MENTAL CALCULATIONS IN THE PROCESS OF OVER PASSING THE FIRST TEN NUMBERS: STRATEGIES AND PERFORMANCES OF 1RST AND 2ND GRADE STUDENTS

PDF (ελληνικά)
Published: Oct 8, 2018
DOI: https://doi.org/10.12681/enedim.18816
Keywords:
mental calculations mental strategies elementary school
Ιωάννης Καραντζής (Ioannis Karantzis)
University of Patras
Abstract

The purpose of the present study was to investigate primarily whether first grade and second grade students have acquired mental calculation capabilities needed in the process of over passing the first ten numbers and the type of strategies they use. At the same time, the study investigated whether there were any significant differences in ti: e performance of students in terms of preferred strategies. Data were collected from 98 first grade students and 58 second grade students from five randomly selected public elementary schools of the city of'Patras. The students participated in three experiments and were tested individually. Results showed that students in both grades employed recall strategies and construction strategies; more specifically, the choice of strategy was found to depend on the type of intermediate sums in the calculation process. In general the findings of the present study seem to confirm the results of earlier studies conducted in Greece or in other countries.

Article Details
  • Section
  • Articles
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors who publish with this journal agree to the following terms:

Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution licence that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g. post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.

Authors are permitted and encouraged to post their work online (preferably in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).

 

 
Downloads
Download data is not yet available.
Author Biography
Ιωάννης Καραντζής (Ioannis Karantzis), University of Patras
Lecturer
References
Baddeley, Α. (1995). Human Memory: Theory and Practice. London: L.E.A.P.
Beishuitzen, M. (1993). Mental strategies and materials or models for addition and subtraction up to 100 in Dutch second grades. Journalfor research in Mathematics Education, 24(4), 294-323.
Cohen, L. & Manion, L. (1994). Μεθοδολογία εκπαιδευτικής έρευνας (μτφρ). Αθήνα:
Μεταίχμιο.
Geary, D., Brown, S., Samaranayake, V. (1991). Cognitive addition: A short longitudinal study of strategy choice and speed-of-processing differences in normal and mathematically disabled children. Developmental Psychology, 27(5), 787-797.
Heirdsfield, A. & Cooper, T. (2004). Inaccurate Mental addition and subtraction: Causes and Compensation. Focus on Learning Problems in Mathematics, 26(3), 43-65.
Heirdsfield, A. & Lamb, J. (2005). Mental Computation: The Benefits of Informed Teacher Instruction. In Clarkson, et al. (Eds), Proceedings MERGA 28 - 2005 Building connections: Theory, research and practice 2 (pp. 419-426). Melbourne.
Jensen, A. & Whang, P. (1994). Speed of accessing arithmetic facts in long-term memory: A comparison of Chinese-American and Anglo-American children. Contemporary Educational Psychology, 19, 1-12.
Καραντζής, I. (2007). Η στρατηγική των όμοιων προσθετέων στο νοερό υπολογισμό κατά τη διαδικασία υπέρβασης της πρώτης δεκάδας. Πρακτικά 2ου Συνεδρίου της ΕΝΕΔΙΜ, Τυπικά και άτυπα μαθηματικά: χαρακτηριστικά, σχέσεις και αλληλεπιδράσεις, στο πλαίσιο της μαθηματικής εκπαίδευσης (σσ. 304-314). Αθήνα: Τυπωθήτω -Γ. Δαρδανός.
Κατσίλλης, Ι. (2006). Επαγωγική στατιστική. Αθήνα: Gutenberg. Κωσταρίδου- Ευκλείδη, Α. (1992). Γνωστική Ψυχολογία. Θεσσαλονίκη: Art of Text. Λεμονίδης, Χ. (2003). Μια νέα πρόταση διδασκαλίας των Μαθηματικών στις πρώτες τάξεις του Δημοτικού Σχολείου. Αθήνα: Πατάκης.
Λεμονίδης, Χ. (2007). Μακροχρόνια μελέτη στην ανάπτυξη των νοερών υπολογισμών στις δύο πρώτες τάξεις του Δημοτικού Σχολείου. Αναζήτηση από το www.google.gr
με τον όρο «νοερός υπολογισμός». Τελευταία προσπέλαση 2-2-2007.
Λεμονίδης, Χ. & Λυγούρας, Γ. (2008). Η επίδοση και η ευελιξία μαθητών της τρίτης τάξης δημοτικού στους νοερούς υπολογισμούς. Ευκλείδης Γ, 68, 20-44.
Leutzinger, L. (1999). Developing thinking strategies for addition facts. Teaching children mathematics, 6(1), 14-18.
Logie, R., Gilhooly, K. and Wynn, V. (1994). Counting on working memory in arithmetic problem solving. Memory and Cognition, 22(4), 395-410.
Macintyre, T. & Forrester, R. (2003). Strategies for mental calculation. In Williams, J. (Ed.). Proceedings of the British Societyfor Research into Learning Mathematics, 23(2), 49-54.
Maclellan, E. (2001). Mental Calculation: its place in the development of numeracy. Westminster Studies in Education, 24(2), 145-154.
Peterson E. R & Deary I. J. (2006). Examining holistic-analytic style using preferences in early information processing. Personality and Individual Differences, 41, 3-14
Πόρποδας,Κ. (2003). Η μάθηση και οι δυσκολίες της (Γνωστική προσέγγιση). Πάτρα: Αυτοέκδοση.
Rensick, L. Β. (1986). The development of mathematical intuition. In M. Perlmutter (Ed.), Perspectives on intellectual development: The Minnesota Symposia on Child Psychology (19, pp. 159-194). Hillsdale, NJ: Erlbaum.
Schoenfeld, A. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (ed.), Handbook of research on Mathematics teaching and learning (pp. 334-370).New York: Macmillan.
Thompson, I. (1995). The role of counting in the idiosyncratic mental calculation algorithms of young children. European early Childhood Education Research Journal, 3(1), 5-16.
Thompson, I. (1999). Written methods of calculation. In Thompson I (ed), Issue teaching numeracy in primary schools (pp. 169-183). Buckingham: Open University Press.
Threlfall, J. (2002). Flexible mental calculation. Educational Sttidies in Mathematics, 50(1), 29-47. ΥΠΕΠΘ-Παιδαγωγικό Ινστιτούτο (2002). Διαθεματικό Ενιαίο Πλαίσιο Προγραμμάτων Σπουδών (τ. 1). Αθήνα: Παιδαγωγικό Ινστιτούτο.
Van de Walle, J. Α. (2005). Μαθηματικά για το Δημοτικό και το Γυμνάσιο: Μιαεξελικτική διδασκαλία (μτφρ). Αθήνα: Τυπωθήτω - Γ. Δαρδανός.
Varol, F. & Farran, D. (2007). Elementary school students' mental computation proficiencies. Early Childhood Education Journal, 35(1), 89-94.
Von Glasersfeld, E. (1989). Cognition, construction of knowledge and teaching. Synthese, 80, 121-140.
Χασάπης, Δ. (2000). Διδακτική βασικών Μαθηματικών Εννοιών - Αριθμοί και Αριθ­μητικές Πράξεις. Αθήνα: Μεταίχμιο.