An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Bush Post Primary School
Dundalk, County Louth
Roll number: 71750U
Date of inspection: 22 September 2009
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Bush Post Primary School, Dundalk. It presents the findings of an evaluation of the quality of teaching and learning in Mathematics and makes recommendations for the further development of the teaching of this subject in the school. The evaluation was conducted over two days during which the inspector visited classrooms and observed teaching and learning. The inspector interacted with students and teachers, examined students’ work, and had discussions with the teachers. The inspector reviewed school planning documentation and teachers’ written preparation. Following the evaluation visit, the inspector provided oral feedback on the outcomes of the evaluation to the principal and subject teachers. The board of management was given an opportunity to comment in writing on the findings and recommendations of the report, and the response of the board will be found in the appendix of this report.
Bush Post Primary School currently has an enrolment of 244 boys and 205 girls. Timetable provision for Mathematics is good with five class periods per week allocated to first, second and third year groups. Fifth and sixth years receive six mathematics lessons weekly. In Transition Year (TY) Mathematics is timetabled for four class periods per week. Four mathematical applications lessons are provided for Leaving Certificate Applied (LCA) students for year one and year two of the programme. The timetabling arrangements for Mathematics are also good; for example, mathematics lessons are concurrently timetabled for all year groups with the exception of first years.
There are three mixed-ability classes and one small Junior Certificate School Programme (JCSP) class group in first year. Students are assigned to higher and ordinary level classes for second, third, fifth and sixth years on the basis of performance in formal examinations and class tests throughout the year. Teacher observation, and student and parental preference also play a role in level choice. TY is optional and one mixed-ability TY mathematics class group is formed each year. A smaller class is created in each year group to facilitate the provision of additional support for students experiencing difficulty with Mathematics. Concurrent timetabling of mathematics lessons occurs from second year through to sixth year. This very good practice is student-centred and allows for flexibility in changing levels. It is mathematics department policy to encourage students to study Mathematics at the highest level possible for as long as possible. The school’s practice in relation to level choice is very good.
The mathematics department comprises eight teachers. Students retain the same mathematics teachers from year to year insofar as possible for the duration of a cycle; maintaining continuity in this way is worthwhile for learners. Levels and programmes are rotated amongst most members of the teaching team which is good practice. Teacher continuing professional development (CPD) is encouraged by management and teachers new to a level or programme are supported by their more experienced colleagues. These good practices help to maintain capacity within the mathematics department and create a supportive environment where teachers can benefit from the sharing of experience and expertise.
The mathematics department is very well provided for in terms of resources. These include geometry equipment, overhead projectors, demonstration calculators, and mathematical games. The commercial posters and student projects that are displayed on classroom walls help to create stimulating mathematical learning environments. In keeping with very good practice students have been encouraged to collect everyday objects such as containers of various shapes and sizes which are used in the study of volume and area. Other resources such as maps, newspapers and holiday brochures are also used. In some cases the internet provides a valuable source of supportive lesson material. Handouts and worksheets were used in many of the lessons observed. In some cases they contained additional questions to supplement the textbook and in others they were designed to support students in reaching a deeper understanding of the concepts of the lesson. It is recommended that a bank of challenging material be created that can be used to provide additional challenge for the better able student.
The information and communications technology (ICT) resources available for the teaching and learning in Mathematics are good. The computer room can be booked for mathematics lessons. LCA year one students are timetabled for two of their four mathematical applications lessons in the computer room. There are three ceiling-mounted data projectors and a number of laptop computers available to mathematics teachers. In addition there is a mobile data projector that can be used on a booking system. Geometry software is available on one of the school’s laptop computers and it is recommended that it be installed on the remaining two. The school’s ICT resources are currently underused by members of the mathematics department; mathematics teachers should take advantage of concurrent timetabling to maximise access to the facilities that are available and to explore ways in which ICT can become a regular feature of mathematics lessons.
The procedures for identifying students who require learning support include pre-entry diagnostic testing, communication with feeder primary schools and with parents, ongoing teacher observation and class testing. Support is provided through the creation of smaller class groups and individual withdrawal where necessary. Students also benefit from the supports provided as part of the JCSP programme. In past years support was provided through team teaching and it is recommended that this model of learning support provision be reconsidered as an option within the range of supports available to students where appropriate. Teachers provide high quality support to students through the provision of individual attention in class on a day-to-day basis. Overall students who experience difficulty with Mathematics or have been identified as requiring learning support in Mathematics are very well supported.
The mathematics department holds planning meetings once per term as part of the whole school planning process. Much discussion also takes place on a day-to-day basis. Minutes are kept of all planning meetings and these are included in the planning documentation. The position of mathematics department co-ordinator forms part of a post of responsibility and is currently held by an experienced member of the teaching team. However, duties and responsibilities are shared by other mathematics teachers. The members of the mathematics department work well together as a team and provide strong support for each other. This is of particular note and value where sharing of experience around classroom practice takes place. This currently happens informally and it is recommended that it be formalised by allocating some time at planning meetings to discussion of teaching methodologies.
Significant progress has been made on planning for Mathematics. The mathematics plan contains the subject department’s policy on student access to levels, timetabling, teaching methodologies, homework, assessment and planning for students who require learning support in Mathematics. It is evident from the review of the minutes of planning meetings that ideas are presented, trialled, reviewed and amended. The method of allocating students to levels provides an example of where this decision-making process has been applied. This reflective approach is in keeping with very good planning practice as it allows the mathematics department to keep student needs at the centre of decision-making.
Schemes of work for each year group and level form part of the mathematics plan. These are set out in terms of learning objectives to be achieved within agreed timeframes. While this is good planning practice it is recommended that, over time, brief sections for methodology, resources necessary and assessment be added to the schemes. This should be undertaken in a collaborative way and should provide mathematics teachers with a valuable opportunity to share ideas on classroom practice. Active, investigative, discovery and research methodologies are currently used in teaching and learning in Mathematics on a limited basis. In TY and in some LCA lessons students work in groups and complete projects, this practice should be reflected in the mathematics plan. It is recommended that the planning process be used to extend the use of such approaches so that they become regular occurrences in mathematics lessons.
The TY programme comprises a list of Leaving Certificate topics to be covered for the year. In keeping with the spirit of a good TY programme, active methodologies, ICT and project work are used to teach these topics. The study of trigonometry involves participation in a project to construct a clinometer and use it to calculate the heights of various structures around the school. Students use Excel to graph linear, quadratic and cubic functions. Games are used in the study of algebra and work on Simpson’s rule involves finding the area of different countries. These are examples of alternative approaches that are included in the TY plan. It is also evident from the TY plan that mathematical puzzles and games are used to encourage student interest in Mathematics. It is recommended that the good practices that already exist in TY be expanded upon over time and that these types of methodologies be extended to teaching and learning in other year groups.
Eight lessons were observed as part of the evaluation. In all cases teachers made very good use of questioning to assess, involve and engage students. Higher-order questions that require reflection were used by some teachers to help students to explore difficult concepts and ideas. Best practice in this regard was observed in some lessons where the use of open questioning led to lively class discussion and a high level of collaboration between the students and their teacher. The further use of higher-order questioning as a strategy to encourage students to fully understand their course material is recommended. All of the lessons observed progressed at a pace that was appropriate to the ability level of the students. The good balance that was achieved between teacher input and student activity contributed to the high levels of student attention and engagement that was observed.
In most cases teachers’ approach focused on encouraging students to understand the underlying concepts presented and explanations and instructions were clear. A good example of this was observed in a lesson on co-ordinate geometry of the circle. The students were expected to find the equation of the tangent to a given circle. The teacher drew two lines which were perpendicular to each other on the board and directed the students to find the equation of one of the lines. The students used previously-learned material and successfully completed this task. A circle was then superimposed on the diagram so that it was easy to see that the equation of the line found was in fact the tangent to the circle. The clarity of this explanation and its strategic focus made it very effective.
In the majority of cases teachers are conscious of providing opportunities for students to develop general mathematical skills such as problem solving and critical-thinking skills. This was particularly evident in a lesson on quadratic equations. Throughout this lesson the students were repeatedly encouraged to focus on what they were given in questions, what additional information they needed and what they were expected to find. This encouraged students to think for themselves and take responsibility for their own learning. This lesson also provides a good example of where the depth of treatment of the lesson material encouraged thorough understanding. Through an investigative approach the nature of the roots of quadratic equations was comprehensively explored and the conclusions that were reached by students resulted from trial and observation. This is an example of best practice because it contributes to a deeper understanding of mathematical concepts and a more extensive use of this approach, through its adoption by all teachers, is recommended.
Two JCSP lessons were observed as part of the evaluation. In both cases the number of students was small and this allowed the teachers to provide support and encouragement to students where necessary. A very high level of individual attention and assistance was provided and it was evident that this was very beneficial to students. However, at times during one of the lessons some students had completed their task while the teacher remained occupied assisting other students. It is recommended that learning be differentiated to allow for variety in ability. This can be achieved by providing graduated worksheets that contain questions that increase in difficulty. In addition, it is suggested that a bank of suitable exercises be created to provide additional work for students when the need arises.
Some teachers use everyday objects such as floor tiles and containers of various shapes and sizes as concrete materials to provide active learning opportunities for students and to clarify explanations. One such lesson was observed during the evaluation. A key objective of this lesson was to explain units of measure. In previous lessons the students had reportedly experienced difficulty with this concept. Acetate handouts had been prepared, each with a grid of four hundred squares, each with sides of one centimetre, photocopied onto it. It was explained that the areas of each of these squares measured one centimetre squared. When students placed it over various shapes it was easy for them to count the squares and hence find the area of the shape. The effect this approach had on student learning was observed to be very positive.
In the LCA lesson observed the students worked on exercises involving percentages and profit and loss, following teacher examples. While there was a good mix of tasks which ensured that students participated well in the lesson’s activities, this methodology was not in keeping with the aims of the LCA programme. In this lesson which was based on the ‘Mathematics for Living’ section of the course, the use of materials such as shopping catalogues, newspaper advertisements, and car sales websites would provide a real life context within which the mathematical topics of this lesson could be explored. It is evident from the overall plan for LCA Mathematics that some topics are covered using active methodologies and that ICT plays a significant role in teaching and learning for LCA year one students. These are representative of approaches that are in keeping with the underpinning principles of the LCA programme. It is recommended that the use of ICT, active, research and investigative methodologies be used in the teaching of LCA Mathematics on a regular basis. Furthermore project, group and pair work are very suitable approaches for use in LCA lessons and should be used wherever appropriate. Lesson material, ideas and resources are available on the Second Level Support Service website (www.slss.ie).
The relationships between students and their teachers were observed to be very good. Teachers are affirming and encouraging of student effort. In some cases, humour was used appropriately to good effect. Teachers have created secure learning environments where students can be supported and become confident with Mathematics.
All year groups are formally assessed at Christmas. Summer examinations are held for first, second, fifth and transition year groups. ‘Mock’ examinations take place in spring for students preparing for the certificate examinations. Once every two months class tests are held for fifth and sixth years. Reports are sent home following all formal examinations and parent teacher meetings are held annually.
It is good that common examination papers are set within levels. There is very good practice in relation to differentiation on examination papers where questions are set to take account of the variety in ability levels in each class group. This practice enhances the quality of the information gained from examination results and is of particular value where results are used to assign students to levels. In some cases the questions on class tests are set so as to ensure that all students have a chance of experiencing some degree of success. This practice provides a valuable way of increasing student confidence in Mathematics and is commended. Overall the mathematics department’s practice in relation to assessment is very good.
Teachers monitor student progress by oral questioning and observation in class. In addition, it is department policy to set class tests at the end of every topic studied. Homework is set regularly and is usually corrected as part of the following lesson. It was evident from the review of student copybooks that the standard of presentation of student work is high. Most teachers include comments in the correction of tests and homework. This is very good practice as such comments can be a very valuable source of advice and encouragement.
Each year the mathematics department carries out an analysis of the school’s performance in the certificate examinations and compares it to the national norms. In keeping with good practice the outcomes of this process are used to inform planning for Mathematics.
The following are the main strengths identified in the evaluation:
· The timetabling arrangements and the school’s practice in relation to choice of levels for Mathematics are very good.
· The mathematics department is very well provided for in terms of ICT and other resources.
· Students who experience difficulty with Mathematics or have been identified as requiring learning support in Mathematics are very well supported.
· Significant progress has been made on planning for Mathematics.
· The good balance that was achieved between teacher input and student activity contributed to the high levels of student attention and engagement that were observed in the classes visited.
· The relationships between students and their teachers were observed to be very good.
· The mathematics department’s practice in relation to assessment is very good.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· The planning process should be used to add more variety of mathematical experience to teaching and learning in Mathematics.
· Brief sections for methodology, resources necessary and assessment should be added to the schemes of work for Mathematics.
· The use of higher-order questioning as a strategy to encourage students to fully understand their course material should be extended to all lessons.
· The good practice of differentiating learning to allow for variety of student ability should be extended to all lessons.
· ICT, active, research and investigative methodologies should be used in the teaching of LCA Mathematics on a regular basis.
Post-evaluation meetings were held with the teachers of Mathematics and with the principal at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published January 2010
Submitted by the Board of Management
Area 1: Observations on the content of the inspection report
The Maths Dept was very happy with the inspection process and with the inspection report.
Area 2: Follow-up actions planned or undertaken since the completion of the inspection activity to implement the findings and recommendations of the inspection
Since the report we have had a Maths Dept meeting where it was agreed that all the recommendations would be taken on board.