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Stimulating pre-service teachers’ content and pedagogical content knowledge on rational numbers

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Abstract

The transition from natural to rational numbers is difficult for most elementary school children. A major cause for these difficulties is assumed to be the “conceptual change” they need to undergo in order to see that several natural number properties do not apply to rational numbers. To appropriately handle pupils’ difficulties, teachers need well-developed content knowledge (CK) and pedagogical content knowledge (PCK). In the present study, a lesson series to promote pre-service teachers’ (PSTs) rational number CK and PCK was developed according to design principles to foster conceptual change. This lesson series was evaluated based on a comparison of the CK and PCK growth of PSTs in the intervention group (n = 138) with the knowledge growth of PSTs in an alternative teacher training course (control group; n = 135). Intervention group PSTs significantly outperformed control group PSTs on CK and PCK, indicating that the intervention was effective in stimulating PSTs’ knowledge on rational numbers. Methodological, theoretical as well as practical implications of the present study are discussed.

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Notes

  1. A rational number is a number that can be expressed by a fraction \( \frac{a}{b} \) in which a and b are whole numbers (with b different from 0).

  2. Ball (1990) does not refer to the separate constructs CK and PCK, but only uses a single notion “subject matter knowledge for teaching” (in later publications labeled as “mathematical knowledge for teaching” or “content knowledge for teaching mathematics”, e.g., Ball, Thames, & Phelps, 2008) comprising content knowledge and pedagogical content knowledge.

  3. The complete set of materials of the intervention study is published in a practically oriented textbook (Van Roy, Hawrijk, Vermeersch, Palmaerts, & Depaepe, 2014).

  4. The tests were scored on 24 points (1 point for each item).

  5. (1) Group × zCK1; (2) group × order; (3) zCK1 × order; (4) group × zCK1 × order

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Authors and Affiliations

  1. Center for Instructional Pscyhology and Technology, Katholieke Universiteit Leuven, 3000, Leuven, Belgium

    Fien Depaepe, Patrick Van Roy, Joke Torbeyns, Wim Van Dooren & Lieven Verschaffel

  2. Christian Albrechts Universitat zu Kiel, Kiel, Germany

    Thilo Kleickmann

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  1. Fien Depaepe
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  2. Patrick Van Roy
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  3. Joke Torbeyns
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  4. Thilo Kleickmann
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  5. Wim Van Dooren
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  6. Lieven Verschaffel
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Correspondence to Fien Depaepe.

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Depaepe, F., Van Roy, P., Torbeyns, J. et al. Stimulating pre-service teachers’ content and pedagogical content knowledge on rational numbers. Educ Stud Math 99, 197–216 (2018). https://doi.org/10.1007/s10649-018-9822-7

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