Developing Algebra Structure Module and Model of Cooperative Learning Helping Concept Map Media for Improving Proofing Ability

This research was purposed to develop module and learning model and instrument of proofing ability in algebra structure through cooperative learning with helping map concept media for students’ of mathematic major and mathematics education in State University and Private University in North Sumatra province. The subject of this research was the students’ of mathematic and mathematics education in Medan State University and Qualitye University. Developmental Research that oriented on developing product at stage and first year was done identification of proofing and positive behavior on algebra structure based on curriculum and was developed module and model cooperative learning with helping concept media map. The result that got at the first stage was the formula of proofing ability and positive behavior on algebra structure with first module and model cooperative learning assisting concept media map that assumed effective, efficient in algebra structure. Module and model of this learning consist of the book of lecturing guiding (lecturing unity schedule, lecturing contract, and lesson plan), module, and book of students’ assignment.


Introduction
Proofing is the main characteristic from mathematical activity that done from since students sat in Elementary School until in the University.This thing was said explicitly in school curriculum so that the students have mathematic competent in forming the ability of arranging prove, that is students of Elementary School and Junior High School to arrange the prove inductively, though students of Senior High School arrange the prove inductively and deductively.
Process of proofing of mathematic on grade the university the form of more formal and more accurate than by proofing in elementary school and Junior high school (Lee, 2004), that is by using deductive method, that is implication, contradiction, contraposition, or prove directly, this thing is very difficult to understand by students, it means that indicate that the ability of proofing need to be a special pay attention and to be key of process in learning.Algebra structure is one of subject need to get a special attention, to remember this subject is one of the subject that join in group/class analysis of mathematic and algebra that have pure and abstract behavior, that is one of the subject that encourage maximal proofing ability.As one of subject from pure mathematic, concepts that consist of inside it commonly are definition, axiom, and theorems that consist on hierarchy.
From the researcher's experience through taking this subject algebra structure shown that many students that feel mistake in processing the prove, for example for proofing the form of implication: if A ⊂ B so B c ⊂ A c.So many students that use B c ⊂ A c for proofing the above problem, even though the form of B c ⊂ A c that will be proved.
From the result of research from Muliono and Syafari (2009) also indicated that was not so far different, many students that did not understand the requirements of grouping from the association, for example H = {a ∈ G | a x = x a, ∀ x ∈ G}, it means that can be seen when it is asked what is the requirement's to be group of association of H? The understanding of the concept is the most important thing in processing of proofing.
To be observed from students' ability, the concept error like the above case is very big probability because of the minimum of requirements knowledge that owned of students, the behavior of students that less of interest/motivation in learning the material, and the students often just keep silent and afraid to ask the questions, The above result pointed that either the good module or proofing ability tests exactly to measure what should be measured based on the taught material.Thus also with reliability test degree that high so that it pointed that either learning equipment's or proofing ability test will produce the same result (ajeg) when it done repetitively.It is supported by opinion of Arikunto (2013) that stated that a valid test and reliability indicate consistent and ajeg from its test, furthermore it said that a test has measured what should be measured, and it will produce the same that ajeg though it done repetitively.Beside that it got some inventions in designing the module and proofing process, they are: 1) In learning activity between group, many students that difficulty in using implication concept (if....so...).
Students do not understand the use of correct score from implication concept and part association concept.
For example: problem if A ⊆ B so B C ⊆ A C .Almost of the students are not able to prove the above problem.They still use the concept B C ⊆ A C however the concept will be proved.However after he given including direction with new implication concept some students can understand the above problem.
2) In equivalent relation concept that is: if f is an equivalent relation association at H association S and a∈S so [ a ] = {x∈ S | (a, x)∈ f } called equivalent class that include a.Most of the student felt difficulty in determining grouping from equivalent class that include a.When it asked who is group from [a}?Most the student are not able to answer, however when the concept included by real life context, for example S association of the students learn algebra structure subject and furthermore asked is the possible group [a] the people in the outside?They are able to answer from [a] is member from S. Furthermore the next questions how is member S? Finally they realized and most of the student are able to answer correctly.
3) The students still difficulty in understanding on concept Center from group G written Z (G) = {a ∈ G | a x = x a, ∀ x ∈ G}.The symbolization from Center concept still very difficult from the student, they do not understand who is member of Z (G).However when the lecturer take the concept in daily life, for example association of G student is following the algebra structure lecturing, then the question who is member of Z(G), there are students do not answer member of G, then the next question continued how is member of G? Almost of all students cannot answer, finally with some helping from given the student cannot answer.Many students felt misconception at the above concept, the students realize that the concept is implication or implication two ways, however when it is in processing proofing concept the students are not able to use two kinds.However after they given explanation that two kinds are close kinds and invers kinds (two of four kind group) already can start the proofing process.
5  Some cases in the above showed that proofing ability that is the main characteristic of mathematic activity for graduate students (S-1) mathematic education was still big problem.So many students still felt difficulty in understanding algebra concepts that are abstract, so that the lecturer need to give an assisting with including the concept in the real context that include in daily life, it designed in forming learning module.Beside it interacted between students and students and between students and lecturer gave positive contribution in doing maximal students' understanding, so that it needs to pay attention.In that process proved many students that assisted in understanding the concept.It is suitable with Arends's opinion (1997) that said that learning cooperatively can be benefit between students with low achievement and students with high achievement that work together in academic assignment, the student can be higher can be colleague's tutor of student's low ability.The benefit of learning cooperatively also supported by the result of research Saragih (2000) that the result that cooperative learning approach in learning algebra structure can help students' understanding either low group or high group.
The including between one concept and another concept also become to pay attention, many students that felt difficulty in understanding concept that abstract and more commonly, for example mutation concept that consist of bijective function, group concept with subgroup, center, and centralizer, kernel or core, isomorphism, and so on.In understanding the concept that more abstract will be easy if the students can understand the simpler concept, all of this need to include and in understanding to the concepts needed concept media map.It is supported by Novak's opinion Novak (1985) that stated so that meaningful learning in cognitive structure students must be any relevant concepts, if there is no new information can be taught memorizing, it can be done with helping concept media map.The benefit of concept media map and students interaction in learning also supported by the research Syafari andSaragih (2001, 2003) that stated that happened minimization and revision misconception students in learning transformation geometry and real analyze through remedial learning by using concept media map and colleagues tutor.

Conclusion
This research concluded they are: 1) From the try out validity tested got learning module in algebra structure subject that consist of seven learning activities and twenty eight formulate the proofing ability that said that valid and have high reliability.
2) Learning model with cooperative approach assisting concept media map by using module can increase the proofing ability.

Suggestion
This research suggested they are: 1) To the lecturer of education mathematic major though another major expected can design learning module in every own subject.
2) To the lecturer mathematic education major though another major expected can design and apply learning model with cooperative approach expected can design and apply learning model with cooperative approach with assisting concept media map in every own subject.
3) To the lecturer mathematic education especially in algebra structure subject though another subject that have analyzed characteristics expected can design the instrument of proofing ability.

4)
Concept the subgroup below: a subset H that is not empty of group G, *  si subgroup of G if and if only: a. ∀ a,b ∈ H so a * b ∈ H ( First Axiom of group definition ) b. ∀ a ∈ H so a -1 ∈ H ( fourth Axiom of group definition) have been said valid by validator and the result of try out in the field pointed the same result that is all the tests have validity and reliability with high category.
) It the same thing with applying subgroup concept: association H that part finite and not empty from group G. H subgroup of G if H contain close kind.Part of the students are not able use the concept subgroup H subgroup, when it fulfilled H association parts are finite of group G, they do not realize that with using Cayley table and fulfill close kind have been enough to conclude that H of subgroup G. 6) Understand the Kernel concept or core of ρ, with ρ is a homomorphism of • , is concept that still difficult to understand by most of the students.However after they drawn a diagram like in the below and some questions they can understand members of association I(ρ) = { a, e} 7) Cycle concept that is: ρ is mutation of association A, said Cycle if ρ has many 1 orbit that contain more than 1 element.Many students that felt difficulty in understanding Cycle concept, however after they given some examples and not example the student have already understood.Furthermore they given assignment for making mutation example that is Cycle and not Cycle.8) Understand and apply concept subgroup of a theorem that sound as: H is part association that finite and not empty of group G. H subgroup of G if H fulfilled close characteristic.Most of the students are not able to understand and apply the concept in processing problem finishing, for example: pay attention group Z 8 ={0,1,2,3,4,5,6,7}.With Cayley table can be observed associations part of H 1 = {0, 4} and H 2 = {0, 2, 4,6} is subgroup of Z 8 .It is not a little students that prove with showing four characteristics of group at association H 1 = {0,4} and H 2 = {0,2,4,6}