Assessment forms and their impact on children's learning in Australian primary schools

1. Problem Posing and Problem Solving

Problem-posing and problem-solving have become significant cognitive practices in learning and teaching mathematics. According to many researchers, the traditional assessment method do really reveal students' knowledge and learning acumen. From the viewpoint of learning and teaching mathematics, problem-posing and problem-solving have become essential instructional techniques to use in class. These practices can be applied in finding out the way people learn mathematics based on the constructivist theory of learning. Nonetheless, meaningful, unique and adaptive evaluations are still not fully developed for the assessment of students' learning, especially for the posing of problems.

2. Authentic Assessment

The alternative suggestion for this purpose was authentic assessment; a rubric for performance is a suitable tool for assessing the ability of students to pose and solve mathematical problems (Rosli, Goldsby, & Capraro, 2013). The practice community needs to move forward to improve the tools for assessment. It also needs to shift from traditional assessment to authentic methods to measure the overall learning of students (Rosli, Goldsby, & Capraro, 2013).

3. Mixed Methods Study

Mixed-methods study involves elements of case study, action research and surveys in examining a child at risk. Through a diagnostic examination, in-take interview, think aloud interview in the clinic and error analysis, the study found the main presenting difficulties of the child (Mundia, 2012). Mixed method designs for research have many disadvantages and advantages; but in this paper, only three merits and three demerits will be listed.

The three major advantages of mixed method designs include (Mundia, 2012):

i. It involves the strong sides of both quantitative and qualitative techniques;

ii. It gives a more complete perspective of the phenomena or problem under study; and iii. It does not restrict the information being gathered.

1. Benefits and Implications

Authentic assessment supposes that students are bound to give something that shows a wide, compartmentalized recurrence of the things offered to them, but a combined scholarship connecting their learning based in other subjects and presented in a situation that matches that where the learning may be potentially most significant (Tanner, 1997). Authentic assessment may entail a combination of authentic assessment and authentic learning experiences. First, one needs to come up with activities which need students to integrate, synthesize and apply skill and knowledge in a way that shows the actual world and goes beyond the classroom. Job study programs and apprenticeships are types of techniques that vocational teachers have applied that are found in environments of authentic learning (Mcalister).

Qualitative perspectives of a mixed design method of research can be used together with quantitative research information to create a statement of belief about the presence of a qualitative study finding (Curllette, 2006). A mixed research method incorporates both qualitative and quantitative methods of research. One advantage of applying a mixed research method is that integrating the two techniques sharpens our knowledge of the study results (Reilly, 2007). A rubric for performance is a major factor in numerous interpretations of authentic assessments. The performance rubric is used through criterion-referenced techniques. Through interpretations that are criterion-referenced, Reynolds et al. stated that assessments of students to a particular performance level within a rubric, which is determined on their knowledge and skill. Analytic, holistic and process rubrics are among the scoring types of rubrics that a practice community usually uses. It qualifies as mathematical since it has several criteria based on students' overall procedural and conceptual insight along with problem-solving procedures. Scores from each criterion are added up to get an overall point as an indicator of performance (Rosli, Goldsby, & Capraro, 2013).

2. Factors Contributing the Use of Assessment Types

The open characteristic of problem-posing and problem-solving has caused an increase in the alternative assessment demand. A rubric of performance is more inclusive for the assessment of students' mathematical processes, concepts, disposition and procedures of mathematics. It changes the application of conventional assessments which are only determined by the rightness of the students' response. A well-developed rubric for performance gives educators reliable and valid information about the progress of students in specific criteria, process and knowledge (Rosli, Goldsby, & Capraro, 2013). Authentic learning assessments emphasize that evaluations of students should enable students to master and understand the skills and knowledge that they achieve from teaching. These assessments include both informal formative evaluations and formal criterion-referenced evaluations like interviews, observations, portfolios, lesson studies, portfolios and evaluations by parents, peers and the self. Even though they are still relatively unknown and new, authentic evaluations are already getting well understood in a few developing countries (Mundia, 2012).

The key specific designs connected to the mixed research method include the following (Mundia, 2012):

i. explanatory design -- takes place when quantitative information is gathered first, and qualitative information gathering follows;

ii. exploratory design - qualitative data information is collected first, followed by quantitative information; iii. Triangulation design -- qualitative and quantitative information are collected at the same time to give a more complete and comprehensive set of information.

As it is with other methods of research, the choice and decision of the investigator to use mixed research methods is often achieved after a careful and long thought, considering several important factors like the nature/type of problem under study, specific research hypotheses or questions to probe, the research strategy feasibility, justification or rationale for applying the technique and skill in using suitable data gathering, evaluation and interpretation approaches. It is redundant and pointless for diverse investigators to apply an unwarranted method of research (Mundia, 2012).

3. Effects of Assessment on Children

Performance is the overt achievement and behaviour of a child. The educator simply wishes to understand if the child generally masters the material, gets it or performs as expected. The educator needs to have an interest in the motivation and effect of the child, although cognitive researchers usually pay very little attention to those factors. Research is not required for one to understand that some children, regardless of age are not attentive, have no interest or are afraid of mathematics, or that teaching needs one to deal with such issues among other factors in the management of behaviour (Ginsburg, 2009). For as long as mathematics education has existed, evaluation has been a major issue. Since early twentieth century, uniform testing is used in the assessment of the performance of students. Performance evaluation needs students to create an assessment task structure, construct responses, apply information, and have the capability to describe the procedures used to get the answers. The applying, structuring, explaining and constructing are observable throughout problem-related learning. Problem-related learning is focussed on conceptual-oriented learning instead of mastery of facts (Reilly, 2007).

Classroom evaluation, both as and for learning, is dependent on discussion between the educator and the child. Primary educators are aware of this fact, and when they are asked what they can do, the learners frequently reply based on the questions that they would ask or their conversations. The assurance of raising the learning outcomes of students through targeted evaluation stimulated Australian education structure along with other systems of education to introduce costly and large-scale programs for assessment like NAPLAN, as a component of a 'support and pressure' technique of academic reform (Callingham, 2010). The effect of influential assessment eventually relies on the mind of the teacher. The educator tries to comprehend the mathematics, the obstacles, the trajectories, the mind of the child and the instruction principles. However, eventually, the educator must apply her own cognition to use all these concepts in an individually meaningful manner to the difficult task of currently educating the individual. The growth psychology of thinking in mathematical terms and the method of clinical interview can majorly contribute to learning by changing the formative assessment process -- the effort to apply information about student performance, motivation and learning potential to inform training (Ginsburg, 2009).