# Methods That Make Small Group Teaching Effective

**INTRODUCTION**

*“I never teach my pupils, I only attempt to provide the conditions in which they can learn.” *― Albert Einstein

The success of a teacher begins when a student develops a curious mind and nurtures him to be a philomath. Teaching mathematics can be truly effective when it positively impacts a student’s learning process. A teacher should be a facilitator to achieve this goal. Some strategies which are found to be more successful than the others are discussed in this article.

**PROBLEM STRUCTURE**

Learning the procedure to solve problems in Mathematics, is knowing what to look for in a problem. Math problems require a deep understanding of concepts and appropriate procedure to arrive at the required solution.

**ENTRY AND EXIT**

Listing down the starting point, the approach to be used, the concept behind it, and how to use the concept to get the required solution are the factors to be kept in mind while solving the problem. An effective teacher should facilitate a student to identify the starting step and an ongoing means for learners to investigate and understand conceptual ideas.

A simple problem like the one stated below might scare primary school kids if they fail to understand the concept behind the problem.

13 + ? = 25

Steps to solve this problem:

- What is the operation to be performed?
- In this operation, which number is the largest? (Tick the correct answer)

ΟAddend 1 ΟAddend 2 ΟSum

- What can you do to get the unknown number?

A facilitator can initially cue the child by asking some probing questions. If only one number and the answer is given, then will the unknown number be more than the answer or less than the answer?

A similar approach of identifying the entry point of the problem and the progress to be made towards the exit point enables all learners to eventually develop the understanding of concepts and more complex skills that facilitate efficient problem-solving. Drawing models to support answers and frame new questions.

Conventional classroom method teaches to solve the problem and to get the answer correctly. The conventional classroom teaching methodology might fail to impart the required conceptual knowledge to the learner. The learner can be asked to draw visual models to support the answers. Writing questions for the answers or framing new questions based on a concept requires a higher level of understanding.

In Cuemath, this is done by making the learners write simple word problems for multiplication and other basic operations. This approach also eliminates the confusion among learners regarding the operation needs to be performed for a particular question.

*Example 1*: ( 4÷ ⅛ )

Step 1: Draw model for this

Step 2: Create a word problem for this

Step 3: Differentiate between 4÷ ⅛ and ⅛÷4

Step 4: Write word problems for both the cases to show the difference

*Example 2:* Mary wants to mix 2½ liters of milk and 1¼ liters of water to prepare a dessert. What is the total quantity of the mixture?

Solution : This can be solved either by adding whole numbers and the fractional part separately or by converting to improper fraction and then adding together. This problem can be solved using visual representations and also with mathematical tools like fraction rods or pattern blocks.

**CUT & PASTE METHOD :**

QUESTION | STICKER |

2 (a+3) = 10 | |

23 x 2a = 29 | |

256 X 429 = 109824 | |

129 + 352 | |

a = 2 | |

a = 6 | |

429 x ? = 109824 |

**Available Stickers**

Learners need to stick relevant stickers below the correct column. This method enables the student to be more active and gets a clear idea of the approach to the problem and the different ways of arriving at an answer.

**ANALYZE MATH ERRORS**

Analyzing the errors act as a great source of learning in Mathematics. It has some benefits and also enables a great level of interaction between the learner and the facilitator.

Example: John has measured the length of a tree in his garden for his science project. The tree is growing by ½ an inch every month and has become 4 inches taller.

For how many months has he measured this tree?

Answer given by the learner:

½ x 4 = 2.

Identify the error in this problem if any and name the error as _________ (Conceptual/Procedural/Factual)

**CORRECT THE PROBLEM IF THERE IS AN ERROR**

This method has countless advantages. Identification of error develops the testing strategies involved. It encourages learners to explore more about errors and various ways of fixing errors. This method shows learners that many Mathematical questions have more than one correct answer. It teaches the importance of careful reasoning and understanding. It builds confidence in all learners that they can learn Mathematics. It helps learners verbalize their ideas.

→ Seminars and real-time projects.

→ Few seminar topics that can be used are:

→ What is the need for fractions, decimals, and other numbers?

→ When and where are they used in daily life?

→ What is the use of data handling?

Prepare a chart with scores of Indian batsmen in the last cricket match. Another learner can prepare a pie chart with the scores of the opponent team in the same match.

Sixth-grade students may be successful in investigating and solving interesting, relevant problems that lead to quadratic and other types of functions.

**CONCLUSION**

Teachers should be able to provide quality feedback to learners and teach learners to receive feedback positively and use the information to effectively improve their work. Assessment for learning and quality feedback promote the learner’s progress. Experts have knowledge that is connected to the conditions in which it can be applied effectively. They not only know what to do but when to do it and how to do it.

Teachers should adopt a positive mindset to encourage learners and motivate them. The positive approach will encourage them to understand or identify their mistakes and make them adopt the actual concept. This will guide them to avoid errors down the line. Teachers should act as facilitators to build confidence in learners and thereby help them to enhance their performance.

- Live one on one classroom and doubt clearing
- Practice worksheets in and after class for conceptual clarity
- Personalized curriculum to keep up with school