Numeracy:

What is reasoning? Why is reasoning and problem solving important to teach in modern primary education?

Reasoning? What is reasoning? Reasoning within maths in education involves using systematic thinking with effective problem solving to come to an answer to a mathematical question. NRICH Primary team (2014) say that reasoning doesn’t only help children with solving strictly maths problems but is seen essentially as the ‘glue’ which helps mathematics make sense to children within education. The primary national curriculum says that the aims for mathematical reasoning are to follow a line of enquiry, conjecting relationships and generalisations, developing an argument and then finally having justification or proof using mathematical language. This may all sound complex however when broken down into a simple formula which it would be for children, all of these points begin to make sense and all form into a neat and tidy formula as such to follow for the children. Why? You might ask well according to Drury (2014), a fifth of all children who happen to fall below national expectations by the end of primary school yet teachers who teach for mastery with using reasoning expect every single child within their classroom to succeed. According to Drury regardless of background, prior engagement, gender or race everyone should achieve. However the modern trait is nowadays that maths is only seen for clever people, which isn’t true, however teachers seem to appreciate equal efforts from everyone in the class when going towards a numerical area which isn’t always the easiest to achieve.

Reasoning is seen as such a critical skill in modern education as it is crucial to succeed within the new curriculums Scholastic Aptitude Test (SAT), which is being introduced within the new national curriculum in Wales and across the United Kingdom (UK) according to Mr Teach (2019) a blogger from within the UK it is his firm belief that primary school mathematics should be not only be about the maths as a whole but should also be about exploring, reasoning and challenging thinking. This should be taught over learning abstract rules for calculations and facts. Even though abstract rules and facts within mathematics are seen as essential I to agree that it should not only be taught for exploring, reasoning and challenging thinking but should also be based around abstract facts and calculations. I believe this as I am also a firm believer in this but also disagree slightly as I think that there should be an equal combination of both within the new curriculum not to only engage the students more which is the most fundamental skills but also to make things more interesting by basing the scenarios and questions upon real life situations.

Whilst recognising how key reasoning is, we also need to acknowledge how essential that allowing the children within modern education to recognise the key skills and facts are within the system. As during the early key stages such as key stages one and two it is important to acquire the basic skills which can then be used by the children to apply in real life situations.

Many sources believe that the reason behind the putting so much importance on reasoning according to Drury (2014) the author of mastering mathematics logical reasoning requires metacognition which in simple terms is thinking about thinking. This influences behaviour and attitude through greater engagement, self-regulation along with seeking conceptual understanding. Drury also states that reasoning seems to promote these traits not only in primary education but throughout it as a whole as it requires children to use their mathematical vocabulary. In basic terms this all essentially means that the key behind reasoning is communication as when using the skill it requires talking whether that be to peers or the teacher. Within my personal experience I feel as though reasoning is essential in getting a deeper understanding in questions especially in certain maths topics where I have struggled in at some point in the past. However during my experience of numeracy during my time in primary education more than ten years ago abstract facts seemed to be a bigger factor rather than reasoning which I feel could have left many peers behind. However with reasoning being implemented more frequently in modern education it could be a chance for a breakthrough along with the new curriculum.

Problem solving according to an ACME report is that ‘problem solving in mathematics: is realising the vision through better assessment’. Problem solving is used every day in modern education throughout primary school as well as secondary, the only problem is that it is a skill that doesn’t seemed to be acquired easily be students and used to its full potential according to Lucy Kilgariff (2018) the head of maths in a successful Devon school, some ways to effectively teach problem solving in modern education can be to use open book tests, these give the students and the teachers the opportunity to assess how far the students are willing to push themselves as she says during an open book test ‘students are much more likely to attempt a question’. Doing these tests personally I can confirm that this is true, having the key information in front of you pushes you to attempt more adventurous questions that you wouldn’t have attempted before through using problem solving. Another key way which is being implemented according to Kilgariff is using free writing is also key when introducing problem solving within education as some pupils seem to fear attempting a question that they don’t seem to know how to get to the answer so they avoid writing anything down at all. This can be very relevant for the children within the class who have a fear getting something wrong or aim highly, Kilgariff said that an easy activity within her own personal lessons to implement this is using a five minute free writing activity to try and combat this fear.

Cotton (2016)

In 2016 the ACME report that was published reported that ‘changes in assessment of problem solving should be introduced incrementally’. Therefore meaning that problem solving will be introduced more heavily within education in primary and secondary school and as mentioned previously this will be essential to pass the new SATs tests that are being implemented into the new curriculum that will be fully in place by 2021. However no matter how much students and pupils try to achieve the skill of problem solving, it is inevitable that it will always be an everlasting problem within education.

In one of our seminar sessions we learnt about the values of problem solving and reasoning and the real life effect they are having on education today. Within this seminar we went over a book designed for year three students by the Welsh Government titled robots, we went over test questions that had previously been used in the 2015 National Numeracy tests for reasoning. These questions weren’t necessarily a difficult task for me and my peers however, they did have us using the skills required to answer them, this only goes to show that being taught reasoning and problem solving at a young age can carry the trait on into higher education. The tasks set within the test often required audio visual aids to be shown (AVAs) to the children prior to them being assessed, which shows the use of technology within the classroom as an additional aid rather than a ‘distraction’ as called by many. Throughout the seminar I and my peers discussed how to not only solve the questions but the thought process that had gone into them to get the end result. I found this particularly intriguing as it allowed me to attempt a modern day test and assess my own ability. The Welsh Government (2014) also now use Literacy and Numeracy Framework (LNF), this has been designed to help students aged five to fourteen with scenarios such as the one I mentioned previously. Some of the key skills they expect leaners to accomplish include:

·         Developing numerical reasoning

·         Using number skills

·         Using measuring skills

·         Using data skills

Welsh Government 20^th Oct 2014

To conclude on this blog post, I personally all of the skills I have mentioned are all equally as important when trying to successfully achieve something in terms of numeracy. These skills are just some of the skills that are currently being taught in our modern education system, it has been intriguing to research these different areas of skills and the reasoning behind actually teaching them as well as being taught them prior to this. I hope this gives you a deeper understanding of the reasoning and problem solving skill sets as a whole.

Reference list:

 Nrich.maths.org. (2014). Reasoning: Identifying Opportunities (Article). [online] Available at: https://nrich.maths.org/10990 [Accessed 20 Mar. 2019].

Drury H, 2014. Mastering Mathematics. Publisher: Oxford University Press [Accessed 21 Mar. 2019]

Third Space Learning. (2012). Developing Reasoning Skills in Maths for KS2 - Third Space Learning. [online] Available at: https://thirdspacelearning.com/blog/developing-reasoning-skills-maths-ks2/ [Accessed 19 Mar. 2019].

 Kilgariff, L. (2018). Teaching Problem Solving. [online] TeacherToolkit. Available at: https://www.teachertoolkit.co.uk/2018/01/30/problem-solving/ [Accessed 19 Mar. 2019].

Learn.cardiffmet.ac.uk. (2018). Cardiff Metropolitan University. [online] Available at: https://learn.cardiffmet.ac.uk/pluginfile.php/905299/mod_resource/content/1/Reasoning%20Resources%20/Unprotected_Year_3_Reasoning_Robots_English.pdf [Accessed 18 Mar. 2019].