relies on specific constructs about what marks represent and the manner in which the significance of marks is elaborated by the pupils ” . ( Radford, 2000, p 239 )

The construct of basic arithmetic operations in variables and invariables in RME:

During work outing the system of algebraic additive equations pupils have some misconception about the basic arithmetic operations in changeless and can take by actioning RME technique because the basic thing in RME is the context through existent life. During RME learning the instructor or teacher can utilize the context and easy work out this misconception.

Since in RME the first measure is horizontal mathematization, and to accomplish the first mark the pedagogue needs to do a realistic environment because harmonizing to Freudenthal ‘s didactical phenomenology realistic state of affairs is really of import to get down the development of mathematical constructs. Realistic state of affairs can be develop by pulling images on the white board or doing some narratives or physically choose some pupils to move. ( Heeley, 2008 ) show the pupils by an first-class manner to distinguish between variable and Numberss and their add-on. He puts some Numberss and some bananas in a jar and invites a male child to happen the variable and add them likewise the Numberss, he can easy happen out the bananas from the jar and individually add them, so this is the manner to unclutter the construct of pupils in variable and numeral Numberss ‘ confusion. There are a batch of other methods to acquire the attending of pupils in the category and heighten the pupil ‘s ability towards mathematics and harmonizing to Freudenthal ( 1973 ) pupils should be the active receiving systems non passives like other traditional categories.This is the best manner to increase the cognitive degree in the pupils larning. Kozulin ( 2003 ) besides in the favour of utilizing symbolic tools in larning and provinces that “ symbolic tools have a rich educational potency, but they remain uneffective if there is no human go-between to ease their appropriation by the scholar ” ( p.35 ) .So instructor ‘s professional development is really necessary in learning and larning through RME and it will be discuss subsequently.

The function of RME for work outing systems of equation:

As we have discussed above that existent context enhance the pupil ‘s ability and the acquisition purposes of this essay is is how to make system of algebraic additive equation with informal and pre-formal methods utilizing the strategy RME.

Corel ( 2003 ) show some illustrations of interchanging goods to develop the construct of equality and how to utilize system of equations in pupils ‘ head.Corel explain her personal experience of utilizing RME and finds a positive consequence in pupils ‘ advancement. She fulfills the first principal of RME and make a context through existent life by utilizing an fanciful narrative in image signifier and nowadayss it in forepart of pupils. In the illustration it is given that a husbandman has two sheep and one caprine animal. He wants to sell them and purchase some bags of wheat but when he goes to the market he finds that he can interchange his one caprine animal by six poulets and same for one sheep and one bag of salt is equal to two poulets. Similarly three bags of salt can be exchanged by two bags of wheat.

Harmonizing to RME regulations after making the realistic context, convert the job in mathematical symbols which is called horizontal mathematization. At this measure pupils should hold some basic cognition of the job. For illustration here they should hold some cognition of equality mark and variables ( as we have already discussed these issues ) . So first she introduce equal mark in algebra and named those things in algebraic notation say degree Celsius for poulet, s for a bag of salt, H for sheep, g for caprine animal and tungsten for wheat. So harmonizing to the inquiry

1g = 6c & A ; 1h = 6c & A ; 2c = 1s & A ; 3s = 2 tungsten

These are four equations which are found by given informations. Until this measure pupils can understand how to do the simple equation.Now the following measure solve the job in mathematical symbols which is called verticle mathematization. At this measure pupils need some supervising of any instractor or instructor.

So altogather the husbandman can exchage his caprine animal and sheep by 18 chicken.For 18 poulet we need to multiply both sides of 3rd equation by 9, because this is the regulation of algebraic equation if you multiply any figure on one side of equality you have to multiply the same figure on the other side as good. so the 3rd equation will go

9 * 2c = 9 * 1s

18 hundred = 9 s

As he has now 18 poulets so they are equal to 9 bags of salt.Now multiply 4th equation by 3 to acquire the reply i.e.

3s * 3 = 2w * 3

9 s = 6 tungsten

It means the husbandman can purchase six bags of wheat when he exchanges his one caprine animal and two sheep.

In this above illustration the pupils can larn three things in basic algebraic system of equation. The first thing is to understand the construct of equal mark and as 2nd how to change over the existent context in to algebraic term ( like variables ) and 3rd how to work out the system of equation to happen the needed consequence.

The Difference between realistic attacks:

The realistic attack Vs the mechanistic attack

In the conventional ( mechanistic ) manner of the acquisition procedure the instructors take control over each activity. In contrast, the RME attack suggests that the students are supposed to take duty for their ain mathematical acquisition and they should be actively engaged in synergistic treatment in the schoolroom. Guided by the instructor, the students reinvent informal and formal mathematics theoretical accounts in a procedure of mathematizing contextual jobs ( Armanto, 2002 ) .

Harmonizing to Heuvel- Panhuizen ( 1998 ) states that In the formal method of learning mathematics, the acquisition capable affair is divided into undistinguished little parts and the students are asked to work out these jobs by fixed processs and are trained by exercisings, often to be done separately. This formal attack to mathematics instruction, which besides rejects the mechanistic, is so a contrast to RME attack. RME has a more complex and meaningful conceptualisation of larning. Active engagement is expressed by pupils in teaching-learning procedure, in which they established mathematical tools and understanding instead than being the receiving systems of ready-made mathematics.

In this position mathematics instruction would be extremely synergistic in which the instructors would hold to construct upon the thoughts of the pupils. It means they have to respond based on what the pupils bring to the bow ( Kooj, 1999 ) .

There is merely one measure more in RME from other formal methods of learning mathematics and this is context from existent life. It is frequently observe that in formal instruction methods the instructor straight off start learning mathematical jobs without any debut from context of existent universe as freudenthal ( 1973 ) declares mathematics as human activity and should be connected to existent life, so every job in mathematics should be related to the existent life and before get downing the inquiries the pedagogue should be make the environment from context of existent life and so show it in forepart of pupils which in unluckily non go on in our formal methods of instruction. “ The leap to the formal degree is made excessively rapidly, and there is about no clip for pupils to develop their ain strategies. The traditional algebra class is seen as unfertile, disconnected from other mathematics and the existent universe ” ( Reeuwijk, 1995, p.1 )

Difference between word job and RME:

When we are speaking about RME, the first inquiries comes in our head about RME is this same like word job? Hade ( 2002 ) describes that in work outing word job it is necessary for the pupils to follow the precise regulations and ordinance, moreover pupils apply the symbols without reflecting the specific context

The contextual jobs in RME aid in construct formation by supplying the pupils an inducement and drive them with a natural attack towards understanding mathematics. These besides provide a cardinal rule and foundation for larning the mathematical processs, symbols, and regulations linked with the other theoretical accounts which act as of import assistance for thought.

Solving system of equations through Comparing Measures:

Our mark is to discourse the schemes for larning system of algebraic additive equation and to accomplish our end we are using different strategies of ancient Greeks and Chinese ‘s to work out system of additive equations presented by Reeuijk ( 1995 ) , Autumn ( 2003 ) and Kooij ( 2001 ) .

These are some basic schemes to develop algebraic believing.They make a span between pupil ‘s old arithmetic ‘s cognition and algebra. By using these schemes pupils can easy understand the tools of doing system of algebraic additive equations. Reeuijk ( 1995 ) called theses strategies a tool which is used to do a nexus between the concrete and the abstract. All strategies are the basic informal schemes for pull stringsing system of additive equation from the chapter ‘Comparing Quantities ‘ of Mathematicss in Context ( MiC ) text edition. An of import facet is that in unit Comparing quantities the thoughts are normally presented as a narrative and therefore the thought is to promote the students to work out the jobs in their ain ways i.e. developing their ain schemes. It has been noticed that by giving the jobs in a natural context, pupils try to utilize the thoughts that they may non hold learned by their instructors at school. At this degree more accent is on pre-formal methods and no formal algorithms are used because this unit is created for the11-12 old ages old pupils who start algebra for the first clip. The more formal form of coincident equations is used in following chapters of the text edition for the following categories. The strategy ( Reuwijeck,1995 ) mentioned four chief schemes __ conjecture and cheque, concluding, combination charts and notebook. .Reeuwijk ( 1995 ) presents an illustration is his paper, in which a diagram of two jerseies and two drinks is given and their monetary value is 44 $ .Similarly in another diagram the monetary value of 30 $ is given for one Jersey and three sodium carbonate H2O. Students are asked to happen the monetary value of one sodium carbonate bottle and one Jersey. This inquiry is looks like a typical word job but as we discuss above that the difference between simple word job and RME is the realistic context and here the context is in the signifier of images. The ‘guess and better ‘ scheme is commonly Figure 1. Structure of Comparing Measures.

( Reeuwijk,1995, p.6 )

used by pupils who have merely basic know-how of the topic. Largely low cognitive degree pupils attempted this inquiry by utilizing this scheme.

The 2nd scheme is concluding through exchanging, this strategy was used by ancient Chinese.It is same like swap system, Students took more involvement in this scheme.The other two strategies are notebook notations and combination charts. These strategy largely used by the pupils holding high cognitive degree. All above strategies are horizontal mathematization. Harmonizing to Gravemeijer ( 1994 ) realistic environment is really of import in the patterned advance of mathematical construct. First, there are many jobs in the universe that are required to be solved, subsequently students apply their mathematical tools to decide them realistically ( Reeuwijk, 1995 )

Reeuwijk ( 1995 ) states that one time pupils endeavor to work out the jobs by their ain informal ways, it was summarized together ( see fig.1 ) and pupils realize that all strategies are interrelated.Now the following measure in perpendicular mathematization.

Our purpose is to alter the traditional construct of algebra and usage context from existent life to do the proper construct of mathematics in pupils ‘ head. Our quandary is that algebra starts at KS3 in twelvemonth 7, so at this phase if we provide the proper apprehension to the pupils so they will ne’er see algebraic equations as a difficult subject. Reeuwijk ( 1995 ) present the above methods to make the sense of coincident equations in the early phase of about 11 old ages old. He uses these schemes and got a really positive consequence.

Harmonizing to Reeuwijk ( 1995 ) if we leave the pupils to let them doing their ain ways to work out the job with their old cognition of mathematics so pupils will utilize their head more and becomes the active participants of the

category and can easy understand algebraic term. Furthermore “ the non-statutory counsel to the National Curriculum states that students at every phase should be encouraged to develop their ain methods and students need to hold chances to develop informal, personal methods of entering and an attack in which students are required to utilize and use their development cognition and accomplishments leads to more effectual acquisition ” ( Antumn,2003, weblink ) as Freudenthal ( 1973 ) declares that the pupils should be an active receiving system in the category, so in this manner pupils will go an active participant in the work outing any job.Moreover this thing will helpful in their existent life job resolution. “ By discoursing and reflecting on the pupils ‘ usage of schemes, they start recognizing that formal schemes of a more general character exist. ” ( Reeuwijk, 1995, p.3 )

In RME a context plays the of import function, by utilizing context pupils prosecute by utilizing contextual jobs the direction is directed to the procedure of reinvention mathematical constructs through horizontal and perpendicular mathematization

Drawback of RME

There are some issues which are raised when we are working with RME.

RME is clip devouring strategy:

The first is that when we are learning by utilizing RME strategy it will take a long clip since the category timing is merely an hr and when a instructor program to learn this method it is surely impossible to understand all the trifles in a fixed period of clip

Teaching this method one time or twice a hebdomad will besides non assist the pupil along. The lessons should be precise and be given on day-to-day footing. The instructors should do certain that the pupils are connoting them practically every bit good.

aˆ?Professionally trained instructors are required to learn RME

aˆ?Are the pupils holding linguistic communication job? Can they understand the narratives or images? The pupils holding linguistic communication job should allow their instructor know about it so they can steer them at the right clip. The English usage in mathematics is simple, clear and concise


Differences in the acquisition and instruction activities made instructors reconsider their former personal thought and beliefs about instruction and acquisition mathematics. At the one manus they believed that the RME attack gave more chances for pupils to larn different schemes, but on the other manus

It seemed that the instructors were afraid to lose their respects as instructors. It is true that the RME attack is non the lone reply for learning all topics in the course of study. However, the RME attack will steer instructors toward a new significance of learning in general footings. Teaching is non for the trial merely, but should construct students ‘ apprehension and cognition of the topics ( cognitive spheres ) . It besides gives students chances to develop their attitude toward larning activities ( affectional spheres ) . These spheres are unusually indispensable to develop students ‘ attitude toward deriving cognition and larning new techniques. But the Netherlands experience shows us that altering from conventional to more realistic pattern will be a long and hard procedure ( de Lange, 1996 ) .