Our Math Textbook is published by Houghton Mifflin Harcourt. The
series is called Singapore Math - Math in Focus. It uses a concrete-pictorial-abstract approach to mathematical problem solving. Students investigate math concepts utilizing interactive
problem solving techniques.
As you can see from the illustration, the basis of the program is Problem Solving. The five inter-related components around the center are further described by the key words written outside the pentagon.
The Concepts component involves students exploring to a great depth numerical, algebraic, geometrical, statistical, probabilistic (concerning probability), and analytical ideas. In Math In Focus textbooks student are given varied opportunities to develop a deep understanding of the concepts and to make sense of mathematical ideas, their connections, and applications. Manipulatives (concrete materials), practical work, and technological aides assist in the acquisition of these concepts.
The Skills component include procedural skills for numerical calculation, algebraic manipulation, spatial visualization, data analysis, measurement, use of mathematical tools, and estimation. The development of skills is essential to the learning of mathematics but should not be overemphasized and overshadow the underlying mathematical principles involved. The attainment of skills proficiency is dependant upon the correct use of technology for problem solving and exploration, thinking skills, and heuristics (what to try when a solution is not evident).
These two components are used for the acquisition and application of mathematical content which spirals (going deeper at each year) throughout the grade levels.
The Processes component refers to the knowledge and process skills necessary to acquire and apply mathematical knowledge: Reasoning, Communication and connections, Thinking Skills and heuristics, and Applications and modeling.
- Mathematical reasoning is a habit of mind in which the process of analyzing situations and constructing logical arguments or solutions is the desire.
- Communication refers to the ability to accurately, intelligently and precisely use mathematical language to express ideas, arguments, and solutions.
- Connections refers to the ability to see between and among mathematical ideas, math and other subjects and life in general. In this way, math becomes part of who we are rather than just what some of us do.
- Thinking skills and heuristics should be used to help solve word problems. Thinking skills are processes such as: classifying, comparing, sequencing, analyzing parts and wholes, identifying patterns and relationships, induction, deduction, generalizing, verifying and spatial visualization.
- Heuristics is what to do or try when faced with a novel problem and beginning the process of trying to solve it when the solution is not obvious. These include but are not limited to: make a list, draw a diagram, guess and test, look for patterns, act it out, working backwards, change or restate the problem, simplify or solve a part of the problem.
- Application of skills should be practiced at every level of math instruction. It provides and important opportunity to deepen understand of mathematical concepts competencies. Students should apply skills to solve a variety of word problems, real world problems, and open-ended problems.
- Mathematical Modeling is the process of taking a standard model and reworking it to make it represent and help solve a real world problem. Inherent in this ability is the choice of appropriate tools and technologies to help make sense of data collection, reporting and representation.
Metacognition refers to the ability to be aware of and control one's thinking. For example, making a conscious choice of which problem solving strategy you might choose to help solve a word problem. This can be developed by providing varied opportunities for exposure to problem solving, thinking skills and heuristics, thinking aloud, planning and evaluation of the plan, alternative ways to solve problems, and checking the reasonableness of answers.
The Attitudes component refers to the affective aspects of learning math such as:
- Beliefs about math and its usefulness to every day life
- Interest and enjoying the learning process
- Appreciation of the beauty and power of math
- Confidence is using math
- perseverance in solving a problem
Singapore Math was chosen in part because the new Core Content Curriculum Standards mention Singapore as a nation doing mathematics education well. Based on the descriptions of the above framework, I look forward to many successful years!
Also see Math Links
Assessments in Mathematics
Building on knowledge and skills gained in preceding grades, students will
use problem-solving strategies to explore mathematical concepts. Assessments
will include textbook and teacher made tests, quizzes, and projects.
These assessments will be combined with an effort grade to give a more accurate
representation of the math student. Grades are reported on trimester basis as:
- A+ 97-100
- A 93-96
- A- 90-92
- B+ 87-89
- B 83-86
- B- 80-82
- C+ 77-79
- C 73-76
- C- 70-72
- D+ 67-69
- D 63-66
- D- 60-62
- F Below 60
Copyright © 2013 John Hampshire