"Several studies involving elementary-grades students (Carpenter et al. 1998; Cobb et al. 1991; Fuson, Carroll, and Drueck 2000; Hiebert and Wearne 1993) have consistently shown the in comparison with student in control groups, students experiencing problem-based instruction usually have higher levels of mathematical understanding and problem-solving skills and have at least comparable basic numerical skills."

**High Quality Tasks**

Why is there a focus on

High Quality Tasks?

What is a High Quality Task?

Essential

Authentic

Equitable

Rich

Feasible

Clear

Scorable

Active

Accessible

What does a High Quality Task Environment Look Like? What Would You Observe In Students ?

Classrooms as mathematical learning communities

Mathematical tasks that engage students' interests and intellect

logical and mathematical evidence as verification

mathematical reasoning

opportunities for students to deepen their understandings of math and its applications

promoting investigation and growth of mathematical ideas through classroom discourse

Conceptual Understanding

problem solving

using technology and other tools to persure mathematical investigations

Making mathematical connections and applications to previous and developing knowledge

students work individually, small groups, and whole class

How to Create a High Quality Task:

Use Core Concepts

Mathematical Skills

Essential Question

Problem Statement or Prompt

Task Criteria

Time Frame for Completion

Scoring Guide/Rubric

Getting to the "Root" of the Matter:

Why did we choose this topic?

We wanted to gain further

understanding and knowledge

so that we would be equipped

and ready when we re-enter

the classroom in the future.

After the time spent in this class

with research, readings, discussions,

and practice we began to believe

this was a valuable way to learn.

We wanted to build our

knowledge base and become

more confident with

high quality instruction.

We chose this topic because

high quality task instruction is

a whole new way of thinking and

learning for us. Both of us were

taught and “taught” procedural

mathematics in a traditional

classroom.

Due to frustration with trying to

understand the new curriculum

teachings of our own personal children, we have felt the understanding of high quality math instruction was needed.

"There is no decision that teachers make that has a greater impact on students' opportunities to learn, and on their perception about what mathematics is, than the selection or creation of the tasks with which the teacher engages students in studying mathematics."

Lappan and Briars, 1995

"Not all tasks are created equal, and different tasks will provoke different levels and kids of student thinking."

Stein, Smith, Henningsen, & Silver, 2000

Connecticut Common Core of Learning, Mathematics Assessment Project

New Jersey Mathematics Curriculum Framework- Keys To Success p.558

7. Assess their work to determine the effectiveness of their strategies, make decisions about alternate strategies to pursue, and persevere in developing and applying strategies for solving a problem in situations where the method and path to the solution are not at first apparent.

6. Make conjectures, pose their

own problems, and devise their

own approaches to problem solving.

4. Participate actively in mathematical activity and discussion, freely exchanging ideas and problem-solving strategies with their classmates and teachers, and taking intellectual risks and defending positions without fear of being incorrect.

3. Develop and maintain a positive disposition

to mathematics and to mathematical activity.

2. Recognize the power that comes from

understanding and doing mathematics.

1. Demonstrate confidence as mathematical thinkers believing that they can learn mathematics and can achieve high standards in mathematics, and accepting responsibility for their own learning of mathematics.

Keys

To Success

8. Assess their work to determine the correctness of their results, based on their own reasoning, rather than relying solely on external authorities.

Reference:

New Jersey Mathematics Curriculum Framework- Keys To Success, p.551-557.

5. Work cooperatively with other students on mathematical activities, actively sharing, listening, and reflecting during group discussions, and giving and receiving constructive criticism.

Examples of High Quality Tasks

PROBLEM OF THE MONTH

AND

OTHER fellow teacher SHARING.

WEBSITES

"OUR" CLASS HIGH QUALITY TASK ASSIGNMENTS

DR. LIVERS HIGH QUALITY PROBLEMS FROM CLASS

In another year long study by Cobb and others in 1991, performance on achievement tests was examined of 10 problem-centered mathematics project classes and 8 non-project classes. The researchers also compared compared students' computational proficiency and conceptual development in arithmetic. They found levels of computational performance to be comparable between the two classes, but the project-based class had higher levels of conceptual understanding than the non-project class.

"Other studies involving elementary school students (e.g., Carpenter et al. [1998]; Hiebert and Wearne [1993]) have obtained similar results: Students learning mathematics through problem solving do at least as well a those student receiving traditional instruction on both basic computation and conceptual understanding."

In middle school studies by Ridgeway (2009) and Romberg and Shafer (2002) has shown that "students with problem based instruction have higher levels of mathematical understanding than students with more traditional instruction, and students in the two groups dis play comparable basic number skills."

"Results from a study by Romber and Shafer (2002) suggest that students using problem-centered curricular materials can maintain basic number skills while developing higher-order thinking skills."

Lester, p.250-251

A

High Quality Task

Teacher

In order to Enable their students mathematical minds to grow ....

nurtures the Minds of their students with High Quality Tasks in Mathematics....

Stephanie Birchmore and

Jessica Howard

CEE-580

Dr. Livers

Thanks!

"In reality, no one can teach mathematics. Effective teachers are those who

can stimulate students to learn mathematics. Educational research offers

compelling evidence that students learn mathematics well only when they

construct

their own mathematical understanding. To understand what they

learn, they must enact for themselves verbs that permeate the mathematics

curriculum: 'examine', 'represent', 'transform', 'solve', 'apply', 'prove',

'communicate.' This happens most readily when students work in groups,

engage in discussion, make presentations, and in other ways take charge of

their own learning."

Everybody Counts, 1989, p.58-59

High Quality Tasks

STephanie birchmore

and

Jessica Howard

CEE-580

Dr. Stefanie Livers

Dr. Stefanie Livers Power Point Slides and References

The New Jersey Mathematics Curriculum Framework, (1996). Standard 17- Keys To Success. New Jersey State School Board of Education, pp.551-557.

**REferences**

Connecticut Common Core of Learning, Mathematics Assessment Project.

mat.aamt.edu.au/.../Designing%20quality%20ended%20tasks.pdf.