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Analysis of Instruments Measuring Values of Mathematics Education

Abstract

Research conducted in the affective domain of mathematics education found that affective variables such as attitude, motivation, anxiety, beliefs and values were strongly linked to the quality of teaching and learning of mathematics. Unfortunately values seem to receive the least attention although it is one of the most stable affective domains. This is due to the fact that most people viewed mathematics as value-free, where in fact it has various values related to it. This paper fills in the missing literature on values in mathematics, particularly in the area of values assessment in mathematics education. The literature review indicated the absence of psychometrically based instruments which adopted holistic well defined constructs in mathematics education between the years 1985 and 2012. The five related instruments were reviewed on definitions of constructs and sub-constructs, designs of instruments, theoretical bases, samples, validity and reliability processes. Definitions on constructs and sub-constructs were found to be mainly based on the western education philosophy and the definition by Bishop (1988) is the most referred to and used by researchers from Australia, Turkey, and Taiwan. Four out of five instruments used survey method to measure values in mathematics education. Targeted respondents were found to be mainly the pre-service and in-service primary and secondary mathematics teachers. Only two out of five instruments went through rigorous processes to enhance validity and reliability. This study is an initial step in developing instrument measuring values in mathematics education for the Malaysian education system which is based on faith and religion as stipulated by the National Educational Philosophy which is not aligned with the western culture. The paper proposed the model of instrument which is in line with the Malaysian Educational Development Plan.

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Procedia - Social and Behavioral Sciences 90 ( 2013 ) 449 – 457

Selection and/or peer-review under responsibility of the Faculty of Education, University Technology MARA, Malaysia.

doi: 10.1016/j.sbspro.2013.07.114

ScienceDirect

nternational Conference on University Learning and Teachin

InCULT 2012

alysis of instruments measuri ng values of mathematics

ati

Nik Azi

Nik Pa

Faculty of Education, University of Malaya, Kuala Lumpur, Malaysia

INTEC Education College, UiTM, Shah Alam, Selangor, Malaysia

tra

in th

aff

main

f math

mati

ati

n f

that aff

aria

h as attitude

tivation, anxiet

, beliefs and values were stron

linked to the

ualit

of teachin

and learnin

ath

mati

nfortunatel

alues seem to receive the least attention although it is one of

aff

main

Thi

hat most people viewed mathematics as valu

free, where in fact it has various values related to it. This paper fills

he missing literature on values in mathematics, particularly in the area of values assessment in mathematics education. Th

rat

re review indicated the absence of psychometrically based instruments which adopted holistic well defined constructs

n mathematics education between the years 198

2012

lat

finiti

onstructs, designs of instruments, theoretical bases, samples, validity and reliability processes.

finiti

onstructs were found to be mainly based on the western education philosophy and the

definition by Bishop (1988) is the

st referred to and used by researchers from Australia, Turkey, and Taiwan. Four out of

five instruments used survey method to measure values in mathematics education. Targeted respondents were found to be

ainly the pr

ervice primary and

econdary mathematics teachers. Only two out of five instruments went

hrough rigorous processes to enhance validit

and reliabilit

This study is an initial step in developing instrument measuring

alues in mathematics education for the Malaysian educati

n system which is based o

faith and religio

as stipulated by the

National Educational Philosoph

which is not aligned with

he western culture. The paper proposed the model of instrument

which is in line with the Malaysian Educational Development Plan

12 Th

Published by Elsevie

Selection and/or pee

eview under responsibility of

Faculty of Education, Universiti Teknologi MARA, Malaysia

Keywords:

alues, Mathematics Education, integrated perspective, instrument, assessment;

Ruzela Tapsir. T

7304

ax: 6-035-522-7109

uzel898@salam.uitm.edu.m

Available online at www.sciencedirect.com

Selection and/or peer-review under responsibility of the Faculty of Education, University Technology MARA, Malaysia.

Open access under CC BY-NC-ND license.

450 Nik Azis Nik Pa and Ruzela Tapsir / Procedia - Social and Behavioral Sciences 90 ( 2013 ) 449 – 457

1. Introduction

One of the fundamental problems in mathematics classrooms is that teaching is aimed at acquisition of

knowledge, giving minimum emphasis on the values in mathematics education (Bishop, 1988). This is because

mathematics has always been seen as a subject which is value free, a primary reason for the lacking of studies in

values in mathematics education (Nik Azis, 2009). Values which is taught explicitly rather than implicitly, is

actually a crucial component in enhancing qualities of mathematics teaching and learning (Seah, 2002).

Furthermore, these values were influential factors on teachers' and students' decisions and behavio urs related to

mathematics (Corrigan et al., 2004). In reality, mathematics is related to various values related to teachers and

students which effect their interest, thoughts, choices and behaviours towards mathematics education.

Motivation, attitude, and belief were found to be the popular affective topics in the field of mathematics

education while values were more or less ignored (Seah & Bishop, 2000).

The research on values in mathematics education started to pick up about a decade ago in areas such as

intended and implemented knowledge on values in mathematics education (Clarkson and Bishop, 1999), values

and culture in the context of mathematics classrooms (Clarkson et al., 2000), role of values in mathematics

education (Leu & Wu, 2000), awareness of the values associated with teaching mathematics (Fitz Simons et al.,

2000; Seah et al., 2001; & Bishop, 2002), mathematics teachers' pedagogical values clarification (Chin & Lin ,

2001), enactment and perceptions of elementary teachers' mathematics pedagogical values (Leu, 2005),

similarities and difference of values between mathematics and science teachers (Bishop, 2006, 2008a), practices

and norms in mathematics instructions (Atweh and Seah, 2008), teachers' mathematical values in developing

mathematical thinking (Bishop, 2008b), mathematics teachers as agents of values (Hoon, 2006), values in

mathematics textbooks (Dede, 2006a), values in learning functions (Dede, 2006b), professed and displayed

values in teaching mathematics (Lin et al., 2006), awareness and development of teaching values (Chin, 2006),

contexts in teaching to develop suitable noble values in mathematics education (Nik Azis, 2009a) and

mathematics values and teaching anxieties (Yazici et al., 2011). Locally, Habsah, et al. (2009) did a study

concerning the translation of the notion of secondary school teachers' belief and devotion to God into real

classroom, Rohani and Mohd Ariff (2010) investigated students' beliefs on their mathematics teachers att ribute in

mathematics teaching where Mathematics-Related Beliefs Questionnaire which was developed by Op'tEynde and

De Corte (2003) was used in the study, Wan Zah et al. (2005) explored the teachers' understanding, perceptions

and beliefs on mathematics values. Nik Azis (2009) did an extensive analysis of values from the universal

integrated perspective which is based on faith and religion. He productively and successfully produced a

framework for the hierarchy of values in mathematics education and even suggested a model for values

development.

It will be less meaningful for us to be adapting and using the existing instruments which were based on the

western education system. There is a dire need for us to have a strong determination in developing a holistic

instrument suitable for our education system which is ba sed on the National Philosophy Education of Malaysia.

This study can be the initial stage in developing the instrument to measure the said values. The instrument can

serve as significant diagnostic potential in which values of students and teachers can be identified. This is

especially important for teachers, since to have some insights into the way teachers understand and teach, one

needs to know their values about mathematics education and mathematics. An instrument of this nature could be

a source of data to assist in designing the curriculum and relevant training to educate mathematics teachers

regarding values in general education, pedagogy, mathematics education and mathematics. It can be a reliable

tool in evaluating the curricular reform effort in mathematics education.

2. Purpose and objectives of Study

The study reports on an aspect from the process of developing an instrument measuring values in mathematics

education. It is the initial stage of the development process where five related instruments were analyzed from

the aspects of: (a) definitions of values in mathematics education and its sub-constructs; (b) theoretical bases used

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Nik Azis Nik Pa and Ruzela Tapsir / Procedia - Social and Behavioral Sciences 90 ( 2013 ) 449 – 457

in discussing the definitions; (c) designs of instruments; (d) samples used for the study and (e) validity and

reliability. The five instruments discussed in this paper are the instruments to measure teachers' value preference

and practice (Bishop, 2006 & 2008), positivist and constructivist values (Durmus & Bicak, 2008 & Dede, 2009),

mathematical educational values (Dede, 2010), teachers' beliefs in mathematics education (Beswick, 2005b), and

perceived values of mathematics teachers (Luthrell et al., 2010).Thorough exploration of relevant information of

reliable sources from books, journals (including online journals), and proceedings were done for material dated

between the years 1985 to 2012. The paper proposed a model of an instrument to measure values which is in line

with the Malaysian Educational Development Plan.

3. Review of the Instruments

Out of the five instruments, all were accessible except for the instrument developed by Dede (2010). The study

found that the concept of value is lacking in terms of commonly agreed definition and is still open to discussion

(Nik Azis, 2009). Defining values is not simple, due to its multidimensionality characteristics. The five

instruments were found to be using different approaches in defining the values related to mathematics education.

The first definition of values pertaining to mathematics education which was proposed by Bishop (1996) was

related to the socio-cultural influences. It was defined as the deep affective qualities to be fostered through

mathematics education and categorized into the general education, mathematics education and mathematics

values (Bishop, 1996; 2001). Mathematics education values were conceptualized as complementary pairs such as

formalistic view and activist view, instrumental understanding and relational understanding, relevance and

theoretical knowledge, accessibility and special, evaluating and reasoning (Bishop, 2004). Mathematics values

on the other hand were thought as three complementary pairs of values to be balanced in the ideological,

sentimental and sociological aspects which were the rationalism-empiricism, openness-mystery and progress-

control values respectively (Bishop, 1988). Bishop did not offer detailed definitions on general education values.

He only suggested that these were values which assisted teachers, schools, culture, society and students to

improve themselves. These values were generally related to ethical values such as good behaviour, integrity,

obedience, kindness and modesty (Bishop et al., 1999; Fitz Simons et all., 2000).

Instruments designed by Durmus and Bicak (2008) and Dede (2009) measured mathematics education and

mathematics values following Bishop's definitions . However the values were discussed from the perspectives of

radical constructivism and categorized them into positivist and constructivist. The positivist values refer to

teachers' objectivity, control, mystery, accuracy, and clarity where the constructivists valued rationalism,

progress, openness, creativeness, enjoyment, flexibility, and open mindedness. The constructivist values were

interpreted as activities emphasized on student-centred learning in teaching mathematics and the positivist

favoured teacher-centred. This limited definition on constructivism do not consider the element of retrieving

prior knowledge and collaborating to acquire new knowledge, instead of focusing solely on students' needs,

abilities, interests, and learning styles, placing the teacher as a facilitator of learning.

Dede (2010) kept to Bishop's definition of mathematics and ma thematics education values to develop the

Mathematics Education Values Questionnaire. The mathematical values examined in the questionnaire are

rationalism– objectivism, control – progress, and openness– mystery. The mathematical educational values are:

formalistic view– activist view, instrumental understanding– relational understanding, relevance – theoretical

knowledge, accessibility– special, and evaluating– reasoning. Beswick used beliefs as the construct to define

values in mathematics education. She defined beliefs generally to be anything that an individual regards as true

and was likely to maintain among one's most central. In examining the connection between beliefs held by

teachers and their mathematics classrooms practices, th e nature of mathematics; teaching mathematics; and

learning mathematics were recognized as relevant. Three categories of beliefs in the nature of mathematics were

instrumentalist, Platonist and problem solving; three categories regarding mathematics teaching were content

focused with emphasis on performance, content focused with emphasis on understanding and learner focused.

Beliefs about mathematics learning were skill mastery, passive reception of knowledge, active construction of

understanding, autonomous exploration of own interest.

452 Nik Azis Nik Pa and Ruzela Tapsir / Procedia - Social and Behavioral Sciences 90 ( 2013 ) 449 – 457

Luthrell et al. (2010) studied the mathematics values from the perspectives of mathematics education. The study

was grounded in the expectancy-value theory of achievement motivation. This theory advocated that individuals'

choices, persistence, and performance were very much influenced by their beliefs on how well they will succeed

and the degree to which they appreciate that particular activity. The mathematics value aspects were viewed as

values that bear directly on a person's motivation for enga ging, persisting, and excelling in mathematics. They

categorized the constructs to be interest, utility, and attainment as task-related b eliefs that would increase the

value students placed on becoming literate in mathematics. Personal cost on the other hand is defined as beliefs

that would lead students to devalue mathematics literacy.

Discussion on the validity and reliability of the instrument designed by Bishop could not be found in the

literature. The instrument designed by Durmus and Bicak went through the process of enhancing face and

construct validity. Feedback from three subjects specialists were used to edit, discard or add items to the initial

pool of items drafted. Principal component factor analysis identified two main factors namely the constructivist

and the positivist for mathematics education values. Twenty (20) of the items were loaded to the sub-category of

constructivist and fourteen (14) were loaded to the sub-category of positivist. The number of items in the

questionnaire was reduced from 40 to 34 after a sequence factor analysis. Cronbach Alpha is used to measure the

internal consistency coefficient of positivist (0.64), constructivist (0.74) and the overall (0.73). The Pearson

correlation coefficient calculated between the positivist and constructivist sub-categories was found to be 0.20.

The Mathematics Education Values (MEV) instrument developed by Dede (2010) started with a pool of 52

items, in which the items were sent to two language experts who were fluent in both English and Turkish

language for the rigorous process of translating the items from Turkish to English and back into Turkish to

maintain consistency. The drafted questionnaire was evaluated by three experts in mathematics education,

educational measurement for openness, fluency, appropriateness of language structure, expression and relevancy

to confirm content validity. The items were revised based on the inputs provided by the experts where some

items needed to be rewritten but no items were deleted. The trial version was pilot tested to 30 pre-service

mathematics teachers where some items were identified as not easily being understood. The trial version was

edited and results were used to produce the experimental version which is called the Mathematical Educational

Values Questionnaire (MEVQ) and distributed to 107 pre-service teachers where the structural and predictive

validities were evaluated. Exploratory factor analysis was employed to identify both the sub-factors and

verification of the structural design of the questionnaire. Item analysis was used in order to verify the

instrument's predictive validity, explore whether individual items measured contributed to the total measure, and

check if items and sub-scales were sensitive to expected differences. The second item analysis compared the

difference between upper and lower performance groups and the sensitivity of the instrument. The 107 pre

service primary teachers respondents were divided into three groups based on the MEVQ scores which are the

top 27%, middle 46% and bottom 27% and the group differences on each sub scale were analyzed by a series of

one way analyses of variance (ANOVA) to determine the consistency of the difference and significance to

establish each sub-scale and item's ability to differentiate between high and low values.

Luthrell et al. discussed the procedure in enhancing the face, content, and construct validity in detail. He

referred the initial 88 items in the Mathematics Values Inventory (MVI) to five experts to improve the clarity of

the facets description of the constructs where items went through two rounds of item sorting where items were

edited, eliminated or adding new ones. After two stages of item sorting, 15 items were eliminated. The

instruments were tested with 38 students in which minimal corrections were made. The first large-scale item

tryout of the 70-item instrument were done on 944 non-mathematics major students where exploratory item level,

factor structure, and internal consistency analyses were done. Each item was evaluated for skewness, kurtosis,

and inter-item correlations where 39 items were eliminated. The normality test, principal components analysis,

factor analysis and Cronbach alpha were used to identify items with high structure correlation. The second large

scale item tryout was done to 1096 non-mathematics major students. Besides performing the factor analysis and

finding the Cronbach alphas, two hypotheses of gender-related differences in math value and reported relations

between task-related value and math participation were studied. The 5-point Likert scale instrument was also

tested for temporal stability over a 2-week period. A test re-test study on the 28 item instrument was also

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Nik Azis Nik Pa and Ruzela Tapsir / Procedia - Social and Behavioral Sciences 90 ( 2013 ) 449 – 457

executed to 55 undergraduate students who are majoring in liberal arts. A discriminate validity of scores of the

instrument against the Marlowe-Crowne Social Diserability Scale (MCSDS: Crowne& Marlowe, 1960) was also

analyzed. The paper discussed the validity and reliability in a rigorous manner. Beswickon the other hand only

shared part of the construct validity procedure using factor analysis, in which problem solving and instrumentalist

were revealed as the sub-constructs.

Four of the instruments used Likert scale and only Bishop used ranking and rating as the response format.

Likert scale is seen as the most suitable method in assessing latent construct like values. The conceptions on

values in mathematics education in these instruments were found to be based on the western education

philosophy which is based on the development of mathematics in the western culture influenced by secularism.

The conceptions of values in mathematics education used in those instruments were not parallel to the National

Philosophy of Malaysian Education (NPME) which focuses on the values, beliefs and attitudes in relation to the

growth process of individuals and society which determines the country's goals and objectives which is based on

belief in God as the first principle stated in the Rukun Negara (National Principles). At present, the only

conception on values in mathematics education which is based on spiritual and faith is the one proposed by Nik

Azis (2009). He viewed values in mathematics education from a holistic perspective where both the physics and

the metaphysics elements were being addressed. His idea is mainly based on the work by Al-Ghazali (1990) and

Syed Muhammad Naquib (1995). This is not parallel to Bishop who regarded all values

As relative and subjective and values were determined by human rational thinking or the society norm

without any standard reference besides ignoring the meta-physics aspects. Bishop represented values in

mathematics education as one's internalization and 'cognitization' of affective variables related to mathematics

knowledge, which is uniquely developed within a certain culture encompassing the societal, institutional,

pedagogical and individual levels. In this case the culture refers to the western education culture.

The instruments discussed were used to measure values on primary and secondary school teachers, pre-

service teachers, in-service teachers and general education students. Thus the studies of values' assessments have

not captured the vast majority of participants in mathematics education domain indicating a gap in the study of

values measurement among various levels of students and teachers. This situation is especially true in Malaysia

as there is currently no substantial research done on assessment in values in mathematics education. Another gap

found in this study is that the instruments available do not cover all aspects involving assessment of values in

mathematics. The obvious aspect lacking is the general education values related to values in mathematics

education which have not been covered in any of the instruments, suggesting lacking of a holistic instrument. The

table below summarized the findings from the literature search from the aspect of the theoretical bases,

definitions of values in mathematics education, constructs and sub constructs used, and the instruments' designs.

4. Future Directions for Measuring Values in Mathematics Education

In order to construct a holistic validated instrument with established psychometric properties which will be an

effective tool in evaluating the corresponding values within teachers and students of Malaysia, the definition of

constructs and sub-constructs chosen for the instruments must be based on a philosophy which is suitable with

the Malaysian education system. Instrument developed must establish psychometric properties to reduce the need

for redundant research design and can be applied across different samples and settings. It is time that

educationists accentuate the effort on developing instrument which is able to measure values in mathematics

education to assist students and teachers to gain their personal and social identities affecting choices they made

concerning mathematics and mathematics education.

The universal integrated approach refers values as co nceptions and beliefs of individuals concerning the

importance of something which act as general guides to their behaviours (NikAzis 2009) and discuss it from the

framework of "adab" in which all other concepts such as norms, ethics, moral and "akhlaq" are the sub -elements

in "adab", brought the definition of values in mathematics education into clear focus. In brief, "adab" refers to the

right action that springs from self-discipline founded upon knowledge whose source is wisdom (Syed

Muhammad Naquib, 1995). NikAzis's idea was based on conceptions definitions of values in education provided

454 Nik Azis Nik Pa and Ruzela Tapsir / Procedia - Social and Behavioral Sciences 90 ( 2013 ) 449 – 457

by Al-Ghazali and Syed Muhammad Naquib, advocators of holistic education. The definition provided basic

elements such as components of values, relationships of values with other relevant domains, the reality of values,

the source of values and the various contexts of values, making values to be very structured and organized.

In the context of classroom settings, values in mathematics education were categorized into the general

educational values, mathematical education values and mathematics values (Nik Azis, 2009a). Nik Azis detailed

out what have been suggested by Bishop from the perspective of universal integrated approach. From the

Hierarchy Categories of Values Model proposed by Nik Azis (2009), faith is proposed to be the fundamental

(values as guidance in life) followed by the core (values as necessity in life), main (values portraying oneself) and

development (self development values). The mathematics education values were divided into the values in

teaching and learning. Teaching was divided into theoretical, utilitarian, functional, and internalization where

values in learning included mastery of skills, information processing, knowledge construction and acquisition of

knowledge. The mathematics values were now being categorized as ideological, sentimental, and sociological

aspects. He further added to the rationalism and the empiricism from the ideological aspect suggested by Bishop

another two values which are pragmatism and integrated approach. The value of civilisation was added to

control and progress of Bishop's sentimental values and the value of integrated was added to the soc iological

aspects which consisted of mystery and openness.

This model assumes that all religions teach human beings to be good, making it imperative that religion is the

most important factor in enhancing our commitment towards values. To conclude, conceptual definition and

framework on values in mathematics education proposed by Nik Azis may be used to produce a holistic

instrument covering the three sub-constructs which are general education values, mathematics education values

and mathematics values suitable for the Malaysian education system which is based on faith and religion.

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Nik Azis Nik Pa and Ruzela Tapsir / Procedia - Social and Behavioral Sciences 90 ( 2013 ) 449 – 457

Table 1

Comparisons of instruments measuring values in mathematics education

Philosophical,

psychological, and

sociological

theory

Definition of values in mathematics

education

Constructs & Sub-

Construct

Rationalism and

Information

Processing

Social

constructivism

Bishop (2005)

Define values as the deep affective

quality nurtured through mathematics

education which is uniquely developed

within a certain culture encompassing

the societal, institutional, pedagogical

and individual levels.

Mathematics Values

Rationalism-Empiricism

Control-Progress

Mysterious-Openness

Mathematics Values

Instrument

point Likert scale

9 questions on values

emphasized.

9 questions on

frequency of

activities

Ranking

12 value items rank

for preferences

Durmus & Bicak (2008) and Dede (2009).

Followed definition by Bishop

Mathematics

education:

Formalistic view-

Activist view

Instrumental-relational

Theoretical knowledge-

Relevance

Accessibility-Special

Evaluating – Reasoning

Mathematics Values

Rationalism-Empiricism

Control-Progress

Mysterious-Openness

(Positivist values

Constructivist values )

Mathematics Value

Scale

14 positivist items

and 20 constructivist

items,

5 point Likert scale

Mathematics

Education Values

Questionnaire

52 items, 5 points

Likert scale

Beswick (2004, 2005b, 2007)

Beliefs as anything that an individual

regards as true and are likely maintained

among one's most central

Nature of mathematics

Instrumentalist

Platonist

Problem solving

Beliefs about

mathematics teaching

Beliefs about

mathematics learning

Teachers' Beliefs

Survey

Beliefs Survey

(26 items,

5 point Likert Scale)

Expectancy-value

theory of

achievement

motivation

Luthrell et al. (2010)

Mathematics value aspects as covering

those values that bear directly on a

person's motivation for engaging,

persisting, and excelling in mathematics.

Interest

Utility

Attainment

Personal cost

Mathematics Values

Inventory (MVI)

(28 items)

5 point Likert Scale

Notes. (*) indicates instrument not available.

456 Nik Azis Nik Pa and Ruzela Tapsir / Procedia - Social and Behavioral Sciences 90 ( 2013 ) 449 – 457

Acknowledgement

The research was supported by INTEC Education College, Shah Alam, Selangor, Malaysia through the High

Impact Research Grant.

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... Desarrollo de un instrumento para evaluar autoconfianza en estudiantes de farmacéutica Fuente: Adaptado de Wongwiwatthananukit et al. (2002) Si bien es perceptible una visión rigurosa en lo metodológico, también se observa una independencia del diseño del instrumento mismo de la comprensión del posterior diseño didáctico. En el campo de la matemática Pa & Tapsir (2013), señalan que es necesario pensar en "construir un instrumento holístico validado con propiedades psicométricas establecidas el cual sea una herramienta efectiva para evaluar los valores que expresan tanto profesores como estudiantes del área" (p. 453). ...

... En general, se establece que los estudios que muestran el diseño de instrumentos se ocupan de un sólo aspecto relacionado con el aprendizaje como autoconanza (Wongwiwatthananukit et al., 2002), valores asociados a lo disciplinar (Pa & Tapsir, 2013), habilidades de pensamiento (Ngang, Nair & Prachak, 2014) y habilidades sociales (Tapia-Gutiérrez & Cubo-Delgado, 2015), para mencionar algunos temas. Parece ser una constante en este tipo de investigación sobre los instrumentos asociados a procesos curriculares y didácticos, que el n especíco es desarrollar el instrumento para medir algo, obtener validez y conabilidad u obtener escalas de medición. ...

Con el ánimo de contribuir al desarrollo de las didácticas de campos disciplinares de la educación, este artículo propone instrumentos para validar ambientes didácticos de aprendizaje (ADA) en el contexto de formación de profesores de lenguaje y comunicación (LyC) en y para la diversidad. En el marco de una arquitectura para validar ADA, se sugieren instrumentos para validar diseños didácticos construidos desde la teoría del diseño así como la inteligibilidad mutua, rectora de las comunidades de práctica que forman profesores de LyC. El resultado, es una batería de instrumentos cualitativos y cuantitativos que tienen como función valorar el ADA en dos momentos: como diseño planeado y como diseño en acción.

... In the literature, there are several studies on values in mathematics education. Some of these studies address the measurement of mathematics educational values (Durmus and Bıçak, 2006;Dede, 2009;Luttrell et al., 2010;Liman et al., 2013;Pa and Tapsir, 2013) the examination of mathematical values in mathematics course books (Cao et al., 2006;2006b) and similarities and differences between the values of mathematics and science teachers Bishop, 2008). Studies on mathematical and mathematics educational values in Turkey are in limited number and their samples consist of preservice teachers attending the faculties of education or in-service teachers (Durmus and Bıçak, 2006;Durmus et al., 2008;Dede, 2009;Durmus, 2011). ...

Nikko Ederio
Sr Marie Rosanne Mallillin SPC
Sr Honorata Sahlee Trinilyn Palijo SPC
Engr Angelus Vincent Guilalas

The study determined outcomes-based mathematics teaching characteristics that mark Paulinian education in St. Paul University Surigao Junior High School. The instruments used were researcher-made questionnaires for the 6 Junior High School Mathematics teachers and 151 Science Class students who taught and enrolled respectively in St. Paul University Surigao during the school year 2019-2020. Data gathered were analyzed using the means, standard deviation, and t-test. Exploratory Factors Analysis was also employed to yield generally significant characteristics based on the data from the responses. The mathematics teachers perceived that the students under study achieved the mathematics learning outcomes and competencies, to some extent. The said students also perceived that they have achieved, to some extent. Hence, the teachers' instructional approaches and perception of their students' achieved mathematics learning outcomes and competencies are validated by the students' actual achievements. It was then revealed that there is no significant difference between the participants' perceptions on the extent of the mathematics learning outcomes and competencies achieved by the students, except for the honesty and truthfulness traits. Exploratory factor analysis revealed five (5) most significant Mathematics learning outcomes and competencies categories that characterize the outcomes-based mathematics teaching in SPU Surigao Junior High School.

Daniel Romano

Bosnia and Herzegovina [B&H] is a very specific socio-political creation. This community is under the protectorate by the so-called international community. In B&H there exist two entities (The Republic of Srpska [RS]-49% of the territory and the Federation of Bosnia and Herzegovina [FBH]-51% of the territory) and the 'Brčko District' in which only three the so-called constitutive people enjoy almost equal rights. Entities and the District have a significant number of elements of statehood. The FBH consists of 10 almost independent cantons (quasi-state). Education is in the full competencies of the RS, the District and each individual canton. In such a political-economic environment, collective education of all levels is realized. Therefore, all kinds of education are under the political and financial (only for public institutions) coverage of the government's administrations of the RS, the District and the cantons. In order to present to the world academic community dilemmas and what kind of challenges the mathematical education is this socioeconomic political situation in, we have intention to open a dialogue on the political and ethical dimensions of mathematics education in B&H. In this, relying on the orientations and attitudes of the international community of researchers in mathematical education, we will try to see the big picture, identify and politically correctly describe the specificity of mathematics education in B&H. We deeply believe that such texts could be one of the supports to our academic community in negotiating with our socio-political community on raising the quality of mathematics education in B&H.

F F Firmansyah
E Y Sunardi
Susanto
Reza Ambarwati

The process of learning mathematics in school has several problems related to the characteristics of mathematics, concepts, principle of mathematics and abstract of mathematical objects. Students also have difficulties in solving geometry of shape and space content. This can be seen from the research carried out by the researchers at one of schools in Thailand. Some students who were at the visualization level still could not do optimally in the level of visualization. However, there was a unique level of students' visualization who could complete several levels above it. The basis that the author had was to examine these students more deeply. The type of this research was qualitative descriptive conducted at one of secondary schools by giving Van Hiele geometry test to get the groups concerning the level of students, then it was proceed by PISA test of shape and space content. SV00 was defined as a code of students' visualization at level 0. At the visualization level, SV00 was able to reach 50% of indicators at the visualization stage and 33.3% at the analysis level.

Daniel Romano

Bosnia and Herzegovina [B&H] is a very specific socio-political creation. This community is under the protectorate by so-called the international community. In B&H there exists two entities (The Republic of Srpska - 49% of the therritory and the Federation of Bosnia and Herzegovina [FBH] - 51% of the territory) and the 'Bricko District' in which only three constitutive people enjoy almost equal right. Entities and the District have a significant number of elements of statehood. The FBH consist of 10 almost independent cantons (quasi-state). Education is in the full competencies of the RS, the District and each of individual cantons. In such a political - economic environment, collective education of all levels is realized.cal situation, we have intention to open dialogue on mathematics education Therefore, all kinds of education are under the political and financial (only for public institutions) coverage of the government's administration of RS, the District and the cantons. In order to present the the word academic community in what dilemmas and what kind of challenges the mathematics education is in this socio-economic-political situation, we have intention to open a dialogue on the political and ethical dimensions od mathematics education in B&H. In this, relying on the orientation and attitudes of the International community of researchers in mathematics education, we will try to see, identify and politically correctly describe the specificity of mathematics education in B&H. We deeply believe that such texts could be one of the support to our academic community in negotiation with our socio-political community on raising th quality of mathematics education in B&H.

Introduction: The aim of this study is to investigate the relation between the pre-service teachers? mathematical values and teaching anxieties in mathematics. Method: The research was carried out on 359 teacher candidates attending the elementary school mathematics, secondary school mathematics and primary school teaching programs. To this end, the 23-item Mathematics Teaching Anxiety Scale and the 34-item Mathematical Values Scale was administered to the pre-service teachers included in the sampling. In the analysis of the data, Pearson Product Moment Correlation Coefficient analysis and regression analysis were utilized to determine the relation between the pre-service teachers? mathematical values and their teaching anxieties in mathematics. Results: As a result of the analysis of data, it was determined that there was a low level, positive correlation between the mathematical values of the pre-service teachers and their mathematics teaching anxieties. According to the regression analysis results, it can be said that constructivist values that are part of the mathematical values are the estimator of mathematics teaching anxieties that arise from self-confidence and attitude towards teaching mathematics. Discussion and conclusions: Among the mathematical values, the constructivist value preferences of the pre-service teachers directly affect their mathematics teaching anxieties, and can be taken as a sign that it is possible to reduce their mathematics teaching anxieties by affecting the mathematical value preferences of the candidates. Therefore, determining other variables that may affect value preferences of candidates gains importance.

Wee Tiong Seah

Values assume an important role in the optimisation of (mathematics) teaching and learning. The most complex / internalised educational objectives in both the cognitive and affective domains of the Taxonomy of Educational Objectives (Bloom, 1956; Krathwohl, Bloom, & Masia, 1964)  namely evaluation and characterisation  are concerned with values. This paper explores the possibility of facilitating teachers' relevant language and conceptualisation relating to values in mathematics education, through an approach which examines beliefs and is complemented by teacher reflection on their own pedagogical practice. Broader implications are outlined.

Alan Bishop

The paper discusses assisting teachers to nurture mathematical thinking in their students by using findings from research on mathematical values. The author begins by sharing three theoretical perspectives on how mathematical thinking develops in a student from Lancy (1989), Billett (1998), and Bishop (1988). Using White"s (1959) three component analysis of culture, the author presents 6 mathematical values which are important to the development of Mathematics, and thus underpinning the development of mathematical thinking in the classroom. An exploratory Values and Mathematics Project (VAMP) shows that teachers found it difficult to discuss values they held about Mathematics education in relation to Mathematics. The introduction of some of the theoretical terminology helped teachers to discuss their teaching. In conclusion, the author proposes some implications for practice and policy.

Chang Lee Hoon

Values education is integral in Malaysian schools as society sees schools as perpetuating and influencing the future development of society, namely in achieving the country's vision of attaining the status of a fully developed nation in terms of economic development, social justice, spiritual, moral and ethical strength, towards creating a society that is united, democratic, liberal and dynamic. This is embodied in the National Educational Policy and Education Act of Malaysia (1996). In implementing values education, the Ministry of Education identified 16 core or noble values that are desirable to be inculcated and developed in Malaysia. The values are drawn from various religions, traditions and norms of Malaysian society that are within the context of the Rukunegara (National Ideology). These values are compassion, self-reliance, humility, respect, love, justice, freedom, courage, physical and mental cleanliness, honesty, diligence, co-operation, moderation, gratitude, rationality and public-spiritedness. The 16 core values are implemented in the school system, both primary and