Assessment and Evaluation in Mathematics (Midterms)

• Assessment


  • Uses empirical data of student learning to refine programs and improve student learning
  • Process of gathering and discussing information from diverse sources in order to develop a deep understanding what can students know, understand, and do with their knowledge
  • Systematic basis for making inferences
  • Systematic collection, use, and review of information about educational programs
  • Uses wide variety of tools in order to evaluate, measure, or document academic readiness or educational needs of the students
• Evaluation


  • Assignment of symbols to phenomenon, characterizing the value or the worth, in reference to a specific cultural or scientific standards
  • Describing something in terms of attributes or judging the degree of acceptability and suitability
  • Systematic collection, analyzing, and interpreting information
• Assessment


  Provides feedback
• Evaluation


  Determines the level of quality or performance and enables decision making based on the level of quality shown
• Functions of educational evaluation

  • Prepares educational objectives
  • Assesses learner's needs
  • Provides feedback to the students
  • Prepares programmed materials
  • Helps in curriculum development
  • Reports progress to the parents
  • Useful in guidance and counseling
  • Helps in effective school administration
  • Helps in school research
• Principles of assessment


  • It should have a clear purpose
  • It is not an end in itself
  • Ongoing, continuous, and formative process
  • It is learner-centered
  • It is both process and product oriented
  • It must be comprehensive and holistic
  • It requires the appropriate measures
  • Assessment should be as authentic as possible
• Principles in assessing mathematics learning

  • Content principle: Assessment should reflect that mathematics is the most important thing for the students to learn
  • Learning principle: Assessment should enhance mathematics learning and support good instructional practice
  • Equity principle: Assessment should support every students the opportunity to learn
• Multi-dimensional approach to understanding to assess students' mathematical knowledge


  • Considers different ways on how a topic will be used and how this forms different perspectives in understanding
  • Defines mathematical proficiency as a tree with five intertwined strands
• Five intertwined strands of mathematical proficiency

  • Procedural fluency: Skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
  • Strategic competence: Ability to formulate, represent, and solve mathematical problems
  • Adaptive reasoning: Capacity for logical thought, reflection, explanation, and justification
  • Conceptual understanding: Comprehension of mathematical concepts, operations, and relations
  • Productive disposition: Habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with the belief in diligence and one's own efficacy
• SPUR approach


  • Skills: Procedures that the students should master with fluency
  • Properties: Principles underlying in mathematics used to justify derivations and proofs
  • Uses: Application of real-world situations or concepts applied in mathematics, ranging from the routinary word problems to the use of mathematical models
  • Representation: Graphs, pictures, and other visual representation to a mathematical concept, including its standard representations or depictions
• George Polya's 4 steps in solving a problem

  • Understand the problem
  • Devise a plan
  • Carry out the plan
  • Check and extend
• Alan Schoenfeld's conceptual framework

  • Cognitive resources: Body of facts and procedures at one's disposal
  • Heuristics: 'Rule of thumb' for making progress in difficult situations
  • Control: Efficiency in which individuals utilize the knowledge at their own disposal
  • Belief systems: One's perspective on a specific discipline and how one goes working about it
• Concept maps


  Drawing or diagrams used by students to represent or organize a knowledge or topic
• Three elements of concept mapping

  • Nodes: Concepts enclosed in ovals or rectangles
  • Links: Shows connection between concepts
  • Linking phrases: Specifies the relationship between pairs of concepts
• Concept maps were first developed by Joseph Novak and his team in the 1970s as a tool to document changes in understanding of wide ranges of concepts held by students
• Ausubel's assimilation theory


  Learning takes place by assimilating new knowledge into the existing concepts
• Four components of concept mapping

  • Concepts
  • Links
  • Linking phrases
  • Map structure
• Types of concept mapping

  • High-directed concept mapping tasks/fill-in-the map: Provides the students with several concepts and requires them to fill in the skeletal structure with the given concepts
  • Semi-directed concept mapping tasks: One or two of the components are missing or the other components are fully or partially provided
  • Low-directed concept mapping tasks/free-style mapping: Students are required to fully construct the map based on a given topic
• Training on concept mapping


  • Introduction: Teachers must provide students a preliminary idea what is a concept mapping, what it is used for, and what are its attributes
  • Demonstrate with examples: Teachers begin with an example of four or five concepts that students have already learned
  • Student practice: Provide students different set of concepts to practice with
  • Consolidation: Teachers will know what the students have already mastered and what concepts they are still struggling with
• Alternative assessment


  Alternative or authentic assessment refers to the alternative to standard pen and paper tests where it provides true evaluation of what the student has learned, going beyond the knowledge by looking into the application of the concepts they had learned
• Three key principles of assessment

  • Assessment for learning: Process in which it is used by the teachers to adjust their teaching strategies for improvement
  • Assessment of learning: Commonly associated with the national or end of semester examination, which gathers evidence for summative judgement of pupils' performance
  • Assessment as learning: Involves students as their own assessors
• Suggested alternative assessment practices

  • Practical test: Pupils are expected to use manipulatives, materials, and instruments to deduce mathematical principles
  • Oral presentation: Enable students to give the solutions orally which it facilitates sharing of thoughts and clarification of understanding
  • Journal writing: Offers the students an opportunity to reflect on their learning by sharing their thoughts and ideas about what they had learned
  • Open-ended task: Elicits range of responses in which the students can show what they know about a specific topic they had learned