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ICE-EM MATHEMATICS SCHOOLS PROJECT
DEVELOPMENT AND FIRST STEPS
Janine McIntosh
Australian Mathematical Sciences Institute,
International Centre of Excellence for Education in Mathematics
TOC \o "1-5" \h \z \u Abstract
A series of mathematics textbooks was developed for Years 5 to 10 and piloted in schools across Australia. Pilot school teachers were involved in professional development designed to enhance their skills and understandings. Teachers found that their students had a deeper understanding of the material, but took longer to get through it. Feedback from teachers was taken into a review of the materials that were then rolled out in commercial versions. A further marketing program is now under way.ICE-EM MATHEMATICS SCHOOLS PROJECT
Introduction
In 2005, the development and trial of a program designed to support the teaching and learning of mathematics with students in Years 5 to 10 in Australian schools was begun. Developed by the International Centre of Excellence for Education in Mathematics (ICE-EM), the program is now in its implementation phase.
ICE-EM was established in 2004 with funding from the Australian Federal Government. The objective was to produce tangible programs to assist students and support teachers in improving teaching and learning in mathematics. As part of this program, a series of integrated textbooks was produced, known as ICE-EM Mathematics, covering Year 5 in primary school to Year 10 in secondary school. These resources were designed to help students make a smooth transition from primary to secondary school mathematics and provide a consistent development of topics through the first four years of secondary school. In conjunction with the development of the ICE-EM Mathematics texts, ICE-EM has also prepared a Professional Development (PD) program for teachers.
DEVELOPING THE MATERIALS
Motivation
There is a noticeable difference in the performance of Australian students against those in other countries. Data from the 2002/03 Trends In Mathematics and Science Study (TIMMS) show that while Australian Year 8 students rank above the international average in mathematics, more than 35 per cent are ranked at a low level or below. This compares with an average of only two per cent of students who rank at a low level or below in the five highest-ranked countries. Similarly, while seven per cent of Australian Year 8 students are ranked at the advanced level in mathematics, this compares with an average of 34 per cent in the five highest-ranked countries.
Many secondary teachers are teaching mathematics without a strong background in the subject. The 2002/3 Trends in International Mathematics and Science Study found that 30 per cent of Australian year 8 students were taught by a teacher who did not have mathematics as their major area of study, 13 per cent of students were taught by teachers who had neither mathematics or science as their major field of study.
Similarly, many primary teachers are under-prepared for the mathematics they will teach. In a 2006 analysis of four-year Bachelor of Education courses, we found that four of 31 Australian universities state on their websites that they require Year 12 mathematics of any type; another eight require year 11 as a minimum. The remaining 19 universities do not state that mathematics is a pre-requisite for the course. It may be said that throughout their course, pre-service primary teachers might top-up their skills in mathematics. It is not clear that this is always the case. The time dedicated to mathematics and mathematics education subjects varies between two per cent and 12 percent of the total contact time. The course content differs between different universities greatly. The nature of the subjects undertaken might include some mathematics as well as psychology, learning theory, curriculum and pedagogy.
Students with difficulties in mathematics often participate in programs that target their learning needs. In Australia, Count Me In and the Early Years Numeracy Project are two programs that identify and target learning needs in mathematics. Of concern is the student who does not take part in intervention programs, who is not identified as needing it. These students might pass tests sometimes and fall in the lower middle band with respect to their success in mathematics and who are simply told that they are not good at mathematics. We know that these students are often teachable, with the right activities and a teacher with a solid understanding they may experience some success. Sadly students who feel that they are not good at mathematics may go on to structure their career planning without mathematics and limit their choices as a result. Interestingly, it is this type of student who may become a primary teacher and go on to teach mathematics.
Textbooks often receive bad press. The message seems to be getting through to teachers that to use a textbook is not a good thing and indeed there is some support for this. Many mathematics textbooks do not provide explanations for the procedures or patterns in mathematics (Newton and Newton, 2007). The aim of developing the ICE-EM Mathematics program was to provide teachers and students with a mathematically accurate, coherent program that would enable students to move from primary to secondary schooling with greater ease and enhanced mathematical knowledge. We believe that this program is unique in that it aims to enhance the mathematical understanding of teachers, build students knowledge and computational and mental skills in a logical and correct mathematical sequence, with investigations and consolidation exercises as they progress through the material. The materials are also aimed at making mathematics at this level accessible to parents.
Scoping meetings
A number of meetings of teachers, teacher educators and mathematicians were held around the country. Discussion centred on the content knowledge of teachers and the need for a high standard of mathematical competence of teachers appropriate to the level they teach (Milgram, 2005). Overwhelmingly the perceived need was for a solid series of textbooks to address the concerns raised above. The mood of these meetings reflected Mas 1999 discussion of the differences between a teacher who understands the mathematics and a teacher who teaches the mathematical procedure without understanding. Teachers need to understand mathematics, they need to have a grasp of the basic ideas; the connectedness and the multiple representations and they must create for themselves and for their students a sense of longitudinal coherence (Ma, 1999).
The ICE-EM Mathematics framework
Sourcing the content
The first task was to review the mathematics curricula in each state. A recent national consistency statement assisted in making sure the syllabus was covered. We also evaluated international mathematics teaching resources such as the JUMP program in Canada (Mighton, 2005), the Singapore primary Mathematics program (Kho Tek Hong, 1997) and documents related to the desired content knowledge of teachers (Milgram, 2005). From these evaluations and drawing on the teaching experience of the team, a list of required and desirable content was made. The concepts were ordered according to their reliance on other areas of content. For example, multiplicative ideas such as multiples, factors and prime numbers came before work on fractions, understanding of which depends upon the earlier concepts.
Structure of the materials
The primary books are structured slightly differently to the secondary as described in Table 1. Each section of each chapter of the books begins with a discussion of the theory to be covered. We call this the mathematics conversation and suggest to teachers that they make this their own by pre-reading and getting to know the big ideas involved in the topic. Professional development sessions develop these big ideas further.
PrimarySecondaryPreparation A list of pre-requisite skills needed for the chapter.Kick off Warm up, skill development, tools session, and beginning of lesson ideas.Show what you know Pre- assessment tasks drawing on content from previous year or stage.Pre-tests are included on the teacher resource CD.Mathematics Conversation- an exploration of the theory related to the topic. Written in language appropriate to the childs year level.Mathematics Conversation- an exploration of the theory related to the topic. Written in language appropriate to the childs year level.Worked examplesWorked examplesConnect apply and build Whole class activities. The teacher models skills and strategies and draws on class members understandings to make connections. Exercises - tagged to worked examples.
Connect apply and build Individual Exercises start gently and build up to some with a degree of challenge.Skills sheets are included on the teacher resource CD. They provide more practice at a level slightly lower than the books.SummarySummaryBlack line masters for those exercises that students would not be expected to copy out of the book. HomeworkHomework sheets are included on the teacher resource CDReflection This is what we did. This is what was important. Posing a question to elicit the summing up conversation. Making connections. Placing our understanding in the mathematics story we have made so far 2. Where will this lead? Students explaining to students.Chapter tests Summative assessments included on the teacher resource CD.Chapter tests Summative assessments included on the teacher resource CD.Table 1
Structure of ICE-EM Mathematics texts.
Developing the materials
Writing began with teams of between five and eight authors, including at least one ICE-EM staff member who oversaw the process of writing, editing, and re-writing the material. The authors were experienced classroom teachers and mathematicians who drafted chapters and brought them to the team for discussion. These discussions contributed to our quality control. At author team meetings the drafts were looked over carefully for mathematical accuracy and consistency as well as practical classroom issues such a viability of activities and coverage of the curriculum. All typesetting was done in-house, allowing for increased creative control and on-the-spot changes to be made following discussions. There was overlap in the author teams for different books to ensure the continuity of definition and smooth development of ideas.
Teacher professional development
Each teacher involved in the pilot program was invited to take part in professional development (PD) session. Four sessions were conducted covering broadly: Number, Arithmetic the algorithms and mental strategies, Fractions and decimals extending whole number thinking and Geometry and Measurement. As well as organized PD, much time was dedicated to building a relationship with teachers in pilot schools. Telephone calls, school visits, classroom sessions and email contact all helped in building this relationship.
The pilot
Each book was extensively trialled in a number of schools for an entire school year. We put out a national call to take part in the Year 7 and 8 pilot for 2006, sending an invitation to 3500 secondary schools. Of those, 350 schools expressed an interest in taking part. Initially it was thought that a pilot of about 50 schools would be adequate, but due to the huge response, 125 schools in 12 clusters the country were accepted. Rural, regional remote, independent, state and catholic schools were well represented. This first group of schools was asked if they would like to continue into the Year 9 and 10 pilot. From an initial group of 125 we then had 65 schools pilot Year 9 and 10 materials in 2007.
We approached the feeder primary schools from the 2006 and 2007 pilot schools and invited them to take part in a pilot of the Year 5 and 6 materials. A total of 80 schools took part in the primary pilot, 69 were primary schools and the remaining 11 schools were secondary schools using the Year 5 and 6 materials to top up the skills of weaker Year 7 and 8 students.
The purpose of the pilots was two-fold. The teachers provided feedback via surveys, email and telephone calls and a large proportion of the time set aside for listening to teacher feedback about the materials during the PD sessions. We also hoped to do some good along the way by meeting with teachers, discussing the teaching of mathematics and thus enhancing their understanding and capability.
Outcomes of the pilot
The pilot allowed us time to take a step back and look at the materials in the light of an entire year of school use with a large variety of classroom settings. Teachers were surveyed once towards the end of the pilot. Much of the feedback in addition to the surveys was verbal, resulting from discussions in PD meeting or during school visits. Feedback provided suggested changes and information about the efficacy of the material. In addition to the teachers, at least one mathematician not involved in the initial drafting of the pilot material took part in the review process.
Changes to the books
The most obvious changes to the program, as the result of the pilot was the textbooks themselves. The following changes were made to the secondary books because of teacher feedback:
Content was revised in line with teachers comments and checked for mathematical accuracy by ICE-EM staff. In some cases, new sections were added, or chapters were split or merged.
Exercise sets were supplemented.
Skills sheets were developed and are available on the teacher resource CD-Rom. Many of the teachers felt that there was more practice needed to ensure skill development.
Exercises were tagged to the worked example so that a student working on a particular exercise might easily find the related worked example if they required assistance.
Changes to the primary books included:
Content was revised in line with teachers comments and checked for mathematical accuracy by ICE-EM staff. In some cases, new sections were added, or chapters were split or merged.
The amount of review material was increased from one review chapter every four or five chapters in the pilot materials to a review section at the end of each chapter.
The amount of challenge material was upgraded from one challenge chapter every four or five chapters in the pilot materials to at least one challenge section at the end of each chapter.
Sorting the questions into three distinct levels and tagging the exercises so that entry level, intermediate and higher order questions were obvious to teachers and students. Far from acting as a labeller of student ability, teachers told us that this motivated students to get to the higher level.
Student progress
Teacher feedback included anecdotal reports of improved student understanding, better school programs and enhanced teacher understanding of and confidence in mathematics. Some of the survey results are shown in Table 2.
Compared with the material I used last year, my students have Highly DisagreeDisagreeUnsureAgreeHighly AgreeTotalDeveloped a better understanding of the mathematical concepts covered.2(1%)46(26%)27
(16%)86
(50%)13
(8%)175Retained the knowledge while moving from one topic to the next3
(2%)45(26%)36
(21%)86
(48%)4
(2%)174Made better or faster progress8
(5%)76
(44%)34
(20%)46
(29%)3
(2%)167Enjoyed the program more
9
(5%)59
(34%)27
(16%)64
(38%)7(4%)165Table 2
Teacher responses to survey questions post pilot.
Some schools felt that the material was too advanced for their students. According to teachers, a significant number of the students are performing at a stage or level of the curriculum below that of their chronological year level in school. This was a main reason teachers gave for pulling out of the program (see below).
Usefulness of the professional development
Schools paid teacher release for the professional development sessions. The attendance was excellent at the start and dropped slightly as the year progressed. This reflected a busy schedule or lack of school funds to allow release more than a desire on the part of the teacher to attend. In a survey of teacher satisfaction with the program, 93 per cent of teachers ticked agree or highly agree to the question, The professional development sessions were useful.
Continuing with the program
Of the 65 schools that continued with the second year of the secondary pilot, 24 (37%) have taken the opportunity to continue with the program and purchase books. These schools will be offered ongoing PD and ICE-EM staff will be in regular contact. Some 15 schools (23%) are still using the pilot books as the main text and a further 7 (11%) are using pilot books and one or more other resources. We continue to be in touch with these schools. We lost 13 (20%) of the secondary schools. These schools gave their reasons for not continuing to use the materials as having had a change of staff since the beginning of the pilot, being unable to purchase due to commitment to other materials or a perceived difference in the ability of the target audience and the students in the pilot school. Six schools (9%) did not respond to requests for information about their intentions.
Of the 80 schools that started the primary pilot, 10 (12.5%) have taken the opportunity to continue with the program and purchase books. These schools will be offered ongoing PD and ICE-EM staff will be in regular contact. Some 36 schools (45%) are still using the pilot books as the main text. We continue to be in touch with these schools. 16 schools (20%) are not using ICE-EM Mathematics in any form. 18 schools (22.5%) did not respond to requests for information about their intentions.
Going forward
We are in the early stages of the marketing program for the materials and have had a number of schools take on the program that have heard of us by word of mouth. To date we have sold
20 000 books. Over 100 individual schools or teachers have purchased one book. We believe they are either looking at us for future use as class texts, or using the books as a teacher reference. A number of parents have also purchased for use at home. Each of these groups will be followed up in the near future
In 2008, BlueScope Steel is supporting 24 schools in the large regional city, Wollongong, to use the ICE-EM program and take advantage of the associated professional development. Already, each school has sent representatives to the first professional development session and has been visited by an ICE-EM staff member.
Discussion
Teachers who participated in the pilot found that their students had a better understanding, but made slower progress. The teachers themselves felt better about their mathematics teaching. A number of schools are purchasing for use as class texts. We take the solid sales record as a further marker of the good name the program is building. We are pleased with the feedback about the efficacy of the materials and look forward to what the future brings.
3495 words
ICE-EM is managed by the Australian Mathematical Sciences Institute, a consortium of 27 Australian university mathematics departments, CSIRO Mathematical and Information Sciences, the Australian Bureau of Statistics and the Australian Mathematics Trust.
A team of three key staff manages the schools project, providing a broad range of experience and practical skills in teaching and in mathematics.
Professor Garth Gaudry is Director of ICE-EM. He was previously Director of the Australian Mathematical Sciences Institute (2003-2005) and Professor and Head of the School of Mathematics at the University of NSW (1993-2003).
Dr Michael Evans manages the ICE-EM Mathematics program. Before coming to ICE-EM, he was Head of Mathematics at Scotch College, Melbourne. Michael works with the Victorian Curriculum and Assessment Authority as examiner for Year 12 mathematics subjects.
Janine McIntosh, ICE-EM schools project officer, is an experienced primary teacher who has lectured in mathematics education at the University of Melbourne, worked as a curriculum writer and currently serves on the Problems Committee of the Australian Mathematics Trust.
References
Kho Tek Hong (1997) Primary Mathematics (Books 3 6) Curriculum Planning and developmental Division, Ministry of Education, Singapore. Times Media Limited, Singapore.
Ma, L., (1999) Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the U.S., Mahwah, New Jersey, Lawrence Erlbaum Associates
Mighton, J., (2005) Jump Math (Workbooks 3 6). Jump Math, Canada
Milgram, R. J., (2005) The Mathematics Pre-service Teachers Need to Know. Department of Mathematics, Stanford University.
Newton, D.P. and Newton, L. S, Could Elementary Mathematics Textbooks Help Give Attention to Reasons in the Classroom? Educational Studies in Mathematics, 64 n1, 69-84
Thomson S., and Fleming N., Summing it up: (2004) Mathematics Achievement in Australian schools in TIMMS 2002 (TIMMS Australia Monograph No. 6) Australian Council for Educational Research, Camberwell, Victoria.
Other resources:
Count Me In Too is an initiative of the New South Wales Department of Education. An explanation of the research conducted and the program itself is available at: http://www.curriculumsupport.education.nsw.gov.au/primary/mathematics/countmeintoo/index.htm
Early Years Numeracy Program is an initiative of the Victorian Department of Education. An explanation of the research conducted and the program itself is available at: http://www.sofweb.vic.edu.au/eys/num/index.htm
The National Consistency Statements of Learning for Mathematics is an initiative of the
Federal Governments Ministerial Council on Education, Employment, Training and Youth Affairs (MCEETYA). It is available at: http://www.mceetya.edu.au/verve/_resources/SOL_Mathematics_2006.pdf
DG 17 Janine McIntosh PAGE 9
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