Generalising the pattern rule for visual growth patterns: Actions that support 8 year olds’ thinking

Abstract

A common approach used for introducing algebra to young adolescents is an exploration of visual growth patterns and expressing these patterns as functions and algebraic expressions. Past research has indicated that many adolescents experience difficulties with this approach. This paper explores teaching actions and thinking that begins to bridge many of these difficulties at an early age. A teaching experiment was conducted with two classes of students with an average age of eight years and six months. From the results it appears that young students are capable not only of thinking about the relationship between two data sets, but also of expressing this relationship in a very abstract form.

Pattern Generalization by Elementary Students

“…These findings concur with those of [21], that elementary school students aged 8 years could think about the relationship between the two groups of data and represent it in a very abstract form. The results also reinforce the research conducted [2] that elementary school students are able to identify the rules or patterns and use them to predict the next values for the given pattern and being able to articulate the general rule verbally.…”

Pathways to Professional Growth: Investigating Upper Primary School Teachers’ Perspectives on Learning to Teach Algebra

“…Many of these incorporate the use of multiple representations of a functional relationship -diagrams of a growing pattern with item numbers, verbal and worded descriptions, symbolic expressions and equations, tables of values, and graphs (e.g., Confrey & Smith, 1994, Kaput, 1999MacGregor & Stacey, 1995). A number of studies advocated the use of concrete materials in constructing growing patterns so that students are able to notice the changes between items and the structure within an item (Markworth, 2010;Moss, Beatty, Barkin, & Shillolo, 2008;Warren & Cooper, 2008). Friel and Markworth (2009) provided examples of several types of geometric patterns of increasing levels of complexity which give students multiple opportunities to experience the process of noticing the structure of the items -answering the question, "What is it that all these instances have in common?"…”

Η Κατανόηση Των Μαθηματικών Μοτίβων Από Παιδιά Γ’ Και Δ’ Δημοτικού Και Οι Στρατηγικές Σκέψης Τους

“…Ωστόσο, η διερεύνηση των επιδόσεων των μικρών παιδιών δείχνει ότι αυτές συχνά εξαρτώνται και επηρεάζονται από το περιεχόμενο και τη δομή του μοτίβου καθώς και από το είδος του υλικού που εμπλέκεται. Σίγουρα, όμως, οι επι-δόσεις των παιδιών εμφανίζονται περισσότερο βελτιωμένες στα επόμενα σχολικά τους χρό-νια, ως αποτέλεσμα των προηγούμενων σχετικών εμπειριών τους από την προσχολική ηλικία (Leung, Krauthausen, & Rivera, 2012), ενισχύοντας την άποψη ότι η καθυστέρηση στην ενα-σχόληση με τα μοτίβα και την αναζήτηση και αναγνώριση δομικών στοιχείων μέσα από αυτά αιτιολογεί τις δυσκολίες των μεγαλύτερων παιδιών στην άλγεβρα (Mulligan & Mitchelmore, 2009. Warren & Cooper, 2008.…”