An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Kilmuckridge Vocational College,
Kilmuckridge, County Wexford
Roll number: 71650Q
Date of inspection: 17 September 2008
Time allocated to Mathematics at senior cycle is good with each class group receiving six class periods of Mathematics per week. However, in each of the three years of the junior cycle programme, class groupings are allocated four class periods of Mathematics with one extra class period of Mathematics allocated to the second year Junior Certificate School Programme (JCSP) class. Generally, class periods are thirty-five minutes but on occasion a thirty-minute class period may be timetabled. This is not a sufficient allocation of time to Mathematics, and does not allow students to develop necessary Mathematics skills. In addition, the school is not providing sufficient instruction time to its students, as highlighted in a previous subject inspection report, and consequently is not in compliance with circular M29/95, Time in School. The school timetable must be amended to ensure compliance with the circular. As part of this process, sufficient time should be allocated to the teaching of Mathematics, particularly at junior cycle. Furthermore the distribution of Mathematics classes should be reviewed to ensure that Mathematics is timetabled more evenly throughout the week.
Currently, there are three teachers providing Mathematics education in Kilmuckridge Vocational College, and most are deployed according to their subject specialism. The allocation of teachers to classes is undertaken by the principal in consultation with the teacher who arranges the timetabling for the school. In so far as is possible, teachers retain the same class grouping within each cycle, which is good practice. It was reported that since the school has recently introduced the JCSP, rotation of teaching of programmes will be a feature in the timetabling of Mathematics teachers in future years. This coupled with the fact that teachers generally have opportunities to rotate the teaching of levels is good practice as it allows all teachers to develop expertise in all programmes and subject levels.
In first year students are taught in mixed-ability class groupings, and in subsequent years depending on the number of students in a year, setting takes place. However, this year the school has introduced the JCSP and has created two distinct class groupings in second year, one of which is a JCSP class. In line with the philosophy of the JCSP, consideration should be given to the placement of JCSP students in mixed class groups. Then JCSP students could be offered appropriate additional support using timetable gaps or periodic withdrawal.
Currently concurrent timetabling of Mathematics takes place in third year and sixth year. Where concurrent timetabling is not in place, it results in the three levels of Mathematics being taught in one class grouping. This is not good practice and it is therefore recommended that consideration be given to extending concurrent timetabling of Mathematics in conjunction with an increase in instruction time. This should ensure that students access Mathematics in accordance with their ability and potential and remain at the highest appropriate level of Mathematics for as long as possible.
In general, students follow the ordinary or foundation level course and there is no discrete higher level mathematics class group in either junior or senior cycle. An analysis of the state examinations results reveals that a sizable number of students are taking foundation level Mathematics, particularly at Leaving Certificate. It was also noted that a significant number of students are achieving below a grade D at ordinary level in both Junior and Leaving Certificate. It is recommended that management and staff review the attainment and performance of students on an annual basis with a view to considering all possibilities that might lead to an increase in students’ performance, including the teaching approaches used and the introduction of more appropriate programmes to accommodate all students.
Equipment to support the teaching and learning of Mathematics was available in most classrooms. This includes data projectors, interactive whiteboards and computers. The acquisition of resources for the teaching of Mathematics is done on an individual basis rather than as a collective request. During the inspection it was reported that the main resources used in Mathematics are calculators and geometry sets. As the school is currently preparing “stock books”, it is therefore timely for the mathematics teachers to collaborate and identify key resources and plan for acquisition of materials to support and enhance the teaching of Mathematics within the classroom. Such resources should be retained centrally for access by all teachers and an ongoing review of resources should be undertaken.
Management is commended for its support for teachers in their continuing professional development. Attendance at in-service is facilitated by management and teachers have attended mathematics in-service, most recently that provided by the Junior Certificate Support Service (JCSS). Upcoming in-service in JCSP is also being facilitated by management. The induction of newly appointed teachers is undertaken by the deputy principal and Co.Wexford Vocational Education Committee also provides training for teachers. In addition the school also partakes in the national mentoring programme for newly appointed teachers.
Currently students do not engage with Mathematics activities outside the classroom. As a means of raising the profile of Mathematics in the school consideration should be given to introducing some Mathematics activities throughout the school year: for example, the first-year Mathematics competition run in conjunction with the Irish Mathematics Teachers Association (IMTA), or involvement in Maths Week. Such activities complement the teaching of Mathematics in the classroom while providing students with an opportunity to experience Mathematics activities in different contexts.
Formal planning time is made available to teachers at the beginning of the year with Mathematics teachers also meeting informally throughout the year. It was reported that two planning days have been arranged by management and will take place in the near future. It is recommended that minutes be taken at Mathematics meetings, thus providing a formal record of issues discussed, decisions agreed and areas for development.
Currently, there is no co-ordinator of Mathematics who would facilitate Mathematics development in the school. It is recommended that the role of coordinator be undertaken by a Mathematics teacher and this position be rotated. This would allow for the sharing of the responsibility for the coordination of the subject.
The long-term plan for Mathematics includes the aims, objectives, reference to textbooks used and general details about the organisation of mathematics in the school. An outline of the programme of work to be studied by each year and grouping and the associated chapters from the textbooks given is included. There are a number of deficits in the current plan. For example, yearly schemes of work should outline intended learning outcomes for each relevant sections of the syllabus for each year and level. Where necessary topics should be ordered to ensure that students study all topics even if they change a level. The aims and objectives for Mathematics should be school centred and take cognisance of the cohort of students and programmes available within the school. Methodologies employed in lessons should be expanded upon, taking account of the range of active methodologies engaged with during in-service courses which teachers attended. Details of continuing professional development and materials/resources received by teachers at such in-services should be included for use by all teachers. Furthermore procedures for students in need of numeracy support should be integrated into the mathematics plan. Subject plans for specific programmes and mathematics initiatives should also be included within the long-term plan for Mathematics. In line with best practice ongoing review of the long-term plan for Mathematics should be undertaken at meetings and all relevant and necessary amendments made. It is therefore recommended that the mathematics teachers collaborate together to develop a comprehensive plan for Mathematics in the school.
During the inspection some individual planning was made available. However, in general teachers follow the programme of work as outlined in the long-term plan for the department.
It was reported that an annual review of state examination results is undertaken by the Principal. However, the analysis of state examinations should also be shared by the Mathematics teachers as it will inform the planning for yearly schemes of work towards enhancing student attainment. When a student decides to change level it was reported that the parent/guardian is consulted. However to ensure that all parties are fully aware of the long-term implications of such a change in level, consideration should be given to developing formal procedures, such as written parental consent.
Topics observed during the inspection included algebra, trigonometry and arithmetic. While the material engaged with within most lessons was generally suitable to the students’ abilities there were situations where the quantity of material studied was limited. It is therefore recommended that, when planning a lesson, teachers select material which is sufficient and suitably challenging for the learning needs of all students while allowing for greater progress to be made in such lessons.
Lessons usually began with the continuation of an example from a previous lesson, or the questioning of students about the material engaged within an earlier lesson. This allowed for the consolidation of previous learning material, while creating links with students’ prior learning experience. Furthermore it demonstrates that Mathematics is a series of topics which are interconnected themes rather than topics learnt in isolation. Best practice would suggest that lessons which begin with shared learning intentions have the advantage of allowing students to be fully engaged with the lesson and that clear expectations are set from the outset of the lesson. It is therefore recommended that this practice be extended to all lessons.
In some lessons observed time management was not effective. The slow pace of the lesson resulted in insufficient material being covered, thereby compromising student progress. On occasion, clear direction and timeframes were not given to students as to what was expected of them when completing assigned work. For example, when students were asked to complete a series of questions during the lesson, no timeframe was apportioned for the completion of this task; instead unanswered questions were assigned as homework. At times, this allowed some students to become disengaged and led to the non-completion of the assigned work. It would have been more beneficial to give specific time to complete an exercise after which corrections would take place, allowing for the identification of common errors or misunderstandings. It is therefore recommended that all lessons be planned and clearly structured to ensure that sufficient time is allocated to the exposition of material and techniques, practice of newly acquired skills, and correction. This structure will allow all students to have a sense of achievement in their classwork and ensure that any errors are addressed in an expedient manner.
In general, whole-class teaching dominated the lessons observed: that is, the teacher demonstrated a technique and students repeated the process by completing a series of questions. However, as not all students benefit from this method, it is recommended that teachers use a range of active methodologies more appropriate to the learning needs of all students. For example, paired work, when used effectively, allows students to learn effectively from one another while developing their reasoning and use of mathematical language. Furthermore, it is recommended that differentiation in the teaching of Mathematics be factored into all lessons to allow for all students to develop at a pace appropriate to their needs while challenging all students. To this end reference should be made to some elements of Assessment for Learning which are described on the National Council for Curriculum and Assessment (NCCA) website.
Questioning frequently focused on recall-type questions with little use of higher-order questions. For example questioning usually sought correct answers to the next line of a mathematics solution rather than probing whether students understood the ideas. The use of global questions did not allow for participation by all in some lessons observed. Furthermore, sufficient time should be given to students to think about their answer before the correct solution is given to them by the teacher. It is therefore recommended that a range of questioning strategies be used in all lessons to encourage the participation of all students in the lesson and to ascertain students’ readiness to progress with new material or to identify students’ misconceptions.
Interactions between students and teachers were, in general, limited to classroom procedures rather than Mathematics. Some students were capable of answering questions posed to them by the inspector during the evaluation and used terminology appropriate to both the level and topic being studied. However, in other situations students had difficulty using correct mathematical terminology. Therefore in all lessons students should be encouraged to use mathematical terminology appropriate to the topic.
In some lessons observed, not all students were engaged fully in their learning, and on occasion this led to students becoming talkative when assigned a task. In other instances some students were reluctant to undertake independent work which was assigned to them. This does not allow for optimal engagement with the subject and strategies should be developed to ensure that students have the confidence to work independently of their teacher. It is recommended that teachers set higher expectations for their students and that these be communicated accordingly to students. Furthermore students should be encouraged to share the responsibility for their learning and to develop competencies in Mathematics commensurate to their abilities.
The main resources used in lessons observed included textbooks, whiteboards and a worksheet. On occasion the use of an overhead or data projector would have enhanced the learning for students and would have been a valuable asset in the aforementioned correction of work. Ongoing review of the resources available and ways of using them in the teaching of Mathematics is recommended.
Some teachers are classroom based with others moving to meet a class group in an assigned room. Some classrooms had displays, but none were mathematical. It is recommended that Mathematics materials be developed and displayed in classroom both as exemplars of best practice and as an aid in the teaching of Mathematics.
Assessment of students takes many forms including in-class questioning, homework and in-school examinations in November and May. In addition examination-year students have ‘mock’ examinations. It was reported that first year students generally have common assessments and this is good practice. Consideration should be given to extending this practice to other year groupings when common levels are being taught in two classes. This practice would allow for students’ achievements within levels to be compared with the entire year group.
Homework was assigned in all lessons observed. However, while the quantity of homework was sufficient in most cases, on occasion it should have allowed for greater challenges for students. The school policy on the recording of homework is clearly outlined in students’ school journals, but frequently students did not record their homework. However, there was evidence that teachers are using students’ journals as a tool to contact parents and to highlight to parents misbehaviour or non-completion of homework. Therefore care should be taken to ensure that as homework is assigned all students accurately record it, in line with the written policy.
During the inspection students’ homework copies were viewed, but it was difficult to distinguish between work completed in school and a student’s attempt at homework. Additionally, many students did not correct their own work but either waited until the teacher corrected it or left it unmarked. As this is not good practice it is recommended that in addition to oral feedback some annotated comments are included in students’ homework copies. In addition students should be encouraged to correct their work as it is corrected in class and to make the necessary amendments.
The following are the main strengths identified in the evaluation:
· In general teachers are facilitated to retain a class grouping within a cycle.
· Management supports teachers to attend in-service in mathematics.
· In general first year students have common assessments in mathematics.
· It was reported the Principal undertakes an analysis of state examination results.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· In the context of ensuring compliance with Circular M29/95, the timetabling of Mathematics should be reviewed and sufficient time allocated to it particularly
at Junior Cycle.
· Concurrent timetabling of Mathematics should be extended to allow students to study mathematics at the highest level possible for as long as possible.
· The mathematics teachers should collaborate to update aspects of the long-term plan for Mathematics to include the learning outcomes for each section of
the syllabus and the identification and purchasing of a range of mathematical resources.
· Strategies to raise the attainment of students in ordinary level Leaving Certificate Mathematics should be developed and adopted by mathematics teachers.
· Teachers should constantly review the content, pace and time management of lessons to ensure that students are suitably challenged by the material presented
and that steady progress is made in all lessons.
· It is recommended that a greater range of methodologies, resources and questioning strategies be explored and developed to engage students more fully in the
lesson while allowing them to become active in their own learning.
Post-evaluation meetings were held with the teachers of Mathematics with the principal and deputy principal, at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published October 2009