Memorisation and/or Processing

 How Important is Memorisation of Tables?

Before we try and answer this question for a school situation, I would like to ask: 

 

When was the last time you use A Dictionary, Thesaurus, Google to check the spelling or meaning of a word or phrase? 

Would you expect you Doctor or Nurse to have memorised every treatment possibility for an illness? 

 

In the first case I would expect that if we had been encourage to think and process, we would not be afraid to say "I Cant Remember, but I know how to find out!"

 

In the second case, I personally would be changing my medical practitioner, if they total relied on memory and did not research/look up the latest or alternative treatments.

 

 

In a school situation how important is the memorisation of tables compared to having Number Sense and an ability to "work it out" when instant recall is not there. I remember sitting in with a teacher who was "testing" my granddaughter(Year 8)!  After the "Test" I asked why the teacher marked 9x8 incorrect. Th response floored me as my granddaughter had got the "answer" correct.  "I marked it incorrect because she did not have instant recall of 9x8" I replied, "But she wrote 8x10 is 80 take away 8 is 72. almost as quickly as many children would say 72"  In this case no change, it was still wrong!!

 

We need to make sure we are not stopping student learning a by a pedantic reliance on Instant Recall. 

 

Problem Solving and Investigations(Thinking/processing) 

Some twenty odd years ago, I attended the graduation of one of my sons who had just completed a B.E. The Guest Speaker told everyone present that an Engineering Degree is the best to have as it teachers Problem Solving and Investigation.  With these skills you can then apply your learning to anything you wish.

 

In a Student I am aware off:  Achieved a B.E(mech)  then became a Patent Attorney, after a few years acheived a MBA(cambridge) and worked as a Business Consultant in Europe. Next step worked for Air New Zealand looking forward for expansion..  Set up a Financial Business with two others, with Offices in NZ, Australia, Singapore, London.

 

Yes they did memorise lots of things but they wouldn't be where they are with out the "processing". 

 

I was pleased to read the latest  Wilkie Way Newsletter which focusses on Memorise or Numbersense?  It is printed below with permission

 

Memorise or Number Sense

This month’s professional reading is based on Fluency without Fear: Research Evidence on the Best
Ways to learn Maths Facts by Jo Boaler
A few years ago a British politician, Stephen Byers, made a harmless error in an interview. The right
honorable minister was asked to give the answer to 7 x 8 and he gave the answer of 54, instead of
the correct 56. His error prompted widespread ridicule in the national media, accompanied by calls for
a stronger emphasis on ‘times table’ memorization in schools. The Conservative education minister
for England, a man with no education experience, insisted that all students in England memorize all
their times tables up to 12 x 12 by the age of 9. This requirement has now been placed into the UK’s
mathematics curriculum and is likely to cause a rise in levels of math anxiety and students turning away
from mathematics in record numbers.

Mathematics facts are important but the memorization of math facts through times table repetition,
practice and timed testing is unnecessary and damaging. The English minister’s mistake when he was
asked 7 x 8 prompted calls for more memorization. This was ironic as his mistake revealed the limitations of memorization without ‘number sense’. People with number sense are those who can use numbers flexibly.

When asked to solve 7 x 8 someone with number sense may have memorized 56 but they would also
be able to use recall of 7 x 7 is 49 and then add 7 to make 56, or they may use recall of ten 7’s and
subtract two 7’s (70-14). They would not have to totally rely on a distant memory. Math facts, themselves, are a small part of mathematics and they are best learned through the use of numbers in different ways and situations. 

 

Unfortunately many classrooms focus on math facts in unproductive   

ways, giving students the impression that math facts are the essence of mathematics, and, even worse that the fast recall of math facts is what it means to be a strong mathematics student. Both of these ideas are wrong and it is critical that we remove them from classrooms, as they play a large role in the production of math anxious and disaffected students.

Some students are not as good at memorizing math facts as others.
That is something to be celebrated, it is part of the wonderful diversity of life and people. In a recent brain study scientists examined students’ brains as they were taught to memorize math facts. They saw that some students memorized them much more easily than others. This will be no surprise to readers and many of us would probably assume that those who memorized better were higher achieving or “more intelligent” students. But the researchers found that the students who memorized more easily were not higher achieving, they did not have what the researchers described as more “math ability”, nor did they have higher IQ scores (Supekar et al, 2013). The only differences the researchers found were in a brain region called the hippocampus, which is the area of the brain that is responsible for memorized facts (Supekar et al, 2013). Some students will be slower when memorizing but they still have exceptional mathematics potential. Math facts are a very small part of mathematics but unfortunately students who don’t memorize math facts well often come to believe that they can never be successful with maths and turn away from the subject. 

 

My own daughter came home in year 5 and stated she was no good at maths because she couldn’t recall
her divisions quick enough - she is now a very successful Financial Manager at a very large institution
and a chartered accountant. What could have happened to her potential if I had let her believe that
speed of recall was a measure of mathematical success? Another interesting fact is she has an inverted
hippocampus (discovered during a brain scan) and was asked by the medical personnel if she had
learning difficulties.

 
When teachers emphasize the memorization of facts, and give tests to measure number facts students
suffer in two important ways. For about one third of students the onset of timed testing is the beginning
of math anxiety (Boaler, 2014). Sian Beilock and her colleagues have studied people’s brains through
MRI imaging and found that math facts are held in the working memory section of the brain. But when
students are stressed, such as when they are taking math questions under time pressure, the working
memory becomes blocked and students cannot access math facts they know (Beilock, 2011; Ramirez,
et al, 2013). As students realize they cannot perform well on timed tests they start to develop anxiety
and their mathematical confidence erodes. The blocking of the working memory and associated anxiety
particularly occurs among higher achieving students and girls. Conservative estimates suggest that at
least a third of students experience extreme stress around timed tests, and these are not the students
who are of a particular achievement group, or economic background. When we put students through this
anxiety provoking experience we lose students from mathematics. Math anxiety has now been recorded
in students as young as 5 years old (Ramirez, et al, 2013) and timed tests are a major cause of this
debilitating, often life-long condition. Timed tests evoke such strong emotions that students can come to
believe that being fast with math facts is the essence of mathematics. There is a second equally important reason that timed tests should not be used – they prompt many students to turn away from mathematics. 

 

In order to learn to be a good English student, to read and understand novels, or poetry, students need
to have memorized the meanings of many words. But no English student would say or think that learning about English is about the fast memorization and fast recall of words. This is because we learn words by using them in many different situations – talking, reading, and writing. English teachers do not give students hundreds of words to memorize and then test them under timed conditions. All subjects require the memorization of some facts, but mathematics is the only subject in which teachers believe they should be tested under timed conditions. Why do we treat mathematics in this way?

It is important when teaching students number sense and number facts never to emphasize speed. In fact
this is true for all mathematics. There is a common and damaging misconception in mathematics – the
idea that strong math students are fast math students. Many mathematicians are rather slow with numbers - this is not a bad thing, they are slow because they think deeply and carefully about mathematics.

The New Zealand 2025 curriculum the potential to cause many students harm, by increasing maths
anxiety, creating mathematically disengaged students who‘s future will be significantly influenced by lack of confidence with mathematics. It is         

essential schools and teachers fully
understand the curriculum. They need to
develop policies that focus on delivering
the curriculum in a least harmful way.
Memorisation is listed as a practice.
The practices are the skills, strategies
and applications to teach. You cannot
teach memorisation - you can only
teach in a way to help students develop
the recall of maths facts - by providing
the opportuity to use the facts in many
different situation. Teachers and students
use the mathematical and statistical
processes to learn knowledge and
practices and develop understanding of
the big ideas. 

 

During first six months
• Memorising addition and subtraction facts up to 5
During the first year
• Memorising addition and subtraction facts up to 10,
• Memorising doubles and halves to 10
During the second year
• Memorising addition and subtraction facts up to 20
• Memorising doubles and halves to 20
• Memorising multiplication and corresponding division facts for 2s, 5s, and 10s
During the third year
• Memorising multiplication and corresponding division facts for 2s, 3s, 4s, 5s, 8s, and 10s
During year 4
• Memorising multiplication and corresponding division facts for 2s to 10s
• Memorising and using the decimal equivalent of ½ and fractions with denominators of 10
During year 5
• Memorising multiplication and corresponding division facts for 2s to 12s
• Memorising and using decimal equivalents of ½, ¼, and ¾ and fractions with denominators or 10 or
100
During year 6
• Memorising decimal and percentage equivalents of common fractions (½, ¼, ¾, 1/5, 2/5, 3/5, 4/5)
including fractions with denominators that are 10 or 100

Teachers should help students develop math facts, not by emphasizing facts for the sake of facts or using ‘timed tests’ but by encouraging students to use, work with and explore numbers. as set out under the Mathematical Processes. (Follow the link on the Mathematics & Statistics curriculum overview page on Tahurangi). As students work on meaningful number activities they will commit math facts to heart at the same time as understanding numbers and math. They will enjoy and learn important mathematics ratherthan memorize, dread and fear mathematics.

Research tells us that the best mathematics classrooms are those in which students learn number facts
and number sense through engaging activities that focus on mathematical understanding rather than rote
memorization.

In conclusion:
As educators we all share the goal of encouraging powerful mathematics learners who think carefully
about mathematics as well as use numbers with fluency.
Unfortunately unproductive and counter-productive classroom practices continue that often accompany
the teaching of math facts – speed pressure, timed testing and blind memorization. High achieving
students use number sense and it is critical that lower achieving students, instead of working on drill and memorization, also learn to use numbers flexibly and conceptually. Memorization and timed testing stand in the way of number sense, giving students the impression that sense making is not important.
We need to ensure the teaching of early number focuses on developing number sense.
If we do not then failure and drop out rates already at record highs will escalate. When we emphasize
memorization and testing in the name of fluency we are harming children, we are risking the future of our ever-quantitative society and we are threatening the discipline of mathematics.
Implementing the 2025 curriculum means you must ensure you have all the parts of the curriculum
which are unfortunately scattered around Tahurangi rather than in a succinct document as were previous
curriculums. Progress?? 

"THE AVERAGE STUDENT 2"

 This article is from "The Wilkie Way" February Newsletter and posted with permission by Charlotte Wilkinson

In 2018 I attended the BCME conference in the UK at Warwick University and attended a session run by Ruth Merrtens (an academic, teacher and writer College of St Mark and St John Plymouth University) and these are the notes I took from her presentation.

The UK under the 2014 mastery curriculum is paying very little consideration to child development and
focusing on a very prescriptive curriculum. Ruth Merrtens pointed out that transferring the Singapore and Chinese methods to UK schools in a bid to raise the UK in international league tables is simplistic. She cites the success of Singapore and Chinese methods in Singapore and China has more to do with high teacher knowledge and status. The amount of time students spend on mathematics is probably double the time spent in UK. Also parental support, no discipline issues in the classroom and the desire/need to be educated in order to make a living. (No welfare systems)

She also highlighted the lack of mathematical pedagogical knowledge in professional learning
opportunities available for primary teachers. Continuing professional learning budgets are being focussed on generic topics like behaviour management, technology use etc.

Publishers are making a lot of money out this approach as UK government are insisting that every student has workbooks and textbooks to work from. One publisher has produced a 100 page workbook and 100 page textbook for each term from year 1 to year 6. Government are providing grants for schools to purchase books – approved by them. Currently there is only one text approved – a direct translation of a Shanghai text. The Education budget will actually bypass schools.

(Michael Gove former UK education secretary (2010 - 2014) has a major advisory role in Stanfords reform programme for NZ schools - See Listener article Educating Erica Jan 31 - Feb 6).

Another session attended at the same conference was a research presentation run over a school year by
the Babcock Centre attached to Exeter University:
The question asked was:
How can we best support teachers to develop their own practice through action research?
Effective professional learning requires the following components:

1. Sustained - weeks and months
2. Subject specific
3. Pro-active – go and play, take a risk
4. Collaborative
5. Supported by an external specialist/credible facilitator
6. Evidence based – created a conflict as teachers engaged on reading research was not effective to PLD
7. Student focused

Barriers to learning identified:
1. Teachers who go through the motions – doing it for someone else, waiting to be told what to do, waiting for the facilitator to control any discussion.
2. Teachers needed to learn to examine their own thinking to move from what they are doing to what is
their impact on student learning.
3. School leadership – this was by far the biggest barrier. Leaders signed their teachers up for the project
then overloaded them with other professional learning contracts and administrative tasks. No consideration or interest is given to the learning needs of their teachers.

UK 2026 Curriculum changes: The UK is updating its national curriculum to modernize education,
moving from a knowledge-heavy focus (2014) to one that emphasizes “applied knowledge,” practical
life skills, and adaptability for a fast-changing, technology-driven world. The review aims to address
educational inequalities and improve engagement for disadvantaged students.

New Zealand is 12 years behind what is being advertised here as drawing on “world
leading curriculums” and is about to repeat what evidence shows is not the answer to
inequity and the resulting inequalities. 

THE AVERAGE STUDENT

 This article is from "The Wilkie Way" February Newsletter and posted with permission by Charlotte Wilkinson

The Average Student

Something to think about as we head down the road of teaching all students in a year group the same
content and new standardized testing.
We’re so accustomed to using averages that we neglect to question whether they’re actually useful. The
End of Average by Todd Rose argues that, when we use averages to judge people, we typically arrive at
inaccurate and harmful conclusions.
(Rose is a developmental psychologist, former Harvard professor)

Rose asserts that one of the areas of society in which judging individuals with averages has done the most damage is the modern education system. Rather than give each student what they individually need to learn the most, we give them a standardized experience that forces them to conform or fail. As a result, students and society both suffer.

Consider what is happening in New Zealand and the politics behind the changes. “What is driving alot of what I’m doing - is that equity piece”(Listener Jan 31 - Feb 6 2026 - Educating Erica). The premise is that the changes being made are to ensure that everyone can live up to their full potential. There is no argument that knowledge is essential but is the knowledge the only aspect to be considered?

According to Rose, our education system is a deeply flawed sorting mechanism because it’s founded on
the false assumption that “general intelligence” exists. We use standardized tests because we assume that students who are better at quickly solving math problems or reasoning through logic puzzles are generally“smarter” than others. In other words, we think they’ll be better at solving all problems than their less“gifted” counterparts. Instead of judging students based on individual skills, we average out their various skills into one-dimensional scores that supposedly reflect their general intelligence.

However, research shows that such scores of general intelligence are completely inaccurate. Rose argues that if you ever judge someone as “generally smart,” you’re probably mistaken. That’s because someone who’s good at one intellectual task is no more likely than anyone else to be good at another intellectual task. For this reason, a student’s standardized test scores or grade point average don’t reliably predict their performance at other tasks, or in their future career.If a student is gifted in ways a standardized test can’t measure, the system incentivizes them to struggle to succeed in the same way as everyone else instead of nurturing the talents they have. This is not only demoralizing for individuals, but also damaging to society at large, as it leaves the labour pool full of underutilized talent.
 

Second, according to Rose, our education system limits students’ potential by teaching all students a fixed curriculum at a fixed pace. This disadvantages those who need more time to effectively learn.

We assume that students who learn more quickly are “smarter” in general, and they’ll also excel at
retaining skills and using them to solve problems. However, research suggests this is false: When given
the freedom to progress through a curriculum at their own pace, almost any student can learn at a “gifted” level. Students benefit from spending more time on the ideas they struggle with and less time with those that come easily to them.

Our entire education system is based on the average learner, when there is no such thing. “So
schools fail at what they’re supposed to do - recognise and nurture talent,” says Rose 

This is what I experienced when going to school from 1948. It is also how I was encouraged to teach when at Wellington Teacher's College 1963-64.  Joan Paske, Maths Adviser, was soanit whole class teaching she with her supporters produced a Differentiated Framework, called Wellington Maths!

Refer back to my previous Blog and the next one "Charlotte Wilkinson's Thoughts" 

Do We Have Standardised (Average) Children?

 As a teacher from 1965 and then a Maths Adviser from the 80's, finishing up as a Private Maths Education Consultant, we were encouraged and expected to teach on the basis that New Zealand had a Child Centred Education System!

THE 'NOW' POSITION 

In the 70's while teaching at Intermediate Schools in Auckland we often called on the Mathematics Advisers to demonstrate in our classrooms or work with them at In-Service Courses. (Jock Day in Auckland, Joan Paske in Wellington etc) In their work they encouraged us to find the "NOW" position of the children and then prepare programmes to build on what they knew.  This often involved some sort of grouping both streamed and cooperative.

RICH MATHEMATICAL ACTIVITIES  Lead to Differentiated Teaching and Learning

In the 80's led by Murray Britt, lecturer at Auckland College of Education (also writer of the 1990 Maths Curriculum) encouraged us all to have our students involved with Problem Solving and Investigations.  Many of these activities were what were called "Rich Mathematical Activities".  An activity that most(all) students could start but were "open" so that more able students could explore further.

At and Auckland Full Primary School (about 2012) they instituted a two year Professional Development Programme focussing on Problem Solving and Investigations, and meeting individual students needs. The visiting Maths Consultant visited fortnightly demonstrating in classrooms and giving feedback and advice for teachers, as well as whole group Inservice. This programme ran for just over 2 years.  Towards the end of the 2 years a call from the local Secondary school to the Principal ask "what are you doing differently in maths as your students are head and shoulders above students from other Contributing Schools.

DO YOU WISH TO BE COMPARED TO A 35 YEAR OLD RUNNER?

In my capacity as an Adviser/Consultant I was often asked to speak with the Parents of schools "about Maths" A very common question/comment was "why do you have students working at different levels, rather than like when I was at school?"

My response often included an Analogy similar to this?  

        "Peter Snell is a 37 year old athlete running the 800 metres"

        "Please stand up if you are Between 35 and 39"

        "If you were in a race with Peter Snell, as we are all "equal" I expect you to be close to Peter at the Finish Line!"

        Is that a fair race?   Why then do we expect 30 children in a class to be at the same level of Maths when they have had different pathways to Standard 5-Year 5?

IS THIS FAIR?

 

Why do I read that the Education System is now instituting the same maths for all students of an Age Group, regardless of the different pathways they have travelled to get there? 

I have been watching in dismay at what has been happening in Mathematics Education, over the past years. Achievement levels have been falling regularly, so each Govt will try and put their answers to the problem into place.  

Where has been the outcry for what is happening at the moment?

Children are NOT Standardised, Average, or at the same level, so dont teach them as if they are!!

CHECK OUT THE NEXT BLOG ABOUT STUDENTS BEING AVERAGE! 

Which Trees and Plants?

 A simple survey leading to a presentation for the school or parents etc.

Spiralling Under Control

 This is card #4 in the series, more to come in the next few days.

I would appreciate any feedback about how useful the cards/activities are 

 

 

 

 

 

 

 

Catlin's Special Plants

* This activity could be an introduction to algebraic rules. 

* When I was at school Algebra was a topic on its own, often not related to anything real or "concrete".  To me, Algebra is about generalisations of patterns and numbers around us.  

* "Rules" we may have learnt about numbers are the beginning of Algebra.  e.g. When we muliply a number by 10 we shift the numbers one place to the left and put a '0' in the 'ones' place, NOT 'Add a Zero' as adding zero doesn't change the number!!!!

* We want and need to students who understand and can apply those understandings to other situations. This means not just teaching rules nand short cuts but using investigations and thinking to develop understanding.