Why ALPHA Works
Is Effective, Measurable and Diagnostic
The pedagogical approach and instructional design of ALPHA Mathematics is based on the best practices of top performing Singapore, Republic of Korea and Hong Kong. The approach and instructional design are proven to be effective in developing conceptual mastery and procedural fluency, and are crafted to enable the teacher and student to evaluate learning and identify areas of remediation, if needed.
Checks for Readiness to Learn
Mathematical knowledge is cumulative in nature and a Let’s Remember Worksheet in the Teacher’s Manual provides valuable feedback to the teacher on the need for remediation or readiness for new learning. Information about the objective of each task, the precursor skill or concept tested and where it is taught in the Coursebook are also provided in the Teacher’s Manual.
Let’s Remember Worksheet
- Items are systematically developed and varied to ensure full review of precursor concepts and skills.
Let’s Remember Worksheet
- Precursor knowledge and mastery of comparison of unit fractions is required in order for students to learn comparison of fractions with common numerators or denominators.
Develops Deep Conceptual Understanding
and Addresses Different Learning Styles and Needs
The 3-stage Concrete-Pictorial-Abstract approach to mathematics instruction and learning enables students to make connections between principles and symbols through concrete activities and visual representation, making mathematical understanding deep and long lasting.
Concrete-Pictorial-Abstract Approach
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Concrete stage - Physical materials such as base ten blocks used in hands-on activities, designed to develop conceptual understanding.
Concrete-Pictorial-Abstract Approach
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Pictorial stage - Visuals that represent previously used physical materials help students visualise concepts and connect mathematical ideas.
Concrete-Pictorial-Abstract Approach
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Abstract stage - Numbers and mathematical symbols are used as final representations of concepts and skills.
Deep Conceptual Understanding and Procedural Fluency
ALPHA Mathematics uses visuals and instructional scaffolding to ensure that students understand concepts and procedures instead of just memorising them and carrying them out in a rote manner.
Concepts and Procedures
- Conceptual understanding is developed through the use of concrete materials in a carefully crafted activity and the pictorial representation shows 3 wholes divided into 4 equally.
- Students understand the relationship between the concept of dividing a smaller number by a bigger number and the procedure for performing the operation. This is important for solving problems and for thinking creatively.
Concepts and Procedures
- Developing conceptual understanding of the perimeter of a rectangle
- Developing procedural understanding of calculating the perimeter of a rectangle
Consistent Lesson Structure Includes
Built-in Formative and Summative Assessment
Each chapter in the Coursebook comprises several lessons. Lessons are structured in two parts: Let’s Learn introduces the concept and Let’s Do provides guided practice and formative assessment of the concept just taught. Practices at the end of each lesson help to consolidate learning.
Let’s Learn
- Concepts are taught in Let’s Learn using the Concrete-Pictorial-Abstract approach.
Let’s Do
- Let’s Do provides guided practice and an opportunity for immediate formative assessment, enabling the teacher to immediately assess students’ understanding of the concept just taught and identify remediation needs.
Practice
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Practice at the end of each lesson consolidates learning and provides opportunities for summative assessment.
Formative and Summative Assessment in the Practice Books
Practice Books are designed to complement and extend learning in the Coursebooks. Practice Book Exercises correlate to the learning objectives in the Coursebook and provide practice and formative assessment.
Practice Books
- Tasks are systematically varied to provide comprehensive practice.
