Five general goals for Mathematics Education
- To learn to value of Mathematics
- To become confident in one’s own ability
- To become a Mathematical Problem Solver
- To learn to communicate mathematically
- To learn to reason mathematically
Singapore Mathematics Curriculum Framework (Pentagonal Model)
Mathematical Problem Solving is central to the teaching & assessment of Mathematics learning. The development of the mathematical problem solving ability is dependent on 5 inter-related components:
- CONCEPTS Numerical, Algebraic, Geometrical, Statistical, Probabilistic, Analytical
- SKILLS Numerical calculation, Algebraic manipulation, Spatial visualisation, Data analysis, Measurement, Use of mathematical tools, Estimation
- PROCESSES Reasoning (ability to analyse mathematical situations & construct logical argument), Communication & Connections, Thinking skills & Heuristics, Applications & modelling
- ATTITUDES Beliefs (about mathematics & its usefulness), Interest (and enjoyment in learning mathematics), Appreciation (of the beauty & power of mathematics), Confidence (in using mathematics), Perseverance (in solving a problem)
- METACOGNITION Monitoring of one’s own thinking, Self-regulation of learning
If you are interested to learn more about Singapore Math Model Drawing for Primary levels, you can check out SMT.
What is Mathematics Heuristics?
Heuristics is a collection of strategies that we can adopt to solve Mathematical Problem Solving. Some strategies are useful to solve our daily problems too, such as looking for patterns and solving part of the problem. There are four steps that we would recommend to problem solving:
- Understand the problem – this includes data or information collection
- Deciding on an approach – with a list of strategies and good questioning techniques, we choose the one that suits the question’s requirement
- Solving the problem – a good knowledge of the approach is necessary to accomplish the task.
- Checking the solution – checking is important to ensure accuracy but most often neglected.
The 8 Cultural Forces that Define Our Learning
- Time – allocating time for thinking by providing time for exploring topics more in depth as well as time to formulate thoughtful responses.
- Opportunities – providing purposeful activities that require learners to engage in thinking and the development of understanding as part of their ongoing learning experience.
- Routines & Structures – scaffolding the learners’ thinking in the moment as well as providing tools and patterns of thinking that can be used independently
- Language – using a language of thinking that provides students with the vocabulary for describing and reflecting on thinking
- Modelling – educators to model as thinkers and learners so that the process of our thinking is discussed, shared, and made visible
- Interactions & Relationships – showing a respect for and valuing of one another’s contributions of ideas and thinking in a spirit of ongoing collaborative inquiry
- Physical Environment – making thinking visible by displaying the process of thinking and development of ideas. Arranging the space to facilitate interactions
- Expectations – setting an agenda of understanding and conveying clear expectations. Focusing on the value for thinking and learning as outcomes as opposed to mere completion of “work”
Adapted from Intellectual Character: What It is, Why It Matters, and How to Get It (Ron Ritchhart, 2002)
Mathematics Freeware/ Websites for Learning
- Graphmatica is a freeware to sketch graphs (http://www.graphmatica.com/)
- Online Calculators (http://www.calculator.net/scientific-calculator.html)
- Online Math lessons & worksheets
Good articles about Mathematics