Linking assessment, instruction and learning in Science and Mathematics

11/15/2012  |  PAGE KEELEY
stem curriculum

Ask a science or mathematics educator what the first word is that comes to mind when they hear the word assessment, and the response is likely to be the “T word”— testing.

Testing, a form of summative assessment, represents only a fraction of the kinds of assessment that occur on an ongoing basis in an assessment-centered science or mathematics classroom. Unlike summative assessment used to document student achievement, formative assessment’s primary purpose is to support learning and inform instruction (NRC 2001). It fits seamlessly into conceptually-based science and mathematics instruction, as emphasized in the Mathematics Common Core (CCSSI 2010) and Framework for K-12 Science Education (NRC 2011) because of its emphasis on questions that elicit deeply rooted misconceptions and common errors and techniques that engage learners in constructing explanations and engaging in scientific argumentation and mathematical discourse. However, for formative assessment to be used effectively, it needs to be purposefully linked to clear and explicit learning goals and rooted in good teaching practices.

One of the questions I am frequently asked when I am working with schools to help teachers implement formative assessment practices is, “When do we use formative assessment and how do we pick a formative assessment technique?” My answer is that formative assessment can be used at any point in an instructional cycle as long as there is a clear purpose in mind. Your purpose informs the type of formative assessment classroom technique (FACT) you choose to meet a particular teaching and learning goal. Regardless of the instructional model teachers use in their classrooms, there are common stages in science and mathematics instruction that my colleague, Cheryl Rose-Tobey and I, have identified in the Science Assessment, Instruction, and Learning Cycle (SAIL Cycle) or the mathematics version — the MAIL Cycle (Keeley, 2008; Keeley and Tobey, 2011).

“A good idea — poorly implemented — is a bad idea” (Ainsworth and Viegut 2006, p. 109). One of the keys to successful implementation of formative assessment is to be purposeful. Explicitly identifying your reason for using a FACT and linking it to the stage of instruction in which it can best support learning is a vital step in selecting a FACT. Using the stages in the SAIL or MAIL Cycle, I will describe some of the ways FACTs can be used to purposefully integrate assessment, instruction and learning.

Engagement and Readiness Stage

In this combined stage, students’ curiosity and interest in the scientific or mathematical content is activated. It is also the stage during which teachers determine students’ readiness to learn the content. For example, a Justified List formative assessment can be used at the beginning of an elementary science unit on seeds to interest students in the content, activate their thinking, and generate curiosity to ask questions about seeds. Students are given a list of things such as water, soil, air, light, darkness, food, gravity, warm temperatures, cold temperatures, and are asked to check off the things seeds need to grow and provide an explanation for why seeds need the things selected from the list. The teacher can quickly scan students’ responses to gather valuable data about students’ prior knowledge and experiences related to living things and needs of seeds. This assessment data helps the teacher determine prerequisite learning goals that may need to be addressed before students are ready to engage with the concepts and skills that make up the learning targets.

Eliciting Prior Knowledge Stage

Elicitation is the process of drawing out students’ existing ideas about a scientific process, phenomenon, mathematical concept, or procedure. During this stage the teacher identifies preconceptions students bring to their learning and uses the information to design appropriate learning experiences that will challenge students’ existing ideas and support conceptual change. At the same time it provides a metacognitive opportunity for students to surface their own ideas, become more aware of others’ thinking, and identify what they know or need to know more about during the teaching and learning process.

For example, a teacher might use a Card Sort strategy to elicit students’ ideas about algebraic variables. Given cards with examples of letters and symbols used for various purposes, students sort them into examples of the use of variables (such as 3b=24) and examples that are not considered a use of variables (such as using the letters a,b,c to label the sides of a triangle). The strategy reveals some of the misconceptions students have about algebraic variables that inform next steps for the lesson.

Exploration and Discovery Stage

In this stage students have an opportunity to explore and discover new ideas through rich scientific or mathematical discussions or investigations. The teacher listens carefully for evidence of students’ thinking as they engage in discussion or interact with materials or manipulatives to explore ideas. A Predict-Explain-Observe (P-E-O) technique can be used to to initiate a prediction, provide an explanation for the prediction, and then launch into making observations to test the prediction. As students make observations, they sometimes see that their observations do not match their prediction, which leads to further investigation or discussion of alternative explanations.

For example, students might be asked whether a thermometer placed inside a mitten would have the same or different temperature reading than a thermometer placed next to the mitten. The P-E-O FACT provides the context for launching into an investigation of heat transfer and temperature as well as valuable information about students’ misconceptions. This information is taken into account as the teacher monitors the investigation and guides students toward the discovery that some objects by themselves do not generate their own heat but rather slow down the transfer of heat.

Concept and Skill Development Stage

After students have had an opportunity to engage in exploration and discovery through investigations or small group discussions, the teacher guides the class through the sense-making process that leads to the development of conceptual understanding of formal scientific and mathematical concepts, skills, and procedures. Assessment probes are used at this critical juncture to determine the extent to which students have grasped a concept or skill, recognized patterns or relationships among ideas, and connected their experiences to appropriate terminology. Assessment data identifies the need for further instructional experiences and readiness to move on to new concepts and skills. For example, assessment probes on measurement may be used to make sure students understand the importance of recognizing how to use a nonzero starting point to measure length or distance traveled. The probe provides data to help teachers decide whether to provide additional opportunities to reinforce this important measurement skill before moving on to the next series of lessons. It is also an opportunity to provide feedback to the student or the class so that they can self-assess or recognize their measurement error and consider ways to correct it.

Concept and Skill Transfer Stage

An important aspect of learning for understanding is being able to transfer ideas learned in one context to a new context. The FACT, Thought Experiments is useful in analyzing how students connect “learned” ideas to contexts not encountered previously.

For example, can students use ideas they learned about gravity to explain how a ball would fall if it were dropped through a hole that went from one side of the Earth to the other. It is called a thought experiment because students could not realistically test it but have to think through what would happen if they could perform the experiment.

This technique also provides a metacognitive opportunity for students to think about how to use their knowledge and skills in new situations. The information often reveals the extent students were bound by the context in which they learned about the content and helps inform the teacher about adjustments that may need to be made to their instructional unit so that students could transfer their learning from one context to another.

Self-Assessment and Reflection Stage

Self-assessment and reflection are critical aspects of any instructional cycle that should take place throughout the learning process to provide opportunities for students to monitor their own thinking and learning. Reflection can also culminate in an opportunity for students to compare what they thought before or during a sequence of instruction to their current understanding. For example, the FACT, I Used to Think __, But Now I Know ___, where students fill in the blanks, promotes metacognition as well as gives the teacher an opportunity to assess the extent of conceptual change before and after instruction.

Reflection is probably the most overlooked aspect of assessment and instruction both in student learning and professional practice. Whether you are a teacher, administrator, or other type of science or mathematics specialist, I encourage you to reflect on your formative assessment experiences and think about what you could do differently to encourage the effective use of formative assessment. What can you do in your classroom or school to build the capacity of science and mathematics educators to use assessment for learning, in addition to assessment of learning? Because reflection is part of a cycle, it doesn’t end with this question. Hopefully your response will feed back into actions you can take to purposefully integrate assessment, instruction, and learning.

Page Keeley is the author of several books on science and mathematics formative assessment and has a web site at that highlights formative assessment. She is the senior program director at the Maine Mathematics and Science Alliance in Augusta, Maine, and a past president of the National Science Teachers Association (NSTA).
References Ainsworth, L., and D. Viegut. 2006. Common formative assessments. Thousand Oaks, CA: Corwin Press.
Common Core State Standards Initiative (CCSSI). 2010. The standards: Mathematics. Available at:
Keeley, P. 2008. Science formative assessment: 75 practical strategies for linking assessment, instruction, and learning. Thousand Oaks, CA: Corwin Press.
Keeley, P. and C. Tobey. 2011. Mathematics formative assessment: 75 practical strategies for linking assessment, instruction, and learning. Thousand Oaks, CA:
Corwin Press. National Research Council (NRC). 2001. Knowing what students know: The science and design of educational assessment. Washington, DC: National Academies
Press. National Research Council (NRC). 2011. A framework for K-12 science education. Washington, DC: National Academies Press.
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