Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1-19 |
| Number of pages | 19 |
| Journal | Educational Studies in Mathematics |
| DOIs | |
| State | Accepted/In press - May 24 2016 |
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Keywords
- Algebraic reasoning
- Distributive partitioning scheme
- Distributive property
- Distributive reasoning
- Fractional knowledge
- Multiplicative concepts
- Unknowns
ASJC Scopus subject areas
- Mathematics(all)
- Social Sciences(all)
Cite this
Students’ distributive reasoning with fractions and unknowns. / Hackenberg, Amy J.; Lee, Mi.
In: Educational Studies in Mathematics , 24.05.2016, p. 1-19.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Students’ distributive reasoning with fractions and unknowns
AU - Hackenberg, Amy J.
AU - Lee, Mi
PY - 2016/5/24
Y1 - 2016/5/24
N2 - 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.
AB - 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.
KW - Algebraic reasoning
KW - Distributive partitioning scheme
KW - Distributive property
KW - Distributive reasoning
KW - Fractional knowledge
KW - Multiplicative concepts
KW - Unknowns
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U2 - 10.1007/s10649-016-9704-9
DO - 10.1007/s10649-016-9704-9
M3 - Article
AN - SCOPUS:84969969877
SP - 1
EP - 19
JO - Educational Studies in Mathematics
JF - Educational Studies in Mathematics
SN - 0013-1954
ER -