Mathematics Didactics

1. Problem solving
   1. Advantages

      Nota:

      • Seven advantages: 1. Places the focus of students attention on ideas and sense making. 2.Develops the belief in students that they are capable of doing maths and that math makes sense 3. Provides ongoing assessment data that can be used to make instructional decisions, help learners suceed, and inform parents. 4. Develops mathematical power. 5.Allows an entry point for a wide range of learners. 6. Engages learnrs so that there are fewer disipline problems 7. It's fun
   2. Developing problem solvers

      Nota:

      • Teacher develops problem solvers by: 1. Create a maths environment 2. Pose worthwhile Math tasks 3. Use models and calculators 4. Use writing and discourse as thinking tools 5. Encourage cooperative learning groups 6. Require justification of learner responses 7. Listen actively
   3. Problem solving lesson
      1. Before phase
         1. Teacher

            Nota:

            • Activate prior knowledge Be sure problem is understood Establish expectations
         2. Student

            Nota:

            • Get ready - connect to personal experiences - understand the problem
      2. During phase
         1. Teacher

            Nota:

            • Lets go Notice students math thinking provide appropriate support Provide worthwhile extensions
         2. Student

            Nota:

            • Works
      3. After phase
         1. Teacher

            Nota:

            • Promote math community listen actively without evaluation summarise main ideas and iD future problems
         2. Students

            Nota:

            • Class discussion
      4. Small groups

         Nota:

         • builds a math community learners collectively establish new ideas from a collection of existing ideas in the group encourages class discussion
2. Understanding

   Nota:

   • Knowing an idea - know about something but cannot really expand on or use it Understanding an idea - when an idea is connected to existing ideas Conceptual knowledge - knowledge that consists of logical relationships constructed internally Procedural knowledge - knowledge of the rules and procedures that one uses in carrying out routine tasks To learn maths with understanding is the measure of the quantity and quality of connections an idea has with existing ideas.
3. Constructivism

   Nota:

   • Students are not blank slates but creators of own learning Through reflective thought people modify existing ideas assimilate accommodate
4. Where student are

   Nota:

   • Teaching should begin with the ideas children already have, the ideas they will use to create new ones
5. Metacognition

   Nota:

   • conscious monitoring and regulation of own thought processes

Nota:

• a continuous planned process gathering info about the performance of learners against Assessment Standards of LO's

1. Characteristics

   Nota:

   • transparent and focused integrated into learning and teaching based on predetermined standards various methods and contexts valid, reliable, fair, student-paced and flexible
2. Pruposes

   Nota:

   • prior learning diagnostic formative summative systematic
3. continuous assessment

   Nota:

   • over a period of time and ongoing supports growth an development provides feedback allows for integrated strategies that cater for learner needs allows for summative assessment
4. Strategies
   1. Observation
   2. Journals
   3. Journals
   4. tests
   5. portfolios
   6. self-assessment