Pedagosko i psiholosko testiranje i procjenjivanje spadaju među najvažnije doprinose znanosti o ponasanju nasem drustvu i pružaju temeljna i znacajna poboljsanja u odnosu na ranije postupke. Iako se ne može ustvrditi da su svi testovi dovoljno usavrseni niti da su sva testiranja razborita i korisna, postoji velika kolicina informacija koje ukazuju na ucinkovitost kvalitetnih instrumenata u onim situacijama u kojima je njihovo koristenje potkrijepljeno validacijskim podacima. Pravilna upotreba testova može dovesti do boljih odluka o pojedincima i programima nego sto bi to bio slucaj bez njihovog koristenja, a također i ukazati na put za siri i pravedniji pristup obrazovanju i zaposljavanju. Međutim, losa upotreba testova može dovesti do zamjetne stete nanesene ispitanicima i drugim sudionicima u procesu donosenja odluka na temelju testovnih podataka. Cilj Standarda je promoviranje kvalitetne i eticne upotrebe testova te uspostavljanje osnovice za ocjenu kvalitete postupaka testiranja. Svrha objavljivanja Standarda je uspostavljanje kriterija za evaluaciju testova, provedbe testiranja i posljedica upotrebe testova. Iako bi evaluacija prikladnosti testa ili njegove primjene trebala ovisiti prvenstveno o strucnim misljenjima, Standardi pružaju okvir koji osigurava obuhvacanje svih relevantnih pitanja. Bilo bi poželjno da svi autori, sponzori, nakladnici i korisnici profesionalnih testova usvoje Standarde te da poticu druge da ih također prihvate.

Standards for educational and psychological testing

미국의 “전국 수학 교사 협의회”(National Council of Teachers of Mathematics, NCTM)는 1989년부터 〈학교 수학의 교육과정과 평가 규준〉(1989), 〈수학 가르침(교수)의 전문성 규준〉(1991), 〈학교 수학의 평가(시험) 규준〉(NCTM, 1995), 〈학교 수학의 원리와 규준〉(2000)을 출판하여 미국의 수학 교육 의 전망(목표, 나아갈 길)과 규준(실행 지침)을 제시하였다. 수학 교사들로 구성된 미국의 NCTM은 학생, 학부모, 학교 행정가 등 많은 사람들과 힘을 합하여 모든 학생들에게 수준 높은 수학 교육을 받을 수 있는 여건(환경, 기회)을 조성하는 데 구심점의 역할을 하였다. 한편 많은 관련 단체들은 여러 배경과 능력을 가진 학생들이 전문성을 지닌 교사(특수 교사를 일컫는 밀이 아니다. 수학 교과를 이해하고 수학의 전문성과 특수성을 가르칠 수 있는 일반 교사를 일컫는 말이다.)로부터 미래를 대비해 평등하고, 진취적이며, 지원이 잘 이루어지고, 공학 도구(IT)가 잘 갖춰진 환경에서 중요한 수학적 아이디어를 이해하면서 학습할 수 있는 수학 교실(미국에서는 우리나라처럼 수학 교사가 수학 시간에 학생의 방(교실: Homeroom)에 찾아가지 않고 학생들이 선생의 방(수학 교실: Classroom)을 찾아온다. 전형적인 수학 교실의 사진은 2쪽에 나와 있다.)을 만들기 위해 함께 힘썼다. NCTM에서 출간한 여러 규준들은 우리나라의 제6차와 제7차 교육과정에도 큰 영향을 미쳤다. 이 글에서는 NCTM(2000)에서 제시한 학습 원리를 간단히 살펴본 다음 이를 중심으로 현재 미국 수학 교육의 교수ㆍ학습 이론의 동향을 살펴본다.

미국 NCTM의 Principles and Standards for School Mathematics에 나타난 수학과 교수,학습의 이론

The emerging field of the learning sciences is one that is interdisciplinary, drawing on multiple theoretical perspectives and research paradigms so as to build understandings of the nature and conditions of learning, cognition, and development. Learning sciences researchers investigate cognition in context, at times emphasizing one more than the other but with the broad goal of developing evidence-based claims derived from both laboratory-based and naturalistic investigations that result in knowledge about how people learn. This work can involve the development of technological tools, curriculum, and especially theory that can be used to understand and support learning. A fundamental assumption of many learning scientists is that cognition is not a thing located within the individual thinker but is a process that is distributed across the knower, the environment in which knowing occurs, and the activity in which the learner participates. In other words, learning, cognition, knowing, and context are irreducibly co-constituted and cannot be treated as isolated entities or processes. If one believes that context matters in terms of learning and cognition, research paradigms that simply examine these processes as isolated variables within laboratory or other impoverished contexts of participation will necessarily lead to an incomplete understanding of their relevance in more naturalistic settings (Brown, 1992).1 Alternatively, simply observing learning and cognition as they naturally Correspondence and requests for reprints should be sent to Sasha A. Barab, School of Education,

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Design-Based Research: Putting a Stake in the Ground

In this study I investigated how collaborative interactions influence problem-solving outcomes. Conversations of twelve 6th-grade triads were analyzed utilizing quantitative and qualitative methods. Neither prior achievement of group members nor the generation of correct ideas for solution could account for between-triad differences in problem-solving outcomes. Instead, both characteristics of proposals and partner responsiveness were important correlates of the uptake and documentation of correct ideas by the group. Less successful groups ignored or rejected correct proposals, whereas more successful groups discussed or accepted them. Conversations in less successful groups were relatively incoherent as measured by the extent that proposals for solutions in these groups were connected with preceding discussions. Performance differences observed in triads extended to subsequent problem-solving sessions during which all students solved the same kinds of problems independently. These findings suggest that t...

When Smart Groups Fail

The World is Flat: A Brief History of the Twenty-First Century

Developing realistic mathematics education

In this contribution, we want to elaborate on an approach to design research
that has been used and refined in a series of design research projects in which
the present authors collaborated over a 10-year period. To locate our contribution in this book, we may categorize our approach as falling within the
broader category of design research that aims at creating innovative learning
ecologies in order to develop local instruction theories on the one hand, and
to study the forms of learning that those learning ecologies are intended to
support on the other hand.1 The research projects we focus on involve a
research team taking responsibility for a group of students’ learning for a
period of time. All projects concern the domain of mathematics education
(including statistics education).

Design research from a learning design perspective

In this article, we describe a methodology for analyzing the collective learning of the classroom community in terms of the evolution of classroom mathematical practices. To develop the rationale for this approach, we first ground the discussion in our work as mathematics educators who conduct classroom-based design research. We then present a sample analysis taken from a 1st-grade classroom teaching experiment that focused on linear measurement to illustrate how we coordinate a social perspective on communal practices with a psychological perspective on individual students’ diverse ways of reasoning as they participate in those practices. In the concluding sections of the article, we frame the sample analysis as a paradigm case in which to clarify aspects of the methodology and consider its usefulness for design research.

Participating in classroom mathematical practices

Participating in Classroom Mathematical Practices

The availability of technology in the mathematics classroom challenges the way teachers orchestrate student learning. Using the theory of instrumental orchestration as the main interpretative framework, this study investigates which types of orchestrations teachers develop when using technology and to what extent these are related to teachers’ views on mathematics education and the role of technology therein. Data consisted of videotapes of 38 lessons taught by three teachers, who also provided information on their views through questionnaires and interviews. Qualitative analysis of these data led to the identification of orchestration types and teacher profiles. The orchestration preferences of the three teachers proved to be related to their views. A detailed analysis of one exemplary episode suggests how other theoretical perspectives might complement the theory of instrumental orchestration.

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Koeno Gravemeijer

Papers

Developing realistic mathematics education

Design research from a learning design perspective

Participating in classroom mathematical practices

Participating in Classroom Mathematical Practices

The teacher and the tool: instrumental orchestrations in the technology-rich mathematics classroom.