Stein, Engle, Smith, & Hughes', (2008) offer a pedagogical model that illustrates five key principles or practices designed for whole class discussions after ...
Developing the observation instruments for the classroom observation and interviews This projects hinges on the frameworks of Schoenfeld’s “Teaching for Robust Understanding in Mathematics (TRU Math) analytic scheme” (Schoenfeld & Floden 2014); Stein et al. (1996) five key pedagogical principles model. Schoenfeld (2014:2) postulates five dimensions of an effective lesson that capture an essential component of “productive mathematics classrooms – classrooms that produce powerful mathematical thinkers” and Kilpatric, Swafford & Findell’s (2001) five strands of good mathematics teachers According to Kilpatrick, Swafford & Findell’s (2001) Teachers with such skills would exhibit ‘five desirable strands of good mathematics teachers and learners’ and that Learners in such classrooms are regarded as mathematically proficient if they possess the following knowledges: • Conceptual understanding – comprehension of mathematical concepts, operations and relations; • Procedural fluency – skill in carrying out procedural flexibly, accurately, efficiently, and appropriately; • Strategic competence – ability to formulate, represent, and solve mathematical problems; • Adaptive reasoning – capacity for logical thought, reflection, explanation and justification; and • Productive disposition – habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and ones’ own efficacy Schoenfeld & Floden ‘s (2014) framework of ‘Teaching for Robust Understanding in Mathematics (TRU Math) summarised below informed both the observation schedule as well as focused interview documents.
The project also used Stein, Engle, Smith, & Hughes’ (2008) Key pedagogical principles for mathematically effective classrooms Stein, Engle, Smith, & Hughes’, (2008) offer a pedagogical model that illustrates five key principles or practices designed for whole class discussions after learners’ work on cognitively challenging tasks namely Anticipating Students’ Mathematical Responses - teachers envisage how learners will approach a problem task and anticipate their responses; Monitoring Learner Responses - involves identifying the strategies or representations used by the learners; Purposefully Selecting Student Responses - teacher uses learners’ particular aspects of mathematics or methodologies to reinforce whole class learning; Purposefully Sequencing Student Responses- Teacher maximise learners achieving their mathematical goals by making purposeful choices about the order in which learners’ work is presented; Connecting Student Responses- Teacher draws connections between learners’ different responses and expands on underlying mathematical ideas. The three frameworks were used to develop and streamline the observation instrument as well as the interview schedules. References Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press. Schoenfeld, A.H., Floden, R.E., & the Algebra Teaching Study and Mathematics Assessment Project. (2014). An introduction to the TRU Math Dimensions. Berkeley, CA & E. Lansing, MI: Graduate School of Education, University of California, Berkeley & College of Education, Michigan State University. Retrieved March, 2014 from: http://ats.berkeley.edu/tools.html. Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning. (10):313-340
