The goal in mathematics has shifted towards an emphasis on both procedural
knowledge and conceptual understanding. The importance of gaining procedural
knowledge and conceptual understanding is aligned with Principles and Standards for
School Mathematics (National Council of Teachers of Mathematics, 2000), which
encourages fluency, reasoning skills, and ability to justify decisions. Possession of only
procedural skills will not prove useful to students in many situations other than on tests
(Boaler, 2000). Teachers and researchers can benefit from this study, which examined
the effects of representations, constructivist approaches, and engagement on middle
school students' algebraic understanding.
Data from an algebra pretest and posttest, as well as 16 algebra video lessons
from an NSF-IERI funded project, were examined to determine occurrences of
indicators of representations, constructivist approaches, and engagement, as well as
student understanding. A mixed methods design was utilized by implementing multilevel
structural equation modeling and constant comparison within the analysis. Calculation of
descriptive statistics and creation of bar graphs provided more detail to add to the findings from the components of the statistical test and qualitative comparison method.
The results of the final structural equation model revealed a model that fit the
data, with a non-significant model, p > .01. The new collectively named latent factor of
constructivist approaches with the six indicators of enactive representations,
encouragement of student independent thinking, creation of problem-centered lessons,
facilitation of shared meanings, justification of ideas, and receiving feedback from the
teacher was shown to be a significant predictor of procedural knowledge (p < .05) and
conceptual understanding (p < .10). The indicators of the original latent factor of
constructivist approaches were combined with one indicator for representations and two
indicators for engagement. Constant comparison revealed similar findings concerning
correlations among the indicators, as well as effects on student engagement and
understanding. Constructivist approaches were found to have a positive effect on both
types of student learning in middle school mathematics.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-1777 |
| Date | 02 June 2009 |
| Creators | Ross, Amanda Ann |
| Contributors | Kulm, Gerald O. |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | electronic, application/pdf, born digital |
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