Underlying Cognitive Components and Conceptual Knowledge in Arithmetic

dc.contributor.advisorRobinson, Katherine
dc.contributor.authorEdwards, William Tomos
dc.contributor.committeememberOriet, Chris
dc.contributor.committeememberPhenix, Tom
dc.contributor.externalexaminerMartin, Ronald
dc.date.accessioned2014-10-17T18:25:10Z
dc.date.available2014-10-17T18:25:10Z
dc.date.issued2013-12
dc.descriptionA Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Arts in Experimental & Applied Psychology, University of Regina. x, 97 p.en_US
dc.description.abstractWithin the field of mathematical cognition there is extensive research on conceptual knowledge of arithmetic operations. There is also extensive research on the link between mathematical ability and spatial ability. This research study seeks to build on both areas of research and identify ways in which they are interrelated. Conceptual knowledge of arithmetic operations is the subject of ongoing research. When solving a three-term problem of the form a x b ÷ b, those who understand the inversion concept do not need to perform any calculations because they know that the multiplication and division operations cancel each-other out. When solving a three-term problem of the form a x b ÷ c, those who understand the associativity concept know that they can do b ÷ c first, or a x b first. Research indicates that there is a complex relationship between spatial ability and mathematical ability. In some studies spatial ability is shown to have an especially strong relationship with certain measures of mathematical performance while in other studies this is not the case. Theories have already been put forth that visual-spatial abilities are initially cardinal to learning mathematics in children, but verbal and general intelligence become more important to mathematical performance later on, after these mathematical skills and forms of knowledge have been well learned. In this study it is theorized that spatial abilities are more important than other cognitive abilities for acquiring new mathematical knowledge across the lifespan, and not just in childhood. Conversely, general intelligence is more important to mathematical performance after the relevant mathematical knowledge has been well learned. This theory is supported by past research as well as the results of this study. This study also provides important clues about the development of conceptual knowledge of arithmetic by showing that knowledge of the inversion concept and the associativity concept are both strongly related to spatial ability. Verbal reasoning ability doesn’t relate to knowledge of these concepts but it is related to performance with mathematical skills that are more basic.en_US
dc.description.authorstatusStudenten
dc.description.peerreviewyesen
dc.identifier.tcnumberTC-SRU-5434
dc.identifier.thesisurlhttp://ourspace.uregina.ca/bitstream/handle/10294/5434/Edwards_William_200275843_MA_EAP_Spring2014.pdf
dc.identifier.urihttps://hdl.handle.net/10294/5434
dc.language.isoenen_US
dc.publisherFaculty of Graduate Studies and Research, University of Reginaen_US
dc.titleUnderlying Cognitive Components and Conceptual Knowledge in Arithmeticen_US
dc.typemaster thesisen
thesis.degree.departmentDepartment of Psychologyen_US
thesis.degree.disciplineExperimental and Applied Psychologyen_US
thesis.degree.grantorFaculty of Graduate Studies and Research, University of Reginaen
thesis.degree.levelMaster'sen
thesis.degree.nameMaster of Arts (MA)en_US

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