## What makes a mathematical task worthwhile?

The National Council of Teachers of Mathematics (NCTM) has defined worthwhile mathematical tasks as those that: Are based on sound and significant mathematics. Use knowledge of students’ understandings, interests, and experiences. Develop students’ mathematical understandings and skills.

**What is mathematical discourse NCTM?**

Page 1. Discourse. Discourse is the mathematical communication that occurs in a classroom. Effective discourse happens when students articulate their own ideas and seriously consider their peers’ mathematical perspectives as a way to construct mathematical understandings.

### What are mathematical tasks?

A mathematical task has been defined as a single problem or a set of problems that focuses student attention on a mathematical idea (Stein et al., 1996). The type of task used in the classroom has an influence on the level of students‟ engagement (Hiebert and Wearne, 1993; Smith et al., 2000).

**What are the six principles for school mathematics according to the NCTM?**

The Principles for school mathematics provide guidance in making these decisions….The six Principles address overarching themes:

- Equity. Excellence in mathematics education requires equity—high expectations and strong support for all students.
- Curriculum.
- Teaching.
- Learning.
- Assessment.
- Technology.

## Why are NCTM standards important?

According to the NCTM, the process standards “highlight the mathematical processes that students draw on to acquire and use their [mathematical] content knowledge.” This allows students to learn through the application of methods they can return to anytime they are approaching a difficult mathematic problem.

**How do you engage students in mathematical discourse?**

Use the tools of mathematical discourse to help students present their ideas. Teachers can engage students in mathematical discourse by posing questions that encourage discussion and debate and that require students to attend to particular aspects of the learning process and explain and justify their thinking.

### How do you promote math discourse in the classroom?

Five Practices That Promote Math Discourse

- Anticipating. “Actively envision how students might approach the mathematics task they will work on,” Smith and Stein write.
- Monitoring.
- Selecting.
- Sequencing.
- Connecting.

**What are open ended math tasks?**

An open ended math question (which is known as an open ended math problem or open ended math task) is a real world math situation presented to students in a word problem format where there is more than one solution, approach, and representation.

## Which task provides the greatest opportunities for students to understand mathematics?

Problem solving provides opportunities for students to demonstrate mathematical proficiency. Identify two ways that teaching through problem solving works for all students. -Practice can deepen conceptual knowledge through more useful connections.

**How do rich assessment tasks support students development of mathematical knowledge?**

The nature of rich tasks gives learners the opportunity to question and develop their understandings of mathematical ideas, and to gain the confidence to apply their knowledge in a range of contexts, even unfamiliar ones.

### Why are the recommendations of groups such as the National Council of Teachers of Mathematics NCTM important?

Why are the recommendations of groups such as the National Council of Teachers of Mathematics (NCTM) important? c. They help to spell out needed changes in mathematical education and shape reform efforts.

**What are the main tenets of the curriculum principle in the NCTM Principles to action?**

What are the main tenets of the Curriculum principle in the NCTM Principles to Action? The tenets of the Curriculum Principle include a coherent curriculum built around big ideas in daily classroom instruction.

## What is an example of discourse in math?

According to the Teachers Development Group, examples of Mathematical Discourse include: A student asks another student or the teacher, “I don’t understand how you got the answer. Could your show your reasoning again?” A student explains, “I first added 20 and 40 to get 60.

**Why are open ended tasks important?**

Importance of Open-Ended Questions Open-ended questions encourage children to: Use language by giving longer answers that help build a wider range of vocabulary. Think about their answers and give details to reasonably answer the question presented to them.

### What are the benefits of planning open ended questions during math instruction?

Use Open-Ended Questions Open-ended questions are beneficial in many ways. First, they encourage and support a variety of approaches and responses to a task. Second, they help build student confidence because they allow each person to respond at their own level, using their own strategies.

**What makes a good math task?**

The tasks in which students engage must encourage them to reason about mathematical ideas, to make connections, and to formulate, grapple with, and solve problems. Students also need skills. Good tasks nest skill development in the context of problem solving.

## What are the three areas of concern in selecting mathematical tasks?

In selecting, adapting, or generating mathematical tasks, teachers must base their decisions on three areas of concern: the mathematical content, the students, and the ways in which students learn mathematics.

**How does the teacher encourage the students to explore mathematical thinking?**

To encourage the students to deepen their understanding of numbers, the teacher has urged them to look for patterns and to make conjectures. She asked them, “Do you see any patterns in the lists you are making? Can you make any guesses about any of those patterns?” The teacher uses this exploratory task to spur students’ mathematical thinking.