Question 1

Which statement best reflects the approach of teaching for problem solving?

Accepted Answer

C

Question 2

Facilitating classroom discourse requires that the teacher be aware of what factors that will affect the level of mathematical talk in the classroom.What statement below would impact the mathematical talk?

Accepted Answer

A

Question 3

How much to tell or not tell is a constant dilemma for teachers.What statement would be the type of information that teachers do need to tell?

Accepted Answer

Teachers should help students clarify their ideas and point out related ideas, as this helps students develop their understanding of the subject matter. While teachers should provide guidance and support, they should also encourage students to struggle and work through challenges as this leads to deeper learning. Teachers should avoid telling students specific problem-solving strategies and instead guide them to develop their own problem-solving skills. Similarly, teachers should avoid providing information that removes the cognitive demand of a task, as this can limit student learning and engagement.

Question 4

Asking effective questions requires planning and teachers become more adept at asking quality questions throughout their careers.What common pattern of questioning fosters a greater chance of classroom discussion?

Accepted Answer

Focusing questioning, which starts with broad questions and zooms in to specific details, has been shown to promote deeper discussions in the classroom. This approach allows students to build on their prior knowledge and work towards a more complete understanding of the topic. Funneling involves starting with specific details and moving towards broader concepts, while Initiating, Responding, Feedback (IRF) is a pattern of questioning that involves the teacher initiating a question, a student responding, and the teacher providing feedback on the response. Correcting questioning involves the teacher correcting a student's answer or behavior.

Question 5

Which statement below best represents worthwhile features of tasks or problems for learning mathematics?

Accepted Answer

Worthwhile features of tasks or problems for learning mathematics should be problematic, meaning they require students to apply their knowledge and problem-solving skills. Additionally, the tasks should focus on concepts and/or misconceptions to help students develop a deep understanding of the material. Finally, the tasks should be relevant to students' lives or future careers to increase engagement and motivation. Memorization, rules, formulas, and routine tasks do not necessarily promote conceptual understanding or critical thinking skills.

Question 6

Researchers have found that teachers' benefit from using an intentional selection process to determine whether a task they chose is worthwhile.One of the criteria of the selection guide is "worthwhile features".Which statement below represents one of the categories in "worthwhile features"?

Accepted Answer

"Relevant context" is a category under "worthwhile features" as it ensures the task is meaningful and applicable to real-world situations, enhancing student engagement and understanding.

Question 7

Selecting problem solving tasks that require higher levels of cognitive demand should include which one of the following?

Accepted Answer

Tasks that require higher levels of cognitive demand should involve the use of complex and non-algorithmic thinking, rather than just following a previously learned procedure or straightforward tasks with little ambiguity. Therefore, option C is the best choice.

Question 8

Drill and practice is present to some degree in every classroom.The definitions of drill and practice demonstrate how they are different and how they link.One of the statements below is representative of practice more than drill.

Accepted Answer

Practice often involves applying concepts in various contexts, which helps in developing a deeper understanding of those concepts. This contrasts with drill, which typically focuses on repetition and memorization of specific procedures or rules.

Question 9

Which statement about the teaching through problem solving approach is most accurate?

Accepted Answer

The answer of Which statement about the teaching through problem...

Question 10

Problem solving tasks that have multiple entry and exit points exhibit what characteristics below?

Accepted Answer

Multiple entry and exit points mean that there are different ways to start and end the task. This implies that there are varying degrees of challenge and methods to approach a solution, making option B the correct choice. Option A is incorrect because the focus is not only on producing a correct answer, but also on the process and methods used to arrive at the answer. Option C is not necessarily true since some problems may require collaboration or group work, and option D is not always necessary as some problems may be solved orally or through other means besides writing.

Question 11

Which is the most accurate statement regarding posing a worthwhile problem?

Accepted Answer

Posing a worthwhile problem should aim to make relationships between mathematical concepts explicit for students. This allows students to connect and apply their knowledge in a meaningful way rather than just memorizing procedures.

Question 12

Teaching through problem solving provides opportunities for all students to become mathematically proficient.Teaching through problem solving benefits all students in what way?

Accepted Answer

The answer of Teaching through problem solving provides opportunities for...

Question 13

The act of writing is a reflective process and involves students in metacognition? What statement is an example of a students' conscious monitoring of how and why they are doing something?

Accepted Answer

The answer of The act of writing is a reflective...

Question 14

Drill of skills has a place in helping students improve procedural knowledge but not conceptual knowledge.Before committing to a solution of "just drill" what do you need to know?

Accepted Answer

Simply drilling without focusing on building understanding can lead to rote memorization without deeper comprehension. Therefore, it is important to choose a type of drill that focuses on developing conceptual understanding.

Question 15

Problem solving provides opportunities for students to demonstrate mathematical proficiency.Identify two ways that teaching through problem solving works for all students.

Accepted Answer

The answer of Problem solving provides opportunities for students to...

Question 16

Children's literature can be a method of creating tasks with context students can connect to other subjects.What statement below demonstrates how a teacher made a connection?

Accepted Answer

The teacher made a connection to children's literature by referring to a Chinese magical pot, which could lead to a discussion about cultural diversity and enrich students' understanding of different cultures. It also makes the lesson more engaging and interesting for students.

Question 17

Teachers can prompt productive classroom discussion through the use of five teacher talk actions.What statement below reflects the type of prompt to elicit student reasoning?

Accepted Answer

By asking "Who also used similar strategy as Ricardo?" the teacher is prompting students to share their own reasoning and strategy, which can lead to a productive classroom discussion. The other statements are either statements of fact or directives, which do not necessarily encourage student participation or discussion.

Question 18

Effective use of classroom discussion has the teacher monitoring the students' strategies and asking questions.What question below would require the student to reflect on their specific strategy?

Accepted Answer

The answer of Effective use of classroom discussion has the...

Question 19

Which of the following is an instructional example of teaching through problem solving?

Accepted Answer

In this example, students are given a problem to solve that requires them to apply their understanding of the concept they have just learned (area of a rectangle) to a new situation (finding the area of a triangle). They are then asked to generalize their process to apply to any triangle. This promotes problem-solving skills and encourages students to think critically and creatively.

Quiz 3: Teaching Through Problem Solving