• Active Learning :
  Students take an active role in their learning rather than learn passively through teacher-directed instruction. Active learning:
  • inspires the senses
  • is sometimes noisy, yet productive
  • encourages learners to experiment and explore
  • fosters critical thinking and inquiry
  • is supportive, safe and encourages risk-taking
  • promotes social interaction and collaboration
  • encourages individual strengths
  • encourages and fosters learning through different mediums
  • may be untidy due to the nature of the work in progress
  • encourages learners to take responsibility for their learning
  • is shaped to promote collaboration
  • provides learning opportunities carefully designed to meet learner expectations and standards
  
  
  
• Algebra:
  The study of general methods for solving equations. The Algebra Standard emphasizes relationships among quantities, including functions, ways of representing mathematical relationships, and the analysis of change. Algebra is about abstract structures and using the principles of those structures in solving problems expressed with symbols.
  
  
• Applet:
  A small computer application program designed to enhance the learning of a concept through animation or the manipulation of parameters.
  
  
• Assessment:
  “Process of gathering evidence about a student’s knowledge of, ability to use, and disposition toward mathematics and of making inferences from that evidence for a variety of purposes” (NCTM, 1995, p. 87).

The process of collecting and interpreting information that can be used to inform:

• students, and their parents/guardians where applicable, about the progress they are making toward attaining knowledge, skills, attitudes, and behaviors to be learned or acquired
• the various personnel who make educational decisions (instructional, diagnostic, placement, promotion, graduation, curriculum planning, program development, or policy) about students (Alberta Joint Advisory Committee, 1993)
  

• Chalk-and-talk:
  Lecture format of instruction whereby the teacher is the dispenser of knowledge and students sit passively, copying notes until the class is over.
  
  
• Computer Assisted Instruction (CAI):
  Simulation of a tutor-tutee relationship in the design of a computer-based instructional program (Kaput, 1992).
  
  
• Constructivist theory :
  The basics of constructivism recognize that people actively construct understanding/knowledge and the process involves interactions among prior knowledge, concurrent experiences, other people, and the environment in a socio-cultural context. It is an amalgamation of Piaget’s, Vygotsky’s, Ausubel’s, and Dewey’s ideas about learning and teaching.
  
  
• Evaluation:
  Evaluation may be criterion-referenced or norm-referenced. “Evaluation is the process of determining the worth of, or assigning a value to, something on the basis of careful examination and judgment” (NCTM, 1995, p. 88).
  
  
• Geometry:
  Study of geometric shapes and structures and how to analyze their characteristics and relationships, including spatial visualization, reasoning, and justification skills and proofs. Geometric modeling and spatial reasoning offer ways to interpret and describe physical environments and can be important tools in problem solving.
  
  
• Manipulatives:
  Item that can be used to help convey a mathematical concept (e.g., bingo chips, playing cards, yardsticks, or dice, etc.).
  
  
• National Council of Teachers of Mathematics (NCTM):
  Founded in 1920, the National Council of Teachers of Mathematics (NCTM) is the world's largest mathematics education organization, with more than 100,000 members and 250 Affiliates throughout the United States and Canada. The mission of NCTM is to provide the vision and leadership necessary to ensure a mathematics education of the highest quality for all students.
  
  
• Numeracy:
  Combination of mathematical knowledge, problem-solving and communication skills required to function successfully within our technological world (British Columbia Association of Mathematics Teachers, 1998).
  
  
• Reform-type mathematics:
  Any mathematical ideas, materials, and resources that have the current problem-solving, student-centered, constructivist paradigm as their foundation.
  
  
• Relational understanding:
  “Knowing both what to do and why,” (Skemp, 1978), as opposed to instrumental understanding, or “rules without reasons” (p. 9). “Mathematical advantages: a) more adaptable to new tasks, b) easier to remember, c) relational knowledge can be effective as a goal in itself, and; d) relational schemas are organic in quality” (Skemp, 1978, pp.12-13; see also Van de Walle, 1990, p. 6).
  
  
• Standards-based mathematics curriculum:
  Curriculum closely aligned with NCTM documents mentioned throughout these modules.
  
  
• Standards and strands:
  “Descriptions of what mathematics instruction should enable students to know and do” (NCTM, 2000, p. 29).
  
  
• Trigonometry:
  Study of how the sides and angles of a triangle are related to each other.