Humans share many similarities with other animal species, but some activities we perform highlight the discrepancy observed between human and non-human animals. For example, although some animals are capable of rudimentary communication with other members of their species, no other animal has mastered intra-species communication to the extent we have. One communicative tool we have used with great success is mathematics. The advancement of our understanding of the universe through science is reliant upon our use of mathematics. Mathematics is also useful in our everyday activities, such as basic decision making (e.g., Do I have enough money to buy groceries when I fill up my car with gas?) and employment (e.g., flipping the correct number of hamburger patties). Mathematical cognition researchers use the scientific method to understand how we mentally perform these mathematical activities. During this process we come to a greater understanding of what it means to be human.
At Campion College at the University of Regina we maintain an active research program in the field of mathematical cognition. As researchers we are interested in the cognitive processes involved in numerical and mathematical abilities (i.e., numeracy). Mathematical knowledge is a key component of our everyday lives as well as in the areas of education, science, and technology, and thus is an important aspect of human thought and productivity. However, the understanding of mathematical cognition has lagged behind that of language processes, and thus the basic and integrative work of cognitive researchers in the MC2 group provides important contributions to knowledge in several areas.
All of our psychology faculty members have ongoing research programs designed to investigate different aspects of mathematical cognition. Some of our research initiatives are geared towards the development of mathematical cognition across the lifespan whereas others are geared towards basic cognitive processes involved in the representation and retrieval of mathematical knowledge.
While faculty members maintain independent research streams in mathematical cognition, we have established close collaborative ties with each other on several research projects. In addition, several students at the undergraduate, master’s and doctoral level are actively involved in mathematical cognition research.
Current research interests include:
1. The representation of arithmetic and mathematical knowledge in memory. Are number facts (e.g., 7 x 5 = 35) stored in the same form as number categories (e.g., 7 & 5 are prime numbers, but 35 is not)? How are mathematical procedures (e.g., order of operations, long division, mathematical ‘tricks’) represented in memory?
2. The retrieval of mathematical knowledge from memory. Does the use of mathematical knowledge rely on general-purpose memory processes, or are there specific processes devoted to numeracy? What role does inhibition play in mathematical retrieval? How do working memory processes operate in mathematical retrieval?
3. The development of children’s strategies (e.g., counting, decomposition, retrieval) and what factors promote the discovery of more sophisticated and efficient strategies.
4. The development of conceptual understanding in children and adults. What mathematical concepts do children understand easily and which ones are more difficult? How do concepts change across development? What tools and techniques can help the development of conceptual knowledge? What conceptual understandings (e.g., inversion, ratio) are well established in educated adults?
5. The developing relations between procedural (strategic), conceptual, and factual understanding or knowledge in children. Current research indicates that the three types of mathematical knowledge are interrelated.
We have full laboratory facilities and testing rooms as well as portable equipment for conducting research in local schools. Our faculty and students are funded through Natural Sciences and Engineering Research Council and/or Social Sciences and Humanities Research Council grants and scholarships. Funding is available for graduate students.
Faculty members
Katherine
Arbuthnott, Ph.D., Full Professor
Tom Phenix, Ph.D., Assistant
Professor
Katherine M. Robinson, Ph.D., Associate
Professor
Sample Publications
Arbuthnott, K.D. (1996). To repeat or not to repeat: Repetition facilitation and inhibition in sequential retrieval. Journal of Experimental Psychology: General, 125, 261-283.
Arbuthnott, K.D., & Campbell, J.I.D. (2003). The locus of self-inhibition in sequential retrieval. European Journal of Cognitive Psychology, 15, 177-194.
Arbuthnott, K.D., & Campbell, J.I.D. (2000) Cognitive inhibition in selection and sequential retrieval. Memory & Cognition, 28, 331-340.
Arbuthnott, K.D., & Campbell, J.I.D. (1996). Effects of operand order and problem repetition on error priming in cognitive arithmetic. Canadian Journal of Experimental Psychology, 50, 182-195.
Campbell, J.I.D., & Arbuthnott, K.D. (1996). Inhibitory Processes in Sequential Retrieval: Evidence from Variable-Lag Repetition Priming. Brain and Cognition, 30, 59-80.
Phenix, T.L., & Campbell, J.I.D. (2004). Effects of multiplication practice on product verification: Integrated structures model or retrieval-induced forgetting? Memory and Cognition, 32, 324-335.
Phenix, T.L., & Campbell, J.I.D. (2001). Fan effects reveal position-specific numerical concepts. Canadian Journal of Experimental Psychology, 55, 271-276.
Robinson, K.M. (2001). The validity of verbal reports in children’s subtraction. Journal of Educational Psychology, 93, 211-222.
Robinson, K.M., Arbuthnott, K.D., & Gibbons, K.A. (2002). Adults’ representations of division facts: A consequence of learning history? Canadian Journal of Experimental Psychology, 56, 302-309.
Robinson, K.M.R., Arbuthnott, K.D., Rose, D., McCarron, M.C., Globa, C.A., & Phonexay, S.D. (2006). Stability and change in children’s division strategies. Journal of Experimental Child Psychology, 93, 224-238.
Robinson, K.M., & Ninowski, J.E. (2003). Adults’ understanding of inversion concepts: How does performance on addition and subtraction inversion problems compare to performance on multiplication and division inversion problems? Canadian Journal of Experimental Psychology, 57, 321-330.
Robinson, K.M., Ninowski, J.E., & Gray, M.L. (2006). Children’s understanding of the arithmetic concepts of inversion and associativity. Journal of Experimental Child Psychology, 94, 349-362.
For further information please contact any of the faculty members listed above.
Dr.
Katherine Arbuthnott
Psychology
Campion College
University
of Regina
Regina, SK
S4S 0A2
fax: (306) 359-1200
phone:
(306) 359-1241
katherine.arbuthnott@uregina.ca
Dr.
Tom Phenix
Psychology
Campion College
University of
Regina
Regina, SK
S4S 0A2
fax: (306) 359-1200
phone:
(306) 359-1257
tom.phenix@uregina.ca
Dr.
Katherine Robinson
Psychology
Campion College
University of
Regina
Regina, SK
S4S 0A2
fax: (306) 359-1200
phone:
(306) 359-1248
katherine.robinson@uregina.ca