Why ALPHA Works
Teaches via problem solving
ALPHA Mathematics teaches via problem solving through the systematic development of problem sets; and by focusing on both aspects of problem solving - the method and the process.
Focus on the Problem Solving Process
ALPHA Mathematics explicitly teaches an efficient 4-step UPAC problem solving process. This process builds good habits for approaching mathematical problems of all levels of difficulty.
1
Understand the problem
- Can you describe the problem in your own words?
- What information is given?
- What do you need to find?
- Is there information that is missing or not needed?
2
Plan what to do
- What can you do to help you solve the problem?
- Here are some things you can do:
- Draw a picture
- Make a list
- Guess and check
- Look for a pattern
- Make suppositions
- Act it out
- Work backwards
3
Work out the Answer
- Solve the problem using your plan in Step 2.
- If you cannot solve the problem, make another plan.
- Show your work clearly.
- Write the answer statement.
4
Check
- Read the question again. Did you answer the question?
- Does your answer make sense?
- Is your answer correct?
- If your answer is not correct, go back to Step 1.
Focus on the Problem Solving Method
ALPHA Mathematics explicitly teaches different problem solving strategies and how to select, express, categorise and compare these strategies.
Problem Solving Strategies
- Draw a Picture
- Make a List
- Choose an Operation
- Guess and Check
- Look for a Pattern
- Make a Supposition
- Act it Out
- Work Backwards
- Solve Part of the Problem
The Bar Model Method
The Bar Model Method is one of the most powerful strategies for mathematical problem solving. It allows students to solve complex word problems using visual representation.
- The Part-Whole Model enables students to understand the concept of addition (given the parts, find the whole).
- The Comparison Model enables students to compare two quantities and shows the difference in quantities.
- The Bar Model Method enables the students to think conceptually, allowing them to do algebraic thinking without having to do algebra.
Example:
Pearl read 10 pages of a book on Monday. She read 1/3 of the remainder on Tuesday. If she still had 24 pages to read, how many pages were in the book?
Varied Problem Sets
Students progress through different types of problem sets including word problems and non-routine problems.
Word Problems
- Enable students to apply knowledge learned and make mathematics relevant to daily life.
- Assess students’ ability to apply knowledge learned.
Non-routine Problems
- Provide opportunities for students to apply knowledge to unusual or complex problem situations.
- Develop higher order thinking skills.
