Measuring Mathematical Knowledge for Teaching: A Longitudinal Study Using Two Measures

From Section:
Assessment & Evaluation
Jun. 01, 2013

Source: Journal of Mathematics Teacher Education, Vol. 16, No. 3, (June 2013) p. 211–236
(Reviewed by the Portal Team)

In this longitudinal study, the authors investigate changes in teachers’ mathematics knowledge during a mathematics content course focused on real-world applications and during a content/pedagogy hybrid course designed specifically for elementary teachers.

In particular, they address the following questions:
1. According to the LMT and DTAMS measures, to what extent does teachers’ common and specialized mathematics knowledge change during a mathematics content course focused on real-world applications versus a hybrid course blending elementary mathematics content and pedagogy?
2. How do the LMT and DTAMS measures compare in their detection of the gains teachers make in algebra—the content area measured by both assessments—during each of the two courses?

The participants were twenty-four K-8 practicing teachers who were employed in fourteen elementary and middle schools across the district and surrounding areas.
All teachers were female, and the majority of the teachers were white.

The authors used two popular assessments in the United States:
(1) Learning Mathematics for Teaching (LMT) and
(2) Diagnostic Teacher Assessments in Mathematics and Science (DTAMS).
They compare the extent to which each assessment captured teacher learning during a K-8 mathematics content/pedagogy hybrid course and a general mathematics content course.


The findings reveal that teachers made large gains on both measures.
Teachers’ DTAMS scores increased significantly during the hybrid course, with both the content knowledge and the Pedagogical content knowledge (PCK) aspects of DTAMS showing similar levels of improvement.
Still, the size of the DTAMS gain during the hybrid course was only half that of the LMT gain. During the mathematics content course, the PCK portion of the DTAMS score remained stable, while the content knowledge portion increased further.

Furthermore, the patterns of change differed during the two courses, with the LMT scores increasing during the hybrid course only and the DTAMS scores increasing over the two courses.
Hence, the two assessments appear to have detected growth in different aspects of teachers’ algebra knowledge, as teachers’ scores became less correlated over time.
The hybrid course seemed to enhance both common and specialized knowledge, while the content course enhanced common content knowledge only.


The findings of this study have several practical and theoretical implications spanning a variety of areas, including research and evaluation, and teacher education.

Implications for research and evaluation
The main theoretical implication of this study relates to whether there is, indeed, a specialized body of mathematics knowledge for teaching.
The correlation between teachers’ LMT and DTAMS scores drastically decreased as they progressed through the two courses, suggesting that these measures captured substantially different aspects of mathematics knowledge.

A practical implication for researchers and program evaluators stems from this study’s evidence that the LMT and DTAMS measures capture substantially different aspects of mathematics knowledge.
Hence, in practical terms, this study suggests that the LMT measure may be a better choice for capturing the learning that occurs in a content/methods course designed specifically for elementary teachers, whereas the DTAMS measure is perhaps a better choice for assessing teacher knowledge gains made in more general mathematics courses.

Implications for teacher education
This study highlights the need to specifically attend to teachers’ specialized mathematics knowledge necessary for teaching, as it is distinct from everyday mathematics knowledge.

The merging of content and pedagogy into a single course might have been particularly effective for the practicing teachers in this study.
Those designing professional development programs for teachers should note that the content/methods hybrid course in this study had a large impact on teachers’ specialized content knowledge.

Updated: Aug. 07, 2018
Blended learning | Comparative analysis | Elementary school teachers | Longitudinal studies | Mathematics instruction | Measures | Pedagogical content knowledge