Preservice Elementary School Teachers' Conceptions of Multidigit Whole Numbers

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Investigating further preservice teachers’ conceptions of multidigit whole numbers: refining a framework (2010, methodology): “In previous work (Thanheiser, 2009), I identified and categorized PSTs‘ conceptions of multidigit whole numbers into four major groups: thinking in terms of (a) reference units, (b) groups of ones, (c) concatenated-digits plus, and (d) concatenated-digits only.”
Prospective teachers’ learning to provide instructional explanations: how does it look and what might it take? (2011, background): “Most show that PSTs provide fragmented, incoherent, and mathematically inaccurate explanations in a gamut of topics ranging from basic elementary concepts such as place value (Ball 1988) to whole-number operations (Thanheiser 2009) to more complex topics, such as (fraction) division (Ball 1988; Bork”
Mathematical Content Knowledge for Teaching Elementary Mathematics: A Focus on Fractions (2014, unknown): “ However, research studies on prospective teachers’ mathematics knowledge have shown that many possess a limited knowledge of mathematics in key content areas such as number (e.g., Ball, 1990a; Thanheiser, 2009; Tobias, 2013).”