Competency 013 - Mathematics Instruction

Divergent questions do not have one specific answer

Using counters to model an addition problem is an example of the concrete stage in mathematics instruction. In this stage, students manipulate physical objects, such as counters, to understand mathematical concepts. Concrete materials help students develop a deep understanding of the concepts before moving on to more abstract representations. By physically adding counters, students can visualize and comprehend the addition process, making it easier for them to transition to more symbolic representations later on.

Changing the counters into tally marks is an example of the representational stage in mathematics instruction. In this stage, students use visual representations such as drawings, diagrams, or models to represent mathematical concepts and solve problems. Tally marks are a visual representation that helps students organize and count objects. This stage allows students to connect the concrete manipulatives (counters) they used in the previous stage to more abstract representations (tally marks) as they develop a deeper understanding of the concept.

Changing the tally marks into numbers is an example of the abstract stage in mathematics instruction. In this stage, students move away from using concrete objects or representations and start working with symbols and numbers. They are able to understand and manipulate abstract concepts and apply them to various mathematical problems. By converting tally marks into numbers, students are demonstrating their ability to work with abstract representations of quantities.

The statement is true because problem solving is indeed a process and not just a topic. It involves using logical and critical thinking skills to identify, analyze, and solve problems. Mathematics instruction aims to develop these problem-solving abilities in students by providing them with opportunities to apply mathematical concepts and skills to real-world situations. By engaging in problem-solving activities, students can develop their problem-solving skills, enhance their understanding of mathematical concepts, and become better equipped to tackle complex problems in various contexts.

The step "Guess, check, and revise" is not a part of the problem-solving process. This step implies randomly guessing a solution, testing it, and then making revisions based on the outcome. However, in the problem-solving process, it is important to have a systematic approach that involves reading and understanding the problem, making a plan, solving the problem using appropriate strategies, and reflecting on the solution. Guessing and checking may be a part of the problem-solving process, but it is not a distinct step on its own.

The given correct answer is "Problem solving strategies". The examples provided, such as finding a pattern, acting it out, drawing a picture, etc., are all different problem-solving strategies that can be used to approach and solve a problem. These strategies help individuals think critically, analyze the problem, and come up with a solution. By utilizing problem-solving strategies, individuals can effectively tackle various problems and find solutions.