Competency 013 - Mathematics Instruction

1) Problem solving is a process, not a topic and is the primary goal of mathematics instruction.

True

False

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.

Explanation

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.

2) The following are examples of what - finding a pattern, acting it out, drawing a picture, guess, check, and revising, working backwards, making a table, using input-output tables, trying a simpler form of the problem, and making a model to solving a problem?

The problem solving process

Problem solving strategies

Concrete-representational-abstract approach

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.

Explanation

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.

3) What unit should we use to measure the weight of this bag of potatoes is an example of what kind of question?

Convergent

Divergent

Convergent questions ask for a specific response

Explanation

Convergent questions ask for a specific response

4) Changing the counters into tally marks is an example of what new topic stage in mathematic instruction?

Concrete

Representational

Abstract

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.

Explanation

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.

5) Using counters to model an additon problem is an example of what new topic stage in mathematic instruction?

Concrete

Representational

Abstract

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.

Explanation

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.

6) Which is not a step in the problem solving process?

Read and understand the problem

Guess, check, and revise

Make a plan

Solve the problem

Look back to reflect

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.

Explanation

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.

7) How could we measure the weight of this bag of potatoes is an example of what kind of question?

Convergent

Divergent

Divergent questions do not have one specific answer

Explanation

Divergent questions do not have one specific answer

8) Changing the tally marks into numbers is an example of what new topic stage in mathematic instruction?

Concrete

Representational

Abstract

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.

Explanation

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.