Teaching, Learning, and Assessment Together

Reflective Assessments for Middle and High School Mathematics and Science

Arthur K. Ellis, David Denton

• Publisher: Routledge
• Year: 2013
• Print ISBN: 9781138162822
• eBook ISBN: 9781317924555
• Edition: 1
• Topic: Education
• Subtopic: Education General

This book offers easy-to-use classroom strategies for middle and high school Mathematics and Science classrooms. They demonstrate how teaching, learning, and assessment are inseparable and seamless. Each strategy will engage your students in activity and reflection, consuming little class time, costing nothing, and uniting the three dimensions of education through reflective practice.

The chapters begin with a reflective teaching strategy, followed by classroom examples. Guiding icons will help you coordinate and implement each strategy. Chapters conclude with a set of learning community discussion questions to guide personal growth as well as faculty discussions.

Strategy 1

I Learned

The reasonable thing is to learn from those who can teach.

— Sophocles

Purpose

The I Learned* statement for assessing learning is a quick and efficient way to get a sense of your students’ grasp of a lesson or activity. It is beautifully simple, and it achieves two assessment goals at once: (1) Each student gives you feedback on what he or she thought was of significance, and (2) the aggregate of the responses informs you to what extent you achieved your teaching goal. Remember that the purpose of school is not teaching—it is learning. Teaching is something one does in order to create opportunities for learning.

Procedure

Here is how the process works. At the conclusion of a class period, with five minutes or so left, ask each student to write down on a sheet of paper, “I learned such and such...” in today’s activity or lesson. For example, if you have just taught students to divide fractions, an I Learned statement by one student might read, “I learned that to divide fractions, you invert the divisor and multiply.” Although such a reflective comment does not answer the “why” or concept of inverting the divisor and multiplying, it does at least get at the skill level or the “how.” The student has shown that he or she knows how to divide fractions. If few or no reflective statements indicate why (the concept) we invert the divisor, this helps you assess the lesson, which is an added purpose of reflective assessment. It could be because you did not explain why. Tomorrow you can do just that. Skip ahead in the text to Strategy 13: Clear and Unclear Windows for some early insight into a way you can get at students’ deeper understandings.

If you have been studying the water cycle with students, an I Learned statement might read, “I learned that water goes through four cycles: evaporation, condensation, precipitation, and collection.” In a unit where students are engaged in cooperative leaning, an I Learned statement could read, “I learned that working together means we have to find out what others think.” Such simple statements are a reasonable place to begin. As students practice writing statements, particularly in the case of older students, their reflections will begin to take on greater depth, but all this comes with time.

These examples come from students who show some basic understanding of significant skills and/or ideas. Of course, not everyone will grasp the main idea, but the point is that even if this is so you are better off knowing that. It doesn’t pay to assume that everyone learned something just because we taught it. And when some students do show a grasp of what was taught and others do not, this becomes a perfect moment for peer teaching.

The first time you try I Learned statements with your class, don’t be surprised if half the papers turned in are blank. This is nothing to be alarmed about. In most cases, students are not asked what they just learned, so they don’t tend to think in those terms. In other words, students are not typically asked to reflect. Also, don’t be surprised if many of the papers contain “irrelevant” or “inaccurate” I Learned statements. Moreover, be sure to share insightful I Learned statements by students with the entire class. All some students need are examples in order for them to grasp the general idea.

We remember having our students write I Learned statements following a presentation by a uniformed naval officer who had spoken to the class. One student’s response sticks in our thoughts to this day. She wrote, “I learned that they have gold buttons on their coat.” It could be argued that this was hardly the main idea of the presentation, which was on the topic of careers, but that is what she said she learned.

One of the joys of I Learned assessment comes from statements by students who not only grasp the intent of the lesson but who see in it really good things that you yourself hadn’t even considered. This is value-added teaching and learning! In other words, they made connections to some prior knowledge or experience. When students write statements that are insightful and even profound, be sure to read those statements aloud to the class. This will help others to understand the process better.

Sometimes what people need most are good examples to get them started. One of the things you will notice if you use this technique over time is that students get better and better at reflection. Of course, keep in mind that learning is a complex process and that students may learn things that you feel were not intended or even to the point. Who knows what prior knowledge a given individual might bring to an activity and how it might affect their learning? It serves as a good reminder that even though we might think we are teaching exactly the same thing to all thirty students, that is simply not the case. Each individual must construct his or her own knowledge. Invariably, people will come up with somewhat different constructions. You need be concerned only if you are convinced that students are not getting the point at all.

It does matter greatly what is taught when it comes to assessing I Learned statements by students. For example, if you are teaching certain skills that you think are crucial, then you do want to be sure that students are grasping those skills. This is known as convergent knowledge; this is especially important in elementary mathematical procedures and in any subject where skills are emphasized. However, if you are teaching complex ideas, then it is quite understandable that students might have varied perspectives on those ideas. You have entered the realm of divergent knowledge. If you are teaching two-place addition, of course, you will hope to receive I Learned statements that are related to the skill. Even in such a case, however, the insights which students generate in learning this can vary considerably. And if you are teaching something as complex as social skills to your class, expect a wide range of insights and personal applications from students.

Outcomes

One use of the I Learned statement is diagnostic. If you receive a large number of statements that you believe are inaccurate or misleading, you will try teaching the same material again, perhaps in a different way. If you receive a mix of statements, you may want to form peer-teaching groups in which those who clearly grasp the content or skill are asked to share their knowledge with students who are having trouble with the material.

The aggregate of the I Learned responses from a class of students is one of the best indicators of your success in achieving your objective in a lesson. Taken together, a classroom set of statements forms a kind of mosaic reflecting the quality of the experience. You can control what you teach, but you cannot control what is learned. Sometimes they are basically the same thing, and on other days, well, they are worlds apart.

How often should a teacher use I Learned statements? The answer is often, but probably not every day. The thing to keep in mind is that you are attempting to raise the level of consciousness of your students. You are asking them to become conscious of what they are learning. In other words, you are asking them to be reflective, to practice metacognition, to think about their learning. Like any technique, the I Learned statement can be overused. It is best to use it intermittently, perhaps three or four times a week; this way students will have it in the back of their minds that you just might use it on any particular occasion, thus helping them to be alert to this possibility and to think about what they are learning just in case they are asked. In time it becomes automatic for them to think that way, in which case you will have achieved a very important educational goal.

Differentiating I Learned Statements

Have students write an I Learned statement cooperatively. One way to accomplish this is to use larger pieces of paper, divide it into four quadrants to add a mathematics spin and then four students can write at the same time. You might find this strategy particularly useful for skill development, for instance, solving one-step algebraic equations. Direct one student to create an equation for the group to solve; then, everyone in the group can solve it showing steps. With additional time, students can discuss their solutions and peer correct. This technique also reduces the number of papers that you have to collect and assess.

Many classrooms are equipped with document cameras and projectors. Use these to show your class exemplary I Learned statements (copying a student reflection onto a transparency as an overhead serves the same purpose). The effect can be dramatic. Select a few praiseworthy reflections to show students at the beginning of the next lesson and the process serves as a visual reminder of the significant learning that took place the day before.

Teachers are busy people and it can be difficult to assess each assignment. Nevertheless, it is important to demonstrate to students that their reflections really matter, and they do. Keep in mind, however, that you can grade I Learned statements in a variety of ways, for example:

♦ Write a quick comment such as “good idea” or “say more.”

♦ Assign a participation grade.

♦ Grade according to the amount written.

♦ Have students assess one another.

♦ Use an I Learned Exit Slip (shown on the next page) to standardize the process.

♦ Visually inspect reflections and mass assign a score.

Consider combining the Post It Up (Strategy 4) and I Learned strategies. For instance, at some point in the lesson, have students write an I Learned reflection, perhaps using an I Learned Exit Slip. Then post the reflections in your room on a piece of poster paper or a section of the dry board. The posted reflections serve as a reference for the next day or as a way to remediate students’ learning during the lesson.

I Learned Exit Slip

From the Classroom

♦ Key Idea: Develop an understanding of heat sources in the earth system. (National Academy Press, 1998)

♦ Instructional Objective: Measure the heat produced by sunlight for 15 minutes. Define heat as a form of energy that can be measured.

♦ Motivational Question: What are some sources of the earth’s heat? Take a moment to define heat as a form of energy that can be measured once students h...

Table of contents

• Cover
• Title Page
• Copyright Page
• Table of Contents
• Meet the Authors
• Acknowledgments
• Preface
• Guiding Icons Defined
• Strategy 1 I Learned
• Strategy 2 Think Aloud
• Strategy 3 The Week in Review
• Strategy 4 Post It Up
• Strategy 5 Jigsaw
• Strategy 6 Key Idea Identification
• Strategy 7 Authentic Applications
• Strategy 8 Parents on Board
• Strategy 9 Search for Meaning
• Strategy 10 I Can Teach
• Strategy 11 Write It Down
• Strategy 12 Learning Illustrated
• Strategy 13 Clear and Unclear Windows
• Strategy 14 Letting Questions Percolate
• Strategy 15 Record Keeping
• Strategy 16 Pyramid Discussion
• Epilogue
• References and Suggested Readings