Academic journal article Educational Technology & Society

Enacting Viewing Skills with Apps to Promote Collaborative Mathematics Learning

Academic journal article Educational Technology & Society

Enacting Viewing Skills with Apps to Promote Collaborative Mathematics Learning

Article excerpt

Introduction

Mathematics competencies are cumulative over time (Jordan, Kaplan, Remineni, & Locuniak, 2009; National Mathematics Advisory Panel, 2008). If not properly addressed and overcome, difficulties encountered at any stage of learning will lead to poor achievement in subsequent mathematics learning. Problem-solving skills in addition and subtraction are dominant aspects of the fundamental competency domains in mathematics. When children practise solving problems, their underlying conceptual and procedural knowledge in addition and subtraction determines their competency (Canobi, Reeve, & Pattison, 2003; Canobi, Reeves, & Pattison, 1998). The causal relations between these two areas of knowledge have been found to be bi-directional; increases in conceptual knowledge will help to increase procedural knowledge, and vice versa (Rittle-Johnson & Schneider, 2015). Therefore, in developing an effective classroom teaching pedagogy, the integration of content knowledge (conceptual and procedural) into learning approaches is important. These approaches must engage children in the target-learning activities while leading to the process of meaning-making using the content knowledge (Hiebert & Wearne, 1996; Schneider, Rittle- Johnson, & Star, 2011).

The conceptual and procedural knowledge of learners is observed explicitly via strategies applied during their routes to problem solutions. Some of the strategies applied in addition problem solving are direct modelling (represented by objects, which are all counted), counting on from the first number, counting on from the larger number, and recall with no apparent counting; those applied in subtraction problem solving are direct modelling (counting objects by separating from the total and counting those remaining), counting down from the bigger number (a backward counting sequence from bigger numbers), and counting up from the smaller number (a forward counting sequence from smaller numbers) (Carpenter & Moser, 1984).

Learning by rote involves imitating. Conversely, creative reasoning engages students by allowing them to develop well-founded mathematically anchored arguments for their choice of methods in non-routine problem-solving processes. In conjunction with challenging non-routine problems, collaboration is often suggested because it can improve students' conceptual understanding (Boaler & GReeno, 2000; Stahl, Rose, & Goggins, 2011). However, to accomplish collaborative creative reasoning, a suitable learning environment needs to be established. In this learning environment, students need to apply new strategies repeatedly, with the objective being the advancement of their competency in addition and subtraction problem solving. Collaboration on a challenging problem cannot be automatically initiated within groups. The utilisation of the process of negotiation to seek the new knowledge (i.e., the correct strategies) must be made visible to the learners during their collaborative efforts. Therefore, mathematics learning that is solely print-based and structured by content printed in a book is inadequate (Clausen-May, 2013). In terms of teaching and learning technology resources, there are a number of readily available free online mathematical problem-solving digital apps. These digital apps mainly afford opportunities to learn interactively with ideas, content and modalities that were not previously possible (Yelland, 2015). However, the place of these apps in formal education in kindergarten has been contentious (Zaranis, Brown, Evans, & Hannula, 2013).

It is believed that working collaboratively with these digital texts may allow participants to jointly acquire knowledge none of them had before (Cress, Stahl, Ludvigsen, & Law, 2015). However, the use of well-established apps and environments alone does not guarantee that

collective knowledge construction will take place. That said, teaching and learning with digital apps could create and facilitate learning contexts but not the actual learning. …

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