The why?
In the context of my teaching practice I undertook a professional enquiry research project to investigate the impact of non-routine problem-solving approaches on Year 6 numeracy reasoning skills. Through classroom observations, I identified a significant need for developing problem-solving strategies within numeracy lessons to foster long-term independence and resilience among learners. Traditionally, problem-solving lessons have been predominantly linear, characterised by routine-based learning of specific skills directed at well-defined problems. This approach appears to inadequately equip students with the skills necessary to tackle diverse mathematical challenges independently. This shortcoming was corroborated by baseline national assessments, pupil surveys, and interviews, revealing that while the majority of pupils performed well in procedural tasks, their scores displayed a marked decline in reasoning.
The Education Endowment Foundation (EEF) highlights the high impact (estimated at +7) and low cost of interventions linked with Metacognition and Self-Regulation. This evidence prompted an exploration of questioning techniques and the implementation of diverse strategies to transform pupils' perceptions and engagement with problem-solving. To quantify the impact of this initiative, an array of analytical methods was applied during daily numeracy sessions and dedicated problem-solving Fridays. The incorporation of experiential learning techniques—such as trial and improvement, systematic working, pattern spotting, working backwards, logical reasoning, visualising, and conjecturing—became central to our pedagogical model, enhancing individual problem-solving abilities while fostering collaborative learning environments.
My research revealed the necessity of nurturing classroom cultures that endorse a problem-solving ethos. It is imperative to shape learners’ approaches to challenges by cultivating an environment conducive to questioning, critical thinking, and the acceptance of mistakes as learning opportunities. As Pennant (2013) asserts, a supportive classroom culture relies on the active engagement of all students, with each contribution valued as fundamental to individual and collective growth. Encountering difficulties should be regarded as an essential element of the learning journey, stimulating meaningful discourse among learners and educators alike.
Reflective practice emerged as a fundamental aspect of evaluating the effectiveness of problem-solving instruction. The use of video recordings facilitated a comprehensive analysis of pedagogical methodologies, directing focus on verbal participation, the quality of questions posed, student responses, listening skills, and the extent to which students’ contributions advanced learning. This reflective process was enhanced by Pennant's essential questioning levels framework, which enabled a detailed exploration of classroom dynamics conducive to effective learning.
Ongoing evaluations of pupils' attitudes towards problem-solving, conducted through structured surveys, provided valuable insights into their perceptions of mathematics, comfort with errors, teaching methodologies, and previous experiences. This data illuminated how individual mindsets influence engagement with mathematical problem-solving.
Questioning emerged as a pivotal component of this enquiry, with questions classified into four categories: starter questions, questions that foster mathematical thought, assessment questions, and concluding discussion questions. This classification was situated within Bloom's taxonomy, which emphasises cognitive engagement from basic recall to evaluative judgement. Following Pennant’s (2013) four-stage process—commencing the problem, engaging with it, delving deeper, and reflecting—our weekly workshops integrated authentic, real-life experiences to enhance student engagement.
While this study had a longitudinal nature, time constraints limited opportunities to observe significant progress. To mitigate this challenge, comparative analyses of reasoning and procedural assessment data collected from late November to early December were juxtaposed with data obtained in June. Concurrent surveys contributed insights into shifts in students’ attitudes towards problem-solving, thereby presenting a comprehensive picture of their developmental trajectory within this essential aspect of numeracy education.
The learning
Looking at procedural and reasoning national assessment in September gave me a good overview of skills pupils needed to practice. An initial pupil survey showed 20% drop in pupils confidence in reasoning from procedural .Mindset, vocabulary used in questions and multistep stages were the main issues according to interviewed pupils. While scores did improve in National assessments, I see the change in mindset as the biggest breakthrough, due to it supporting more resilience and independence.
Recording and reviewing my own teaching, questioning and the dispersal of questions throughout the class was very informative. Learning what questions to pose and when to pose them. Creating a culture of learning from mistakes was transformative for the pupils mindsets and resilience. Developing a classroom culture of sharing approaches and methods freely enabled pupils to improve their oracy skills and numeracy vocabulary. Trial and improvement and pattern spotting were key strategies along with key questions and identifying key stages of the process. Pupils explored these strategies during 'safe space' problem solving Fridays sessions. We also linked it to our our outdoor learning SDP and allow pupils to trial concepts in a more 'hands on' concrete method. Problems from Nrich website with no right answer gave pupils the opportunity to use conjecture and build confidence.
Pupils began to use key questions in both the problem solving and the evaluation of their attempts. Have I seen something like this before? What are the key facts? What is it asking me to find out? What did I do well? how do I know? what are my targets?
This built up a very informative dialogue with the pupils and I, it also facilitated their identification of next steps.
Confidence up by 20%
Pupils developing a more positive mindset is crucial. At the start of project pupils had a 60% positivity rating for reasoning by the end of the process this had risen to 80%. Pupils were less scared of making a mistake. Learning to break the problem solving into the stages supported by questioning was also important. Reasoning scores on average increased by 3 marks with some pupil making big steps forward. Numeracy dialogue and collaboration had big impact on pupils confidence. My own development of questioning and when best to use it, while still progressing has been transformative.
What worked
Recording a baseline from national tests was a useful start, also creating a suitable survey to gather pupil opinion at various interval gave me some insights into progression. Planning lesson using Nrich resources gave me a library of lessons which allowed me to mix the type of problems the pupils were solving. I will build a set of resources for the different key stages. Identifying the importance of classroom culture around the subject and mindset were initial targets and the lesson evolved as we all grew in confidence. Looking at it over the space of a year allowed time to see some development in mindset and approach. Linking to our oudoor learning and school marking policies allowed pupils more of freedom in assessing their own approach and target.
Challenging times
As advised in the seminars it was important to develop a timetable of data collection, interviews and assessments to keep on track with the longitudinal study. Working on survey timings, questions and styles is something I would like to investigate further. Keeping a good flow and variation with the Friday workshops was a challenge as it was also important to break down negative mindsets. It was important to be proactive but patient to enable classroom culture to develop. I think that a longer period of time is needed to assess development properly. A schoolwide move to creating positive problem solving culture would also help in addressing negative mindsets
What next?
As part of an initial enquiry each class teacher in following a PEP. A summary of each seminar has been shared during staff meetings. The NPEP coordinator has consulted with staff on their questions and on their initial outcomes. This precedes a more in depth enquiry next year tying into an element of the the SDP.
An Inset day is planned to look using PEPs to develop the school as a learning organisation (SLO). A brief survey of the staff indicates a need to embed the culture of investigation further.
So what?
As mentioned the initial pupil survey revealed a concerning 20% drop in pupils' confidence in reasoning compared to procedural tasks. Interviews conducted with the students highlighted mindset, vocabulary used in questions, and the complexities of multistep processes, identified the primary barriers to their understanding.
Recording and reviewing my own teaching practices, particularly my questioning techniques and the distribution of queries across the class, proved to be highly informative. Understanding what questions to ask and the optimal timing for these inquiries facilitated a culture of learning from mistakes, which transformed pupils' mindsets and bolstered their resilience. Nurturing a classroom atmosphere where approaches and methods were shared openly contributed significantly to their oracy skills and numeracy vocabulary.
Key strategies such as trial and improvement, pattern spotting, and identifying crucial stages of problem-solving became foundational to our learning. 'Safe space' problem-solving sessions on Fridays allowed pupils to explore these strategies and connect their learning to our Outdoor Learning Strategic Development Plan, engaging with concepts through more tactile methods.
Furthermore, utilising problems from the Nrich website that offered no definitive answers enabled pupils to employ conjecture and build their confidence. As students began to integrate key evaluative questions into their problem-solving processes, constructive dialogues emerged between us, effectively clarifying their next steps for progression. Following a final survey pupils confidence in numeracy had improved by 20% with a general improvement on national assessment scores
Pupil voice
Now I know it's ok to make and learn from mistakes, I feel more confident.
I feel a lot more confident than I did at the start. I was a bit scared before but feel better now.
Our teacher has gone through lots of strategies and I have worked hard. I feel a lot better.
Using trial and improvement really helped me get started. I didnt always get it right but I was on right track.
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