Developing Conceptual and Procedural Knowledge of Mathematics

Rittle‐Johnson, Bethany; Schneider, Michael

doi:10.1093/oxfordhb/9780199642342.013.014

Cited by 194 publications

(282 citation statements)

References 96 publications

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“…With these, initiatives around the world have introduced a range of innovative and interactive learning technologies such as graphic software (Robutti, 2010;Lavizca, 2010) and computer algebra system (Özgün-Koca, 2010;Mignotte, 2012;Durán, Pérez & Varona, 2014) to explore Calculus concepts. The use of these technologies offer new ways to learn and teach Calculus that help deepen students' understanding of abstract and complex ideas (Arango, Gaviria & Valencia, 2015;Šumonja, Veličković & Šubarević, 2015;Zakaria & Salleh, 2015) which include conceptual understanding (Bartell, Webel, Bowen & Dyson, 2013;Richland, Stigler & Holyoak, 2012) and procedural skills (Rittle-Johnson & Schneider, 2014;Cragg & Gilmore, 2014) and also increases positive attitude of students towards the subject (Sang, Valcke, Van Braak & Tondeur, 2010;Yuan & Chun-Yi, 2012). Further, it helps students to better visualize the concepts through graphical representation (Moses, Wong, Bakar & Mahmud, 2013).…”

Section: Introductionmentioning

confidence: 99%

Improving students' attitude, conceptual understanding and procedural skills in differential calculus through Microsoft mathematics

Mendezabal

Tindowen

2018

J. Technol. Sci. Educ.

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This study examined the effects of using Microsoft Mathematics on students' attitude, conceptual understanding, and procedural skills in Differential Calculus. A quasi-experimental research design was used in which two different learning environments were compared. The participants of the study were two classes of Electrical Engineering students enrolled in Differential Calculus course, assigned randomly as control and experimental groups with 30 students in each group. The control group was taught using the traditional approach of teaching Differential Calculus while the experimental group was taught the same lessons using the Microsoft Mathematics embedded activity sheets. The experimental group learned through exploration and discovery of various concepts. The findings indicated that the participants had little understanding of the concepts and processes of Calculus prior to the conduct of the study. A significant improvement in their performances was noted after the experimentation. This suggests that the use of Microsoft Mathematics in teaching and learning Differential Calculus improves students' conceptual understanding and procedural skills. It is also found that the use of Microsoft Mathematics in teaching and learning calculus is equally effective as the traditional approach. In terms of attitude, the experimental group demonstrated a "favorable" to "very highly favorable" attitude along the five (5) domains of the MTAS. A significant difference exists between the pretest and posttest attitude of the participants on the domain "learning Mathematics with technology".

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Section: Introductionmentioning

confidence: 99%

Improving students' attitude, conceptual understanding and procedural skills in differential calculus through Microsoft mathematics

Mendezabal

Tindowen

2018

J. Technol. Sci. Educ.

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“…Lack of comprehension could hinder the learning of fractions. Several research studies have brought up conceptual and procedural knowledge because both are essential to understanding whole numbers and fractions (Hiebert & LeFevre, 1986;Rittle-Johnson & Siegler, 1998). Numerical development clearly includes many important acquisitions other than knowledge of numerical magnitudes, such as learning to count and to solve arithmetic problems (Siegler, Thompson, & Schneider, 2012).…”

Section: Contributions Of Whole Number Division To Learning Fractionsmentioning

confidence: 99%

Developing Deaf Students Fraction Skills Requires Understanding Magnitude and Whole Number Division

Mousley¹,

Kelly²

2017

JEL

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Research has shown that fraction magnitude and whole number division are important precursors to learning and understanding fractions. Deaf and hard-of-hearing (DHH) students are consistently challenged with learning fractions from K-12 through college. Sixty DHH college students were tested for both their understanding of magnitude between two fractions and their ability to calculate whole number division. The results showed that both understanding the magnitude between two fractions and whole number division are significantly associated with accurately calculating arithmetic functions of fractions with like denominators and different denominators that required them to add, subtract, multiply, and divide two fractions. Understanding fraction magnitude and whole number division were also significantly associated with their self-rated confidence of math performance with fractions. Tangentially, DHH college students' English reading ability was significantly, but modestly associated with their fraction performance.

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“…Based on the development of conceptual and procedural knowledge (for a recent review, see Rittle-Johnson & Schneider, 2015) [29], Rittle- Johnson and Koedinger (2009) [9] compared the effects of lesson sequence on sixth-graders' conceptual knowledge of place value and procedural knowledge in decimal arithmetic. Compared to a group who received all concepts lessons before the procedures lessons ("blocked" sequence), iterative sequencing resulted in better learning and transfer of procedural knowledge, but no difference was found between conditions on the transfer of place value concepts.…”

Section: Representational Sequencing In Instructionmentioning

confidence: 99%

Effects of Instructional Guidance and Sequencing of Manipulatives and Written Symbols on Second Graders’ Numeration Knowledge

2017

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Concrete objects used to illustrate mathematical ideas are commonly known as manipulatives. Manipulatives are ubiquitous in North American elementary classrooms in the early years, and although they can be beneficial, they do not guarantee learning. In the present study, the authors examined two factors hypothesized to impact second-graders' learning of place value and regrouping with manipulatives: (a) the sequencing of concrete (base-ten blocks) and abstract (written symbols) representations of the standard addition algorithm; and (b) the level of instructional guidance on the structural relations between the representations. Results from a classroom experiment with second-grade students (N = 87) indicated that place value knowledge increased from pre-test to post-test when the base-ten blocks were presented before the symbols, but only when no instructional guidance was offered. When guidance was given, only students in the symbols-first condition improved their place value knowledge. Students who received instruction increased their understanding of regrouping, irrespective of representational sequence. No effects were found for iterative sequencing of concrete and abstract representations. Practical implications for teaching mathematics with manipulatives are considered.

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Developing Conceptual and Procedural Knowledge of Mathematics

Cited by 194 publications

References 96 publications

Improving students' attitude, conceptual understanding and procedural skills in differential calculus through Microsoft mathematics

Improving students' attitude, conceptual understanding and procedural skills in differential calculus through Microsoft mathematics

Developing Deaf Students Fraction Skills Requires Understanding Magnitude and Whole Number Division

Effects of Instructional Guidance and Sequencing of Manipulatives and Written Symbols on Second Graders’ Numeration Knowledge

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