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Status of Teachers’ Proficiency in Mathematical Knowledge for Teaching at Secondary School Level in Kenya

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Abstract

Mathematical knowledge for teaching (MKT), defined by Ball (Elementary Journal, 93, 373–397, 1993) as knowledge that is needed to teach mathematics, has been used as a framework by researchers to interrogate various aspects of teaching and learning mathematics. In this article, which draws from a larger study, we show how an in-depth analysis of MKT can illuminate what teachers know and need to learn. This study described here uses MKT theory (Ball, Thames & Phelps, Journal of Teacher Education, 59(5), 389–407, 2008) to develop an assessment tool, the MKT proficiency status tool, to measure and describe teachers’ MKT by proficiency status. The study explores Kenyan teachers’ interpretations of secondary school students’ unusual problem solving solutions from across five mathematics strands. In this article, we share findings from data collected using a MKT task questionnaire. Data were analyzed using descriptive statistics and interpreted against the MKT proficiency status tool continuum of fluent, partially fluent, and inadequate. The teacher was the unit of analysis. Findings from the study indicate that teachers’ levels of fluency were not consistent either by mathematical strand or by assessed MKT component. A fluency rate of 9.1 % for mathematical strands and 1.7 % for MKT components was found. The overall description of MKT proficiency status for this study was found to be partially fluent. From this study, we argue that the MKT proficiency status tool details and illuminates teachers’ professional development needs and enables an in-depth analysis of their MKT proficiency status.

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Authors and Affiliations

  1. Marang Centre, School of Education, University of Witwatersrand, Private Bag 3, 2050, Johannesburg, South Africa

    Marguerite Miheso-O’Connor Khakasa & Margot Berger

Authors
  1. Marguerite Miheso-O’Connor Khakasa
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  2. Margot Berger
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Corresponding author

Correspondence to Margot Berger.

Appendix: MKT Tasks

Appendix: MKT Tasks

Please answer the following as exhaustively as you can. (N.B.: No response will be recorded as nil MKT).

Task 4:

STEM: A student solved the equation 3 (n − 7) = n + 4 and obtained the solution n = 2.75.

MKT Task: What might the student have done wrong?

Task 5:

STEM. Swimming pools are sometimes surrounded by borders of tiles. The drawing below shows a square swimming pool with sides of length S meters. This pool is surrounded by a border of 1 m by 1 m square tiles.

figure a

How many 1 m square tiles will be needed for the border of this pool?

MKT Task:

  1. a)

    Paul wrote the following expression: 2S + 2(S + 2).

    Explain how Paul might have come up with this expression.

  2. b)

    Bill found the following expression; (S + 2)2 − S 2 .

    Explain how Bill might have come up with this expression.

How would you convince the students in your class that the two expressions above are equivalent?

TASK 6

STEM: Ms Wamalwa asked her students to explain why the sketch below does not represent a proportional relationship.

figure b

Her students’ explanations are given below.

MKT Task: Which of the following student statements explains why the sketch does not represent a proportional relationship (mark all that apply)

  1. (a)

    You can’t have a curve in a graph

  2. (b)

    The relationship between the distance and the time is not always constant

  3. (c)

    The graph is not labeled correctly

  4. (d)

    The ratio of rise over run is different at different points on the curve

  5. (e)

    At every point on the curve, the d/t is not always the same ratio

  6. (f)

    None of the above

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Miheso-O’Connor Khakasa, M., Berger, M. Status of Teachers’ Proficiency in Mathematical Knowledge for Teaching at Secondary School Level in Kenya. Int J of Sci and Math Educ 14 (Suppl 2), 419–435 (2016). https://doi.org/10.1007/s10763-015-9630-9

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  • DOI: https://doi.org/10.1007/s10763-015-9630-9

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