Central for all Learners in 21st Century
The 21st Century with all its change, challenges and opportunities means that children need a skill set that encompasses problem solving, independence as a learner and curiosity about the world that mathematics is well placed to help develop. Positive attitudes to mathematics are key in a world where mathematics is central to so many careers. The quantitative demands of almost all university courses are increasing; even subjects like history, which traditionally had involved no mathematics, now recognise the importance of statistics. Also, soon, youngsters will be required to take some mathematics classes until the age of 18.
The nature of mathematics
When we were young we may have experienced a narrow version of mathematics, centred round correct computation using standard algorithms. The new National Curriculum (2014) states that,
‘Mathematics is a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.’
The development of independent thinking and the ability to be a successful problem-solver are key skills for 21st living and employability. This is highlighted in the Advisory Committee for Mathematics Education (ACME) report (2011) Mathematical needs: Mathematics in the workplace and in Higher Education. This report found that in the workforce there is a steady shift away from manual and low-skill jobs towards those requiring higher levels of management expertise and problem-solving skills, many of which are mathematical in nature.
The three aims of the new National Curriculum for mathematics: fluency, problem solving and reasoning, underline the government’s intention to prepare our youngsters for the 21st century world of work that waits them. This world of work is likely to be very different from the one that greeted us when leaving school or university.
A problem-solving curriculum demands a different teaching approach since dialogue, questioning, learning from dead ends and reviewing progress to date are all central to the process. These can be fostered very effectively in a mixed-ability context. Such a curriculum also demands the use of Low Threshold, High Ceiling (LTHC) tasks which means that, ‘pretty well everyone in the group can begin, and then work on at their own level of engagement, but which have lots of possibilities for the participants to do much more challenging mathematics’ (Lynne McClure Director NRICH). Few of us are likely to have experienced such tasks in the majority of our schooling.
The new National Curriculum is a mastery curriculum where all children are to be taught together as much as possible and extension and enrichment is by going deeper into the core material.
This approach to developing our most able mathematicians is championed by the ACME report (2012), Raising the Bar.
‘Ofsted evidence shows that the most effective strategy for generating students’ interest in and commitment to mathematics is through planned enrichment and extension work with the minimum of acceleration. The Mathematical Association has also argued the need for the most able students to be routinely expected to master essentially the same material as their peers – but more robustly, fluently and deeply, and with a greater emphasis on making connections. They should also focus on communicating mathematically and on developing better problem solving skills both within and beyond mathematics. That is, if students are ultimately to go even further in mathematics, they need to achieve a deeper, more rigorous mastery of core material before moving on.’
Every lesson is a problem-solving lesson where children are developing their proficiency with the problem-solving skills such as trial and improvement and working systematically.
A problem-solving approach to mathematics where all children can contribute and explore ideas can be very effectively fostered in mixed ability classrooms. The approach needs to be underpinned by fluency in key mathematical facts and processes. This can sometimes be called ‘plonk’. Within the class, children need to be able to be grouped flexibly on a daily basis, according to the outcomes of the previous day’s assessment for learning, the task and the topic. The classroom culture needs to be one where mistakes are fine, even celebrated for the learning opportunity they offer, where children can change their mind, where everyone’s ideas are valued and children challenge themselves to be the best they can be at mathematics. The mindset needs to be one where all can achieve and where feedback celebrates the achievement rather than the innate ability of the child.
Central to the mathematics classroom are representations such as the numberline, arrays, Dienes apparatus, the fraction wall and beadstrings. These help children to ‘see’ the mathematics and they support the development of deep conceptual understanding. Representations need to be used consistently across the school so that children are very familiar and fluent with their use.
‘Pen in hand’ marking is fundamental to every classroom as teachers and TAs talk with the children throughout the lesson about their learning and record successes in their books, offer next steps and comment on mathematical thinking. Both written feedback and verbal feedback are valuable to support learners in developing their practice.
TAs and additional adults are deployed effectively to support children with their learning throughout the lesson. They may be supporting the main class tasks or working with individual or small groups of children to consolidate or extend their learning. They work with the whole range of attainment in the class over the week and support children through effective questioning and use of representations.
Beyond the Daily Mathematics Lesson
Children need to have frequent and regular opportunities to practice key skills such as times tables and the associated facts (8 x 6 = 48, 0.8 x6 = 4.8, 80 x 60 = 4800, 4 x 12 =48, 48 divided by 6 = 8), conversion of units, matching analogue and digital times etc. These are built in beyond the Daily Mathematics Lesson and may be supported by games and appropriate card matching activities. It is essential that children also practice these skills at home. Each child has a maths box which has appropriate facts they need to learn.
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