Chapter 9 Notes

"There is a need to create a learning environment in which mathematical sense is natural." Arcavi and Schoenfield.  Mathyogi partnered with teachers aims to create that environment.

Basic Mathematical Skills

1. Computation
2.  Problem Solving

Computation

This is the manipulation of given numbers according to a preset of rules to determine a predictable outcome. 

Computation can be divided into three;

1. Readiness Skills
2. Number  Facts
3. Algorithms

Readiness Skill

• Can lead to or block future number manipulation - How does a student acquire this skill?
• consist of the ability to recognize numbers and comprehend them
• Students should be able to to recognize one to one correlation and the joining of sets of object. This skill must be internal to a child's system before anything.

Number Facts

Number facts are build upon readiness skills.

• They consist of isolated bits of information that can be used in the computation process much the same as sight vocabulary is used in reading process.
• Number facts must be recalled immediately during the computation process if they are to be used.

Number Computation

• Manipulation of number facts according to a set of rules whose application will result in some predictable results

• Can be divided into;
1. Whole numbers, Fractions, Decimals
2. Each of the above can be divided into; Subtraction, addition, multiplication and division 

For Mathyogi

How can we detect if a student is struggling in one of the areas above? When a student is confused about one section, that confusion will carry over to the rest. 

Problem Solving

This is the application of a process or organized framework of thinking in order to understand some previously unknown situation.

Problem Solving Approach

1. Study the problem and find out what it sought
2. Organize the information within the problem
3. Develop an action strategy for solving the problem
4. Select and apply the correct computational and other skills
5. Evaluate the answer for correctness and reasonableness

This approach is great because it allows mathyogi to accurately determine the cause of an incorrect answer. 

The premise of error analysis is that students develop an incorrect method of solving problems like students develop a correct way of solving a problem. 

In maths wrong answers may be the result of basic number fact error, an error in the computational algorithm, or an error in not understanding the question being asked.

Mathyogi should be able to;

1. interpret data collect during indirect assessment means
2. formulate diagnostic hypotheses
3. establish assessment priorities 
4. develop streamlined plans for direct assessment