Educational assessment is the process of documenting, usually in measurable terms, knowledge, skills, attitudes and beliefs. Assessment can focus on the individual learner, the learning community (class, workshop, or other organized group of learners), the institution, or the educational system as a whole. According to the Academic Exchange Quarterly: "Studies of a theoretical or empirical nature (including case studies, portfolio studies, exploratory, or experimental work) addressing the assessment of learner aptitude and preparation, motivation and learning styles, learning outcomes in achievement and satisfaction in different educational contexts are all welcome, as are studies addressing issues of measurable standards and benchmarks".

It is important to notice that the final purposes and assessment practices in education depends on the theoretical framework of the practitioners and researchers, their assumptions and beliefs about the nature of human mind, the origin of knowledge and the process of learning.

The following table summarizes the main theoretical frameworks behind almost all the theoretical and research work, and the instructional practices in education (one them being, of course, the practice of assessment). This different frameworks have given rise to interesting debates among scholars.

TOPICS EMPIRICISM RATIONALISM SOCIOCULTURALISM Philosophical orientation Hume, British Empiricism Kant, Descartes, Continental Rationalism Hegel, Marx, Cultural Dialectic Metaphorical Orientation Mechanistic/Operation of a Machine or Computer Organismic/Growth of a Plant Contextualist/Examination of a Historical Event. Leading Theorists B. F. Skinner (behaviorism)/ Herb Simon, John Anderson, Robert Gagne (Cognitivism) Jean Piaget/Robbie Case Lev Vygotsky, Luria, Bruner/Alan Collins, Jim Greeno, Ann Brown, John Bransford Nature of Mind Initially blank device that detects patterns in the world and operates on them. Qualitatively identical to lower animals, but quantitatively superior. Organ that evolved to acquire knowledge by making sense of the world. Uniquely human, qualitatively different from lower animals. Unique among species for developing language, tools, and education. Nature of Knowledge

(epistemology)

Hierarchically organized associations that present an accurate but incomplete representation of the world. Assumes that the sum of the components of knowledge is the same as the whole. Because knowledge is accurately represented by components, one who demonstrates those components is presumed to know General and/or specific cognitive and conceptual structures, constructed by the mind and according to rational criteria. Essentially these are the higher-level structures that are constructed to assimilate new info to existing structure and as the structures accommodate more new info. Knowledge is represented by ability to solve new problems. Distributed across people, communities, and physical environment. Represents culture of community that continues to create it. To know means to be attuned to the constraints and affordances of systems in which activity occurs. Knowledge is represented in the regularities of successful activity. Nature of Learning (the process by which knowledge is increased or modified) Forming and strengthening cognitive or S-R associations. Generation of knowledge by (1) exposure to pattern, (2) efficiently recognizing and responding to pattern (3) recognizing patterns in other contexts. Engaging in active process of making sense of (“rationalizing”) the environment. Mind applying existing structure to new experience to rationalize it. You don’t really learn the components, only structures needed to deal with those components later. Increasing ability to participate in a particular community of practice. Initiation into the life of a group, strengthening ability to participate by becoming attuned to constraints and affordances. Features of Authentic Assessment Assess knowledge components. Focus on mastery of many components and fluency. Use psychometrics to standardize. Assess extended performance on new problems. Credit varieties of excellence. Assess participation in inquiry and social practices of learning (e.g. portfolios, observations) Students should participate in assessment process. Assessments should be integrated into larger environment

• ThatQuiz
  thatquiz.com
  Free math practice and testing site for students with complete class record keeping and grading for teachers.
• Diagnostic Test of Pre-Algebra Math
  aprtestingservices.com
  Test is available to school systems to purchase to help make year-end placement decisions, or to diagnose weaknesses in students.
• MARS - Mathematics Assessment Resource Service
  nottingham.ac.uk
  Balanced Assessment Project: Michigan State - Berkeley - Shell Centre. MARS works with districts and states on performance assessment design and implementation, and on professional development for designers and teachers. The aim is to help the local leadership develop local capability to meet local needs.