4. Express Misconception and Errors Struggles involving the students’ misconceptions appeared to be instances when mistaken ideas were used as a basis for solving problems rather than students’ confusion or possible error due to carelessness. Teacher Response I situate the four types of teacher responses on a continuum. Figure 1: Teacher Response Continuum I then examine how the following three dimensions of the interactions were affected by the of teacher responses: The level of cognitive demand of the mathematical task; • The attention to the student’s struggle; and • The building on student’s thinking. • The following table summarizes the four types of teacher responses. Table 2: Teacher Response Summary Teacher Characterizations Frequency Dimensions Response Supply 27% Cognitive Demand 1. Telling information Lowered Suggest strategy Attend to Student Correct error Struggle Evaluate student Remove struggle work efficiently. Relate to simpler on Student problem Thinking Decrease process Suggest an time explicit idea for student consideration
4. Express Misconception and Errors Struggles involving the students’ misconceptions appeared to be instances when mistaken ideas were used as a basis for solving problems rather than students’ confusion or possible error due to carelessness. Teacher Response I situate the four types of teacher responses on a continuum. Figure 1: Teacher Response Continuum I then examine how the following three dimensions of the interactions were affected by the of teacher responses: • The level of cognitive demand of the mathematical task; • The attention to the student’s struggle; and • The building on student’s thinking. The following table summarizes the four types of teacher responses. Table 2: Teacher Response Summary Teacher Response Characterizations Frequency Dimensions 1. Telling Supply information Suggest strategy Correct error Evaluate student work Relate to simpler problem Decrease process time 27% Cognitive Demand Lowered Attend to Student Struggle Remove struggle efficiently. on Student Thinking Suggest an explicit idea for student consideration
NCTM_ResearchConference_2014_final.docx