A heuristic approach to assess change in mathematical knowledge for teaching geometry after a practice-based professional learning intervention

ABSTRACT

We show how we used a national distribution of responses from 416 practicing teachers to items of a test of mathematical knowledge for teaching geometry to estimate changes in knowledge by a group of 11 practicing teachers who participated in a 2-year practice-based professional development programme. To draw a reliable interpretation of the change, we use multiple measurement models under different assumptions on the scale of MKT-G. We demonstrate how Diagnostic Classification Modelling was used to determine whether participants had grown. The participants’ gain (status change in achievement profile) was also examined in relationship with the amount of time participants spent during the PD, which was estimated using log data recorded by the online platform. We discuss the findings from these explorations, in the context of the broader problem of improving conceptualizations of MKT.

KEYWORDS:

• Teacher knowledge
• geometry
• secondary teachers
• diagnostic classification modelling
• practice-based professional development

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 These domains are called common content knowledge (CCK), specialised content knowledge (SCK), knowledge of content and students (KCS), and knowledge of content and teaching (KCT). Along with horizon content knowledge (HCK), CCK and SCK are grouped in what Ball et al. (2008) call subject matter knowledge (SMK). Likewise, along with knowledge of content and curriculum (KCC), KCS and KCT are grouped in what Ball et al. (2008) call, after Shulman (1986), pedagogical content knowledge (PCK). For the purposes of our study, it is important to note that there has been an interest in assessing knowledge of different types, with those types being either the domains or the groups of domains. It is also important to note that while SMK includes only mathematical knowledge, PCK includes blends of mathematical and education knowledge. It is less important for us here that the reader understand the differences across domains within the same group – the interested reader could consult Ball et al. (2008).

2 The responses from 416 teachers (among the 602 teachers) who completed all the items used in this study were used to scale the PD participants’ MKT-G.

3 A testlet (Wainer & Kiely, 1987) is defined as an aggregation of items that are based on a single stimulus.

4 Three of the four True/False items of the testlet showed correct response rates 0.88, 0.89, and 0.95.

5 Three of the four True/False items of the testlet had lower than 0.15 item-rest correlation.

6 Weighted Least Squares Means and Variances.

7 Marginal Maximum Likelihood.

8 As the chi-square value for WLSMV cannot be used for chi-square difference testing in the regular way, the DIFFTEST option of Mplus was used to compare two models (Muthén & Muthén, 1998–2015).

9 A table specifying which attributes are measured by which item in terms of numeric value (1s for an attribute measured by an item and 0s for an attribute not measured by an item; Rupp et al., 2010, p. 54).

Additional information

Funding

The data analyzed for this project comes from the project EMATHS (Embracing Mathematics, Assessment, Technology in High School) through LessonSketch StoryCircles, a Mathematics Science Partnership project awarded to Deborah Ferry at the Macomb ISD and funded through the State of Michigan. The national sample of teacher responses to the MKT-G items was collected with support of the US National Science Foundation grant DRL- 0918425 to Patricio Herbst.