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What are essential learnings in mathematics?

Often people ask how can I help my child in mathematics. We know there are many key indicators in mathematics that can determine later success and the likelihood of children further pursuing a career in maths. Di Seamon, mathematical researcher uses the term Big Ideas in Number. She has identified key areas in maths that students need to master to continue their development. In Primary school, students are exposed to most of these ideas within the first seven years of their education whilst further developing them when moving into high school. Unfortunately, research tells us that many students will move to high school without some of the core knowledge needed to access higher levels of mathematics. 

So what are these 'Big Ideas' in maths? 

Trusting the Count is the foundation of all other work with numbers: in particular, it refers to a learner’s capacity to access flexible, mental models for the numbers 0–10 (Siemon, Beswick, Brady, Clark, Faragher & Warren, 2015). It's the ability for students to see a collection and recognise how many there are without counting individual units (subitising) and to understand the part part whole relationship of numbers to ten i.e. 7 is 5 and 2 and 1 less than 8. 

Place Value is the understanding of our number system as base 10. The structure of the base 10 number system is essentially multiplicative, involving different-sized groups that are powers of ten. Students can recognise that various numbers have different values. Students can often read two-digit numbers before understanding that 5 in 52 represents 50 rather than 5. Place value underpins fluency in arithmetic calculations and supports ongoing learning with larger numbers and decimals.

Multiplicative Thinking involves thinking about multiplication in a number of different ways. Multiplicative thinking is a prerequisite for the understanding of rational number and proportional reasoning: fractions, decimals, ratio, percent and proportion (Siemon, Izard, Breed & Virgona, 2006). Multiplicative thinking occurs when students can hold the number in each group (multiplicand), the number of groups (multiplier) and the total amount (product), in their minds at the same time (Jacob & Willis, 2001). Being able to picture multiplication as an array, region, or area model is important, as this helps learners to recognise and use equal groups in rows and columns, and teaches them that a collection can be rearranged whilst the quantity stays the same (Norbury, 2002). 

Partitioning is the process of dividing an object or objects into equal groups or equal parts. The idea that a collection or quantity can be expressed in terms of its parts is fundamental in developing a strong sense of number. 

Proportional Reasoning is the ability to think and reason proportionally. It is an essential element for understanding and applying mathematics. People use proportional reasoning to calculate best buys; to perform measurement or monetary currency conversions; to adjust recipes; and to work with drawings and plans.

Generalisation begins when learners start to notice patterns and spot aspects that stay the same when other aspects change. Identifying pattern and structure in mathematics is at the heart of mathematics. When learners are faced with a mathematical problem they are often required to identify a pattern and then give a general rule for what they see.

Students won't just learn one Big Idea before moving to the next. Students in Reception will be exposed to generalising as our older students will still be required to Trust the Count and use Place Value. What we know is the importance of knowing where our students currently are in their learning. Many students going to high school are still consolidating their multiplicative knowledge even though the majority of work at high school involves proportional reasoning and generalising. 

The best way to assist students is to make sure they have strong understanding in their mental knowledge of numbers up to ten. Does your child know how many ways there are to make 8, or what comes before and after the number? The ability to subitise collections and know part-part whole knowledge to twenty is essential for mathematical success in all years.

For more information, please come and see me or speak to your child's teacher about how your child is doing in maths.