Mathematical self-schema: a framework for analyzing adults’ retrospection on high school mathematics

Nonprofessional mathematics tutoring for low-achieving students in secondary schools: A case study

“…Field notes from instructional sessions document comments such as: "I must tell you, I hated this in high school but now it seems rather nice (Sharon, during session on equations)" or "I wish that they had explained it this way when I was a student, it makes much more sense to see it visually first" (Naomi, during session on the slope concept). Yet, as can be expected, shifts in attitudes (if occurred at all) were not deep enough to alter the tutors' mathematical selfschemas, since this construct is assumed to be persistent (Karsenty, 2004).…”

“…On the contrary, most of them, although generally being successful as former mathematics students, stated they were pleased to be finished with mathematics upon graduation from high school. Only one tutor was characterized by the positive mathematical self-schema (Karsenty, 2004) while six tutors were characterized by the indifferent mathematical selfschema. Thus, it is most unlikely that students were motivated by tutors through conveying positive feelings towards mathematics per se.…”

“…Other observed characteristics are poor note-taking and homework habits and short concentrating periods. Some low achievers in mathematics develop a negative mathematical self-schema (Karsenty, 2004), i.e., feelings of fear, stress, and resentment towards mathematics. Lastly, low achievers in mathematics tend to view mathematics as an esoteric, unattractive subject, detached from their common sense (Karsenty & Arcavi, 2003).…”

“…Of the nine tutors, seven chose the statement "Glad I don't have to do this anymore" as one representative of their feelings towards mathematics. Using the categorization offered by Karsenty (2004), the statement choices suggest that only Gabriel can be characterized by the positive mathematical self-schema; Miriam and Sam may by characterized by the semi-positive mathematical self-schema, and the other six tutors seem to be characterized by the indifferent (or even somewhat negative, as in Hanna's case) mathematical self-schema. This characterization is confirmed by field notes from individual meetings with tutors.…”

Exploring informal mathematical products of low achievers at the secondary school level

“…This practice not only decreases the students' chances to benefit from helpful instruction, but is also harmful in terms of affective results. The following citation, taken from a study investigating adults' retrospection on high school mathematics (Karsenty, 2001(Karsenty, , 2004, illustrates this point. Ilan, a 40-year-old businessman, describes the teacher who taught his mathematics class more than 25 years ago.…”