[MMW] Part 4: Math Investigation

Mathematical investigation

refers to the sustained exploration of a mathematical situation. It distinguishes itself from problem solving because it is open-ended.

Mathematical investigation

is the use of mathematical processes to pursue an inquiry about a situation which must be understood or a set of data which must be organized.

Standard exercises

These are activities with clearly defined procedure/strategy and goal. Are used for mastery of a newly learned skill like computational, use of an instrument, and even new terms or vocabulary.

Problem-solving

These are activities involving clearly defined goals but the solutions or strategies are not readily apparent. The student makes a decision on the latter. It is said that _____ is at the heart of mathematics.

Mathematical investigation

is a divergent (open) activity, i.e. there are no known outcomes either for the students or the teacher.

Problem-solving

is a convergent (closed) activity where students have to reach a solution to a problem.

1. Exploration

2. Gathering and recording data

3. Looking for patterns

4. Making and testing conjectures

5. Testing the conjecture and then refine it and test

again

6. Explaining and proving results

7. Making generalizations

8. Extending the problem

9. Communicating findings

Mathematical investigations involve the following

processes: (9)

Communication Processes

(e.g. explaining, talking,agreeing, questioning)

Reasoning Processe

(e.g. analyzing, recognizing patterns, conjecturing, proving)

Recording Processes

(e.g. drawing, writing, listing,graphing, symbolizing)

Operational Processes

(e.g. data collecting, sorting, ordering, classifying)

Conjectures

are inferences or judgments based on inconclusive or incomplete evidence. (American Heritage Dictionary, 2006). These are statements, opinions or conclusions based on guesswork.