Prospective Teacher Learning: Recognizing Evidence of Conceptual Understanding
Source: Journal of Mathematics Teacher Education, Vol. 16, No. 1, February 2013, p. 57-79.
(Reviewed by the Portal Team)
The goal of this study is two-fold:
1) to examine the role content knowledge plays in prospective teachers’ (PSTs) ability to recognize children’s conceptual understanding of mathematics, and,
2) to examine examined PSTs' ability to recognize evidence of children’s conceptual understanding of mathematics in three content areas before and after an instructional intervention designed to support this ability.
Methods
Fifty-four PSTs from a university in the mid-Atlantic region of the United States participated in this study.
All of the students were enrolled in a 4-year undergraduate program for elementary school teacher education.
PSTs’ mathematics preparation within this program consists of three mathematics content courses followed by one or two mathematics methods courses.
The results of this study revealed that content knowledge did not seem to support PSTs’ analyses of children’s procedural responses, as many PSTs with good content knowledge initially characterized procedural solutions as evidence of conceptual understanding. Similarly, content knowledge did not seem to support PSTs’ analyses of children’s responses with features commonly associated with understanding but not evidence of understanding.
Yet content knowledge did seem to support PSTs’ analyses of children’s responses in two cases.
In the first case, PSTs’ content knowledge about comparison of fractions seemed to support them in analyzing the response demonstrating conceptual understanding.
In the second case, PSTs’ content knowledge of comparison of fractions seemed to support their ability to analyze a child’s response exhibiting a misconception.
This study suggests that content knowledge is necessary but insufficient in supporting PSTs’ ability to recognize evidence of children’s conceptual understanding of mathematics.
These interventions may support PSTs in moving away from attributing conceptual understanding to procedural responses or those containing conceptual features but no evidence of conceptual understanding.
While the intervention did prove significant, the fact that even after the intervention, many PSTs considered procedural responses or those containing conceptual features as evidence of conceptual understanding shows room for further growth.
These results also suggest that teacher education programs should engage PSTs in such analyses early on, perhaps simultaneously with their content knowledge development.
Since, evaluating student understanding is an essential skill for teaching with which PSTs need experience.