3 What were our aims? learning and teaching opportunities for the To develop practical, contextualisedlearning and teaching opportunities for thedelivery of key mathematical conceptswithin Curriculum for ExcellenceTo engage all pupils through the delivery ofhigh quality, interactive lessons whichpromote discussion and challenge thinking
4 How did we begin? By asking ourselves ....... Are we really teaching the concepts, or simply how to answer the textbook/workbook question?How able are pupils to transfer and apply their learning?How early does mathematics need to be recorded, and does the emphasis on recording impede the learning?
5 What did we want to happen? For our pupils:to find learning engaging, stimulating, challenging and funto see relevance and meaning in what they are learningto spend more time discussing, thinking and evaluatingand less time writingto learn from each other by working co-operativelyFor ourselves:to find teaching engaging, stimulating, challenging and funto see relevance and meaning in what we are teachingand less time marking
7 Pupils use a sand tray to complete What did we do?Purposeful PlayLorraine Smith teaches P1-3 at Carmyllie, a two teacher Primary School on the outskirts of Arbroath. She considers herself very fortunate to have large spaces to accommodate practical activities both inside and outside her classroom. These spaces have been developed into play areas and each week Lorraine sets her pupils a practical maths challenge to be completed in one of them.Pupils use a sand tray to completework on co-ordinatesSymmetry is investigated in “Artists’ Corner”
8 Pupils are introduced to a new challenge each Monday Pupils are introduced to a new challenge each Monday. The mathematical concept behind the challenge is taught and pupils brainstorm their ideas on how the challenge might be tackled. Working in ability groups, pupils take turns to complete the challenge sometime during the course of that week.Lorraine has pupils of wide ranging ability, and maturity, within her multi-composite class. For this reason, challenges are presented on laminated sheets, making them easy to adapt for differing needs and aptitudes.Pupils weigh ingredients for a magic spell in the “haunted house” and, as zoo keepers, calculate the feeding times for animals in their charge
9 On finishing the activity pupils self and peer assess and complete a simple evaluation sheet. Agreement must be reached on how well they coped with the task, and how well they feel they functioned as a group.Although materials required for this approach are many and varied, few have had to be purchased; Lorraine is simply making better use of what is already there! All challenge cards and photographs are kept on file, and should prove a helpful resource in the future.Most Shape, Measure and Data Handling concepts are now developed through play. The school has adapted their planning sheets to cater for this, the column identifying workbook pages having been replaced with one entitled “Cross Curricular Links and Links to Play Activities”.The “Small World” area is used to practisefollowing directionsBudding scientists measure out quantities of“chemicals” in the water tray
10 Lorraine has also produced an information leaflet for parents and plans to hold a “Maths Evening” early next session so that the parents may experience the approach first hand, with their children. Discussions are also currently taking place as to how the scheme may be extended into the P4-7 class.Although this project has been implemented over a relatively short timescale, Lorraine is convinced it has had a positive impact on attainment:“My pupils have a new enthusiasm for maths and can readily recall concepts that they have covered in this way. I’ve also noticed they are far better at co-operating and working together. There were lots of silly squabbles amongst groups at the beginning but these have not happened for a long time. The children now work as a team and learn from each other.”“I am not finding that practical maths gives me any greater workload. On the contrary, the challenges are quite simple to prepare and set up, and once this has been done the children are able to complete them without any teacher help. There is in fact less preparation (and marking!) than there is when textbooks and workbooks are used.”
11 Early Stages“At first I felt apprehensive about my workbooks being removed so, when my head teacher asked if I would like to be involved in PACT , I was interested straight away. I wanted to see what others were doing and how they were doing it!” Jill“Before the project I was dissatisfied with the way I taught maths as I felt the children weren’t being given enough fun. My current stage partner was keen to make changes too. This has added to the success of the project as it has been great to have someone to share ideas with.” SylviaSylvia Beisok and Jill Duncan teach P1 classes in large, town schools. The way in which they approached PACT, and their reasons for doing so, are similar in many ways:both felt that commercial schemes werethe driving force behind their teachingboth felt that an inordinate amount of timewas being spent on written tasks, in orderto “get through the scheme”, and thatoften these worksheets/workbook pageswere indeed inappropriate, or unnecessary.both were keen to change their practice,and meet teachers of a similar mindset.
12 Both teachers place a high focus on Interactive Mental Maths, using a variety of practical resources: number fans, digit cards, flip flops, number squares, etc. Commercially produced, and teacher devised, games are used for reinforcement.Every effort is made to set the learning within real contexts. Sylvia’s pupils worked together to turn a round table in their classroom into an analogue clock. The clock is “set” at various times in the day and serves as a useful teaching and assessment tool. In number, pupils already showing confidence in handling larger amounts are given responsibility for collecting and counting the dinner money, under supervision.Much discussion has centred aroundthe names and properties of shapes.Pupils took part in a “Shape Walk”and worked co-operatively to identifyshapes within their environment.Observations were later recorded inthe form of 2D pictures and 3D models.
13 This year, Jill’s school has used no commercially produced workbooks/ worksheets at all in P1 and P2. Sylvia and her stage partner have been given the autonomy, by their senior management team, to use these resources only when they feel it is appropriate to do so. This was explained to parents in order to relieve any anxiety caused by incomplete workbooks going home! Though the emphasis is clearly on oral and practical work, pupils in both classes use dry wipe boards and jotters to record their thinking.The teachers now have a daily, focused“Maths Time” where pupils are taughtas a class or in ability/mixed abilitygroups, depending on the activity.Where group work is deemednecessary, classroom assistants,parents and nursery nurses provideinvaluable support, simply by talkingto the children about their learning.In addition, the introduction of“Thinking Pairs” and “Talk Partners”has enabled pupils to becomelearning resources for each other.
14 Both Jill and Sylvia believe that being free from the “burden” of endless worksheets/workbook pages, which pupils often found difficult to complete independently, has bought them quality teaching time. They feel far better informed about what their pupils understand, and can see straight away those who require extra support.“The children are achieving good results and show confidence in what they are doing. When check ups/assessments are given they tackle them with fewer mistakes. I really feel this is due to the fact that the concepts have been taught thoroughly.” Sylvia“The children are progressing well. I feel I can challenge them and they enjoyit.” Jill
15 Co-operative Learning Training in Co-operative Learning has had a huge impact on the practice of hundreds of Angus teachers this session, no more so than on that of Kathleen Meldrum, Carlene Kidd,Simon Gallon and Scott Haxton.Despite recognising the value ofstructured play and experientiallearning, most felt that a lack ofconfidence in the teaching ofmathematics had resulted in them,too, becoming “scheme driven”.“When I am less confident I find it easier, and more convenient, to be led page by page through a scheme. However, I was not convinced that the children were accessing and interacting with learning experiences that would ensure number concepts would become embedded. I was in no doubt that they were learning, but how meaningful that learning was to their life experiences, I wasless sure about.” Kathleen
16 Each lesson begins with the sharing of learning intentions and success criteria. In true co-operative learning style, these are identified as academic goals (WALT) and social goals (WILF). Groups are formed accordingly and “Task Roles” allocated.Lessons are carefully planned to ensure all members of a group feel connected to each other in working towards a common goal; groups are only considered successful if every member can demonstrate accomplishment of the learning. Peer support is encouraged through strategies such as, “Ask three before asking me.” Pupils consolidate their learning and understanding through demonstrating, recounting and explaining concepts, processes and strategiesto each other. Teachers and classroom assistants actas facilitators, challenging the thinking appropriately.“The co-operative approach enables me to monitorlearning and understanding by listening to theinteraction between the children as they work.” Simon“I have consciously begun to use more open endedquestioning techniques which promote higher order,independent thought.” Scott
17 All tasks are time constrained All tasks are time constrained. On completion, pupils use various forms of self and peer assessment (thumb tool/fist of five, traffic lights, learning logs etc) to evaluate how well they feel they have achieved both their social and academic goals.In Scott’s class, pupils are encouraged to devise activities for assessing each other’s learning and understanding, e.g. by preparing a quiz. Carlene and her pupils record their thoughts about lessons in a class journal.As well as assessment comments in planning folders, all teachers retain photographic evidence hence they have a full record of the work undertaken.
18 Solving “Real” Problems In collaboration with his P6 class, Simon looked at problem solving activities from new sources, including the Northumberland Grid for Learning and Using Maths: Real Contexts for Problem Solving (Tick Tock Publications), as well as problems within contexts devised by himself.He believes that involving his pupils in the evaluation and selection of these resources not only gives them ownership of the task but contributes significantly towards the process of personal learning planning.Contexts have included a “Shopping Parade” which looked at the skills required by different trades/shopkeepers (counting, weighing, measuring), working for a “Juice Company” to develop packaging (area, volume, 3D shape) and a “Travel Bureau” dealing with exchange rates (multiplication and decimals).
19 Simon feels the project has had a major impact on the way he teaches mathematics: “Before becoming involved in PACT I taught a textbook page without much thought for what else the children might need………. The maths contained in these activities is almost hidden in the presentation and has encouraged even the most reluctant mathematician to participate………. The children are making connections and transferring the strategies they have learned to other areas.”His comments are reiterated further by Kathleen’s Head Teacher, ClassroomAssistant and Support for Learning Assistant who observed her teaching an interactive, co-operative learning lesson on money to her P2 class:“Pupils who would normally have difficultysettling to individual tasks were absorbedand became “invisible”.”“More meaningful than the workbook page.Most children will have put money in a piggybank at some point and will therefore be ableto relate this to their own life experiences.”“Allocating roles ensured that pupils whowould normally dominate had to relinquishthis position in favour of co-operation.”
20 Cross Curricular Links Opportunities for cross curricular work occur daily in our classrooms, yet are often not exploited to their full potential. Certainly, we do not want to revert back to days of yore, where a theme was chosen and all subject areas contrived to fit around it, yet to ignore links which occur naturally is to waste valuable opportunities to streamline and“de-clutter”. To this end, Carlene and Scott have focused on developing co-operative, problem solving tasks linked to Science and Social Subjects.Carlene has devised a series of lessons for her P3/4 class around the theme of Living Things. Pupils conducted surveys to collect information, organised it using tally charts, displayed the information as bar charts, and interpreted and evaluated each other’s efforts. Symmetry in nature was also explored.Carlene was one of three Angus teachers involved in piloting the new Let’s Think Through Maths materials last session. This resource fits perfectly with PACT, and the Co-operative Learning approach, and Carlene has made good use of it to teach key concepts in number, and position and movement.
21 Scott decided to build a series of mathematics lessons, for his P7 class, around the theme of Earth and Space. An understanding of the relationship between diameter and radius was initially established through a “Halloween Pumpkin Prediction Challenge”. This prompted discussion on the relative size of the planets in our Solar System, and pupils worked co-operatively to construct solar system mobiles. Negative numbers was taught through looking at temperature differences; research on satellite and rocket launches provided a stimulus for work on graphs, databases and spreadsheets; planet distances from the Sun, and distances travelled by probes, linked to work on place value and measurement and a discussion on space exploration led to the examination of probability, e.g. the likelihood of finding alien life forms!Like Simon, Scott used “Mission toSpace” from the Using Maths seriesas a stimulus for both his pupils and himself to plan their learning and teaching. Pupils were encouraged to follow their interests, and supported in adapting tasks to suit their preferred learning style. This, Scott feels, has had a marked impact on pupil motivation and confidence.
22 Were we successful?The focus for each practitioner involved in PACT has varied according to their own strengths and development needs, and the stage at which they teach. However, in every classroom there is clear evidence of:direct, interactive teachingcontextualised, meaningful learningchallenging activities that promote thinking, discussion andco-operationan increase in understanding, pace, motivation and enthusiasmongoing assessment, evaluation and reflectionTeachers have become more aware of what they need to do to help their pupils become successful learners, confident individuals, responsible citizens and effective contributors. Textbooks and workbooks, though still in use, no longer dictate what we teach……..we really are marking less to achieve more!
23 The pupils decide!“I think maths was good today because I learned more about shapes.” P3/4 pupil“When I come to school I can’t wait to see if it’s going to be my group’s turn to dothe challenge today.” P2 pupil“Whiteboards are good for practising on…..if you make a mistake you can tryagain.” P1 pupil“Maths was fun today because we was doing hundreds, tens and units.” Less ableP3/4 pupils with behaviour difficulties“I liked it because if we didn’t know the answer then we worked it out together.”P2 pupil“I like playing maths games because they are fun and they help me to learn aboutnumbers.” P1“I enjoyed it, and it was good, and I was obsessed with it!” P3/4 pupil“Maths is better now because there is not as much textbook.” P3/4 pupil“I like mental maths and I like doing my workbook too (teacher asks why) …….because I like writing and I like getting a smiley face on my work!” P1 pupil
24 What happens now?Undoubtedly, all who have participated in PACT have found it a worthwhile, enjoyable experience. But perhaps the real challenges are yet to come. How do we sustain and build upon the progress we have made, and what are the implications?Discussion with the group has highlighted a number of needs:time: to discuss, resource, prepare and share ideassupport: from management, colleagues and the education authorityhigh quality CPDSteps have already been taken towards addressing some of these needs. This session, all Angus primary teachers were given the opportunity to participate in a networking opportunity entitled “Let’s Talk Numeracy”. Several project participants have shared their experiences at these meetings, and arrangements are currently being made to enable them to talk at a training day for probationer teachers.
25 An interim report on the group’s work was also described in VIEW, the Angus Education Department newsletter. This has resulted in teachers from both sectors visiting participants in their classrooms to see PACT “in action”.Teachers throughout Angus will be able to access lesson plans and resources, devised by project participants, via the Angus Education Department Intranet and Innovative Teachers’ Blog. We hope to use remaining funds to provide further CPD training, and to task a ShortLife Working Group with adding to the lesson/resource bank.Final ThoughtsWith the onset of A Curriculum for Excellence there is a need for all teachers, primary and secondary, to review how they deliver key mathematical concepts. And, with the introduction of a new Early Level, collaborative planning between nursery and P1 staff will be essential.The challenge may be great but one thing is certain: with a force of enthusiastic and dedicated teachers such as those involved in PACT, the future of Scottish Education looks bright.
26 Practical Applications of Contextualised Teaching Carol Lyon, Staff Tutor(01241)