Framework

Values in mathematics classrooms refer to the values in the teaching and learning of mathematics in the context of classrooms and values which are implicit or explicitly embedded in the curriculum, textbooks, and anything related to the teaching and learning of mathematics. The construct is categorized into general education values, mathematics education values, and mathematics values.

General education values are qualities which are not directly involved with the knowledge of mathematics or mathematics education, instead it focuses on developing good characters in man. These are values associated with the norms of a particular society and also the practices and system of the educational institution (Bishop, 2008). These values help teachers, schools, culture, society and students in character building of a good man. The ethical values include good behavior, integrity, obedience, kindness and modesty (Mark, 2016). For example, the topic on time discussed in class, may include the discussion on importance of appreciating time, the meaning of appreciating time that respecting other people’s time. The general education values are values which are very much influenced by the norm of a certain community, in particular the institution of education.

The Hierarchy Model of the General Education:

1. Basic values: Foundation principles of life where faith and religion play a big role where the concept of God and His relationship with His creation (the world and mankind) (Al-Ghazali, 1996). The opposite values to the basic values are values which are against the shariah and Allah and not believing the existence of God and religion.
The value indicators:
1. attention to values – interested and pay attention to aspects of values
2. respond to values – react to all values demonstrated
3. evaluate values – direct and indirectly assessing values
4. build values and act out values – display (act out) and being consistent with the value system chosen.


2. Core values: These are the basic guides to each individual in life, are also described as the akhlaq by Islam (Al-Ghazali, 1992). Concomitant action on the part of man to behave in accordance with the suitable requirements of what have been recognized (Naquib, 1997).
The value indicators:
1. fulfilling life needs ethically - excellent personality for example is being shaped and developed according to the necessities in life
2. fulfilling safety needs ethically - bravery is developed in respond of wanting to be safe and secured.
3. wisdom - developed as a reaction to the social, emotional, self-achievements and purifying the spiritual and the physical challenges in life
4. justice - The harmonious condition of things being in their right or proper places


3. Main values: These are the primary value system which can be seen through individuals’ characteristics and personality like cleanliness, truthful, trustworthiness, sincere, respectful, integrity, loyal, humble, moderate, thankful, steadfast, tolerances and diligent. Characteristics such as dishonesty, bribing, bad thoughts on others, looking down at people, treacherous, pride, arrogant, not serious, are values to be avoided.
The value indicators:
1. Discipline - Abiding rules, discipline, norms, or codes of conduct are important in performing activities in mathematics classrooms
2. team work - Performing tasks together, helping and needing each other
3. accountability - Performing duties with full responsibilities, justifying one’s action and performance, taking responsibilities.
4. innovativeness - Able to try and introduce new ways of doing something, bold enough to try new ideas, and being a pioneer in one’s own field, are important values in mathematics classrooms.


4. Expanded values: The expanded values are combinations of two or more of the basic, core or main values and contains worth of knowledge, success of perseverance, importance of quality, virtue of precision (Nik Azis, 2009a). The greater the amount of self-discipline and effort in the individuals the higher the level of perfection one would attain as one progresses in life.
The value indicators:
1. culture of knowledge - Love of knowledge where thoughts, decisions and actions were in accordance with knowledge, always in the process of getting updated knowledge, and always being challenged intellectually are important values in performing mathematics activities in the classrooms.
2. culture of diligence - Prosecuted with careful attention and effort; careful; painstaking; not careless or negligen
3. culture of quality - Put quality as priority in work, have clear standards, and have realistic key performance indicator, are very important when doing activities in mathematics classrooms.
4. culture of precision - Prioritizing the virtue of precision in decision making, thinking, knowledge, explanation, and judgment is very important in mathematics classrooms.
5. culture of integrity - Honesty, efficient, truthful, consistent, transparent, open mind, and trustworthy are important in the context of mathematics classroom

Mathematics education values refer to the values which occur during the processes of teaching and learning mathematics. Classrooms situations are multi-dimensions, dynamic, and complex and values in mathematics education involved several different aspects. These values refer to values which occur during the teaching and learning in mathematics classrooms which are generally motivated and supported by teachers, textbooks, and school culture. Besides being very dynamic, classroom situations are also very complicated and multi-dimensional making it very important to pay attention to.

The Hierarchy Model of the Mathematics Education Values:

1. Teaching values: Values which are the foundations of the teaching of mathematics. Teaching Mathematics - can be utilized not only through the teaching and learning activities but they can be embedded into other classrooms activities such as assessment, evaluations, homework, textbooks, softwares and lesson plans. It is also important to be able to understand what to stress on when one is performing mathematics representation, reasoning, relation, or communicating Nik Azis (2009). The values also include accurateness, clarity, making conjectures, consistency, working systematically, flexible in thinking, diligent, creative, check the working, following procedures, neat and following the regulations of certain algorithm.
The value indicators:
1. theoretical values - teaching mathematics with the main intention that student can understand higher level mathematics later.
2. utilitarian values - teaching of mathematics which focuses on daily utility and application
3. functional values - teaching of mathematics to encourage students to build sophisticated mathematics for specific usage.
4. internalizing knowledge - teaching of mathematics to fulfill the responsibility toward the Creator, oneself, community, and the environment.


2. Learning values: Values which are the foundations or the psychological of learning mathematics.
The value indicators:
1. behaviorism - memorizing, drilling, doing lots of exercises, skills, and receiving knowledge.
2. Cognitivism - more into sharpening of thinking skills, information processing, meta-cognitive thinking, and problem solving.
3. Constructivism - who actually build and develop the knowledge
4. Integrated perspective - mastering of skills, problem solving, constructing knowledge, developing and internalizing knowledge

Mathematics values rise from the way mathematicians and mathematics educators develop the discipline of mathematics based on different culture setting. These are values produced by mathematicians who have grown up in different cultures (Bishop, FitzSimons, & Seah, 1999). All aspects of values contexts were given duly attention and being constructed and developed in an integrated manner based on the faith and believe in Allah. The universal integrated perspective believes that values in mathematics can be taught in an implicit or explicit manner, however, for the pupils to obtain them it needs to be constructed. The implication is that teachers’ role are limited to preparing suitable activities, provide encouragement, portray examples and assist students to experience the constructions of mathematics knowledge efficiently.

The Hierarchy Model of the Mathematics Education Values:

1. Ideological: Values which underlie the epistemology of mathematical knowledge
The value indicators:
1. Empiricism - Empirical experience, applications of mathematical ideas, analogy thinking and manipulation of concrete materials are important values in mathematics. Teachers encourage her pupils to develop their ability in expanding the idea of mathematics by concretizing and using the symbol, model, figures, tables, graphs to collect empirical data.
2. Rationalism - Mathematical knowledge based on intellectual arguments, hypothetical reasoning, logical analysis, theory and logical thinking when making explanations and conclusions is important in mathematics classrooms. Teachers normally would use the mathematics ideas, allow arguments, encourage thinking logically and stress on hypothetical reasoning.
3. Pragmatism - Mathematical knowledge which focuses on reflections on information to assist in problem solving and social interactions among individuals in managing mathematical ideas, is an important value in mathematics. Mixture of both the rationalism and empiricism values.philosophical of Islam - the combination of empiricism, relational and spiritual, in which the knowledge of mathematics is based on beliefs in God and a tool to surrendering oneself to God.


2. Sentimental: Values which are concern with the relationship between individual and mathematics.
The value indicators:
1. Control - Activities involving rules, prediction and mastery are able to provide a sense of control, confidence, security and stability are important values in mathematics. Situation where there are rules to be followed, able to predict results or procedures, able to apply ideas to situation within the environment. The complementary of control is progress. This value involves the activities involving abstraction and generalization in understanding knowledge.
2. Developmental - development mathematical knowledge through generalization process, deep understanding, usage of alternative theory, scrutinizing existing ideas and development of new ideas and methods, and integration of mathematical knowledge with religion.
3. Civilization - Values focusing on spiritual discipline, cognitive, and physical that allows individuals to identify and place mathematics at the right position to create harmony and justice within oneself and community, are important values in mathematics. The effort of fulfilling responsibilities to God, nature, society and oneself through developing of self-discipline and appreciating superior civilization


3. Sociological: The customs, institutions, rules and patterns of interpersonal behavior values which are concern with the relationship between society and mathematics.
The value indicators:
1. Mysterious - Astonishment, admiration, mystery, and being abstract towards mathematics where human involvement is minimal are important values in mathematics. Wonders, mystifying, wonderful, and surprises in the quest of learning mathematics.
2. Openness - public verification of mathematical ideas by proofs, articulation, sharing of ideas and demonstration.
3. Integrated values - Mathematics knowledge is from God and given to man through construction of knowledge and only turned into meaningful knowledge when individuals acquire meaning through intuition or inspiration is important mathematics values. Encourages exploring the mathematical knowledge by utilizing facts, procedures, mathematics criteria, development mathematical knowledge through generalization process, deep understanding, usage of alternative theory, scrutinizing existing ideas and development of new ideas and methods, and integration of mathematical knowledge with religion