Borko & Livingston 1989 Cognition and improvisation: Differences in mathematics instruction by expert and novice teachers.

Borko, H., & Livingston, C. (1989). Cognition and improvisation: Differences in mathematics instruction by expert and novice teachers. American Educational Research Journal, 26(4), 473-498. Doi: 10.3102/00028312026004473


Summary: This qualitative study examines in the differences between novice and expert pedagogical expertise in planning, teaching, and reflecting. They found stark differences and conclude that teacher preparation programs need to consider developmentally-appropriate practice. It is interesting to note that the authors talk about pedagogical expertise but do not reference current notions of noticing, yet their work is really about noticing. It seems as if this article is a precursor to the work of noticing.


  • four student teachers and their corresponding cooperating teachers
  • interviews
  • observations of teaching
  • reflection documents


Main Findings from Abstract:

  • “Novices showed more time consuming, less efficient planning, encountered problems when attempts to be responsive to students led them away from scripted lesson plans, and reported more varied, less selective post lesson reflections than experts” (p. 473).
  • This means that “novices cognitive schemata are less elaborate, interconnected, and accessible than experts’ and that their pedagogical reasoning skills are less well developed” (p. 473).


Terms and Definitions:

  • Schema: “A schema is an abstract knowledge structure that summarizes information about many particular cases and the relationships among them (Anderson, 1984).
  • Shavelson (1986) descried three types of schemata that seem to characterize teachers’ knowledge systems: scripts, scenes, and propositional structures” (p. 475)

    • “A script is a knowledge structure that summarizes information about familiar, everyday experiences. Relationships in a script are temporal. Expert teachers have scripts for common teaching activities such as checking homework, presenting new information, providing guided practice, and conducting class discussions” (p. 475).
    • “Scenes represent teachers’ knowledge of people and objects in common classroom events such as whole-gropu instruction, small-group work, and independent seatwork. The relationships in scenes are spatial” (p. 475).
    • “Propositional structures represent teachers’ factual knowledge about components of the teaching-learning situation such as the students in their classrooms, subject matter, and pedagogical strategies” (p. 475).
  • “Leinhardt and Greeno (1986) hypothesized that experts’ teaching is based on operational plans or ‘agendas’ for lessons. These agenda consist of specific versions of the schemata in their knowledge systems” (p. 475).


Important Quotes:

  • Teaching as Improv

    • “Yinger (1987) suggested that we can understand some aspects of interactive teaching as improvisational performance. When improvising, a teacher begins with an outline of the instructional activity. Details are filled in during the class session as the teacher responds to what the students know and can do. Preparation for such improvisation entails the creation of general guidelines for lessons that are designed to be responsive to the unpredictability of classroom events. When planning for a structure lesson, in contrast, the teacher attempts to predict and then identify ways to control classroom events and action” (p. 476).
  • Experts engaged in long term planning whereas novices rarely did that. Their planning was day-to-day and much more detailed. Experts used planning as a framework for teaching whereas novices used it more as a script. Experts still had mental plans but they allowed for flexibility and anticipated contingencies based upon student performance as compared to prescribed decisions.
  • In post lesson reflection conferences, experts were more concise and focused on student misconception and understanding of the material whereas novices’ reflections were more varied and focused more on themselves and management as compared to students and student understanding. While both had elements of students, experts focused on understanding whereas novices focused on participation and active involvement.
  • “Like improvisational actors, [expert] teachers work from mental scripts that consist of general outlines of their lessons. They fill in the outlines during interactive teaching to ensure that their instruction is responsive to student performance” (p. 483).
  • “The success of the expert teachers’ improvisation seemed to depend on their ability to quickly generate or provide examples and to draw connections between students’ comments or questions and the lesson’s objectives. In terms of cognitive structure, successful improvisational teaching requires that the teacher have an extensive network of interconnected, easily accessible schemata. Further, he or she must have the ability to select particular strategies, routines, and information from these schemata during actual teaching and learning interactions based on specific classroom occurrences” (p. 485).
  • MY THOUGHTS – It appears that these differences are also related to career stage and stages of concern. For example, the novices were preparing for tomorrow, which is indicative of the survival stage.
  • Planning for novices took a greater amount of time and novices were much more inefficient than experts in their planning.
  • “Several of the difficulties the novice teachers encountered, such as the time-consuming nature of their planning and the inability to anticipate student problems, are difficulties encountered by most teachers the first time they teach a course or body of knowledge. Any teacher will think and act like a novice, to some extent, the first time he or she attempts to teach a particular body of knowledge. This observation suggests that the patterns seen in novices’ teaching rest on differences in knowledge, which can in turn be analyzed in terms of cognitive structures” (p. 489).
  • “If novices’ cognitive schemata are less elaborate, interconnected, and accessible than experts’ we can account for several patterns seen in novice teachers that are not observed among experts: more time-consuming, less efficient planning; deviations from scripted lesson plans when attempting to be responsive to students; and varied, less selective postlesson reflections. Experts can plan more quickly and efficiently than novices because they are able to combine information from existing schemata to fit the particulars of a given lesson” (p. 490).
  • “Experts are also better able than novices to predict where in a course students are likely to have problems. Their better-developed propositional structures for content knowledge, pedagogical content knowledge, and knowledge of learners, and the more extensive interconnections among these schemata, enable them to predict misconceptions the students may have and areas of learning these misconceptions are likely to affect” (p. 491).
  • “Novices’ cognitive schemata often must be elaborated during the decision-making process itself, so they are less able to determine whether information is relevant to the decision. They therefore consider much more information than do experts when planning. Similarly, they are less selective in the cues to which they attend during interactive teaching and less focused in their reflections following the lessons” (p. 491).
  • “Finally, difficulties that novices encounter when deviating from scripted lesson plans can be understood as limitations in their ability to improvise. As we suggested earlier, successful improvisational performance requires an extensive network of interconnected, easily accessible cognitive schemata. Novices do not have as many potentially appropriate scripts for instructional strategies to draw upon in any given classroom situation as do experts. Nor do they have sufficiently well-developed propositional structures for pedagogical content knowledge to enable the construction of explanations or examples on the spot. Also, because their scripts and propositional structures are not well connected, when they are drawn away from the lesson agenda they have difficulty getting back on track” (p. 491). MY THOUGHTS – Hence the important need for co-teaching.