Evaluation |
Performance tasks, such as the example above, are an effective way to assess mathematical understanding and processes (Reys et al., 2012). This task in particular provides a real-world scenario that is related to the content-specific area of financial mathematics, and is sufficiently open so all students can be creative in attempting the task (Quinnell, 2010; Sullivan, Griffioen, Gray & Powers, 2009). Providing a real-world problem enriches the activity and increases student engagement (Siemon et al., 2015). Students use the concept of money authentically while also using higher-order thinking skills to find a solution (Varygiannes, 2014). Higher-order thinking skills include critical thinking, problem solving, reasoning and justifying solutions (Reys et al., 2012). Open-ended tasks are beneficial for developing a classroom culture that embraces mathematical conversations which are important for increasing students’ confidence (Varygiannes, 2014; Van de Walle, Karp & Bay-Williams, 2014). During mathematical conversations students should be encouraged to make valuable connections by analysing and comparing their strategies with those of their peers (Van de Walle, Karp & Bay-Williams, 2014).
However, open-ended tasks have limitations and can be problematic. When activities have multiple pathways and solutions, and are not based on “memorisation or repetition” (Reys et al., 2012, p.56) students can become frustrated. It is important to pose tasks as a challenge and not a problem (Quinnell, 2010). Some will also become frustrated if they are not sure which strategy is required to solve the problem (Quinnell, 2010). Additionally, students may not fully understand the problem or lack the knowledge to solve it, which could result in “incorrect use of mathematical ideas” (Quinnell, 2010, p. 38). Classroom talk can eliminate issues of understanding the problem though (Reys et al., 2012). Open-ended tasks can also be problematic as not all of them have a written solution, in which case it is critical that teachers engage with students to gain insights to their procedural thinking, understanding of the concepts, and reasoning for solutions (Van de Walle, Karp & Bay-Williams, 2014; William, 2013). The above open-ended task provides a differentiated approach to learning and assessment. It can be accessed at different levels with more proficient students finding all solutions, while students having difficulties can focus on strategies to find one solution (Quinnell, 2010). Students can also be supported by solving problems with concrete manipulatives or pictures. This informs the teacher what level of understanding students have (Jamieson-Proctor and Larkin, n.d.). It is suggested that enabling and extending prompts should be planned ahead, which is not evident in this task (Siemon et al., 2015). However, the enabling prompt could involve the provision of concrete manipulatives as opposed to providing materials up front, or provision of a calculator once other strategies have been attempted (Sullivan, Griffioen, Gray & Powers, 2009). The extending prompt could involve a $100 note, or a different currency to address the cross-curriculum priority regarding engagement with Asia (ACARA, n.d.). It is important to be conscious of the level of support as too much support can lower the “value of the task” (Quinnell, 2010, p. 38). Lastly, the time to complete the task can be adjusted to suit all learners (Tomlinson & Moon, 2013).
Summative assessments are generally used at the end of units of work as a record of student progress and to provide a grade (Callingham, 2010; Tomlinson & Moon, 2013). They are often measured against the achievement standards of the national curriculum (Siemon et al., 2015). This task provides opportunities for students to demonstrate the Year 4 achievement standard “students solve simple purchasing problems” (ACARA, 2016, Year4 Achievement Standards). However, additional problems may be required to fully address all skills and strategies required to meet the achievement standard, as detailed in the learning progression. For example, students may not demonstrate their ability to record notes, coins or combinations of notes and coins if their strategy is based on mental computation.
The task could also be considered an assessment ‘for learning’. The purpose of the assessment could be to identify opportunities for future teaching and learning, and to provide prompt feedback (Callingham, 2010; William 2013). Records of observations or written processes will inform additional teaching and learning of the concept, skills and strategies regarding money (Van de Walle, Karp & Bay-Williams, 2014). The value of an open-ended task for teachers is realised through observations of the mathematical processes students use (Van de Walle, Karp & Bay-Williams, 2014). Additionally, when tasks are conducted as cooperative learning, conversations between students can be just as informative (Van de Walle, Karp & Bay-Williams, 2014). The relevance of the task could be improved by providing students a set budget and grocery catalogues to complete a grocery shop. Students with difficulties adding money could shop for one item and explain the change they will get. |