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Brainstorming is a teaching strategy for releasing ingenuity and for enhancing critical thinking, especially in mathematics wherein higher order thinking skills of students should be more developed. Students can use this to come up with ideas until the group decides for the best solution.
Motivation in a mathematics class is indispensable, although it is a reality that all students should be properly motivated, especially the poorly motivated ones, the teacher should not ceased in finding ways to deliver the lesson at hand deliberately and accurately. One way to do this is through brainstorming, more so, when a teacher wants to expand a subject matter into the values arena, he or she can often use the power of brainstorming to uncover non obvious connections.  For example, a teacher might conclude a lesson in multiplication by asking students to  brainstorm real-life situations in which using multiplication would be helpful.  The teacher can also ask students to think  open-mindedly about a topic  to generate lots of ideas without worrying if any of their ideas  is reasonable or not. He or she might asks students  sitting in a small or large group, to create as long a list of alternatives, say balancing the home budget or doing mental long division.  If a mathematics teacher truly hope to release ingenuity and encourage productive thinking, then he or she need to use brainstorming techniques.  Brainstorming is a key tool that applies to most problem-solving and complicated mathematical concepts.  In fact, brainstorming strategy is an assumed component in  many subject areas not only in education, but also in other sectors of the society. Here are some basic rules for the teacher:
•    Encourage free expression of ideas.  The teacher explains that everyone’s ideas will be heard and recorded. One thing to make clear is that the only bad idea is the one that isn’t expressed.  The goal is productive thinking.
•    Encourage everyone’s participation.  Be sure everyone who is involved, or as many as possible, actually participates in the process.  A recorder writes down every idea in a way that can be readily understood.
•    Avoid killer phrases that close down communication.  Killer phrases are comments such as these:” What a silly idea!” ,” I     wouldn’t do that in a million years.”” You’re crazy. That’s a rotten idea! “                        
•    Sort the results.     When the brainstorming portion of the group/s is/are completed, you may want them to have the group sort the suggestions by considering their probability, impact, implications, advantages, disadvantages and priorities. This part is optional.  What is important is to select the best results/answers to the problem being solved. It’s good if all groups have best answers.                                

SAMPLE BRAINSTORMING ACTIVITY                                                                        

Activity---Brainstorm and Analyze
Organizer:  This is a way to get a lot of ideas out about        
Objective:  Identify information known and ideas about and integrate it with new                                                        information (for instance : any complex content topic particularly where they may be misconceptions)                                                                                                               
Time:           20 minutes
Techniques/Equipments:  Personal experience, written information, flipchart, felt pens.     Monitor and encourage participation. Augment ideas to ensure comprehensive list    
.Process:        In pairs or triads
-    Brainstorm the various types of that they know about.  This is an all ideas are welcome, no analysis session.
-    Record the information.
In the whole group:                                                       
Share the examples of from each group, rotating the response so that everyone contributes
Document      on a flipchart.
Discuss ideas that are triggered  by the examples.
Use examples and documented information to expand on their ideas.
Group Success:  Everyone in the group can explain the ideas put forward
Accountability:   Identify how previous information fits into the expanded information.
Debrief:           Identify how what was known already nassists understanding of new
Summing it up, remember:
1.    Accept all ideas without judgment.
2.    Write down all ideas as they are mentioned.
3.    Generate ideas quickly.
4.    Sort options by desirability.
5.    Examine the group who made the best choices.