President's Message - December 2011

Using Rich Assessment Tasks

Growing success: Using multiple sources of evidence to evaluate student Achievement

With the release of the Growing Success document (Ontario Ministry of Education, 2010), mathematics educators have been provided with the opportunity to reexplore assessment practices and consider what these look like specifically within the context of mathematics.

In the Evaluation section of the policy document, we are presented with what it means to evaluate student achievement. "Evidence of student achievement for evaluation is collected over time from three different sources-observations, conversations, and student products. Using multiple sources of evidence increases the reliability and validity of the evaluation of student learning. 'Student products' may be in the form of tests or exams and/or assignments for evaluation.

Assignments for evaluation may include rich performance tasks, demonstrations, projects, and/or essays." (Ontario Ministry of Education, 2010, p. 39)

Rich performance tasks provide teachers with the opportunity to observe process and examine product. But what might a rich performance task look like in mathematics?

A Look at Criteria for rich Assessment tasks

NCTM's Mathematics Assessment: Myths, Models, Good Questions, and Practical Suggestions (Stenmark, 1991, p. 16), presents us with some suggested criteria for performance tasks. The list, which is adapted from one developed by Steve Leinwand and Grant Wiggins, offers us a number of characteristics for examining and developing such tasks. As we explore the characteristics presented, I invite you to consider rich "assessment" tasks as our broader lens for exploring these characteristics, rather that just "performance" for evaluation.

ESSENTIAL vs. TANGENTIAL

• The task fits into the core of the curriculum.
• It represents a "big idea."

Rich assessment tasks offer teachers with the opportunity to focus on a "big idea" through the clustering of grade/course expectations. Carefully designed, these tasks enable students to make connections based on important mathematics.

AUTHENTIC vs. CONTRIVED

• The task uses processes appropriate to the discipline.
• Students value the outcome of the task.

Rich assessment tasks engage students in the actions of mathematics, otherwise known as the mathematical processes. Through problem-solving, reasoning and proving, reflecting, representing, connecting, selecting tools and computational strategies, and communicating, students appreciate the utility and power of mathematics as they apply their knowledge and skill to solve meaningful problems. They value the time that they are given to engage in their best mathematical thinking.

RICH vs. SUPERFICIAL

• The task leads to other problems.
• It raises other questions.
• It has many possibilities.

As students engage in such assessment tasks, they uncover the complexity of mathematical thinking that is needed to solve problems. As students pose questions, such as, "What if...?," "How would... affect...?," "Why does this work?," "Do we need to consider...?," they set the stage for their inquiry and envision the possibilities.

ENGAGING vs. UNINTERESTING

• The task is thought-provoking.
• It fosters persistence.

An engaging assessment task is one that will stimulate student interest and engage students in a "good struggle," fostering motivation, perseverance, and resilience.

ACTIVE vs. PASSIVE

• The student is the worker and decision maker.
• Students interact with other students.
• Students are constructing meaning and deepening understanding.

In contrast to a quiz or test, rich assessment tasks offer students the opportunity to interact with other students. As students work collaboratively to explore the task presented, students "bump up" ideas with others. The teacher can focus his or her attention on listening to students as they clarify their mathematical thinking, present conjectures, and share reasoning. In addition, he or she can pose questions to help students make their thinking explicit. Rich assessment tasks enable students to be active in the work as they negotiate meaning and deepen their understanding.

FEASIBLE vs. INFEASIBLE

• The task can be done within school and homework time.
• It is developmentally appropriate for students.
• It is safe.

Rich assessment tasks are safe and offer an entry point for all students, while preserving the intent of the assessment of curriculum expectations. As students continue to construct meaning by making connections, they seek out opportunities to revise and/or refine their work. Naturally, this can provide opportunities for work on the task within school and home environments.

EQUITABLE vs. INEQUITABLE

• The task develops thinking in a variety of styles.
• It contributes to positive attitudes.

In honour of the diverse ways in which students think and make sense of mathematics, it is important to design an assessment task that reflects this diversity. Whether students are systematic in their approach to solving problems or "out of the box" thinkers who cycle through different processes before solving a problem, the task must be accessible to a range of diverse learners. The design of the task offers opportunities for students to enter into the problem, using ways of thinking that are familiar or comfortable to them, and encourages students to explore different ways of thinking. Students develop confidence in their ability to approach and solve problems, and as a result, develop positive attitudes toward mathematics.

OPEN vs. CLOSED

• The task has more than one right answer.
• It has multiple avenues of approach, making it accessible to all students.

Rich assessment tasks that are open give permission to students to think creatively and divergently. Given that there is more than one way of solving the problem and more than one right answer, students recognize that understanding mathematics is not about memorizing rules and procedures, but about developing the flexibility and mathematical habits of mind that will equip them with the tools needed to solve problems within and beyond the classroom. When we create assessment tasks that provide multiple avenues of approach, we honour the mathematical knowledge and understanding that students bring.

Developing an Assessment Task On page 17, Stenmark (1991) offers educators some suggestions for developing assessment tasks.

Start with an idea.	What existing resources could I use? With whom might I work to brainstorm such ideas?
Test the idea.	Does it meet the criteria for Rich "Assessment" Tasks? Will my students engage in the context?
Begin converting the idea.	Where does it fit in the curriculum? What will my students have to know? Describe the task and furnish information to students on the criteria. Will these be clear to students?
Consider response formats.	Will I require written and/or oral components? What group discussions and activities are needed?
Develop teacher notes.	What do students need to know ahead of time? What materials and equipment are needed? What amount and kind of guidance should I provide?
Draft an assessment approach.	Look for process and product. How will I assess these? What attitudes and attributes do I hope to see? Why are these important? How will I assess these? Define levels of performance, as appropriate. Do these reflect the categories of achievement?
Try out the task.	Which colleagues will I ask to review the task and provide feedback? Administer the task in a few classrooms and seek out feedback from students. How will I use this feedback?
Revise where necessary.	Based on the feedback, what revisions should I make?

Some Final Thoughts

As you reflect upon how, when, and why you might incorporate rich assessment tasks into your program, I invite you to consider the implications for you as an educator and for your students.

• How might these tasks reveal student thinking in a different way than a test or quiz?
• What kind of support do you anticipate that students will need when they begin working on such tasks?
• What support will you need as you create and assess such assessment tasks?

I wish you well as you consider implementing rich assessment tasks in your grade/course, and look forward to hearing from you about your journey.

References
Ontario Ministry of Education. (2010). Growing success: Assessment, evaluation, and reporting in Ontario schools - first edition, covering grades 1 to 12. Toronto: Queen's Printer.
Stenmark, J.K. (Ed). (1991). Mathematics assessment: Myths, models, good questions, and practical suggestions. Reston, VA: National Council of Teachers of Mathematics.

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