2019
DOI: 10.1016/j.jmathb.2019.03.001
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Calculus students’ fraction and measure schemes and implications for teaching rate of change functions conceptually

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Cited by 18 publications
(13 citation statements)
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“…It is important to help teachers understand the limitations of teaching the idea of slope as angle measure and to help teachers develop more productive lessons on slope ( Byerley and Thompson, 2017) . We also suggest that mathematics teachers at the high school and college level pay particular attention to their students’ understanding of secondary school topics such as place value and fractions ( Byerley, 2019 ). The high school mathematics teacher, Gertrude, showed us that it is possible to pass many advanced mathematics courses without becoming confident in concepts such as place value and relative size of quantities.…”
Section: Discussionmentioning
confidence: 99%
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“…It is important to help teachers understand the limitations of teaching the idea of slope as angle measure and to help teachers develop more productive lessons on slope ( Byerley and Thompson, 2017) . We also suggest that mathematics teachers at the high school and college level pay particular attention to their students’ understanding of secondary school topics such as place value and fractions ( Byerley, 2019 ). The high school mathematics teacher, Gertrude, showed us that it is possible to pass many advanced mathematics courses without becoming confident in concepts such as place value and relative size of quantities.…”
Section: Discussionmentioning
confidence: 99%
“…The data representations varied (e.g., text, graphs, charts, tables) and relied on mathematical concepts including rate of change, comparisons of relative size, exponential growth, probability, accumulation, and mathematical modeling. Mathematics education researchers have created models of how students and teachers understand these representations and concepts ( Behr, Harel, Post, & Lesh, 1992 ; Byerley & Thompson, 2014 ; Byerley, 2019 ; Castillo-Garsow, 2013 ; Ellis, Ozgur, Kulow, Dogan, & Amidon, 2016 ; Harel & Confrey, 1994 ; Johnson, 2012 ; Konold, 1989 ; Lesh & Lehrer, 2003 ; Lobato & Siebert, 2002 ; Moore, Stevens, Paoletti, Hobson, & Liang, 2019 ; Steffe & Olive, 2009 ; Steffe, Liss, & Lee, 2014 ; Thompson, 1994a , 1994b ; Thompson, Hatfield, Yoon, Joshua, & Byerley, 2017 ), but independent of the COVID-19 pandemic and data. These same researchers have argued people’s schemes for these concepts and representations vary in their productivity, but again these claims have been independent of a major event like the COVID-19 pandemic.…”
Section: Introductionmentioning
confidence: 99%
“…The learning of calculus draws on students' school experiences with pre-calculus notions such as functions, algebraic expressions, geometrical objects and representations (Biza, 2021;Frank & Thompson, 2021;Grant et al, 2016;Hitt & González-Martín, 2016;Thompson & Carlson, 2017). Such experiences are related to the curriculum students encounter (Biza, 2021;Byerley, 2019) and to their teachers' expectations (Ayalon & Wilkie, 2019). Byerley (2019), for example, discusses the implication of three students' fraction and measure schemes for their understanding of rate of change, while Biza (2021) looks at how tangent lines to circles and conic sections influence how students argue about tangent lines in calculus.…”
Section: Transition Across Notions From Pre-calculus To Calculus or W...mentioning
confidence: 99%
“…Such experiences are related to the curriculum students encounter (Biza, 2021;Byerley, 2019) and to their teachers' expectations (Ayalon & Wilkie, 2019). Byerley (2019), for example, discusses the implication of three students' fraction and measure schemes for their understanding of rate of change, while Biza (2021) looks at how tangent lines to circles and conic sections influence how students argue about tangent lines in calculus. In addition, essential ideas of calculus can be introduced with algebraic and geometrical routines without the use of limits.…”
Section: Transition Across Notions From Pre-calculus To Calculus or W...mentioning
confidence: 99%
“…This roughly corresponds to Kieren's (1976) "measurement" interpretation of a fraction. Many people struggle to develop understanding of fractions as magnitudes or measures (Byerley, 2019;Ni & Zhou, 2005;Stafylidou & Vosniadou, 2004;Stigler et al, 2010;Torbeyns et al, 2015). This is unfortunate, as scholars from multiple theoretical perspectives have argued that this knowledge is critical for children's expanding view of the number line and the continuity of all real numbers (e.g., Moss & Cass, 1999;Siegler et al, 2011;Vamvakoussi et al, 2018).…”
Section: Measuring Knowledge Of Fraction Magnitudesmentioning
confidence: 99%