Learning involves changes in knowledge, skills and the sophistication of the strategies employed ... more Learning involves changes in knowledge, skills and the sophistication of the strategies employed by the learners. To measure these changes we need at least two relevant measures. One assessment must document the level of achievement prior to a particular stage of learning and a later assessment must document a higher level of achievement. But improving achievement requires more than good assessment. To use a farming analogy: the farmer's maize will grow better if appropriate nutrients and water are provided in timely fashion. Measuring the height of the maize frequently is not going to improve the yield at all. To provide effective learning opportunities for all pupils we need assessment strategies that will be teacher -friendly (helpful in identifying what has to be taught) and teaching strategies to ensure students learn what they currently do not know. This paper looks at the requirements for using assessment for teaching and learning and addresses threats to the validity of assessments to evaluate progress. These threats include failure to use appropriate samples of tasks in assessments, use of uncalibrated tasks, and inappropriate scoring procedures and methods of interpreting data.
To provide effective learning opportunities for all pupils we need assessment strategies that wil... more To provide effective learning opportunities for all pupils we need assessment strategies that will be teacher-friendly and that encourage learning. Teacher-friendly assessment strategies are those that are helpful in identifying what has to be taught. Encouraging learning requires teaching strategies that use the assessment information to ensure students learn what they currently do not know. Izard has discussed teacher-friendly assessment strategies but warns that problems may arise in the choice of test items for tests for assessment for learning purposes. This paper considers theoretical and practical requirements for using assessment for teaching and learning, and reviews the use of a published test series to meet these requirements in a local primary school.
... Robert Hunting & Brian Doig); "Affective Considerations in Assessing... more ... Robert Hunting & Brian Doig); "Affective Considerations in Assessing Mathematics" (Beth Southwell & Mon Khamis); "Classroom Practicalities ... Learning Mathematics" (Andrew Waywood); "Spatial Mathematics: A Group Test for Primary School Students" (Kay Owens); "Patterns ...
Abstract: Whether poor knowledge of evolution among Singapore students might be linked to low lev... more Abstract: Whether poor knowledge of evolution among Singapore students might be linked to low levels of content knowledge about evolution among junior high school and senior high school teachers was studied. A teacher questionnaire on biological evolution was ...
How do we decide whether students have learned? Learning involves changes in knowledge, skills an... more How do we decide whether students have learned? Learning involves changes in knowledge, skills and the sophistication of the strategies employed by the learners. How do we gather the relevant evidence of learning? To measure these changes we need at least two relevant measures, one prior to a particular stage of learning and a later assessment documenting a higher level of achievement. This paper looks at the requirements for using such assessment for teaching and learning and addresses threats to the validity of assessments to evaluate progress.
Abstract Research has shown that many students in Years 5 to 9 experience considerable difficulty... more Abstract Research has shown that many students in Years 5 to 9 experience considerable difficulty with rational number, algebra, and the application of multiplication and division to a broader range of problem types. While each of these has been the focus of considerable research, there is little advice about how these ideas are connected and jointly develop over time. This paper describes the genesis of a learning assessment framework for multiplicative thinking based on Rasch analysis of student responses to a range of rich tasks to inform ...
This study uses Rasch modelling to link student out comes over the decade since the introduction ... more This study uses Rasch modelling to link student out comes over the decade since the introduction of chance and data into the curriculum of an Australian state in 1993. Although improvement is observed over time for intact groups of students, and between grade levels in a given year, improvement across co horts for given grades over time is not observed. The distribution of the items used in the 2003 survey across the statistical literacy variable supports earlier models of the hierarchica l nature of statistical thinking obtained from a larger pool of items. Three factors contributed to the research reported in this study. First was the introduction of chance and data into the mathematic s curriculum in an Australian state in 1993, following its appearance in A National Statement on Mathematics for Australian Schools in 1991 (Australian Education Council (AEC), 1991; Department of Education and the Arts, 1993). Because very little research had c ontributed to the definition of the c...
This study uses Partial Credit Rasch analysis to study a complex data set of student responses to... more This study uses Partial Credit Rasch analysis to study a complex data set of student responses to survey items relating to chance and data. The items were administered in the classroom and collected from 1993 to 2003 in the Australian state of Tasmania. Data were collected from a total of 5514 individual students across Grades 3 to 11 over the decade and of these students 896 provided at least one repeated measure. As students completed a core of common items, Rasch analysis could be performed and all students were subsequently placed on the same logit scale for comparison. The purpose of the analysis is to consider average cohort change over time and trends in performance during the first 10 years after the curriculum was introduced in Tasmania. Implications for the education system and curriculum implementation are considered.
The provision of valid evidence of learning achievement and the need for accountability are two c... more The provision of valid evidence of learning achievement and the need for accountability are two crucial factors in assessment. Projects and investigations, which provide evidence of communication in mathematics are discussed as a means to the direct assessment of the true objectives of the curriculum meeting the criteria of Eisner (1993). Using the methodology of , developed for adult literacy and numeracy scales, research in UK universities addresses the assessment of such tasks in mathematical modelling, pure mathematics and statistics. Analysis from this research, using item response modelling and the techniques of and , describes student, judge and descriptor behaviour on rating scales which attempt to assess student achievement comprehensively. This paper focuses on the example of oral communication skills as an illustration. Implications of the research are discussed and questions are raised which require further investigation.
Research has shown that many students in Years 5 to 9 experience considerable difficulty with rat... more Research has shown that many students in Years 5 to 9 experience considerable difficulty with rational number, algebra, and the application of multiplication and division to a broader range of problem types. While each of these has been the focus of considerable research, there is little advice about how these ideas are connected and jointly develop over time. This paper describes the genesis of a learning assessment framework for multiplicative thinking based on Rasch analysis of student responses to a range of rich tasks to inform ...
Learning involves changes in knowledge, skills and the sophistication of the strategies employed ... more Learning involves changes in knowledge, skills and the sophistication of the strategies employed by the learners. To measure these changes we need at least two relevant measures. One assessment must document the level of achievement prior to a particular stage of learning and a later assessment must document a higher level of achievement. But improving achievement requires more than good assessment. To use a farming analogy: the farmer's maize will grow better if appropriate nutrients and water are provided in timely fashion. Measuring the height of the maize frequently is not going to improve the yield at all. To provide effective learning opportunities for all pupils we need assessment strategies that will be teacher -friendly (helpful in identifying what has to be taught) and teaching strategies to ensure students learn what they currently do not know. This paper looks at the requirements for using assessment for teaching and learning and addresses threats to the validity of assessments to evaluate progress. These threats include failure to use appropriate samples of tasks in assessments, use of uncalibrated tasks, and inappropriate scoring procedures and methods of interpreting data.
To provide effective learning opportunities for all pupils we need assessment strategies that wil... more To provide effective learning opportunities for all pupils we need assessment strategies that will be teacher-friendly and that encourage learning. Teacher-friendly assessment strategies are those that are helpful in identifying what has to be taught. Encouraging learning requires teaching strategies that use the assessment information to ensure students learn what they currently do not know. Izard has discussed teacher-friendly assessment strategies but warns that problems may arise in the choice of test items for tests for assessment for learning purposes. This paper considers theoretical and practical requirements for using assessment for teaching and learning, and reviews the use of a published test series to meet these requirements in a local primary school.
... Robert Hunting & Brian Doig); "Affective Considerations in Assessing... more ... Robert Hunting & Brian Doig); "Affective Considerations in Assessing Mathematics" (Beth Southwell & Mon Khamis); "Classroom Practicalities ... Learning Mathematics" (Andrew Waywood); "Spatial Mathematics: A Group Test for Primary School Students" (Kay Owens); "Patterns ...
Abstract: Whether poor knowledge of evolution among Singapore students might be linked to low lev... more Abstract: Whether poor knowledge of evolution among Singapore students might be linked to low levels of content knowledge about evolution among junior high school and senior high school teachers was studied. A teacher questionnaire on biological evolution was ...
How do we decide whether students have learned? Learning involves changes in knowledge, skills an... more How do we decide whether students have learned? Learning involves changes in knowledge, skills and the sophistication of the strategies employed by the learners. How do we gather the relevant evidence of learning? To measure these changes we need at least two relevant measures, one prior to a particular stage of learning and a later assessment documenting a higher level of achievement. This paper looks at the requirements for using such assessment for teaching and learning and addresses threats to the validity of assessments to evaluate progress.
Abstract Research has shown that many students in Years 5 to 9 experience considerable difficulty... more Abstract Research has shown that many students in Years 5 to 9 experience considerable difficulty with rational number, algebra, and the application of multiplication and division to a broader range of problem types. While each of these has been the focus of considerable research, there is little advice about how these ideas are connected and jointly develop over time. This paper describes the genesis of a learning assessment framework for multiplicative thinking based on Rasch analysis of student responses to a range of rich tasks to inform ...
This study uses Rasch modelling to link student out comes over the decade since the introduction ... more This study uses Rasch modelling to link student out comes over the decade since the introduction of chance and data into the curriculum of an Australian state in 1993. Although improvement is observed over time for intact groups of students, and between grade levels in a given year, improvement across co horts for given grades over time is not observed. The distribution of the items used in the 2003 survey across the statistical literacy variable supports earlier models of the hierarchica l nature of statistical thinking obtained from a larger pool of items. Three factors contributed to the research reported in this study. First was the introduction of chance and data into the mathematic s curriculum in an Australian state in 1993, following its appearance in A National Statement on Mathematics for Australian Schools in 1991 (Australian Education Council (AEC), 1991; Department of Education and the Arts, 1993). Because very little research had c ontributed to the definition of the c...
This study uses Partial Credit Rasch analysis to study a complex data set of student responses to... more This study uses Partial Credit Rasch analysis to study a complex data set of student responses to survey items relating to chance and data. The items were administered in the classroom and collected from 1993 to 2003 in the Australian state of Tasmania. Data were collected from a total of 5514 individual students across Grades 3 to 11 over the decade and of these students 896 provided at least one repeated measure. As students completed a core of common items, Rasch analysis could be performed and all students were subsequently placed on the same logit scale for comparison. The purpose of the analysis is to consider average cohort change over time and trends in performance during the first 10 years after the curriculum was introduced in Tasmania. Implications for the education system and curriculum implementation are considered.
The provision of valid evidence of learning achievement and the need for accountability are two c... more The provision of valid evidence of learning achievement and the need for accountability are two crucial factors in assessment. Projects and investigations, which provide evidence of communication in mathematics are discussed as a means to the direct assessment of the true objectives of the curriculum meeting the criteria of Eisner (1993). Using the methodology of , developed for adult literacy and numeracy scales, research in UK universities addresses the assessment of such tasks in mathematical modelling, pure mathematics and statistics. Analysis from this research, using item response modelling and the techniques of and , describes student, judge and descriptor behaviour on rating scales which attempt to assess student achievement comprehensively. This paper focuses on the example of oral communication skills as an illustration. Implications of the research are discussed and questions are raised which require further investigation.
Research has shown that many students in Years 5 to 9 experience considerable difficulty with rat... more Research has shown that many students in Years 5 to 9 experience considerable difficulty with rational number, algebra, and the application of multiplication and division to a broader range of problem types. While each of these has been the focus of considerable research, there is little advice about how these ideas are connected and jointly develop over time. This paper describes the genesis of a learning assessment framework for multiplicative thinking based on Rasch analysis of student responses to a range of rich tasks to inform ...
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