Year 7 students’ approaches to understanding and solving NAPLAN numeracy problems

This study investigated how the interpretation of mathematical problems by Year 7 students impacted on their ability to demonstrate what they can do in NAPLAN numeracy testing. In the study, mathematics is viewed as a culturally and socially determined system of signs and signifiers that establish the meaning, origins and importance of mathematics. The study hypothesises that students are unable to succeed in NAPLAN numeracy tests because they cannot interpret the questions, even though they may be able to perform the necessary calculations. To investigate this, the study applied contemporary theories of literacy to the context of mathematical problem solving. A case study design with multiple methods was used. The study used a correlation design to explore the connections between NAPLAN literacy and numeracy outcomes of 198 Year 7 students in a Queensland school. Additionally, qualitative methods provided a rich description of the effect of the various forms of NAPLAN numeracy questions on the success of ten Year 7 students in the same school. The study argues that there is a quantitative link between reading and numeracy. It illustrates that interpretation (literacy) errors are the most common error type in the selected NAPLAN questions, made by students of all abilities. In contrast, conceptual (mathematical) errors are less frequent amongst more capable students. This has important implications in preparing students for NAPLAN numeracy tests. The study concluded by recommending that increased focus on the literacies of mathematics would be effective in improving NAPLAN results.

The effect of calculators on the numerical problem-solving skills and attitudes of primary students towards mathematics /

The purpose of this study was to determine the effect that calculators have on the attitudes and numerical problem-solving skills of primary students. The sample used for this research was one of convenience. The sample consisted of two grade 3 classes within the York Region District School Board. The students in the experimental group used calculators for this problem-solving unit. The students in the control group completed the same numerical problem-solving unit without the use of calculators. The pretest-posttest control group design was used for this study. All students involved in this study completed a computational pretest and an attitude pretest. At the end of the study, the students completed a computational posttest. Five students from the experimental group and five students from the control group received their posttests in the form of a taped interview. At the end of the unit, all students completed the attitude scale that they had received before the numerical problem-solving unit once again. Data for qualitative analysis included anecdotal observations, journal entries, and transcribed interviews. The constant comparative method was used to analyze the qualitative data. A t test was also performed on the data to determine whether there were changes in test and attitude scores between the control and experimental group. Overall, the findings of this study support the hypothesis that calculators improve the attitudes of primary students toward mathematics. Also, there is some evidence to suggest that calculators improve the computational skills of grade 3 students.

Time limitations in NAPLAN numeracy tests

The article discusses evidence that time prevented many students from showing what they could do in the 2010 Year 7 and 9 NAPLAN numeracy tests. In addition to analysing the available data, the article discusses some NAPLAN numeracy questions that contribute to this problem. It is suggested that schools should investigate whether time limitation is a problem for their own students. The article discusses the implications of these findings for teachers preparing students for NAPLAN tests and for the developers of the tests.

After the testing : talking and reading and writing the world

This critical essay discusses the challenges and prospects for the reform of school-based literacy programs. It begins with an overview of the effects of a decade of test-driven accountability policy on research and teachers’ work, noting the continuing challenges of new demographics, cultures and technologies for literacy education. The case is made that whole school literacy programs can make a difference in improving the overall education of students and youth from low socioeconomic and cultural minority backgrounds. But this requires a strong emphasis on engagement with substantive readings of cultural, social and scientific worlds through talk, reading and writing. The key questions facing teachers, then, are not simply around basic skills instruction and acquisition, but about sustained, intellectually demanding and scaffolded talk around texts, print and multimodal.

Group metacognition during mathematical problem solving

Although various studies have shown that groups are more productive than individuals in complex mathematical problem solving, not all groups work together cooperatively. This review highlights that addressing organisational and cognitive factors to help scaffold group mathematical problem solving is necessary but not sufficient. Successful group problem solving also needs to incorporate metacognitive factors in order for groups to reflect on the organisational and cognitive factors influencing their group mathematical problem solving.

Primary school teacher’s noticing of students’ mathematical thinking in problem solving

Professional noticing of students’ mathematical thinking in problem solving involves the identification of noteworthy mathematical ideas of students’ mathematical thinking and its interpretation to make decisions in the teaching of mathematics. The goal of this study is to begin to characterize pre-service primary school teachers’ noticing of students’ mathematical thinking when students solve tasks that involve proportional and non-proportional reasoning. From the analysis of how pre-service primary school teachers notice students’ mathematical thinking, we have identified an initial framework with four levels of development. This framework indicates a possible trajectory in the development of primary teachers’ professional noticing.

Testing After Worked Example Study Does Not Enhance Delayed Problem-Solving Performance Compared to Restudy

Four experiments investigated whether the testing effect also applies to the acquisition of problem-solving skills from worked examples. Experiment 1 (n=120) showed no beneficial effects of testing consisting of isomorphic problem solving or example recall on final test performance, which consisted of isomorphic problem solving, compared to continued study of isomorphic examples. Experiment 2 (n=124) showed no beneficial effects of testing consisting of identical problem solving compared to restudying an identical example. Interestingly, participants who took both an immediate and a delayed final test outperformed those taking only a delayed test. This finding suggested that testing might become beneficial for retention but only after a certain level of schema acquisition has taken place through restudying several examples. However, experiment 2 had no control condition restudying examples instead of taking the immediate test. Experiment 3 (n=129) included such a restudy condition, and there was no evidence that testing after studying four examples was more effective for final delayed test performance than restudying, regardless of whether restudied/tested problems were isomorphic or identical. Experiment 4 (n=75) used a similar design as experiment 3 (i.e., testing/restudy after four examples), but with examples on a different topic and with a different participant population. Again, no evidence of a testing effect was found. Thus, across four experiments, with different types of initial tests, different problem-solving domains, and different participant populations, we found no evidence that testing enhanced delayed test performance compared to restudy. These findings suggest that the testing effect might not apply to acquiring problem-solving skills from worked examples

A multiple case study of NAPLAN numeracy testing of Year 9 students in three Queensland secondary schools

This thesis reports on a multiple case study of the actions of three Queensland secondary schools in the context of Year 9 NAPLAN numeracy testing, focusing on their administrative practices, curriculum, pedagogy and assessment. It was established that schools have found it both challenging and costly to operate in an environment of educational reform generally, and NAPLAN testing in particular. The lack of a common understanding of numeracy and the substantial demands of implementing the Australian Curriculum have impacted on schools' ability to prepare students appropriately for NAPLAN numeracy tests. It was concluded that there is scope for schools to improve their approaches to NAPLAN numeracy testing in a way that maximises learning as well as test outcomes.

The life of data: Evolving national testing

To this point, the collection has provided research-based, empirical accounts of the various and multiple effects of the National Assessment Program – Literacy and Numeracy (NAPLAN) in Australian schooling as a specific example of the global phenomenon of national testing. In this chapter, we want to develop a more theoretical analysis of national testing systems, globalising education policy and the promise of national testing as adaptive, online tests. These future moves claim to provide faster feedback and more useful diagnostic help for teachers. There is a utopian testing dream that one day adaptive, online tests will be responsive in real time providing an integrated personalised testing, pedagogy and intervention for each student. The moves towards these next generation assessments are well advanced, including the work of Pearson’s NextGen Learning and Assessment research group, the Organization for Economic Co-operation and Development’s (OECD) move into assessing affective skills and the Australian Curriculum, Assessment and Reporting Authority’s (ACARA) decision to phase in NAPLAN as an online, adaptive test from 2017...

National testing from an Australian perspective

Introduction This book examines a pressing educational issue: the global phenomenon of national testing in schooling and its vernacular development in Australia. The Australian National Assessment Program – Literacy and Numeracy (NAPLAN), introduced in 2008, involves annual census testing of students in Years 3, 5, 7 and 9 in nearly all Australian schools. In a variety of ways, NAPLAN affects the lives of Australia’s 3.5 million school students and their families, as well as more than 350,000 school staff and many other stakeholders in education. This book is organised in relation to a simple question: What are the effects of national testing for systems, schools and individuals? Of course, this simple question requires complex answers. The chapters in this edited collection consider issues relating to national testing policy, the construction of the test, usages of the testing data and various effects of testing in systems, schools and classrooms. Each chapter examines an aspect of national testing in Australia using evidence drawn from research. The final chapter by the editors of this collection provides a broader reflection on this phenomenon and situates developments in testing globally...

Local experiences, global similarities: Teacher perceptions of the impacts of national testing

Since 2008, Australian schoolchildren in Years 3, 5, 7 and 9 have sat a series of tests each May designed to assess their attainment of basic skills in literacy and numeracy. These tests are known as the National Assessment Program – Literacy and Numeracy (NAPLAN). In 2010, individual school NAPLAN data were first published on the MySchool website which enables comparisons to be made between individual schools and statistically like schools across Australia. NAPLAN represents the increased centrality of the federal government in education, particularly in regards to education policy. One effect of this has been a recast emphasis of education as an economic, rather than democratic, good. As Reid (2009) suggests, this recasting of education within national productivity agendas mobilises commonsense discourses of accountability and transparency. These are common articles of faith for many involved in education administration and bureaucracy; more and better data, and holding people to account for that data, must improve education...

Cracking the language code : NAPLAN numeracy tests in years 7 and 9

Focusing on the use of language is a crucial strategy in good mathematics teaching and a teacher’s guidance can assist students to master the language of mathematics. This article discusses the statements with reference to recent year 7 and 9 NAPLAN numeracy tests. It draws the readers’ attention to the complexities of language in the field of mathematics. Although this article refers to NAPLAN numeracy tests it also offers advice about good teaching practice.

Making meaning in mathematics problem solving using the Reciprocal Teaching approach

This paper examines the application of the Reciprocal Teaching instructional approach to Mathematical word problems in the middle years. The Reciprocal Teaching process is extended from the four traditional strategies of predicting, clarifying, questioning and summarising, to include further cognitive reading comprehension strategies applied to the context of solving Mathematical word problems.

Computers and mathematical programming : proceedings of the Bicentennial Conference on Mathematical Programming held at the National Bureau of Standards, Gaithersburg, Maryland, November 29-December 1, 1976 /

Includes bibliographies.