Encountering Proportional Reasoning During a Single Algebra Lesson: A Microgenetic Analysis

• This case study explores how 12-13-year-old students encounter proportional reasoning while working with geometric patterning tasks using concrete materials. The focus is on the students’ use of spontaneous concepts when first dealing with such patterns in the context of collaborative work. Based on video recordings of a single lesson, a microgenetic analysis was performed to identify students’ learning trajectories, starting with students familiarizing themselves with pattern structure, followed by engagement in proportional reasoning, and ending with students perceiving a new technique to handle a situation where proportional reasoning did not suffice. While some student groups were able to move along the whole trajectory, most groups, when facing challenges, regressed to simpler techniques. The results provide new insights into students’ learning trajectories, which can be used to support students’ progress in the context of student-teacher interaction.

Subject headings

SAMHÄLLSVETENSKAP  -- Utbildningsvetenskap (hsv//swe)

SOCIAL SCIENCES  -- Educational Sciences (hsv//eng)

SAMHÄLLSVETENSKAP  -- Utbildningsvetenskap -- Lärande (hsv//swe)

SOCIAL SCIENCES  -- Educational Sciences -- Learning (hsv//eng)

SAMHÄLLSVETENSKAP  -- Utbildningsvetenskap -- Didaktik (hsv//swe)

SOCIAL SCIENCES  -- Educational Sciences -- Didactics (hsv//eng)

SAMHÄLLSVETENSKAP  -- Utbildningsvetenskap -- Pedagogik (hsv//swe)

SOCIAL SCIENCES  -- Educational Sciences -- Pedagogy (hsv//eng)

NATURVETENSKAP  -- Matematik -- Annan matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Other Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

Keyword

algebra

geometric pattern

learning trajectory

microgenesis

proportionality

proportional reasoning

algebra

Publication and Content Type

ref (subject category)

art (subject category)