東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Connecting proportionality and slope...

Cheng, Diana S.,

FindBook

Google Book

Amazon

博客來

Connecting proportionality and slope: Middle school students' reasoning about steepness /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Connecting proportionality and slope: Middle school students' reasoning about steepness // Diana S Cheng.
作者:	Cheng, Diana S.,
面頁冊數:	1 electronic resource (212 pages)
附註:	Source: Dissertations Abstracts International, Volume: 72-01, Section: A.
Contained By:	Dissertations Abstracts International72-01A.
標題:	Mathematics education. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3405966
ISBN:	9781109726213

Connecting proportionality and slope: Middle school students' reasoning about steepness /
Cheng, Diana S.,

Connecting proportionality and slope: Middle school students' reasoning about steepness /Diana S Cheng. - 1 electronic resource (212 pages)

Source: Dissertations Abstracts International, Volume: 72-01, Section: A.

This study investigates the relationship between middle school students' proportional reasoning abilities and their understanding of steepness, since steepness may be a key developmental understanding that students need in order to understand slope in algebra. This study uses mixed methods, with a large-scale survey and one-on-one interviews with students. The large-scale survey involves two tests: an adapted version of the Ratio and Proportion Test administered in England for the Concepts in Secondary Mathematics & Science (CSMS) and Increasing Competence & Confidence in Algebra and Multiplicative Structures (ICCAMS) projects, and a steepness test which I created and for which I established content validity and test-retest reliability. The problems on the steepness test involve a comparison of two roofs, two staircases, or two lines. The problems vary by structural difficulty based upon the values of the slopes involved. Analysis of 413 research participants' survey data indicate that approximately 25% of the variability in students' scores on the Steepness test is explained by their performance on the Ratio and Proportion Test. Linear regression has shown that there is a positive correlation between participants' proportional reasoning abilities and their abilities to solve steepness problems. Using paired t-tests, there is evidence of significant difference in students' performance on the three contexts. The difficulties of contexts in the order of difficulty from hardest to easiest are: stairs, roofs, lines. Analyses of interviews with middle school students solving steepness problems indicate that they do use different strategies to solve problems based upon their proportional reasoning levels. Participants who attained higher levels of proportional reasoning used quantitative considerations of two measurements, norming, and rates and ratios to determine relative steepness more frequently than participants who attained lower levels of proportional reasoning. It was concluded that participants' abilities to solve steepness problems are related to their abilities to reason proportionally. The findings of this research contribute to literature on early algebraic reasoning that explores ways in which algebraic topics such as slope can be made accessible to students prior to their formal studies of algebra.

English

ISBN: 9781109726213Subjects--Topical Terms:

641129
Mathematics education.
Subjects--Index Terms:

Algebra

Connecting proportionality and slope: Middle school students' reasoning about steepness /
LDR:03808nmm a22004693i 4500 001 2391405
005 20250923061215.5
006 m o d
007 cr|nu||||||||
008 251029s2010 miu||||||m |||||||eng d
020 $a 9781109726213
035 $a (MiAaPQD)AAI3405966
035 $a AAI3405966
035 $a 2391405
040 $a MiAaPQD $b eng $c MiAaPQD $e rda
100 1 $a Cheng, Diana S., $e author. $3 3759252
245 1 0 $a Connecting proportionality and slope: Middle school students' reasoning about steepness / $c Diana S Cheng.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2010
300 $a 1 electronic resource (212 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 72-01, Section: A.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisors: Chapin, Suzanne.
502 $b Ed.D. $c Boston University $d 2010.
520 $a This study investigates the relationship between middle school students' proportional reasoning abilities and their understanding of steepness, since steepness may be a key developmental understanding that students need in order to understand slope in algebra. This study uses mixed methods, with a large-scale survey and one-on-one interviews with students. The large-scale survey involves two tests: an adapted version of the Ratio and Proportion Test administered in England for the Concepts in Secondary Mathematics & Science (CSMS) and Increasing Competence & Confidence in Algebra and Multiplicative Structures (ICCAMS) projects, and a steepness test which I created and for which I established content validity and test-retest reliability. The problems on the steepness test involve a comparison of two roofs, two staircases, or two lines. The problems vary by structural difficulty based upon the values of the slopes involved. Analysis of 413 research participants' survey data indicate that approximately 25% of the variability in students' scores on the Steepness test is explained by their performance on the Ratio and Proportion Test. Linear regression has shown that there is a positive correlation between participants' proportional reasoning abilities and their abilities to solve steepness problems. Using paired t-tests, there is evidence of significant difference in students' performance on the three contexts. The difficulties of contexts in the order of difficulty from hardest to easiest are: stairs, roofs, lines. Analyses of interviews with middle school students solving steepness problems indicate that they do use different strategies to solve problems based upon their proportional reasoning levels. Participants who attained higher levels of proportional reasoning used quantitative considerations of two measurements, norming, and rates and ratios to determine relative steepness more frequently than participants who attained lower levels of proportional reasoning. It was concluded that participants' abilities to solve steepness problems are related to their abilities to reason proportionally. The findings of this research contribute to literature on early algebraic reasoning that explores ways in which algebraic topics such as slope can be made accessible to students prior to their formal studies of algebra.
546 $a English
590 $a School code: 0017
650 4 $a Mathematics education. $3 641129
650 4 $a Secondary education. $3 2122779
650 4 $a Middle school students. $3 3435319
650 4 $a Middle school education. $3 969762
653 $a Algebra
653 $a Early algebra
653 $a Proportional reasoning
653 $a Ratio
653 $a Slope
653 $a Steepness
690 $a 0280
690 $a 0450
690 $a 0533
710 2 $a Boston University. $e degree granting institution. $3 3759253
720 1 $a Chapin, Suzanne $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 72-01A.
790 $a 0017
791 $a Ed.D.
792 $a 2010
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3405966