In an effort to assess the quality of mathematics and science instruction in U.S. classrooms, our Horizon Research team spent 18 months observing more than 350 representative lessons and conducting follow-up interviews with teachers to explore their instructional decision making. The assertion by Burstein and colleagues (1995) that educators cannot measure some aspects of instruction without observing teacher-student interactions expresses the need that inspired our Inside the Classroom study (Weiss, Pasley, Smith, Banilower, & Heck, 2003). We documented, analyzed, and assessed lessons according to specific indicators in several areas: the quality of the mathematics and science content, the quality of implementation, and the extent to which the classroom culture facilitated learning (see Sample Indicators, p. 27).
The observers rated individual indicators in each area on a 1–5 scale, with 1 designating poor and 5 designating excellent, and then looked across these indicators to categorize the lesson's overall quality as low (1, 2), medium (low 3, solid 3), or high (high 3, 4, 5). Low-quality lessons were unlikely to enhance students' understanding of important mathematics or science content or their ability to engage successfully in the processes of science or mathematics. At the other end of the scale, high-quality lessons were structured and implemented in a manner that engaged students with important mathematics or science concepts; such lessons were very likely to enhance student understanding of these concepts and to develop their capacity to do mathematics or science successfully.
Lack of Rigor and Excellence
The findings of our study suggest that U.S. schools fall very short of the ideal of providing high-quality mathematics and science education for all students. Observers classified only 15 percent of K-12 mathematics and science lessons as high in quality; 27 percent were medium, and 59 percent were low.
On the plus side, most mathematics and science lessons included accurate, significant, and worthwhile content, and teachers generally appeared confident in their ability to teach mathematics and science. Fewer than one in five lessons, however, were intellectually rigorous, included effective teacher questioning, or guided students appropriately in making sense of the lesson's content.
Our analyses indicated that the quality of lessons did not depend on whether the teacher used a “reform-oriented” approach or a traditional approach. Some lessons judged to be effective were traditional in nature, using lectures and worksheets; others were reform-oriented, involving students in open inquiries. We also saw both traditional and reform-oriented lessons that were far lower in quality.
We also observed a troubling pattern of differential quality of instruction across types of communities, in classes with varying proportions of minority students, and in classes of varying ability levels. Compared with lessons taught in suburban and urban schools, those taught in rural schools tended to be lower in quality on such key indicators as intellectual rigor and sense making. Similarly, lessons in classes with high percentages of minority students tended to be lower in quality than lessons in other classes. Finally, lessons in classes composed of students considered “low ability” or “middle ability” tended to be lower in quality than those in heterogeneous and high-ability classes.
Features of High-Quality Classrooms
To determine which characteristics were most important in determining quality, we conducted an in-depth analysis of lessons rated very effective and very ineffective. The following factors distinguished the most effective lessons from the least effective ones.
Student Engagement with the Content
One of the most important aspects of effective mathematics and science lessons is significant, worthwhile content. The majority of lessons in the study did, in fact, include such content: observers rated 89 percent of lessons at 3 or above on this indicator.
But important content is not enough. High-quality lessons also invite students to interact purposefully with the content. Effective mathematics and science lessons use various strategies to involve students and to build on their previous knowledge, often using real-world examples or engaging students in firsthand experiences with the concepts or phenomena. For example, in a lesson on fractions and as an introduction to percentages, one teacher in a 7th grade mathematics class asked three students to come to the front of the class for a demonstration. One student measured the height and arm spread of a second student while the third student wrote the measurements on the board. The students used these numbers to express the relationships both as a ratio and as a percentage.
Lessons also need to be at the appropriate level for students, taking into account what students already know and challenging them to learn more. Some lessons go further than simply providing content at an appropriate level for students. Many lessons judged to be highly effective include a variety of experiences that enable students to tap into multiple pathways in developing or reinforcing a concept.
Culture Conducive to Learning
High-quality classrooms are both respectful and rigorous. Students feel free to contribute their ideas and questions, but they are also challenged to engage deeply with the content. Findings from the study suggest that teachers have difficulty combining these two elements: 45 percent of lessons received high ratings for respect, but only 13 percent of lessons were both respectful and rigorous.
Of course, the development of a respectful and rigorous culture does not occur in a single lesson. The teacher must foster this climate over the course of the school year. In observing individual lessons, observers noted evidence of a culture conducive to learning when teachers asked questions that challenged and broadened students' thinking, when students felt free to contribute new ideas and to question the ideas of their peers, and when students exchanged constructive criticism about the findings of an investigation. For example, students in a 5th grade science class worked well in pairs. One student concluded that a rubber band conducted electricity, but her teammate pointed out that she had accidentally touched the wire to one of the clips, completing the circuit. The pair of students then tried the experiment again, taking care to touch only the rubber band, and found that the rubber band was not a conductor. The observer wrote,The teacher eagerly answered questions and encouraged exploration. There was—pardon the pun—an air of electricity and excitement in the room, and the students had to be shooed away from their activities for recess. It would be hard to imagine a classroom more conducive to learning.
Equal Access for All Students
A crucial aspect of the teacher's role is ensuring that no students slip between the cracks. When observers rated the extent to which lessons encouraged active participation of all students, they found that approximately half of the lessons did provide access for all students, but 29 percent of lessons were rated low in this area. Observers described cases in which some students were left out of the lesson as well as cases in which the teacher succeeded particularly well at engaging learners with differing needs.
A 3rd grade lesson provides an example of a teacher ensuring access for all students by altering her lesson plan to accommodate the varying levels of her students. She required all students to depict their observations of the experiment that they had conducted during the class. The more able students completed a six-part, step-by-step description, with pictures, of the experiment. Other students, who had more difficulty with writing, were allowed to express their understanding through a drawing.
Effective Questioning
Teachers' questions are crucial in helping students make connections and learn important mathematics and science concepts. Effective questioning—the kind that monitors students' understanding of new ideas and encourages students to think more deeply—was relatively rare in the mathematics and science classes we observed. One 8th grade mathematics class illustrates a teacher's question that led students to examine and deepen their understanding:When searching for examples of tessellations around the room, one student proposed the border of the bulletin board, which was made of circles.Student: “How about the border?”Students: “No . . . that won't work.” (Several students talk at the same time and reject this contribution.)Teacher: “Why won't it work? Can the circle ever work?”The discussion became focused on why the circle did not create a pattern that fit the definition of a tessellation. Although the student who suggested the border had been focusing more on patterns, the disagreement helped him redirect his analysis back to the definition of tessellations presented earlier in the lesson.
Unfortunately, teachers more often used low-level, “fill in the blank” questions asked in rapid-fire fashion with an emphasis on getting the right answer and moving on rather than helping students make sense of the concepts, as in this 1st grade mathematics lesson:The teacher distributed crayons and worksheets and began the lesson by noting, “Today, we're going to find differences for facts of five. When we say difference, does that mean add or subtract?” (Calls on a student.)Student: “Add?”Teacher repeats what she said.Another student says: “Subtract?”Teacher: “That's right. Before we start, I want to pass out these mats and counters. Take five counters out of the bag. Place them on the top line of the mat. Now put three white counters on the bottom.If I tell you 5 + 3, are you going to add everything or take something away?”Students: “Take away.”Finally a student says: “Add.”Teacher: “If I say 9-5, how many are you going to take away?”Students call out every number except five.Teacher (getting impatient): “You're not listening.”
Assistance in Making Sense of the Content
Teacher questioning is not the only way to help students understand mathematics or science content. A teacher's ability to provide clear explanations at appropriate junctures as the lesson unfolds often determines students' opportunities to learn. Effective lessons engage students in doing intellectual work, with the teacher helping to ensure that students are making sense of the key mathematics and science concepts.
Most of the lessons that we observed lacked an adequate emphasis on sense making. Only 16 percent of lessons observed received high ratings in this area. In some lessons, however, teachers did help students make sense of the content and see connections among ideas. The teacher in a high school human anatomy and physiology class, for example, began a lecture by drawing a diagram of a nerve receptor connected by a nerve fiber to the brain. He explained the concept of the threshold for a receptor, noting that stimuli could be either sub-threshold, threshold, or super-threshold; he stressed that the receptor responds to the stimulus and sends a signal to the brain only after the threshold is reached. He spent most of the remainder of the lesson explaining that receptors vary in threshold, emphasizing that “your brain recognizes the highest threshold receptor stimulated.” The teacher summarized the lecture by reiterating the threshold principle and the differentiation of nerve receptors by threshold. The observer commented,This lecture was extremely engaging, accessible, and focused on worthwhile content. The teacher emphasized sense making throughout the lesson, using examples familiar to the students and connecting the content to their lives.
Instructional Decisions of Teachers
In planning lessons, teachers are influenced by a multitude of factors that determine what content they teach, how they teach it, and what materials they use to engage students with the content. We need to understand these instructional influences as a precursor to improving curriculum and instruction.
Following our observations, we conducted extensive interviews with the teachers to determine what factors influenced their instructional design decisions. Our findings indicated that someone other than the teacher usually made the decisions about the content of mathematics and science lessons. Teachers cited state- or district-level curriculum standards, textbooks and curriculum programs selected at the district level, and accountability systems related to student achievement as influences on their decisions about what to teach. For many teachers, pressure for their students to do well on high-stakes testing drove their selection of topics.
These external policy instruments appeared to have a smaller influence, however, on the selection of instructional strategies in lessons. Although most teachers relied to some extent on the textbook or curriculum program in their school or district, for the most part teachers reported designing their instruction with little external guidance. They used resources and strategies grounded in their beliefs about mathematics and science, about effective pedagogy, and about the students they taught.
Preparing and Supporting Teachers
The findings of the Inside the Classroom study have implications for the continuing education of the mathematics and science teaching force and for the support provided to teachers.
Teachers need a vision of effective instruction to guide the design and implementation of their lessons. Findings from this study suggest that rather than advocating one type of pedagogy over another, the vision of high-quality instruction should emphasize the need for important and developmentally appropriate mathematics or science learning goals, instructional activities that engage students with the mathematics or science content, a learning environment that simultaneously supports and challenges students, and attention to appropriate questioning and sense making. A number of interventions would help teachers understand this vision and improve instructional practice in their specific contexts.
First, teachers need opportunities to analyze a variety of lessons in relation to these key elements of high-quality instruction. Lesson study conducted with skilled, knowledgeable facilitators would provide teachers with helpful learning opportunities.
Second, the support materials accompanying textbooks and other instructional materials should provide more targeted assistance for teachers—clearly identifying the key learning goals for each suggested activity, sharing the research on students' cognitive development in each content area, suggesting questions and tasks that teachers can use to monitor student understanding, and outlining the key points that the teacher should emphasize to help students make sense of the mathematics or science concepts.
Third, workshops and other teacher professional development activities should reflect the elements of high-quality instruction with clear, explicit learning goals, a supportive but challenging learning environment, and ways to ensure that teachers are developing their understanding. Without question, teachers need to have sufficient knowledge of the mathematics and science content they teach. The teacher's content knowledge, however, does not guarantee high-quality instruction. The Inside the Classroom observations indicate that teachers also need expertise in helping students develop an understanding of that content. Teachers need to know how students typically think about particular concepts, how to determine what a particular student or group of students thinks about those ideas, and how to help students deepen their understanding.
Fourth, policymakers need to explore the apparent inequities in quality of instruction and, if these inequities are confirmed, take steps to resolve them. All students must receive high-quality instruction, regardless of the location of their schools or the demographic composition of their classes.
Finally, administrators and policymakers need to ensure that teachers receive a coherent set of messages. Only when preservice preparation, curriculum, student assessment, professional development, and teacher evaluation policies at the state, district, and school levels are aligned with one another, and in support of the same vision of high-quality instruction, can we expect to achieve the goal of excellence and equity for all students.
