Rationale

This year has been challenging – in addition to the regular challenges of teaching GCSE resits (from those who sat an exam), this year has been compounded by having learners who have not formally sat GCSEs due to the Centre Assessed Grades (CAGs) in 2020. We therefore decided to shift our focus away from the initial proposed intention of the work to investigate techniques of online pedagogy.

Engagement of learners has been something we wanted to address from the start of the project. Learner engagement has been a problem for both GCSE and Functional Skills lessons, which is one of the common issues we have in the FE environment.

One key aspect of our project initially was to investigate how learners might effectively communicate answers to us. Once we started using our new lesson plans (created prior to this year and adapted from the 5Rs by Julia Smith (2020)), we considered engagement alongside effective assessment.

We also investigated how, what (and why) our learners think about maths and learning of maths, along with effective assessment for learning that can be delivered remotely. Literature indicates there are two possible consequences when learners fail their maths – increased perseverance which helps improve the learner’s performance, or fear of failure which leads to a decline in performance and anxiety (Johnston-Wilder, et al., 2015).

Every year, around one thousand learners must study maths at The College of West Anglia. Around half of these learners, because of the Government’s condition of funding policy, are required to continue studying towards GCSE maths (Education and Skills Funding Agency, 2014). The current national GCSE pass rate in FE is around 20% (Linford, 2019), which means approximately one hundred learners will achieve grade 4 or above.

The focus in this action research was developed via Cambridge Maths Hub’s (Cambridge Maths Hub, 2021) Post16 workshops, particularly their session on maths anxiety. Our learners often say they cannot do maths and that it makes them anxious. We wanted to understand what learners meant by this statement, what their understanding of maths anxiety is, how it manifests in our classrooms and finally if there is correlation between misconceptions (that are so very common in FE maths re-sitters) and maths anxiety.

Approach

Spot the question type digital quiz

1. Initial Planning phase – identifying how we can adapt to the online learning environment.
   a. Adapting lesson resources from traditional style into 5Rs (Smith, 2020) and accommodating Variation Theory (Barton, 2020).
   b. Finding online technologies that can be used for effective Assessment for Learning.
2. Focusing on Learner Engagement – how can we maximise it?
   a. Different variation sequences and questioning
   b. Trying multiple digital methods to engage and assess learners: What to use apart from our own VLE? Are there any technologies that learners refuse to use?
   c. Which systems are best to use, and are there any learners who cannot access lessons due to digital poverty?
   d. Can we ensure learners are present – ideas from behavioural science. Investigating how we enforce attendance and engagement within lessons – how do we keep those less motivated?
   e. Additional challenge – second large scale lockdown January – March 2021.
3. Identifying maths anxiety and misconceptions – now we have engagement, what can we find out?
   a. Assessment for learning throughout the year with Diagnostic Questions (Barton, 2018). Use of this questioning approach gave inspiration for the misconception investigation.
   b. Direct misconception buster sessions delivered in March and April with ~50 learners. Evidence of improvement across the session and one week after evident.
   c. Surveys completed on maths anxiety.
   d. Two learners chosen for interview on maths anxiety.
4. Synthesis of findings to a conclusion

Professional Learning: Evidence of changes in teaching, learning and assessment practices

Previously the maths department had used a ‘Top 15’ (Grimsby Institute C4ME team, 2020) approach to delivery of GCSE resit maths. ‘Top 15’ is a focus on the 15 most common topics that appear in exams. This allowed us to reduce the scope of the GCSE specification delivered as we only have nine months to deliver two years of teaching and learning.

This approach had been successful in the previous academic year as it allowed the maths department to transition from teaching the full curriculum (in a very short period) to teaching the most important skills needed to be successful in GCSE examination, as well as everyday maths.

This transition made us realise our learners are not able to connect different topics and apply their skills in different scenarios, for example ‘translating’ a worded problem into a solvable algebraic equation (Appendix 5). Our teaching approach had to change to give learners the opportunity to develop this skillset. We started a transition to 5Rs based lesson plans (still using the Top 15) when lockdown started.

The 5R model focuses on five elements: “Routine, Recall, Revise, Repeat and Exam Ready?”. It was first introduced to us in 2017, at the same time as the ‘Top 15’ approach. At the time, ‘Top 15’ seemed more important to implement into our delivery, and implementation of the 5R model across our team was inconsistent. Since then, we have modified Julia’s 5R model to suit our learners and delivery methods and we re-designed our lesson structure around it.

The new sessions also incorporated variation theory to encourage learners to think about the mathematical methods and processes they would be manipulating in their lessons. Variation theory relies upon question sequences where a crucial aspect changes while others stay the same – such that learners should discern the crucial part (Barton, 2020). Full usage of this theory requires learners to reflect upon and consider how their answers change, and stronger learners may be able to explain ‘why’. We decided to integrate this into our delivery as these allowed learners to draw connections between topics, that at first might seem disconnected, but are all interlinked (Appendix 6).

At the start of our research project we had already put the above systems in place, though the variation sequences had only been used in a simple way, and as a source of useful questions. One modification to our session design in the project was to use the ‘Rule’ type of question set (Barton, 2020), where typically only 3 answer options would be available. This reduction in plausible answers helped to facilitate engagement with learners, and creative use of this style of question was useful for developing engaging activities for learners on more challenging topics such as identifying ‘reverse percentage’ questions (Appendix 7).

We quickly established that misconceptions have a clear impact upon learner outcomes. Carl was studying his PGCE this year and researched the theories of misconceptions as a key part of his subject specialism. In turn, these theoretical findings were applied within our action research and put into practice.

“Maths, more than any other subject, has the power to crush children’s confidence and to deter them from learning important methods and tools for many years to come” (Boaler, 2015)

The majority, if not all, of our maths learners come to us with negative emotional baggage surrounding maths. Research into maths anxiety shed an interesting light on the importance of learner perception of maths and their willingness to keep trying – ‘maths resilience’. Although we were not able to fully investigate how anxiety or resilience manifests within our classroom due to remote lesson delivery, we were able to collate some learners’ views on the matter and will be looking at continuing this research next academic year. As a team, we are very keen to ensure learners’ previous experience in learning mathematics is not a barrier to learning it with us.

Evidence of improved collaboration and changes in organisation practices

One of the biggest changes in our delivery this year was remote working and live online lessons as well as our new lesson structure, which, having been developed for face-to-face delivery, had to be adapted.

In September 2020, after very careful planning of our resources with variation theory and prior learning at the heart of everything, we found ourselves adapting resources to allow online delivery. Most of our resources were produced with the assumption that learners will have access to teaching and learning tools such as whiteboards, books, and maths equipment.

Due to the nature of online delivery and the fact that we were not in our usual classroom environment, unable to provide physical learning aides, we had to research and trial online software that would replicate them virtually.

One barrier to effective teaching and assessment has been a lack of verbal learner communication via Zoom. This has been due to technological issues (such as digital poverty or use of mobile phones to access online lessons) as well as some learners being uncomfortable with it. Most learners were also not using their cameras, for the same reasons. This meant we were not able to rely on body language which could indicate they need assistance and restricted our methods for assessing their learning.

The maths team researched a range of different software applications that would enable us to effectively assess learning. Our preferred tools were Whiteboard.fi, DrFrost Maths, OneNote and Microsoft Forms. As a team, we put together several training sessions to present and try those out before we used them in lessons.

Successful tools were in turn communicated to the rest of the college in Continued Professional Development (CPD) events. None of those were as effective as physical tools, partly because we did not have a single approach as a team but also, it relied on learners being able to switch between different tools on their devices, at times more than two in a lesson.

As mentioned above, we found out it was difficult to gauge learners’ understanding at first. Carl developed his quizzes to help understand what learners have learnt after the lesson, which then turned into prior learning check and ‘what have you learnt this lesson?’ tasks. This allowed us to a) understand learners’ starting point and b) see in-lesson progression. Those quizzes were available to the team to use as they see fit. Some members of the team used Carl’s approach and produced quizzes of their own, which they then shared with others.

Carl and Aga had regular meetings to discuss findings and decide on next steps. This time was also designated to discuss any changes needed to our approach, such as use of quizzes as a prior learning check as well as lesson plenary. We also looked at other possible interesting avenues in mathematics education such as comprehensive reading and understanding questions, confidence levels in answering questions, and formal and informal methods of concept delivery. While we did not investigate these aspects in this project, we could do so in the future – a focus on reading and understanding questions could be very beneficial to our learners.

Our team is very fortunate to have been allocated weekly teaching, learning and assessment sessions. The maths team meets Friday afternoon as part of CPD. We use that time to collaborate on resources and new ideas, take part in maths specific professional training, and team discussions on teaching and learning approaches. We also use that time to share good practice with one another.

Evidence of improvement in learners’ achievements, retention and progression

We initially identified two learners in the same group for a case study. One of these learners entered the GCSE November 2020 series and passed with a grade 5. Her feedback (Appendix 8) was that learning synchronously over Zoom was beneficial as it reduced the noise in her learning environment and helped her to understand concepts. Utilising the Zoom messaging system was described as beneficial as it meant that explanations could be read multiple times.

An early piece of assessment – before and after teaching fractions – demonstrated the two misconception types well and can be seen in Appendix 2. The results demonstrated that learners progressed better where errors came from reading the question accurately, rather than those where the process itself was poorly understood prior to the topic being covered. We concluded that learners expect that mathematical operations with addition should be straightforward. Since the addition of fractions is not simple, it seemed that learners treated it as if it were, and despite learning the correct process, did not tend to retrieve this knowledge when tested. It seems likely that our learners were able to apply the skill when taught it (procedural understanding), but unable to correctly identify when to use the skill (conceptual understanding (Rittle-Johnson, et al., 2016)).

In the later stages of the project, we investigated algebraic misconceptions – specifically, erroneous simplification, for example:

For this task, a diagnostic quiz was used to determine which misconceptions a group had, before tackling the misconception with Frayer models (Quigley, 2018). The correct answer to this first algebraic simplification was ‘Does not simplify’ – it seemed that learners may be reluctant to select this option. A follow up short low-stakes quiz at the end of the session was used to determine if learners had progressed in the short term. The following week an additional quiz was used that used modified versions of the original questions, and another quiz was to be used after a month to test retention. In general, after a week, more correct answers were given, and some errors were almost eliminated. A detailed breakdown of the results we were able to gather can be seen in Appendix 9.

As mentioned previously, we also wanted to investigate how our case study learners feel about maths as a subject and what emotions maths education brings as well as if there is correlation between misconceptions.

Johnston-Wilder et al., (2019) describe maths anxiety as:

“a negative emotional reaction to mathematics that acts as an ‘emotional handbrake’ and holds up progress in maths.”

Aga found that from 41 learners who answered a questionnaire on maths and maths anxiety, 20 learners had either not heard about it or had no idea what it was. (Appendix 3). Other answers varied between

“Nervous to do maths”, “When you get stressed and worry about maths” or “When people hate maths, but they are forced to do it”.

Although learners often say ‘maths makes me anxious’, responses in the questionnaire did not support this claim amongst those asked. One key question used was “What do you understand by “maths anxiety”?” – an example response given was “I assume its where it gives you anxiety, like what I have”. This learner was invited to an interview in which she admitted she didn’t know ‘maths anxiety was a thing’. (Appendix 4). When asked to elaborate on this statement, the learner said:

“I wouldn’t say the whole thing in general (maths), but some parts of maths make me anxious, I just want to completely shut off and I just get worked up about it”.

Johnstone-Wilder et al talk about the brain-hand model (Johnston-Wilder, 2021); Siegel (Siegel, 2012) introduced this method as a way of explaining what happens in our brains when faced with a threatening situation, in our case, learners’ fear of failure.

In our survey, we asked “What were the signs/ changes in their behaviour? (of people experiencing maths anxiety)”, only 16 learners were able to answer this question. Some responses were “Get angry and loose the temper and keep worrying”, “They Go quiet”, “not want to do it as they think there not good at it”, “get quieter and stressed”. This is a typical ‘fight, flight, freeze’ response. There are a number of possible ways to address this and help build their maths resilience to minimise occurrence of feeling helpless:

1. ensuring teachers are aware of the emotions surrounding a particular task
2. recognising when emotional stress is overtaking and
3. working on relaxation response.

This year, due to online lesson delivery, the only possible way of knowing if learners are experiencing emotional distress was for them to communicate it directly with us via their preferred communication method and, so, this part of the research was not successful. We were not able to introduce relaxation methods either as we have not been aware of possible emotional difficulties.

The survey also asked learners if they think “maths anxiety relates to reading and understanding exam questions?” (Appendix 3) and if so, how. Twenty-four learners answered this question and some of their responses were “You don’t read the question right and rush through questions and get them wrong”, “You feel a big amount of pressure, you get flustered, which overall creates a negative mindset. no one will do well in exams with this mind set”, “makes you nervous which blocks of your whole understanding and makes you think you’re doing things wrong”.