Large-scale mathematics assessment : looking globally to act locally

In this paper, I will argue that it is possible to use data from large-scale international and national mathematics assessment programmes, whose attention is on summative achievement, to provide formative information that informs teachers about the effects of their classroom practice. However, to have impact on, and be useful for, classroom practitioners, these achievement data need to be reworked and re-presented in ways that are plausible, provide a basis for inferences about practice, and be appropriate for the intended audience. This paper examines achievement-focused assessment programmes in terms of their aims and approaches, and develops the argument that formative assessment possibilities are present, within these programmes, although usually hidden. Examples are drawn from several sources to support this argument, and demonstrate a variety of approaches that have been taken in the past. Suggestions for further action are made.

Towards an integration of theories of achievement motivation

This thesis investigated children's school achievement in terms of an integration of three theories of achievement motivation. The three theoretical outlooks were expectancy-value theory (EVT), implicit theories of intelligence (ITI), and flow theory (FT). The first of two studies was an exploratory investigation of the effectiveness of each theory independently and combined to predict children's achievement in four school subjects. The subject areas were maths, reading, instrumental music and sport. Participants were 84 children (40 females and 44 males) aged 9 to 10 years, one of each child's parents, and school teachers of each child in the four subject areas. All data were collected through questionnaires based on the three models. The results indicated that EVT and FT but not ITI accounted for a significant amount of the variance in children's achievement, including effects for subject area and gender. A second confirmatory study tested EVT, FT and an integrated model for the prediction of achievement in maths, reading and instrumental music. The participants were a further 141 children (74 females and 67 males) aged 10 to 11 years, and a parent and teachers of each child. Data collection using questionnaires occurred early in the school year (Timel) and approximately five months later (Time2). For EVT, children and parents’ competence beliefs were significant predictors of children's achievement in each subject area. Females tended to believe themselves more competent at reading and instrumental music and also valued these subjects more highly than boys. Modeling results for flow theory indicated that children's emotional responses to classes (happiness and confusion) were significant predictors of achievement, the type of emotion varying between subject areas and time periods. Females generally had a more positive emotional reaction to reading and instrumental music classes than males did. The integrated model results indicated significant relationships between EVT and flow theories for each subject area, with EVT explaining most achievement variance in the integrated model. Children's and parents’ competence beliefs were the main predictors of achievement at Timel and 2, Subject area and gender differences were found which provide direction for future research. Anecdotal reports of parents and teachers often attest to individual differences in children's involvement in various school domains. Even among children of apparently similar intelligence, it is not uncommon to find one who likes nothing better than to work on a mathematics problem while another much prefers to read a novel or play a musical instrument Some children appear to achieve good results for most of the activities in which they are engaged while others achieve in a less consistent manner, sometimes particularly excelling in one activity. Some children respond to failure experiences with a determination to improve their performance in the future while others react with resignation and acceptance of their low ability. Some children appear to become totally absorbed in the activity of playing sport while others cannot wait for the game to end. The primary research objective guiding the current thesis is how children's thoughts and feelings about school subjects differ and are related to their school achievement. A perusal of the achievement motivation literature indicates several possible models and concepts that can be applied to explain individual differences in children's school achievement. Concepts such as academic self-concept, multiple intelligences, intrinsic and extrinsic motivation, self-beliefs, competence beliefs, subjective task values, mastery and performance goals, ‘Flow’ experiences and social motivation are just some of the constructs used to explain children's achievement motivation, both within and between various activity domains. These constructs are proposed by researchers from different theoretical perspectives to achievement motivation. Although there is much literature relevant to each perspective, there is little research indicating how the various perspectives may relate to each other. The current thesis will begin by reviewing three currently popular theoretical orientations cited in achievement motivation research: subjective beliefs and values; implicit theories of intelligence, and flow experience and family complexity. Following this review, a framework will be proposed for testing the determinants of children's school achievement, both within each of the three theoretical perspectives and also in combination.

Improving middle years mathematics and science

The overall aim of the Improving Middle Years Mathematics and Science (IMYMS) project was to explore the explore the nature and significance of subject cultures in framing teacher and school practice in mathematics and science and to develop a middle years school improvement model that takes account of these subject cultures in influencing school and teacher change. The project also investigated ways in which effective pedagogies in mathematics and science can be monitored; and ways in which higher order learning outcomes in mathematics and science can be reliably assessed.

The project has worked with more than 30 schools in four clusters to support them in planning for and implementing change. A framework describing effective mathematics and science pedagogies was developed, and used as the basis for auditing procedures that track classroom practice. Instruments were developed and used to probe: teacher classroom practice; student perceptions of classroom practice and learning preferences; knowledge outcomes; reasoning in science and mathematics; understanding of the nature of science and mathematics; and performance skills in mathematics and science investigations. Data sources have also included questionnaire data, interviews, school reports and field notes. Video data was also collected and used for stimulated recall interviews concerning teacher beliefs and practices.

In order to support teachers and schools to improve their practice, the project team worked with cluster educators in each of the clusters, and with school coordinators, through a number of network meetings including an initial ‘leading change’ workshop, through cluster visits, and the provision of auditing and planning instruments supported by data analysis support. The nature of the subject cultures of, and effective pedagogies in, mathematics and science, was explored using interview data with effective teachers, literature exploration, interviews with project teachers to map characteristics of their practice, the team’s experience of the construction and analysis of achievement tests, a video and interview study of teachers of mathematics and science, and student perceptions data.

Precise Mathematical Language: Exploring the Relationship Between Student Vocabulary Understanding and Student Achievement

In this action research study of my classroom of fifth grade mathematics, I investigate the relationship between student understanding of precise mathematics vocabulary and student achievement in mathematics. Specifically, I focused on students’ understanding of written mathematics problems and on their ability to use precise mathematical language in their written solutions of critical thinking problems. I discovered that students are resistant to change; they prefer to do what comes naturally to them. Since they have not been previously taught to use precise mathematical language in their communication about math, they have great difficulty in adapting to this new requirement. However, with teaching modeling and ample opportunities to use the language of mathematics, students’ understanding and use of specific mathematical vocabulary is increased.

Improving Communication about Mathematics through Vocabulary and Writing

In this action research study, where the subjects were my 6th grade mathematics students, I investigated the impact of direct vocabulary instruction on their communication and achievement. I strategically implemented the addition of vocabulary study into each lesson over a four-month time period. The students practiced using vocabulary in verbal discussions, review activities, and in mathematical problem explanations. I discovered that a majority of students improved their overall understanding of mathematical concepts based on an analysis of the data I collected. I also found that in general, students felt that knowing the definition of mathematical words was important and that it increased their achievement when they understood the words. In addition, students were more exact in their communication after receiving vocabulary instruction. As a result of this research, I plan to continue to implement vocabulary into daily lessons and keep vocabulary and communication as a focus of my 6th grade mathematics class.

Attitudes, Confidence, and Achievement of High-Ability Fifth Grade Math Students

In this action research study of my fifth grade high-ability mathematics class, I investigated student attitudes of mathematics and their confidence in mathematics. Student achievement was compared to two different confidence scales to identify a relationship between confidence and achievement. Six boys and eleven girls gave their consent to the study. I discovered there seems to be a connection between confidence and achievement and that boys are generally more confident than girls. Most students liked math and were comfortable sharing answers and methods of solving problems with other students. As a result of this study I plan to use my survey and interview questions at the beginning of the school year with my new class in order to assess their attitudes and confidence in math. I can use this information to identify potential struggles and better plan for student instruction.

Writing Relevant Word Problems: Seeking to Increase Student Mathematical Achievement

In this action research study of eighth grade mathematics, I investigated my students’ use of writing and solving word problems. I collected data to determine if writing and solving word problems would have a positive effect on students’ abilities to understand and solve word problems. These word problems are grade-level appropriate and are very similar to the problems on the eighth grade online assessment of state standards. Pre- and post-test data, weekly word problems that focus on specific mathematics topics, beginning and end surveys about word problem perceptions, and a teacher journal reveal that student engagement in this weekly practice of writing and solving word problems did influence the students’ overall abilities for, achievement in and attitudes toward solving word problems. Except for some students’ perceptions, the influence was largely positive. This suggests that word problems can be a constructive feature in eighth mathematics instruction.

Using Descriptive Feedback In a Sixth Grade Mathematics Classroom

In this action research of my 6th grade math class, I investigated whether or not my students would improve their ability to reflect on their learning process when they received descriptive feedback from a peer. I discovered the process of giving and receiving feedback was challenging for the students to initially learn, but eventually using the feedback was highly beneficial. Descriptive feedback allowed the students to learn and understand their mistakes immediately, which in turn improved their learning. In my action research, I also began to discover more ways to implement descriptive feedback in my instruction so it could be more effectively for the students and efficiently so there would be less time taken out from instruction. As a result of this research, I plan to continue having students provide and receive descriptive feedback and to find more evidence of how descriptive feedback could influence student achievement.

Written Communication in a Sixth-Grade Mathematics Classroom

In this action research study of my sixth grade mathematics classroom, I investigated what happened to students’ mathematical achievement when they had increased practice on written explanations to problems. I wanted to see if writing out solutions to problems helped them overall in daily mathematics. By using specific mathematic vocabulary more frequently and deliberately during my instruction, I wanted to investigate whether students would correctly use specific math vocabulary in their written explanations. I also increased my expectations of the students’ written explanations throughout the research project. I wanted to determine whether students would try to meet or even exceed my expectations. I discovered that students used vocabulary more frequently in their written explanations by providing definitions of vocabulary versus using the vocabulary in context. I found little to no evidence suggesting that my students’ mathematical achievement changed through more practice on written communication; however, I did find as my expectations for the quality of students’ written explanations increased, most of my students improved their written explanations of problems and my teaching became more deliberate and specific. As a result of this research, I plan to continue having students communicate their mathematical ideas through written communication while continuing to focus on specific mathematical vocabulary and its purpose in written communication.

Cooperative Learning in Relation to Problem Solving in the Mathematics Classroom

In this action research study of my classroom of 5th grade mathematics, I investigated cooperative learning and how it is related to problem solving as well as written and oral communication. I discovered that cooperative learning has a positive impact on students’ abilities in problem solving and their overall impression of mathematics and group work. I also found that my students’ communication skills improved in oral explanations of their work. As a result of this research I plan to continue my implementation of cooperative learning in my classroom as a general method of teaching. I also plan to continue to use cooperative learning in working with my students to increase their achievement in problem solving and communication of mathematics.

Student Understanding and Achievement When Focusing on Peer-led Reviews

Math in the Middle Institute Partnership, Action Research Project Report, In partial fulfillment of the MAT Degree. Department of Mathematics. University of Nebraska-Lincoln. July 2009.

Oral Communication and Presentations in Mathematics

In this action research study of my classroom of eighth grade mathematics, I investigated the attitudes of students toward mathematics along with their achievement levels with the use of oral presentations in my Algebra class. During the second semester the class was divided into groups of two for each presentation, changing partners each time. Every other week each group was given a math problem that required more work than a normal homework type problem. On the last day of that week the students gave a short presentation on their problem. I discovered that while there was no significant evidence that student achievement increased, the students did enjoy the different aspect of presentations in a math class. I plan to implement presentations in my classroom more often with the intent to increase student enjoyment.

Reading as a Learning Strategy for Mathematics

In this action research study of 55 sophomore and junior students in my Algebra II/Trigonometry classrooms, I investigated a reading strategy of learning mathematics. Students were given background information about reading and explored the benefits of reading for themselves. Next, students were taught to read their textbook, analyzing one section of the textbook at a time. Throughout the research project, students were given reading guides to fill out during class with whole class discussion following the reading time. I discovered that students are able to read a mathematics textbook with understanding and students who are gone for activities can learn independently. Teacher observations, student surveys, and student interviews provide quantitative evidence of increased student understanding and achievement. As a result of this research, I plan to continue utilizing the reading guides and incorporating reading as a method of learning mathematics within my classrooms.

A causal model of mathematics performance in early adolescence: the role of sex

Using path analysis, the present investigation was done to clarify possible causal linkages among general scholastic aptitude, academic achievement in mathematics, self-concept of ability, and performance on a mathematics examination. Subjects were 122 eighth-grade students who completed a mathematics examination as well as a measure of self-concept of ability. Aptitude and achievement measures were obtained from school records. Analysis showed sex differences in prediction of performance on the mathematics examination. For boys, this performance could be predicted from scholastic aptitude and previous achievement in mathematics. For girls, performance only could be predicted from previous achievement in mathematics. These results indicate that the direction, strength, and magnitude of relations among these variables differed for boys and girls, while mean levels of performance did not.

Children's performance estimation in mathematics and science tests over a school year: A pilot study

The metacognitve ability to accurately estimate ones performance in a test, is assumed to be of central importance for initializing task-oriented effort. In addition activating adequate problem-solving strategies, and engaging in efficient error detection and correction. Although school children's' ability to estimate their own performance has been widely investigated, this was mostly done under highly-controlled, experimental set-ups including only one single test occasion. Method: The aim of this study was to investigate this metacognitive ability in the context of real achievement tests in mathematics. Developed and applied by a teacher of a 5th grade class over the course of a school year these tests allowed the exploration of the variability of performance estimation accuracy as a function of test difficulty. Results: Mean performance estimations were generally close to actual performance with somewhat less variability compared to test performance. When grouping the children into three achievement levels, results revealed higher accuracy of performance estimations in the high achievers compared to the low and average achievers. In order to explore the generalization of these findings, analyses were also conducted for the same children's tests in their science classes revealing a very similar pattern of results compared to the domain of mathematics. Discussion and Conclusion: By and large, the present study, in a natural environment, confirmed previous laboratory findings but also offered additional insights into the generalisation and the test dependency of students' performances estimations.