Understanding Number Series and Problem-Solving in Basic Education
Understanding Number Series
Series Concept
A set of things that follow each other and are interrelated. These series can be made with pictures, numbers, symbols, or objects.
Number Series
This typically involves learning to interpret a sequence of integers given the first few terms. Series can be finite or infinite. The goal is to find the missing terms by identifying the underlying rule. Series can be purely numerical or contain letters, symbols, or combinations thereof.
Examples:
- 3, 3, 4, 6, 5, 4, 5, 4…
- 3, 3, 5, 4, 4, 3, 5, 5…
- U, D, T, C, C, S, S…
- E, F, M, L, M…
- L, M, M, J…
- 2, 3, 6, 7, 16…
- 1, 2, 3, 5, 8…
Basic Education Series
These primarily focus on the following criteria in ascending and descending order:
- Counting by 1s
- Counting by 2s
- Counting by 5s
- Counting by 10s
Predecessor and Successor
The predecessor is the number immediately before a given number on the number line. To find it, subtract 1. The successor is the number immediately after a given number. To find it, add 1.
Mathematics Education
Formal mathematics utilizes the deductive method, while basic education employs the inductive method. Mathematical knowledge should be adapted to the child’s developmental level.
Numeric Sizing
Before formal math, students undergo numeric sizing, which includes:
- Sorting
- Completing patterns
- Creating space
- Establishing relationships between parts and the whole
- Storing continuous and discontinuous quantities
Teaching Number Concepts
Children need to:
- Count: A collection corresponding to natural numbers, where each element has a symbol, and the final symbol names the collection. Counting methods include moving, touching, giving, looking, and mental counting.
- Understand quantity conservation
- Identify the additive structure of numbers
- Establish relationships of <, >, and =
- Read and write numbers
They must also visualize the repeating pattern of 1, 2, 3… after each multiple of ten (11, 12, 13…, 21, 22, 23…, etc.) and continue to 99 in the first year, then from 100 onward in the second year.
Decomposing Numbers
This involves recognizing that a number is the sum of smaller numbers.
Entry Behaviors
- Knowing place value
- Understanding units, tens, and hundreds
- Applying basic addition
- Mastering quantity conservation
- Reading and writing numbers
Materials for Decomposing Numbers
Base 10 blocks and the national monetary system can be used, following the same steps as teaching counting: moving, touching, looking, and mental manipulation.
What is Decomposing Numbers?
Decomposing numbers additively (expressing a number as a sum) in the first year reinforces decimal system understanding. For example, 15 as 14 + 1 demonstrates the successor function, while 15 as 10 + 5 highlights the decimal nature.
Vertical Fundamental Objective (OFV)
Recognize that numbers can be ordered and expressed in various ways as sums of smaller numbers.
Troubleshooting
- Monitoring tools for each subsector axis
- Applying learned concepts
- Stimulating critical, creative, and metacognitive thinking
Problem-Solving in Basic Education
A mathematical problem presents a question or situation requiring a mathematical procedure for resolution.
Steps to Solve Problems
- Read the problem
- Understand the meaning
- Clarify unfamiliar words
- Identify data
- Understand the question
- Identify relevant data
- Formulate a plan
- Perform operations
- Compare the answer to the question
Methodology for Problem-Solving
- Recite number sequences
- Check procedural understanding
- Employ counting strategies
- Verbalize quantities
- Demonstrate quantities
- Write quantities
- Locate fundamental counting principles
- Compare collections
- Decompose
- Compose