> wyv` vubjbjss 2v2, 4 a6f!^z!z!z!z!z!z!z!5555555$7h/:5Q"z!z!""5z!z!6###"z!z!1#"5##V+@B,z!!0u o#R+b,160a6+T;#;B,;B, z!0!"#!!z!z!z!55#z!z!z!a6"""" DG21: Current problems and challenges in lower secondary mathematics education
Naomi Ingram
University of Otago, New Zealand
HYPERLINK "mailto:ningram@maths.otago.ac.nz" ningram@maths.otago.ac.nz
Key questions addressed
What are the most important current problems and challenges pertaining to the teaching and learning of mathematics at the lower secondary level (that is, for 12 to 15 year olds)?
What issues impact the mathematics learning experiences of students?
What dilemmas confront teachers of mathematics at this level?
Age range of students concerned
13-15 years
Research
I am an experienced secondary mathematics teacher and have become frustrated and increasingly dismayed by the numbers of students who seem to have the ability to engage in the activities of the mathematics classroom but do not. This led me to PhD study, which has grown from initial thinking about mathematics anxiety into understanding students affective development in mathematics through an exploration of their mathematical identities. It is a longitudinal study of 31 students, all New Zealanders of European descent. I aim to complete the PhD at the end of 2008, supported by my supervisors, Derek Holton and Tamsin Meaney.
Context and Setting
My research is situated in an urban coeducational school in the South Island of New Zealand. The school caters for Year 7-13 students (10 to 18 years) and has around 950 students. In Year 9 (age 13), students in New Zealand no longer take their core subjects in home-rooms and move around the school. Mathematics is a compulsory subject for all students until the end of the students Year 11 year when they attempt to complete internal and/or external achievement standards towards a National Certificate of Educational Achievement. For this research, the students were followed during their Year 10 and 11 years. The students, in 2006, were together in a Year 10 class (aged 13-14 years) for their core subjects of Mathematics, English, Science and Social Studies. In 2007, the Year 11 students split into a seven different mathematics classes depending on their chosen option subjects, and timetabling considerations.
Data collected
This research was classroom based because it was important that I spent time with the students in this environment to try and understand their processes of engagement and interaction, and collect evidence of their developing mathematical identities and indicators of affective responses. Data was collected from a wide variety of sources over two school years. Further detail can be found in Ingram ADDIN EN.CITE Ingram200715915947Ingram, NaomiWatson, JaneBeswick, KimA story of a student fulfilling a role in the mathematics classroomMathematics: Essential research, essential practice450-4591Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia, Tasmania2007AdelaideMERGA(2007),
Research toolsPre-200620062007ObservationsMathematics classes""English classes"Observational artefacts""Student interviewsIndividual"Group"Students written responsesMetaphors for mathematics"Drawing of mathematicians"Personal journey graphs"Journals"End of unit evaluations"Student questionnaires""Exercise books"School documentsMathematics class attendance"""Reports"""Enrolment information"Assessment results"""Disciplinary reports"""Internal assessment results"""Subject choices""TeacherTeacher feedback""Interviews""Metaphors for mathematics"Teacher s drawing of a mathematician"Parent questionnaire"
Theoretical Background
Not only is learning fundamentally social, it is an emotional practice. Students affective responses to mathematics are often negative and are thought to influence students learning, achievement, and subject and career choice. It is the notion of identity that to me has exciting implications for the affective domain. Sfard and Prusaks ADDIN EN.CITE Sfard200523523517Sfard, AnnaPrusak, AnnaTelling identities: In search of an analytic tool for investigating learning as a culturally shaped activityEducational researcherEducational researcher14-223442005May, 2005(2005) operational view of identity is being used as both an analytic tool in my research and a theoretical framework. Sfard and Prusak believe identities to be reifying, endorsable, and significant stories about a person. People have a number of stories told about them by a variety of narrators, including themselves; each person has multiple identities. Sfard and Prusak ADDIN EN.CITE Sfard200523523517Sfard, AnnaPrusak, AnnaTelling identities: In search of an analytic tool for investigating learning as a culturally shaped activityEducational researcherEducational researcher14-223442005May, 2005(2005) split these multiple identities into two sets of actual identity (I am, he is - stories about the actual state of affairs) and designated identity (I should be - a state of affairs expected to be the case now or in the future). The authors claim that learning may be thought of as closing the gap between actual and designated identity. When there is a perceived and persistent gap between a students actual and designated identities, there is likely to be a sense of unhappiness in that person. My research views all students emotions and feelings, rather than just unhappiness, to be situated in the gap between actual and designated identities. A main part of the analysis of the data therefore consists of recognising identifying stories and their associated indicators of affective response.
Discussion
The lower secondary level is a particularly vulnerable time for mathematics learning. There are many factors that contribute to this vulnerability: a mathematics syllabus dominated by textbooks and a chalk and talk style of teaching; physical and psychological changes in students; a perceived regurgitation of previous mathematics topics with little new content; increasing social pressure from peers; increasing academic pressure with exams, if not imminent, looming; increasing pressure from parents, especially because of a historical leaving age for the parents generation of 15 years; a new qualification system sometimes little understood by parents; other pressures such as self-harm, home-life, and part-time employment. Indeed, the complex culture of the mathematics classroom is really a small subset of a teenagers very complex life.
The gap between a students actual and designated identities is very complex and dynamic. The data shows how the gap between each students designated and actual identities narrows and widens as what is actually happening in the mathematics classroom differs from what the student expects to happen. For some students their expectations of mathematics are exceeded by what happens in the classroom and they experience positive affect. For many others, their expectations of their own mathematical ability are not met and they experience negative affect. Some of the students use learning about mathematics and the mathematical context to control or lessen the gap, while for others, the pendulum swings the other way and their expectations drop to meet what is actually happening so they can feel better about the mathematics.
The data from this research illustrates how the teachers judgements and expectations of the students directly affect the mathematical experience of the students. These judgements and expectations are communicated mostly within classroom interactions but also through assessments, parent interviews and school reports. There is evidence to show the impact that teacher-related stories have on each student and how these stories contribute directly to students affective responses to mathematics. Teachers need to understand the direct impact that they have on a students mathematical experience by being a significant narrator of that students stories. Furthermore, the students in the research directly express the need for their teachers to get to know them, and their mathematics, better. In New Zealand, where a secondary teacher may teach up to 160 students (sometimes in one day) this presents a dilemma for the teacher. The issue of teacher experience often compounds this dilemma. Only one of the eight teachers involved with the students during the research period was both a qualified and experienced mathematics teacher. The other teachers, while possibly experienced teachers in a mathematics classroom, were all either primary trained or teaching outside of their subject area.
The data also highlights the effect of seating arrangements on students affect and learning. The results show that students need to be surrounded by others whose behaviour do not disrupt or distract them, and who they like and feel comfortable with. The adolescents in this study did not have the power or control to stop other peoples behaviour affecting them, nor did they have the power to sit where they wanted to ensure their academic identities are being fulfilled. This has direct implications for teachers in terms of monitoring behaviour and instituting seating plans.
ADDIN EN.REFLIST Ingram, N. (2007). A story of a student fulfilling a role in the mathematics classroom. In J. Watson & K. Beswick (Eds.), Mathematics: O~E
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