Classroom assessments can actively promote access to learning. In fact, assessments might be the best way to connect more students to conversations and activities directly related to standards. But not all assessments promote equitable access. Assessment must invite rather than exclude, catalyzing the spread of ideas and skills throughout the classroom.
The assessment strategies we suggest for promoting equitable access grew out of our field tests of a project-based math curriculum, the Middle School Math through Applications Project (MMAP). MMAP is a comprehensive, standards-based middle school math curriculum developed at the Institute for Research on Learning with funding from the National Science Foundation. MMAP students learn math by engaging in design projects based on the work of math-using professionals, such as architects and biologists. For example, in one 7th grade unit, the Antarctica Project, students design a research station for scientists in Antarctica. As they draw their floor plans and optimize insulation levels and heating costs against building costs, they learn important and powerful mathematics concepts: scale, area, function, and variable. Concept-focused units follow the design project, clarifying and extending the mathematics.
Improving equity was one of our primary goals in developing MMAP. MMAP is designed to draw traditionally underserved students, such as minorities and girls, into higher mathematics. An assessment strategy that would enhance students' access to mathematics was crucial to the success of our curriculum.
- What are we learning?
- What is quality work?
- To whom do we hold ourselves accountable?
- How do we use assessment tools to learn more?
What Are We Learning?
"Let's talk about some of the math words you heard or used today as you worked on your projects," says Judy Calise to begin the last five minutes of her 8th grade math class. As students call out mathematical terms or phrases, Judy writes them on the chalkboard, solicits examples, and has students ask clarifying questions.
"Function," calls out one student. Judy repeats, "Function. . . . What is function?" One kid says, " How two things go, ya know, with each other." Judy asks for an example. He explains that it's "like heating cost and amount of insulation . . . what they do to each other . . . one going up and one going down."
Judy says "F-U-N-C-T-I-O-N—a relationship" as she writes the words on the chalkboard. "Great. That's right in your investigation, and it's a very important math idea that we'll spend a lot of time on this year, so let's get it up here on the list and let's keep coming back to it with more examples and definitions. This is a big idea for algebra. For tonight I want each of you to write down the word function in your math log and to try to give me the definition and an example. I'll check it tomorrow."
In this example, Judy uses assessments—debriefing and journaling—to engage students in naming, cataloging, categorizing, and relating to help them explicitly connect mathematics and related classroom investigations. Making the connections explicit is particularly important as students face new material. Judy is aware that mathematical skills, concepts, and representations can seem isolated and unrelated to one another and without application in the students' world. She debriefs with the intention of helping students make connections among the materials, the activities, and the math concepts.
How is this assessment process related to equity? The debriefing results in a public and detailed display of connections that is accessible to everyone in the class. Combining this public display with private reflection helps each student process the information and connect it to a larger picture. When kids begin to see the big picture, they receive multiple entryways to the process of meeting standards, regardless of their previous achievement levels.
What Is Quality Work?
The question about what students learn asks students to identify the discipline-related perspectives and practices in which they are engaging. The next step is to deliberate on what constitutes quality work within that discipline. Certain assessment techniques are useful for making standards for quality work explicit and meaningful, which is an essential feature of an equitable learning environment (Delpit, 1995). Goals and standards become clearer, and creating a forum for a public analysis of concepts increases exposure and access to the mathematics content.
During one of our assessments—a whole-class review of group floor plans for the Antarctica research station—a student pointed out that one plan depicted stairs ascending eight feet over just three feet of horizontal space, resulting in an unrealistically steep staircase. Jessica: How big are your stairs? 'Cause they go down and you only have them three feet by three feet so you have three feet to go down the stairs.Araceli: [examining the floor plan] I don't get what you're saying.Jessica: The stairs have to be like this [shows with hands] and an average ceiling is eight feet and you have to get down stairs.
Several groups had drawn stairs in a similar manner, that is, not accounting for the space that a staircase requires. Jessica challenged this thinking and clarified how and why the students needed to change their floor plans. She helped make explicit one criterion for a quality design: A staircase needs sufficient space for a person to walk up and down.
This whole-group review demonstrates how assessment can create meaningful and shared definitions of quality work. Learners apply externally defined standards while creating standards to evaluate the authentic work in which they are involved. Equity is enhanced because standards are made explicit to all students.
Other common assessment techniques facilitate identifying quality and making criteria more meaningful. In many classrooms, for example, students work together to create a rubric for evaluating their work and then apply their rubric in peer and self reviews. The conversations that define the rubric, together with the act of deciding how a particular piece of work fares against that rubric, create a vocabulary and a standard for evaluation that become a known and shared definition of improved practice. It is in explicit conversation and use that rubrics and standards take on meaning.
To Whom Do We Hold Ourselves Accountable?
In an equitable learning situation, everyone has a clear sense of the audience or beneficiary of the work that he or she does (Wiggins, 1998). Everyone also has a clear sense of the nature and consequences of evaluations. But simply telling students to whom and for what they are accountable does surprisingly little to clarify accountability relationships. A well-planned assessment opportunity, in contrast, is surprisingly powerful for both establishing and clarifying accountability.
Teachers often organize design review presentations midway through the floor-plan component of the Antarctica project so that each group can presents its design. Students in the audience quickly home in on important problems, ranging from functional to mathematical: "According to your scale, that bed is 15 feet long!" or "The scientists need more than one exit—what if there's a fire?" Within a few presentations, critiques become shorter as mistakes become rarer. Students begin to hold themselves accountable to their peers for meeting the standards of functionality and correctness.
- The assessment gives students shared practice at being accountable. Each criticism and response teaches everyone present something about the nature and consequences of evaluation.
- It is tied to revision opportunities. Design groups get what they need to hold up their end of the accountability relationship: a chance to revise with clear criteria for doing so.
- It is tied to a cycle of assessments by the same assessors. Students know that they will present their designs again at the end of the project. The peer accountability relationship becomes palpable and ongoing, and thus effective and efficient.
- It includes multiple perspectives. Through the peer accountability relationship, other sources of accountability are defined: accountability to the fictitious inhabitants of the building, accountability to students' cultural sense of functionality, and accountability to standards of mathematical correctness. Equity is enhanced because any perspective can be an entry into the accountability relationship. Once students are hooked, they learn to take on the full range of perspectives.
In short, accountability becomes both something that students practice and an ongoing relationship.
How Do We Use Tools of Assessment to Learn More?
A student who uses written journal entries to understand new mathematical concepts expressed an appreciation for assessment: When we [take notes], all we are doing is copying what the teacher is writing down, and we're not learning anything, but when we . . . write it in our own words, we are beginning to learn things about it.
In an equitable learning situation, students become proficient drivers of the assessment process. They have the tools to improve their skills and understanding. Even when they lack control of assessments (as in standardized tests), they are savvy consumers of assessment data and know the consequences of their performances. A major goal of authentic assessment is to help students develop the capacity to evaluate their own work against public standards, to revise, modify, and redirect their energies, taking initiative to assess their own progress. (Darling-Hammond, Ancess, & Falk, 1995, p. 12)
Students come to own the assessment by practicing and reflecting on it. The teachers with whom we work teach assessment while they teach math. They critique sample journal entries as a class. They role-play effective peer reviews. They ask students to discuss the purposes and strengths of each assessment technique and to design their own assessments.
For example, Pam Ensign uses whole-class assessment to help students learn to write productive journal entries. She asks students to critique an anonymous entry from a student who is not part of the class. Pam asks, "Does anyone notice anything about the second paragraph?" A student says, "They said what they did [in class] but they didn't say anything about what they learned."
Pam walks to the chalkboard. "How could we rewrite this paragraph to be about what they learned?" The students work together to construct a better entry. They all copy the entry and use it to revise their own journal entries.
Pam knows that not all students come to class knowing how to write journal entries. Without support, these students won't be able to use journals to learn more, and the assessment will unintentionally widen equity gaps. Group reflection, combined with individual practice, helps make journaling a tool that everyone can use to learn effectively.
Achieving Equity
We can achieve our equity goals only by drawing every teacher and student into the process of making standards meaningful. The four questions we propose as assessment strategies promote inclusion by making concepts, processes, relationships, and techniques explicit and openly shared rather than implicit and shrouded.
Classroom assessments, used thoughtfully and continually, bring students into the standards conversation. When students and teachers use assessment together to define practices, quality, accountability, and evaluation, a standard becomes a powerful tool for those who are learning. When standards serve those who are learning instead of those who have already achieved, we are on the road to promoting equity.
