Converting among fractions, decimals, and percents: an exploration of representational usage by middle school teachers

 Title: Converting among fractions, decimals, and percents: an exploration of representational usage by middle school teachers Author: Muzheve, Michael Tapfuma Description: Using both quantitative and qualitative data collection and analyses techniques , this study examined representations used by sixteen (n = 16 ) teachers while teaching the concepts of converting among fractions , decimals , and percents . The classroom videos used for this study were recorded as part of the Middle School Mathematics Project (MSMP ) . The study also compared teacher -selected and textbook representations and examined how teachers‘ use of idiosyncratic representations influenced representational choices on the number test by the teachers‘ five hundred eighty -one (N = 581 ) students . In addition to using geometric figures and manipulatives , a majority of the teachers used natural language such as the words nanny , north , neighbor , dog , cowboy , and house to characterize fractions and mathematical procedures or algorithms . Coding of teacher -selected representations showed that verbal representations deviated from textbook representations the most . Some teachers used the words or phrases bigger , smaller , doubling , tripling , breaking -down , and building -up in the context of equivalent fractions . There was widespread use of idiosyncratic representations by teachers , such as equations with missing or double equal signs , numbers and operators written as superscripts , and numbers written above and below the equal sign . Although use of idiosyncratic representations by teachers influenced representational choices by students on the number test , no evidence of a relationship between representational forms and degree of correctness of solutions was found . The study did reveal though that teachers‘ use of idiosyncratic representations can lead to student misconceptions such as thinking that multiplying by a whole number not equal to 1 gives an equivalent fraction . Statistical tests were done to determine if frequency of representation usage by teachers was related to the textbook , highest degree obtained by teacher , certification , number of years spent teaching mathematics , number of years teaching mathematics at grade level , number of hours completed on professional development related to their textbook , and total number of days spent on the Interagency Education Research Initiative (IERI ) professional development . The results showed representation usage was related to all the above variables , except the highest degree obtained and the total number of days spent on the IERI professional development . URI: http : / /hdl .handle .net /1969 .1 /ETD -TAMU -2941 Date: 2013-03-12

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