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How Does the 'PACE Maths' Approach Impact on the Practice of School Staff?

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Title: How Does the 'PACE Maths' Approach Impact on the Practice of School Staff?
Language: English
Authors: Burt, Emma, Stringer, Phil
Source: Educational Psychology in Practice. 2018 34(3):245-261.
Availability: Routledge. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
Peer Reviewed: Y
Page Count: 17
Publication Date: 2018
Document Type: Journal Articles
Reports - Research
Education Level: Elementary Education
Descriptors: Mathematics Skills, Mathematics Instruction, National Curriculum, Metacognition, Small Group Instruction, Cooperative Learning, Program Effectiveness, Problem Solving, Foreign Countries, Mathematics Achievement, Elementary School Students, Elementary School Teachers, Teacher Role
Geographic Terms: United Kingdom (England)
DOI: 10.1080/02667363.2018.1431767
ISSN: 0266-7363
Abstract: Mathematical skills are essential for young people to attain academic results needed for further study and employment. Recent changes to the English National Curriculum have put an increased emphasis on pupils explaining the reasoning behind answers in maths. This is a skill that can be developed by improving metacognitive skills. The authors report on an in-class programme for small group work, based on prior studies that utilised metacognition to support maths. An evaluation was conducted including a focus group interview and observation, modelling and feedback sessions over approximately 10 weeks. Results from interview analysis showed a positive impact both on staff practice and pupils' independent problem solving. Adaptations based on research findings were made to the programme and handbook. This programme represents a flexible, inclusive and low resource option for schools to address new challenges posed by the National Curriculum in times of budget cuts and increased time pressure.
Abstractor: As Provided
Number of References: 44
Entry Date: 2018
Accession Number: EJ1190673
Database: ERIC
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  Value: <anid>AN0131751775;b8g01sep.18;2018Sep15.09:49;v2.2.500</anid> <title id="AN0131751775-1">How does the “PACE Maths” approach impact on the practice of school staff? </title> <p>Mathematical skills are essential for young people to attain academic results needed for further study and employment. Recent changes to the English National Curriculum have put an increased emphasis on pupils explaining the reasoning behind answers in maths. This is a skill that can be developed by improving metacognitive skills. The authors report on an in-class programme for small group work, based on prior studies that utilised metacognition to support maths. An evaluation was conducted including a focus group interview and observation, modelling and feedback sessions over approximately 10 weeks. Results from interview analysis showed a positive impact both on staff practice and pupils’ independent problem solving. Adaptations based on research findings were made to the programme and handbook. This programme represents a flexible, inclusive and low resource option for schools to address new challenges posed by the National Curriculum in times of budget cuts and increased time pressure.</p> <p>Metacognition; Maths; Intervention; Inclusion; Programme; Problem-solving</p> <hd id="AN0131751775-2">Introduction</hd> <hd id="AN0131751775-3">The Scale of the Problem</hd> <p>Mathematical knowledge and skills enable access to a range of opportunities. A maths qualification can support employment or a place in further or higher education because employers and educational establishments use maths skills as a “sifting criteria” (Wolf, [<reflink idref="bib43" id="ref1">43</reflink>] ). Mathematical qualifications also affect the earnings of an individual; for example, in the UK, adults with a level 1 qualification in maths (equivalent to General Certificate of Education, GCSE, grades A-C) earned on average 26% more than adults with lower level qualifications (Every Child A Chance Trust, [<reflink idref="bib15" id="ref2">15</reflink>] ). The cost of difficulties in maths is experienced by the individual and also by society. The lifetime cost of unemployment in the UK due to numeracy difficulties per annual cohort (based on a yearly school intake of 35,843 pupils) was estimated by the Every Child A Chance Trust ([<reflink idref="bib15" id="ref3">15</reflink>] ) report to be approximately £1872.7 million through lost national insurance, income tax and payment of benefits.</p> <p>The importance of maths skills in allowing an individual to access opportunities in later life has led those connected to education to examine current performance in schools to see where improvements can be made. A report by the National Foundation for Educational Research (National Foundation for Educational Research (NFER), [<reflink idref="bib30" id="ref4">30</reflink>] ) called for a review of the mathematics education system due to levels of underachievement, and highlighted the need to tailor mathematical provision to the needs of different groups of pupils, rather than offering a “one size fits all” approach. Tailored provision involves being clearer about the skills, attitudes and knowledge that are needed to teach young people so that they are more able to use what they know, which can then enable them to move to different levels of maths provision (for example, more challenging tasks). This report suggests that the way in which maths is taught needs to make children more aware of how they can apply what they have learnt, thus developing their metacognitive skills.</p> <p>In response to evidence gathering over time, the English National Curriculum, and thus the mathematical programme of study, was updated in 2013 to tackle the growing trend of underachievement in mathematics (Department for Education, [<reflink idref="bib9" id="ref5">9</reflink>] ). The new mathematical programmes of study: key stages 1 and 2 (Department for Education, [<reflink idref="bib10" id="ref6">10</reflink>] ), put an increased emphasis on pupils being able to explain their reasoning, work through mathematical processes and to check their working. These skills have been shown to be difficult for children since they struggle to extract relevant information and can be unaware that an answer is incorrect because they do not understand the mathematical process sufficiently to check it (Gooding, [<reflink idref="bib17" id="ref7">17</reflink>] ). Metacognition has been identified as supporting children to develop these types of reasoning skills.</p> <hd id="AN0131751775-4">Maths Learning and Metacognition</hd> <p>Demetriou, Christou, Spanoudis, and Platsidou ([<reflink idref="bib8" id="ref8">8</reflink>] ) proposed that maths knowledge improves through learning opportunities facilitated by factors such as metacognition, because it aids planning, monitoring and evaluation. Metacognition may be defined as being aware of what you know (metacognitive knowledge) and how best to use that information (regulation of performance) (Lai, [<reflink idref="bib24" id="ref9">24</reflink>] ).</p> <p>Metacognitive knowledge can be split into three parts (Schraw & Moshman, [<reflink idref="bib35" id="ref10">35</reflink>] ):</p> <p>Procedural knowledge = knowing appropriate strategies</p> <p>Conditional knowledge = knowing when and why to use a strategy</p> <p>Declarative knowledge = knowing what affects how well you do</p> <p>Regulation of performance can also be divided into three parts (Schraw & Moshman, [<reflink idref="bib35" id="ref11">35</reflink>] ):</p> <p>Planning = thinking about what you need to do</p> <p>Monitoring = checking your strategy is working</p> <p>Evaluating = Reflecting on task performance</p> <p>Several studies from a range of countries have shown a link between improving metacognition and performance in maths. There are slight variations in the design of each study but typically interventions consisted of a series of metacognitive questions, which were posed to pupils by an appropriately trained adult during a maths lesson (Cardelle-Elawar, [<reflink idref="bib6" id="ref12">6</reflink>] , [<reflink idref="bib7" id="ref13">7</reflink>] ; Hoek, van den Eeden, & Terwel, [<reflink idref="bib19" id="ref14">19</reflink>] ; Kramarski & Mevarech, [<reflink idref="bib22" id="ref15">22</reflink>] ; Kramarski, Mevarech, & Arami, [<reflink idref="bib23" id="ref16">23</reflink>] ; Mevarech, [<reflink idref="bib25" id="ref17">25</reflink>] ; Mevarech & Amrany, [<reflink idref="bib26" id="ref18">26</reflink>] ; Mevarech & Kramarski, [<reflink idref="bib27" id="ref19">27</reflink>] , [<reflink idref="bib28" id="ref20">28</reflink>] ). All of these programmes showed a positive impact on maths achievement. A number of interventions are currently available which develop reasoning skills through metacognition, but a number of these have limitations in terms of time, cost or in ease of integration into a lesson; for example, Feuerstein’s Instrumental Enrichment programme is a well-evidenced, long-term curriculum programme with structured exercises that can be used in the classroom (Feuerstein, Rand, Hoffman, & Miller, [<reflink idref="bib16" id="ref21">16</reflink>] )). However, in order to use the approach, participants must undergo a three-day training programme; therefore this can be costly in terms of time and money.</p> <p>The “Thinking Together” programme by the University of Cambridge teaches children in adult-led groups to discuss problems. The approach provides guidance on how to set ground rules for talk and children are explicitly taught about exploratory talk in separate lessons. Exploratory talk emphasises the importance of providing reasons for responses and encourages children to ask questions and share knowledge to create collaborative solutions (University of Cambridge, [<reflink idref="bib40" id="ref22">40</reflink>] ). There is guidance on how to encourage discussion, but the technique of using exploratory talk in lessons is open ended and may take some time for teachers to fully integrate it into their lessons, as they develop their own set of questions that would suit this approach. The additional lessons to teach this approach also present a demand on curriculum time, albeit a relatively small demand.</p> <p>Given the time constraints in the curriculum, due to the introduction of the new national curriculum (Association of Teachers & Lecturers, [<reflink idref="bib1" id="ref23">1</reflink>] ) and the budget constraints on schools (Sellen, [<reflink idref="bib36" id="ref24">36</reflink>] ), it appeared that a need existed to develop an approach that made minimal demands on curriculum time and school resources, whilst facilitating metacognitive skills.</p> <hd id="AN0131751775-5">Developing a Flexible, Cost Effective Intervention</hd> <p>The opportunity to develop such an approach was provided by the first author’s work as a school’s contact educational psychologist (EP) in a local authority traded service. The school had identified pupils who struggled in maths but had developed skills to mask this by looking like they were working. A meeting was held with the special educational needs coordinator, head teacher and deputy head teacher, and the first author negotiated that she would create a question-based intervention based on reviewed metacognitive studies and then provide training to all staff.</p> <p>A ninety-minute training session was devised and delivered to all staff, and a handbook detailing the approach was provided. The programme developed by the first author from this training is called “PACE” maths (Planning, Applying, Checking and Evaluating) and is designed to develop metacognition to deepen pupils’ understanding of mathematical concepts so they can be more independent problem solvers.</p> <hd id="AN0131751775-6">The PACE Maths Programme</hd> <p>The PACE Maths programme is a manualised, metacognitive programme, where an adult works in a specific way with a small group following the whole class input. PACE Maths has been developed by the first author based on a literature review on maths and metacognition. It was developed through her work as a local authority educational psychologist and the purpose of this evaluation was to determine if the approach was effective, before offering the programme as a product that would form part of the local authority’s traded service offer. For a school to be able to use the PACE Maths programme they receive:The adult has guidance from the manual as to how to divide up this group working-time into four phases; that is, planning, applying, checking and evaluating. Each stage has its own set of questions, which are detailed in the manual, although different questions can be asked, provided they cover the main areas in the handbook. The structure of the session is as follows: planning, applying, checking, and then the applying and checking stages are revisited as a whole group throughout the lesson to ensure children have a good understanding. The evaluation stage is just before the end of the lesson. It is important that all stages are conducted as a group rather than just with an adult and a child, because the group element helps children to learn from each other and to be less reliant on adult support.</p> <p>A handbook written by the first author, detailing the background to the approach, how the lesson needs to be structured, the type of questions that need to be asked at each stage of the lesson and the way in which the questions should be asked (that is, starting with open questions and making them increasingly closed if the child needs more information in order to be able to give a response).</p> <p></p> <p>A whole school training session written by the first author about the background of the approach and how to use it. This covers the theory of metacognition and goes through each stage of the programme and how to apply it. The training comes with full presenter notes so that there is consistency of content regardless of who is delivering the presentation.</p> <p>Two observation and modelling sessions during a normal maths lesson with at least two members of staff (therefore a minimum of four lessons observed - two for each member of staff). These sessions take place during a normal maths lesson, with the EP observing the session until he or she thinks it would be helpful to intervene and model how to use an aspect of the approach so that staff can see it in practice. This allows staff to apply what they have learnt and to receive practical support to resolve any potential issues in application. This support thus helps to establish at least two members of staff who are familiar with the approach so that over time other trained staff members have someone in school they can refer to for immediate questions about applying the approach. The school’s contact EP can also be approached for support. This model should help to ensure fidelity through the correct application of the programme.</p> <p>The PACE maths programme uses the structure provided by the headings from metacognitive theory, specifically regulation of performance (plan, monitor, evaluate). There were a number of reasons for adopting this structure. Firstly, planning, monitoring and evaluating mapped well onto the “Plan, Do, Review” model often used within teaching, especially for those with special educational needs (Nasen, [<reflink idref="bib29" id="ref25">29</reflink>] ). Furthermore, this type of approach maps well onto existing structures within the metacognition intervention literature; for example, Schraw ([<reflink idref="bib34" id="ref26">34</reflink>] ) proposed the categories of planning, monitoring and evaluation, which have been found to have a positive impact on metacognition and mathematical development (Pennequin, Sorel, Nanty, & Fontaine, [<reflink idref="bib32" id="ref27">32</reflink>] ). The approach is low in time and resources and only requires ninety minutes of training followed by a minimum of two observation, modelling and feedback sessions with the educational psychologist during a normal lesson for at least two key members of staff to provide a “bridge” from training to implementation.</p> <p>The questioning used in this approach aims to uncover how much children really understand, therefore a think aloud protocol is used whereby children are required to “say aloud” what they are thinking (Jacobse & Harskamp, [<reflink idref="bib20" id="ref28">20</reflink>] ; Teong, [<reflink idref="bib37" id="ref29">37</reflink>] ). The way in which the questions are asked may be termed a “funnelled questioning” approach, whereby questions begin as relatively open but, if pupils struggle, increasingly closed questions are asked to focus them on important information - without actually giving them the answer.</p> <p>This is based on the style of questioning used during dynamic assessment (Tzuriel, [<reflink idref="bib39" id="ref30">39</reflink>] ) and the theories underpinning this type of questioning are detailed in Tzuriel ([<reflink idref="bib38" id="ref31">38</reflink>] ); for example, within Vygotsky’s ([<reflink idref="bib41" id="ref32">41</reflink>] ) sociocultural theory the “graduated prompt” approach is influential because different levels of prompts are given to help a child solve a problem. Feuerstein et al.’s ([<reflink idref="bib16" id="ref33">16</reflink>] ) mediated learning theory is also linked to this type of questioning. For example, mediation of meaning is where an adult highlights the importance of certain task characteristics so that children learn to actively attach meaning to new information.</p> <hd id="AN0131751775-7">The Evidence Base for Metacognitive Questioning</hd> <p>The specific questions used in the PACE maths approach derived from a number of peer reviewed studies. The interventions within these studies were all delivered as part of small group work during the independent working section of a normal maths lessons after the whole class input, where adults provided support by asking questions based on metacognition (Cardelle-Elawar, [<reflink idref="bib6" id="ref34">6</reflink>] , [<reflink idref="bib7" id="ref35">7</reflink>] ; Hoek et al., [<reflink idref="bib19" id="ref36">19</reflink>] ; Kramarski et al., [<reflink idref="bib23" id="ref37">23</reflink>] ; Kramarski & Mevarech, [<reflink idref="bib22" id="ref38">22</reflink>] ; Mevarech, [<reflink idref="bib25" id="ref39">25</reflink>] ; Mevarech & Amrany, [<reflink idref="bib26" id="ref40">26</reflink>] ; Mevarech & Kramarski, [<reflink idref="bib27" id="ref41">27</reflink>] ). The PACE maths approach aimed to capture key elements of these programmes to provide easy-to-use, evidence-based interventions. The PACE maths programme uses the principle of collaborative working where peers learn from each other, based on the approach used in Mevarech and Kramarski’s ([<reflink idref="bib27" id="ref42">27</reflink>] ) IMPROVE method: Introducing new concepts, Metacognitive questioning, Practising, Reviewing and reducing difficulties, Obtaining mastery, Verification, and Enrichment. This programme is a small group, within class, intervention that takes place following the whole class input. The programme requires the adult to ask the group comprehension questions (about the understanding of the class), strategic questions (about what strategy to use) and connection questions (making links to previous learning). The structure of the IMPROVE method (whole class input then small group support with metacognitive questions) is similar to the interventions listed above, and this is the structure that PACE Maths adopts.</p> <p>The question areas used in the PACE Maths approach incorporate elements of different metacognition interventions used in a range of studies, as will be detailed in the remainder of this section. The structure of the PACE Maths programme comes from the main areas of metacognitive theory, specifically regulation of cognition (that is, plan, monitor and evaluate). The PACE Maths programme also includes “apply”, to use the thoughts from the planning stage. The questions in each area are as follows:</p> <p>Planning (prediction, comprehension, connection, strategies and conditional)</p> <p>Applying</p> <p>Checking (checking and conditional)</p> <p>Evaluating (prediction, comprehension, connection and checking)</p> <p>The inclusion of these different types of questions is based on the content of the following studies. Prediction questions in both the planning and evaluation sections are based on a study by Desoete, Roeyers, and De Clercq ([<reflink idref="bib11" id="ref43">11</reflink>] ). Prediction enables children to anticipate task difficulty, which can make them persist on tasks that they know will be difficult but work quicker through tasks they know to be easier (Desoete, Roeyers, & Huylebroeck, [<reflink idref="bib12" id="ref44">12</reflink>] ). In Desoete et al. ([<reflink idref="bib11" id="ref45">11</reflink>] ) prediction is included because this skill was only found to develop when explicitly trained. The comprehension questions in the planning and evaluation sections are based on the IMPROVE method which notes that pupils should explicitly understand what the problem is (Mevarech & Kramarski, [<reflink idref="bib27" id="ref46">27</reflink>] ).</p> <p>The IMPROVE method has been used in a number of studies which have found positive effects on maths (Kramarski et al., [<reflink idref="bib23" id="ref47">23</reflink>] ; Mevarech & Amrany, [<reflink idref="bib26" id="ref48">26</reflink>] ; Mevarech & Kramarski, [<reflink idref="bib28" id="ref49">28</reflink>] ; Mevarech, [<reflink idref="bib25" id="ref50">25</reflink>] ) and therefore a range of question types were based on this approach: for example; the strategic questions in the planning and checking sections which encourage pupils to find appropriate strategies, and the connection questions in the planning and evaluation section where pupils are encouraged to find similarities and differences between the current problem and previously encountered problems. Conditional questions are included in the planning and checking sections of the programme, which are based on the conditional area of metacognitive knowledge (Schraw & Moshman, [<reflink idref="bib35" id="ref51">35</reflink>] ). The checking section of the programme is based on the monitoring aspect of metacognitive theory, which focuses on checking how an approach is progressing (Schraw & Moshman, [<reflink idref="bib35" id="ref52">35</reflink>] ). No questions were developed for the applying section of the programme because this is intended for independent working.</p> <hd id="AN0131751775-8">Current study</hd> <p>An evaluation was conducted following the implementation of the programme in order to answer the following questions;</p> <p>What impact does the PACE maths approach have on staff practice?</p> <p>Does the PACE maths approach have an effect on children’s participation in their learning?</p> <p>How can the approach be adapted to be more effective?</p> <p>This paper reports on the findings of this research and the subsequent impact and development of the programme.</p> <hd id="AN0131751775-9">Method</hd> <p>Participants were selected from the school where the first author had delivered the initial PACE maths training. The school senior leadership team selected four participants who were thought to be good practitioners of the approach. All participants were invited to take part through a letter and a participant information sheet. Consent forms were returned to the researcher. Participants were all female; two worked as teachers and two worked as learning support assistants. One teacher had a number of years’ experience and one teacher was newly qualified, whereas both learning support assistants had been in post for about four years. The age groups of the pupils whom the staff worked with were year three (aged 7-8 years) and year five (aged 9-10 years).</p> <p>The initial phase of the research involved observations and modelling from the first author. This was followed by two-way feedback sessions where both the author and participants could discuss areas for change and those areas that were working well. All participants were observed using an observation schedule designed by the first author, based on the key elements of the programme. An observation-modelling-feedback approach was chosen for three reasons: to gain feedback on how to improve effectiveness, to ensure fidelity and to help staff to bridge/generalise skills from training into the classroom. Support to staff to generalise taught skills is important in building confidence and helping to develop the right conditions for implementation (Blase, Van Dyke, Fixsen, & Wallace Bailey, [<reflink idref="bib3" id="ref53">3</reflink>] ). Support from staff to improve effectiveness is important with a new approach because key individuals should be actively involved in gathering information about the design of the intervention and any changes that may need to be made (Kelly, [<reflink idref="bib21" id="ref54">21</reflink>] ).</p> <p>This research adopted a critical realist position because it aimed to uncover causal mechanisms but acknowledged that the data may not provide complete access to this “reality” (Willig, [<reflink idref="bib42" id="ref55">42</reflink>] ) because some identified factors are specific to a particular context, in this case, a school (Kelly, [<reflink idref="bib21" id="ref56">21</reflink>] ). For example, the research aimed to find factors that impacted on the effectiveness of the PACE maths programme and it was assumed that through discussion and interaction with the participants the authors would be able to identify these factors. It was acknowledged, though, that these factors will vary between participants because they will be affected by their environment and by those with whom they are interacting.</p> <p>Upon completion of the observation and feedback sessions a focus group was conducted at the school with all four participants. A focus group was chosen because group dynamics can help to focus on important aspects of the data, participants can feel more comfortable in a group and the method is time efficient (Robson, [<reflink idref="bib33" id="ref57">33</reflink>] ). A semi-structured interview schedule was used. As per the recommendations in Bannister, Burman, Parker, Taylor, and Tindall ([<reflink idref="bib2" id="ref58">2</reflink>] ) certain ethical components were included such as: seeking permission to record the interview, anonymising the data by removing names and other identifying characteristics, the option to terminate the interview should any participant request this and the option to remove a participant’s data from the transcript. At the end of the interview all participants were given a debriefing sheet.</p> <p>The interview was recorded and then transcribed. All data were anonymised through the use of pseudonyms. The transcript was analysed using thematic analysis, following the six-stage process outlined by Braun and Clarke ([<reflink idref="bib4" id="ref59">4</reflink>] ). The first step was familiarisation with the data-set, moving to the second stage where initial codes were generated. Coding was mainly inductive because the codes identified were strongly linked to the data rather than being driven by theory; however, there was inevitably some coding which was more deductive due to the authors’ prior familiarity with research and theory in this area (Braun & Clarke, [<reflink idref="bib5" id="ref60">5</reflink>] ). Themes and sub-themes were developed and an initial thematic map was created. The themes and sub-themes were reviewed to create a second and final thematic map. These themes are explored in the results section.</p> <hd id="AN0131751775-10">Results</hd> <hd id="AN0131751775-11">Observation Schedules</hd> <p>Information collected through the observation schedules and feedback discussions reinforced the use of certain aspects of the programme or provided examples of good practice that could be incorporated. Areas that needed amendment and ways in which this may be achieved were also highlighted. This aspect of the research was intended to update and improve the programme rather than necessarily evaluating it. Examples of good practice incorporated into the programme related to the following two areas:</p> <p>Questions</p> <p>Additional questions for small group and whole class teaching</p> <p>Greater emphasis on funnelled questioning</p> <p>Ordering of some questions was given greater flexibility</p> <p>Summarising</p> <p>Adults to summarise and number the steps of a strategy</p> <p>Areas that required adaptation were also highlighted and subsequent improvements were created through discussion with participants. These improvements related to the following five areas:</p> <p>Additional prompts</p> <p>More prompts for children to “say aloud” their thinking</p> <p>Visual prompts to summarise task information to reduce working memory demands</p> <p>Connection (to previously learnt information)</p> <p>Adult verbally highlights similar areas pupils have covered, but asks them to identify the strategies</p> <p>Colour coding different areas of maths in children’s books using post-its to speed up finding related work</p> <p>To point out key markers that indicate an area is related, for example, particular notation for calculations (+, −, × etc.)</p> <p>Applying</p> <p>Time limit for independent work to improve focus</p> <p>Checking</p> <p>More regular checks</p> <p>“Pacey” discussion to increase engagement</p> <p>Emphasis on the whole group checking a problem</p> <p>Evaluation</p> <p>Using smiley faces to indicate task difficulty predictions so they can be easily revisited</p> <p>Encouraging reasons behind predictions</p> <hd id="AN0131751775-12">Focus Group Interview</hd> <p>A focus group was conducted with all four participants when observations were completed. The focus group interview was analysed using thematic analysis as per the guidance provided in Braun and Clarke ([<reflink idref="bib4" id="ref61">4</reflink>] ). The information collected from these interviews was very positive about the impact on both staff practice and pupil learning behaviour in the maths lessons where the programme was used. Additional benefits were also highlighted, such as improvements in staff questioning in other lessons and evidence of children retaining strategies over time. The following themes and sub themes were created through analysis in order to capture the key messages of the data.</p> <hd id="AN0131751775-13">Improving the Learning Process</hd> <p>This theme represents the changes in skills and attitudes that help children improve their approach to learning and help adults to become more effective facilitators. This overall theme is split into three sub-themes to more clearly explain the benefits that the programme had on the learning process.</p> <p>(a) A Guide to Approach Teaching. This sub-theme is about the changes to teacher practice during maths lessons. Benefits to staff practice included the programme giving adults a guide to structure a task so as to help pupils know how to approach it.</p> <p>P3: Yeah... specially for those that struggle to implement the skills we’ve taught them previously, sort of give them something that, oh... like, ‘Oh, I’ve got something to start’, so having the conversation really helps.</p> <p>The guide that adults give pupils involves helping children to think of a strategy before they start trying to do the task and giving them more opportunities to check their work so that they are set up for “next steps”. Through this more in depth process of children thinking about their work the adults felt that children “internalised” their teaching to a greater degree, allowing them to move through the task without having to revisit things as much.</p> <p>P1: The children you can see, or certainly I can see, each time, there were certain bits they picked up and they had internalised and were using themselves and you could kinda focus on the next bit, which they then internalised.</p> <p>The programme not only helped adults give children a guide through the learning but it also helped adults guide what they needed to do. Sometimes this was something as simple as stepping back and allowing the children time to implement discussed strategies.</p> <p>P1: I also think it’s easier to sit back and let them have that independence, I often think we’re guilty, certainly with the other children, of leaping in and helping too soon, whereas it enables us to step back and let them try all of that before we actually get involved in it.</p> <p>Sometimes the benefits related to helping the adult to know what they should be focusing on to help children get the most out of the lesson.</p> <p>P2: “I said the other day that the three lessons I did with PACE questions were probably the best three lessons I’ve done because I actually… I was far more focused on what I was doing.”</p> <p>One of the mechanisms that helped to achieve this focus was the type of questioning in the programme because this helped staff to ask a range of meaningful questions. Because they were written down this meant that adults could choose which ones they thought were most useful at that time. The quality of the questions was also higher because staff did not have to “make them up” on the spot.</p> <p>P2: “Yeah, cos if they weren’t all there... da da da da! Something like that out of your head, it’s just having the prompts....”</p> <p>(b) Independent Problem-Solving. As a result of the way in which adults were able to guide their teaching, pupils began to develop into more independent problem solvers. This sub-theme is therefore about children learning the skills and strategies that helped them to be more independent. These skills included using resources more effectively and knowing how to check their work.</p> <p>P2: Because you’ve obviously got the rote learning reply: ‘How do you do it?’ ‘Check the inverse’, yeah, but that doesn’t work! (laughs). So they’ve just learned something to say, whereas now they’re actually thinking about it.</p> <p>Children were also more likely to ask peers for help in a constructive way so that they learnt from each other, which is consistent with previous research.</p> <p>P1: Actually, if we’re in a group they’ve got that security that actually I can go and say to someone else, ‘What did you do because my strategy’s not working.’</p> <p>Once children learnt or internalised strategies from adults or peers, they would then apply them in subsequent tasks, or they were enabled to work more independently for the remainder of the current task.</p> <p>P4: There’s one of yours in particular that impressed us, in one of our focus groups, she’s still using the same strategies and doing really well.</p> <p>(c) Wider Benefits. Through the acquisition of new skills in both staff and pupils there were improvements in both teaching and learning behaviour in maths lessons, but the approach had wider benefits. These benefits refer to positive changes and gains that were not solely skill based or that did not necessarily occur in the maths lesson. For example, the way in which children talked about learning changed, because they had been given the skills to think about the task by themselves and could now self-regulate their discussions so that they were about the learning.</p> <p>P3: And the conversation is more relevant to the task than it probably was before, they’re sort of focused and actually communicating with each other about what they’re doing.</p> <p>Due to the skills the children had been taught they had learnt to continually adapt their strategies by monitoring how well they were working. This had helped children learn that there was not necessarily one right answer and that they did not have to reach it straight away. Due to this, children’s confidence to “give things a go” improved.</p> <p>P2: It’s confidence building as well. They’re not so frightened to take a risk because they know it’s ok.</p> <p>As children had made additional gains through learning the skills in the programme, so too did the staff. Wider benefits for adults included improvements in practice outside of maths group work. This involved using the questions from the programme in other lessons, which was possible because the questions are built on metacognition, which applies to all areas of learning.</p> <p>P3: And those questions do come out in other lessons, like topics and things as well.</p> <p>Similarly, the questions used during group work were also beginning to be used in the whole class input. The inclusion of these questions was not always planned and seemed to become an “organic” part of practice.</p> <p>P1: Do you, do you find this...I find an awful lot of those questions come out in whole class teaching as well, without realising it.</p> <hd id="AN0131751775-14">Factors Affecting Future Implementation</hd> <p>This theme aims to move the programme forward from what is working now, to how to ensure its continued effectiveness. This is explored through the following sub-themes:</p> <p>(a) What Helps make the Programme Work. This sub-theme details practical factors, that is, not skills based, that help the programme to have an impact on staff practice and children’s learning. Factors that affected staff practice were related to how easily the approach could be implemented given the time and resource constraints in schools. Time pressures were thought to be low because it did not take a long time to work out how to use the programme and because there were no additional resources needed in order to use it;</p> <p>P2: I don’t have to make/do anything extra - it’s there.</p> <p>It was also noted that the approach is flexible which makes it more practical to use in a range of ways.</p> <p>P4: You’ve already adapted mine so I can use it on a day to day basis, going round each table.</p> <p>Other factors related to how staff could keep using the approach effectively. These related to the need for continued reflection, because the way in which the children responded or the way in which the adults may need to adapt questions may change slightly each time.</p> <p>P2: Yeah. Yeah. And obviously every time I did it, it was totally different. So, unless you did it for every single lesson, and reflected on it.</p> <p>The process of reflection was noted to be a difficult one and therefore the importance of outside guidance was highlighted. This is a theme that was also commonly expressed from participants during feedback after the observation and modelling sessions.</p> <p>P2: Other things may come up... I don’t know. You just have to be on hand - help me! (laughs)</p> <p>The focused, group-based nature of the programme was also thought to be an important factor in the success of the approach. The notion of working with only a small group of children and really focusing on their development rather than trying to “spread” oneself amongst all of the class every lesson, was thought to lead to greater learning gains.</p> <p>P2: I found that, some, like, sometimes it is just better to, work with six children, and those six children benefit greatly, rather than 10 of them, get a little bit.</p> <p>(b) What Areas Still Need to be Developed. This sub-theme explores factors that were identified which needed adaptation to make the approach more effective. A number of factors that needed adaptation were also noted as part of the observation/modelling and feedback sessions and are discussed in the corresponding results section.</p> <p>Connection questions (linking past and current learning) were highlighted as more difficult to implement. This is because due to changes to the new national curriculum and the subsequent “catch up” that all children are expected to do, there is often not space in the curriculum to regularly revisit learning (ATL, 2013) and therefore children are less used to this skill. This is even more difficult if it is a less common topic.</p> <p>P2: And parts of the curriculum you don’t see very often, they found it hard then to take something from something they’d done before, or something like that, so sort of with statistics or geometry, they don’t see that particularly frequently... so I think that was harder.</p> <p>A further area that needed adaptation was the wording of the questions. The approach is quite language based and this can be harder to access for children whose levels of language are not as developed, often due to age:</p> <p>P1: And the age of the children I think as well, because we had to adapt quite a lot in terms of, the … reword the questions for the year threes so they understood it whereas year fives probably understood it.</p> <p>Finally, there was some consideration about how the approach could be more child-led in order to further reduce the demand on adult time.</p> <p>P2: However, if there was... some... of adapting it to do it for themselves. I don’t know. Obviously that depends on the age of the children.</p> <hd id="AN0131751775-15">Discussion</hd> <p>This research aimed to answer three main questions:</p> <p>What impact does the PACE maths-approach have on staff practice?</p> <p>Does the PACE maths approach have an effect on children’s participation in their learning?</p> <p>How can the approach be adapted to be more effective?</p> <p>To address these questions a series of observation, modelling and feedback sessions were conducted with four members of staff who worked with small groups of children during maths lessons. A focus group was then conducted and analysed using thematic analysis.</p> <p>Regarding the first question, a number of benefits to staff practice were found. The approach helped staff guide pupils through a task by giving them the structure of planning, applying, checking or evaluating work, which made adults clearer about what they should be focusing on. This focus was aided by the provision of example questions they could ask at each stage. Due to the clear structure that existed in the lesson, adults were more comfortable to “stand back” and “let children have a go”, which facilitated a greater level of independent learning.</p> <p>Benefits were found, not only to practice within small group work in the maths lesson, but to other lessons and to the whole class input. It was reported that the questions used in the approach could be implemented in other lessons, for example, topic lessons, and that they “naturally” began to form part of whole class teaching. Other factors were also identified that did not directly contribute to improving staff practice but which enabled staff to use the approach. These included how easily the approach could be implemented due to its flexibility and low resource and time demands. Staff also noted the importance of reflection in being able to continually use the approach in an effective way. The importance of having an external person to facilitate this was highlighted in both the focus group and the feedback sessions. This finding is consistent with literature in the field of implementation science, which notes that it is important to have a “knowledgeable purveyor” who can help identify and problem solve any ongoing issues in implementation (Blase et al., [<reflink idref="bib3" id="ref62">3</reflink>] ; Kelly, [<reflink idref="bib21" id="ref63">21</reflink>] ).</p> <p>Regarding the second research question, a number of benefits to pupils’ participation were reported, which were largely consistent with benefits found in other metacognitive intervention research. The approach was thought to improve children’s ability to “internalise” learning, so that adults did not have to “go back over” information as much as they believed they had to previously. This is consistent with findings by Mevarech and Amrany ([<reflink idref="bib26" id="ref64">26</reflink>] ) who found that pupils could apply taught metacognitive procedures to a testing situation that occurred a couple of months after the intervention took place. As a result of the way in which adults were able to guide their teaching, pupils began to develop into more independent problem solvers who could check their work in a meaningful way. This benefit was also found in Kramarski et al. ([<reflink idref="bib23" id="ref65">23</reflink>] ) who noted that pupils who were encouraged to talk about mathematical problems were more able to justify their reasoning. Furthermore, Cardelle-Elawar ([<reflink idref="bib7" id="ref66">7</reflink>] ) found that students who had followed a metacognitive approach were more critical of their approach than students in a control group, which is consistent with reports in this research. Pupils in the current research were reported to be more likely to work with peers and try to learn from each other, which is consistent with the findings of Mevarech and Kramarski ([<reflink idref="bib27" id="ref67">27</reflink>] , [<reflink idref="bib28" id="ref68">28</reflink>] ).</p> <p>The current research also noted reports of increased confidence to “have a go” from pupils, and being increasingly comfortable with “making mistakes”. This finding is consistent with the development of a growth mindset (Dweck, [<reflink idref="bib13" id="ref69">13</reflink>] , [<reflink idref="bib14" id="ref70">14</reflink>] ), which is part of the PACE maths programme. The importance of a growth mindset may be in the level of resilience it can foster in a child, helping them to try new things when their approach has not been successful (Yeager & Dweck, [<reflink idref="bib44" id="ref71">44</reflink>] ).</p> <p>With regards to the third research question, there were a number of factors identified that would make the approach more effective. The connection questions were highlighted as being more difficult to use, especially if the lesson was about a less common topic. Strategies to overcome this barrier were discussed and subsequently incorporated in an updated version of the PACE maths handbook. The wording of questions for younger children was discussed as something that staff had needed to adapt and it was noted that the adult often needed to summarise a pupil’s strategy in order for them to remember it. Further adaptations were the need to prompt children more regularly to “say aloud” their thinking and to encourage children to check their work. These adaptations have also all subsequently been incorporated into an updated version of the PACE maths handbook.</p> <hd id="AN0131751775-16">Implications for practice</hd> <p>The framework for inspection (Ofsted, [<reflink idref="bib31" id="ref72">31</reflink>] ) notes that outstanding teaching will evidence: highly effective questioning, provision of adequate time for practice to embed pupils’ understanding and skills and develop pupils who love a challenge and are resilient to failure. These are all outcomes that this research has highlighted as being connected to the use of the PACE maths approach. The congruence of what the PACE maths approach can offer with what is being expected of schools demonstrates that, if used regularly, this approach has the potential to develop both staff practice and children’s responses.</p> <p>This intervention does not require many resources or for children to be withdrawn from class and is therefore a relatively easy to use, inclusive option. Consistent with previous research into metacognitive interventions delivered during maths lessons (Cardelle-Elawar, [<reflink idref="bib6" id="ref73">6</reflink>] , [<reflink idref="bib7" id="ref74">7</reflink>] ; Hoek et al., [<reflink idref="bib19" id="ref75">19</reflink>] ; Kramarski et al., [<reflink idref="bib23" id="ref76">23</reflink>] ; Kramarski & Mevarech, [<reflink idref="bib22" id="ref77">22</reflink>] ; Mevarech, [<reflink idref="bib25" id="ref78">25</reflink>] ; Mevarech & Amrany, [<reflink idref="bib26" id="ref79">26</reflink>] ; Mevarech & Kramarski, [<reflink idref="bib27" id="ref80">27</reflink>] , [<reflink idref="bib28" id="ref81">28</reflink>] ), this research has indicated that there are positive effects on pupils’ problem solving ability. This research is distinctive because it also explores the impact on staff practice, which provides helpful information for schools planning staff development.</p> <hd id="AN0131751775-17">Limitations</hd> <p>There are a number of limitations to this study. First and foremost, it was a relatively pragmatic and expedient study in terms of the first author’s time and the resources available to her. Ultimately, the priority was to conduct an evaluation, accepting the limitations rather than to do nothing. The first author works as the local authority contact EP within the school where the research took place and therefore is in some sense a part of the school context. The interpretation of these research findings must therefore be made with this in mind and in particular the effects of confirmation bias.</p> <p>In fact, there are a number of potential sources of bias of which the authors are mindful. As Guest, MacQueen, and Namey ([<reflink idref="bib18" id="ref82">18</reflink>] ) note, bias is inevitable and, in this case, undoubtedly more could have been done to manage this. For example, the first author conducted all the lesson observations and the focus group; independent observation and focus group facilitation would have reduced bias. A small number of participants already identified as effective practitioners. These practitioners of the approach were chosen so that research actually evaluated the PACE Maths approach being used. By this it is meant that as the approach is essentially the structure that the staff give the small group work (that is, plan, apply, check then evaluate) and the questions that they ask in each of these stages, if staff are not structuring the lesson correctly or asking the right type of questions then the approach is not really being used and therefore the impact of it cannot be properly evaluated.</p> <p>While it would seem counter-intuitive to identify participants who might not effectively deliver the programme, a future study might learn much about strengthening fidelity and improving staff training and support if a random sample of participants were identified. Inevitably, there may also have been implicit if not explicit pressure on the participants to please the head teacher and the first author. Again, independent researcher involvement might have gone some way to managing this. Bias will also affect analysis and although another educational psychologist checked the coherence and content of final themes, it must be acknowledged that the interpretation of data is largely subject to the values, beliefs and knowledge of the authors.</p> <p>Finally, this research also took place in only one school and therefore it must be acknowledged that from a critical realist perspective, the mechanisms and factors identified may be specific to contextual factors in that school (Kelly, [<reflink idref="bib21" id="ref83">21</reflink>] ) and therefore may not generalise to significantly different settings (for example, secondary schools).</p> <hd id="AN0131751775-18">Future research</hd> <p>This research has highlighted the positive impact of the programme on staff practice and although positive effects on pupils have been reported, these have not been directly investigated. However, information gathered from the school where the research took place did suggest that almost all children made expected progress over the time span of the intervention. Future research may therefore focus on the impact of the programme on pupils’ performance, approach to problem solving and their attitude to learning.</p> <p>This research was conducted with key stage 2 pupils (aged 7-11 years), therefore future research could look at how the approach would need to be adapted if used in a key stage 1 (5-7 years) or secondary (11-16 years) setting. Another area for future research would be to explore how pupils could be trained to use this approach more independently. Additionally, given the indicators within the current research that elements of the PACE maths programme could be effective in lessons other than maths, future research could investigate how the approach would need to be adapted for different subject areas.</p> <hd id="AN0131751775-19">Concluding comments</hd> <p>This article has described a small-scale evaluation of the PACE Maths approach which aims to focus on the metacognitive aspects of learning. Although the study has its limitations, the authors are sufficiently encouraged by the evaluation to consider that the programme represents a flexible, inclusive and low resource option for schools to address new challenges posed by the National Curriculum in times of budget cuts and increased time pressure. 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  Data: <searchLink fieldCode="AR" term="%22Burt%2C+Emma%22">Burt, Emma</searchLink><br /><searchLink fieldCode="AR" term="%22Stringer%2C+Phil%22">Stringer, Phil</searchLink>
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  Data: <searchLink fieldCode="SO" term="%22Educational+Psychology+in+Practice%22"><i>Educational Psychology in Practice</i></searchLink>. 2018 34(3):245-261.
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  Data: Routledge. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
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  Data: Mathematical skills are essential for young people to attain academic results needed for further study and employment. Recent changes to the English National Curriculum have put an increased emphasis on pupils explaining the reasoning behind answers in maths. This is a skill that can be developed by improving metacognitive skills. The authors report on an in-class programme for small group work, based on prior studies that utilised metacognition to support maths. An evaluation was conducted including a focus group interview and observation, modelling and feedback sessions over approximately 10 weeks. Results from interview analysis showed a positive impact both on staff practice and pupils' independent problem solving. Adaptations based on research findings were made to the programme and handbook. This programme represents a flexible, inclusive and low resource option for schools to address new challenges posed by the National Curriculum in times of budget cuts and increased time pressure.
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