Mathematics Conceptual Knowledge for Teaching (MCKT)#
See also: teaching-mathematics
Li et al (2019) define MCKT as key to helping students learn with understanding and define it as
topic-based conceptual knowledge packages that are needed for understanding, explaining, as well as teaching specific mathematics content topics with connections.
Three topic-based components#
And it consisting of three topic-based knowledge components.
| Component | Description |
|---|---|
| 1. K&S directly associated with a specific content topic | common CK which students will learn |
| 2. Ability to connect and justify the main points of a content topic, and to place it in wider contexts | place the content topic in the broader knowledge structure |
| 3. Knowing and being able to use various representations for teaching the content topic and being able to teach the relations between them | Mainly to pedagogical aspects of the topic |
The second component is problematic for some of the same reasons raised around exploring-australian-curriculum. It is also seen as the one with which PSTs are least familiar.
More often than not, (2) is presented as great challenges to prospective and practicing teachers as it often requires conceptual understanding across different content topics that are connected.
Related ideas#
The distinction with PCK is in the packaging. PCK separates based on pedagogy and content. MCKT separates based on content topic. e.g. PCK is knowledge separated into pieces, not packages (topics).
Ball extends Schulman's PCK work by refining
- PCK into
- knowledge of content and students;
- knowledge of content and teaching;
- knowledge of curriculum.
- CK into
- common content knowledge
- specialised content knowledge
- horizon knowledge
Argument is that MCKT escapes the further refinement/complication of Ball's work and also unites the content and pedagogical knowledge into topics.
Similarly work around teachers' knowledge constructs in large scale assessments breaks the knowledge into
- mathematics content knowledge
- mathematics pedagogical content knowledge
- general pedagogical knowledge
Knowledge quartet (Rowland et al, 2019) developed for observation and assessment. MCKT is intended to knowledge are needed when teaching specific content topics.
| Dimension | Description |
|---|---|
| Foundation | Propositional knowledge and beliefs. mathematics and pedagogy. |
| Transformation | Knowledge-in-action used in planning and teaching. Mostly PCK |
| Connection | Knowledge-in-action unifying subject matter and coherence. |
| Contingency | Knowledge-in-interaction - thinking on feet |
Background#
Three types of knowledge often mentioned: mathematical CK and PCK and general pedagogical knowledge.
On the difficult of gathering and weaving (gather-weave) between disparate knowledge strands
However, if salient connections among different knowledge components are left unspecified in their knowledge preparation, prospective teachers would be left to make such connections by themselves after learning separate pieces of knowledge.
Make the argument that teachers need topic-based integrated knowledge that allows them to make content connections between different topics and representations. A key skills is the ability to gather and weave (pack) the knowledge into "key pieces".
References#
Rowland, T. (2019). Researching Mathematical Knowledge in Teaching. In International Handbook of Mathematics Teacher Education: Volume 1 (pp. 105--128). Brill. https://doi.org/10.1163/9789004418875_005
Li, Y., Pang, J., Zhang, H., & Song, N. (2019). Mathematics Conceptual Knowledge for Teaching: Helping Prospective Teachers Know Mathematics Well Enough for Teaching. In International Handbook of Mathematics Teacher Education: Volume 1 (pp. 77--104). Brill. https://doi.org/10.1163/9789004418875_004