Browsing by Author "Lee, Mi Yeon"

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PRE-FRACTIONAL MIDDLE SCHOOL STUDENTS’ ALGEBRAIC REASONING
(Proceedings of the Thirty-fourth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 2012-11) Hackenberg, Amy; Lee, Mi Yeon
To understand relationships between students’ quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. Six students with each of 3 different multiplicative concepts participated. This paper reports on the 6 students with the most basic multiplicative concept, who were also pre- fractional in that they had yet to construct the first genuine fraction scheme. These students’ emerging iterating operations facilitated their algebraic activity, but the lack of a disembedding operation was a significant constraint in developing algebraic equations and expressions.
Relationships Between Students' Fractional Knowledge and Equation Writing
(Journal for Research in Mathematics Education, 2015-03) Hackenberg, Amy; Lee, Mi Yeon
To understand relationships between students' fractional knowledge and algebraic reasoning in the domain of equation writing, an interview study was conducted with 12 secondary school students, 6 students operating with each of 2 different multiplicative concepts. These concepts are based on how students coordinate composite units. Students participated in two 45-minute interviews and completed a written fractions assessment. Students operating with the second multiplicative concept had not constructed fractional numbers, but students operating with the third multiplicative concept had; students operating with the second multiplicative concept represented multiplicatively related unknowns in qualitatively different ways than students operating with the third multiplicative concept. A facilitative link is proposed between the construction of fractional numbers and how students represent multiplicatively related unknowns.
Students' distributive reasoning with fractions and unknowns
(Educational Studies in Mathematics, 2016) Hackenberg, Amy; Lee, Mi Yeon
To understand relationships between students' quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. The study included six students with each of three different multiplicative concepts, which are based on how students create and coordinate composite units (units of units). Students participated in two 45-min semi-structured interviews and completed a written fraction assessment. This paper reports on how 12 students operating with the second and third multiplicative concepts demonstrated distributive reasoning in equal sharing problems and in taking fractions of unknowns. Students operating with the second multiplicative concept who demonstrated distributive reasoning appeared to lack awareness of the results of their reasoning, while students operating with the third multiplicative concept demonstrated this awareness and the construction of more advanced distributive reasoning when they worked with unknowns. Implications for relationships between students' fractional knowledge and algebraic reasoning are explored.
STUDENTS’ DISTRIBUTIVE REASONING WITH FRACTIONS AND UNKNOWNS
(Proceedings of the Thirty-third Annual Meeting of PME-NA, 2011-10) Hackenberg, Amy; Lee, Mi Yeon
To understand relationships between students’ quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. The study targeted a balanced mix of students with 3 different multiplicative concepts, which are based on how students coordinate composite units (units of units). Students participated in two 45-minute semi-structured interviews and completed a written fractions assessment. This paper reports on how students with the second and third multiplicative concepts demonstrated the use of a distributive operation in fraction and algebraic problem solving.