The Wilkie Way:September Newsletter TABLES OR ALGEBRA?

Charlotte Wilkinson in her latest Newsletter challenges us as teachers to consider the broader picture rather than the narrow on; "Learn your Tables in Primary School and all well be well for Maths at Secondary!"

Those of you over 40 (and those younger as well) need to reflect on your achievement and attitude to mathematics while at school and before University.  

        How many of your friends hated Maths?

        How many of your friends still say they cant do maths? 

        How many of you were encouraged to take other subjects instead of Maths at Secondary School                 ((Just one young lady in my 6th form maths class in 1960) 

And now we are being told to make sure students memorize their tables in the first months of schooling.

Charlotte is advocating for understand the tables and their relationships and not to learn 100'2 of isolated facts.  We have all seen the despair on children's faces when they dont get "10 out of 10 " of they can remember something that has been asked.  

Picture this: I am a visiting Consultant/Advisor of Mathematics in a Central Auckland School's Year 6 class:

        "Please Sir can you help me I have forgotten what 6 x 4 is?" 

        "Have you any counters in your room?"  "Yes!" and rushes to get them

        "What do you notice with the counters?"        "THank you Sir the answer is 10!"

        This of course led to a discussion about what the signs + and x meant and how display with counters

        Wilkie Way September 

 

 

Basic Facts or Algebra?

Many teachers view primary mathematics as computation, learning the basic facts. Our new curriculum with its wording of memorising basic facts quite early in a students mathematical journey is adding weight to this view.
The Ministry of Education are pushing the need to as turn out pupils who know their basic addition and subtraction facts and know their multiplication tables. The perception being that armed with these crucial mathematical skills children will be successful in secondary school mathematics. 

Parents also set this as an expectation on primary schools and most primary school
assessments support this view of primary mathematics.
While knowledge of addition, subtraction, multiplication and division facts
are essential to mathematical success they are only part of the story.
Recent results from the UK (who implemented a compulsory multiplication test at year 4 many year
ago) have recorded the lowest pass rate at GCSE maths (year 11) since records began. Mathematical
knowledge and looking good on narrow primary assessments does not guarantee success at later maths.
Consider the early addition experiences presented to young children.
I have three red teddies and two blue teddies. How many teddies altogether?
This will often be recorded as 3 and 2 makes 5 and 3 + 2 = 5. The use of signs at this stage implies a
meaning on the equals sign as “makes”. Teachers in their teaching continue to develop the understanding of equals as “makes” by the language they use. They may use the word “makes” or “is” or even use the word “equals” or “is the same as”, however children will construct meaning from what they already know.
Learners will construct the meaning of the equals sign to be “makes” from the context in which it is used.
The focus of children’s learning is on the result of the combination of two or more numbers.
Some teachers introduce signs as a way of avoiding the issue of children being unable to read words and
the signs are far easier for children to learn to write than words. By using signs children can be quickly
propelled into carry out mathematical activities involving the use of worksheets and pencils which allows the teachers to keep children occupied on tasks independent of the teacher.
Some teachers may themselves believe in the importance of teaching equality and that the equal’s sign
indicates a relationship between 3 + 2 and 5 in the equation 3 + 2 = 5. They will often use scales or a
number beam balance to convey the idea of equality but while a number sentence is only portrayed as
3 + 2 = 5 the understanding of the meaning of the equals sign as “makes” seems to pervade children’s
thinking for years to come.
Children’s first generalization regarding equations is constructed incorrectly with the assistance of their
teachers. They practice pages of “sums” all reading “number + number = total” or “number – number =
what’s left”. Occasionally they may be presented with the equation in reverse 5 = 3 + 2. For children who still write letters and numerals back to front this is just the same equation presented back to front, 3 and 2 still make 5. The focus is on the result of joining 3 and 2 and not on the relationship between 3 and 2 and 5. Their learned expectations of an equation result in children’s responses to equations presented as 4 + ___ = 7 as completing the missing number as 11 instead of 3. How often do you see this in a primary school classroom? Children see the + which tells them the operation is addition, they see two numbers, 4 and 7 and an equal’s sign which means what do these two numbers make?

Plenty of research exist identifying huge issues with children’s understanding of the equals sign and even more importantly teachers lack of understanding regarding the children’s misconceptions.
Research evidence would suggest delaying the introduction of the equals sign until it can be introduced ina way that encourages an understanding of a relationship between two quantities rather than as a signal o perform an operation. The equals sign should not be seen as “what’s the answer”.
However - our curriculum expects students to be using the addition and subtraction operational symbols
and the equals symbol in their first year. (and multiplication and division symbols in year 2)
The junior teaching programme for mathematics needs to include a focus on the relationships and
patterns inherent in numbers and through studying these relationships and patterns children will become
competent in knowing their basic addition and subtraction facts and then their multiplication and division facts. Basic facts practice must also be included as children need time to learn these essential facts in order to use them as tools for working with higher mathematics relationships and patterns. Completing equations is not practice for recall.
Teachers need to transform their current arithmetic activities and word problems from problems
with a single numerical answer to opportunities for discovering patterns and making conjectures or
generalizations about mathematical facts and relationships and justifying them. (Blanton & Kaput 2003)
For example: A year one class working on facts to five. The basic facts they need to learn are 0 + 5, 1 +
4, 2 + 3, 3 + 2, 4 + 1 and 5 + 0. You may question whether 1 + 4 is the same or different to 4 + 1. To five
year olds they are different as they will compare by direct observation of the numbers, they have not yet
generalized that addition is commutative and the result is unchanged by reversing the numbers in the
equation. Nor will they see the relationship between 4 + 1 and 3 + 2.
(The curriculum expects students to have memorised these facts by the end of 6 months - this does not
mean recording the equations.)
When introducing this work I would start with looking at number five and begin with the partitioning rather than the joining of two sets. How many ways can you break up five objects into two groups? From this the children will discover there are only three ways, 5 and 0 or 0 and 5, 4 and 1 or 1 and 4, and 2 and 3 or 3 and 2. (There are many songs and poems around the number 5 that make good contexts)
Model the use of the addition sign and use the equals sign to record 4 + 1 = 1 + 4. In this way you
are using the equals sign to show equality and promoting the mathematical property of addition being
commutative. (Expected year 1 knowledge)
While learners seem to experience little difficulty with operational signs like addition or subtraction the
equals sign needs to be used in a variety of contexts to promote the understanding of equality. Children
can be presented with the equation 4 + 1 = 3 + 2. Questions to promote thinking about the relationship
between the two sides of the equation need to be asked which focus the children on the changes that
have occurred. These questions should also be supported by concrete evidence. A line of double sided
counters showing four yellow and one red could be changed by turning one counter to red to show three
yellow counters and two red counters. Ask the children if the number of counters altogether has changed.
Emphasize 4 + 1 is equal to 3 + 2, supported by the recording. How have the numbers changed? The
counters assist children to describe the change, four yellow counters is now one less, there are three
yellow counters and the red counters have one more so one red counter is now two red counters. Initially children may not have the language to explain the change. Part of the teacher role is to develop the children’s language to explain the changes. Language underpins all mathematical thinking.
Children must understand that equality is a relationship that expresses the idea that two mathematical
expressions hold the same value. If they can use relationships in mathematics then mathematical
reasoning involved in finding the result to 5 + 6 they can say “ I don’t know what 5 + 6 is but I know 5 + 5 is 10 and one more is 11.” Using mathematical relationships will enable children to recall basic addition and subtraction facts. If the right answer is what children (and teachers) believe is the most importantaspect of mathematics then methods employed will stay in the safe option. Counting will always give me the right answer, thinking about relationships is not required and therefore will not be used.
The relational patterns begun with numbers up to ten continue with all numbers. If children
have been able to generalize the relationships with small numbers then using them with bigger
numbers is not as difficult as trying to undo misconceptions learnt in their first year of school mathematics

AIMS: Activities in Mathematics and Science

 In the 1980's there was a move by many educators to provide contexts for Mathematics Learning, this including looking at the Maths within Science as well as stand alone Maths.

At the same time there was a push for more Girls to be involved in these  subjects as traditionally they were considered for boys alone!!!!

A great deal of movement was begun in California out of Lawrence Hall of Science Berkeley where EQUALS and Family Math were born.  At the same time happening in Fresno Pacific University AIMS was born

I was fortunate to visit AIMS in Fresno (1987) and through their generosity came away with many practical resources for sharing in New Zealand. I also attended a Week Long Workshop in Perth facilitated by AIMS Tutors.

It has changed over the past 40 years but I am glad that it is still doing some great Professional Development for Teachers.  In fact they have just turned 40.

Elementary School Teachers, check out their latest Newsletter at AIMS 40th Newsletter you may then wish to join their Mailing List.

Congratulations AIMS on reaching 40, just a little short of half my time on this earth. 

 

 

 

Capturing Penguins- Ordered Pairs

 I came across this activity many moons ago so thought it was timely to resurrect as another way to introduce or practise using Ordered Pairs.

Personally hope you are still encouraging children/students to play "Battle Ships" and similar games that I can remember playing, some 70 years ago. 

It does require a little preparation but I hope the outcomes are worth it  And it could spark interest in finding out about Penguins, especially the Hoiho as it is very endangered. 

 

Mathematical "Trick" with a Calculator

 I have to admit I am not a great fan of too much Technology with children, as I believe students learn best by doing, talking about what they have been doing and then writing(in maths language).

DO

SAY

WRITE 

It is difficult for me to understand how students can learn to Measure if all they have is a Tablet in their hand. Measurement is about Stepping, Holding, Weighing(Balance scale) etc.

That said her is a Fun Calculator Activity for you to try on your students or children.   After repeating it a number of times you may wish to ask them to see if they can work out "why it works."

Enjoy.  

Three Gazinta

 Often when encouraging students to learn/memorise tables we do not always look at some of the maths "hidden" in the numbers.

I can remember seeing the "Lights go on" when exploring with students various Divisibility Rules.  I still use the Divisible by Four rule for working out which years are Leap Years, or when the Olympic Games are scheduled.

Three Gazinta could be the springboard for further investigations as well as a context for simple additions and division by 3.  Tables with a Purpose! 

 

The Mathematics of Kaleidoscopes

 With the New Zealand Mathematics Curriculum of the 1990's each Achievement Objective was prefaced by words such as; "Through problems and investigations students will achieve.."

This was a time when those involved in Mathematics Education Teaching and Learning also encouraged "Contexts for Studying Mathemathics" so that the maths skills and ideas had real life ideas to explore and learn the mathematics.

On Thursday I visited an Oral Surgeon, and before he filled y mouth with Instruments he asked me what I used to do. This of course opened a quick discussion about "How Children Learn Maths and My Philosophy"  When I mentioned Contextual Learning he said that he did Orienteering with his daughter! Wow what a great physical as well as mathematical activity. Geometry and Measurement in CONTEXT! I then offered to send him some repeatable maths activities for the family to do together, otherwise he was going to go online to find Maths Pages. I encouraged the games as they would be learning together, they are fun and they would be "talking mathematicss" 

This then got me thinking about other activities that students and families could become involved with. The first is KALEIDOSCOPES. I have never come across anyone who doesn't like at the wonderful patterns made by a Kaleidoscope.  But how many of us have explored the mathematics?  The attached PDF might be the start of a great exploration ending up with making your own kaleidoschope in the future.  Kelston Intermediate back in the 80's had a Metal Work Teacher who had a unit about the making of a Kaleidoscope but no real exploration of the mathematics that help make the patterns.

 

Enjoy your dip into the wonderful world of Kaleidoscopes (Acknowledgement to Creative Publications-Dale Seymour-for Kaleidoscope Math by Joe Kennedy and Diane Thomas)

 

 

 

Beware The Science of Maths

I am on Charlotte Wilkinson's mailing list, as I respect her research and writings, and have her permission to share her thoughts and writings. 

Her latest epistle (April Newsletter) https://www.wilkieway.co.nz/blog/post/163475/april-newsletter-2026/ asks us to Question and Reflect on Teaching Approaches we may have thrust on us or encouraged to implement as its "best for the students"  see her final paragraph.

Beware The Science of Maths

Riding on the wave of the popular “Science of Reading” there is now a movement calling itself the Science of Maths.

Information for this newsletter is taken from The Science of Maths Reconsidered: A critical examination of foundational claims. by Kate Raymond (University of Oklahoma USA) and Melissa Gunter (Central Connecticut State University USA)

While there is much common ground between the “Science of Maths” (SOM) and current research in maths education most arguments made by SOM are based on scant evidence.

Areas of agreement: There is a need for high quality instruction, large scale research of instructional practices, and clear goals and direction for students.

SOM conclude that these goals can only be achieved through the use of direct instruction, they fail to demonstrate that inquiry, discovery, or other student-centred approaches cannot accomplish the same goals.

SOM claims it is a myth that students should not be exposed to procedural instruction until they have demonstrated adequate conceptual understanding.
This is a long standing debate within maths education - when in fact effective mathematics teaching focuses on the development of BOTH conceptual understanding and procedural fluency. Conceptual knowledge and procedural knowledge work in tandem and are often intertwined. To use an algorithm well, students have to have a strong foundation in understanding of numbers and place value. They need a strong foundation in understanding of what it means to add, subtract, multiply or divide before introducing an algorithm.

SOM claims it is a myth that inquiry learning is the best approach.
The argument given is very thin in that the view of inquiry based learning is interpreted as an approach that offers no support or guidance to students. Inquiry with support and scaffolding for student success is of benefit to students. There is little evidence to suggest that inquiry methods with support and scaffolding are inferior to explicit instruction methods.

Further myths claimed by SOM include:

• Teaching algorithms is harmful
• Productive Struggle is important
• Growth mindset increases achievement
• Executive training function is important
• Timed assessments cause maths anxiety

The emergence of SOM as a contempory contributor to the discourse of mathematics education should be treated with caution especially when picked up by politicians, policy makers and the media. Their inclination to support SOM is probably because of its focus on procedural fluency (which is easily measured) rather than sense making, reasoning, or problem solving for which is harder to gather “hard data” as evidence of this occurs over time and in application outside of the school setting. (Becoming numerate!)

We should focus on the common ground:
Timed assessments: - be wary of timed assessments when used ineffectively in providing useless data, creating high stakes assessment practices, used to compare students, or used as a means of withholding something, e.g. morning tea break.
Explicit instruction: defined as “an instructional design and delivery approach characterized as unambiguous, structured, systematic and scaffolded.” This approach can equally be applied to inquiry, problem based learning or other student-centred approaches. However to add to the definition should be “responsive and flexible to individual learning needs.”

It is imperative that as educators we do our due diligence with all new ideas, examining each critically and always ask ourselves why?

We need to make sure we go beyond asking ourselves;
What do I need to teach? (the curriculum)
How am I going to teach it (which resource am I going to use?)

2 ©Copyright N C Wilkinsons Ltd 2026 All rights reserved.

I would like to add a phrase, "Courses for Horses" in other words there is no one instruction that will fit the needs of all students. We as Teachers/Educators need to be aware of this and adjust our teaching strategies to meet the needs of all students in our classrooms.

Consider the learning styles or the students: 

Primary Learning Styles (VARK Model)

• Visual (Spatial): Prefer maps, diagrams, graphs, charts, and patterns to understand information.
• Auditory (Aural): Learn best through listening, discussions, lectures, and speaking.
• Reading/Writing (Verbal): Consume information best through text-based input and output, such as reading notes and writing.
• Kinesthetic (Physical): Learn through experience, hands-on practice, simulations, and movement.

 "I can remember being asked to demonstrate how I would teach simple line graphs to a Year 10 group of girls in a private girls school.

I explained to the class that we were going to start the "maths lesson" outside on the tennis courst, where I had prepared a number line including negative numbers.

Once outside I asked some of the girls to stand on a number on the number line and then proceeded to give them an equation such as:  y = 2x + 3

The students standing on the various numberline points had to look at the number between their feet and do the calculation:   2(-2) +3 =-1,  2(0) + 3 = 3,  2(3) + 3 = 9   etc.

Once the calculations had been completed with assistance from others especially for the negative numbers I instructed.   "When I say "go" if your total is negative step that many steps backwards, if positive  then step those many steps forward.   Go

What have we made?  A straight line!

After a number of these activities including a quadratic equation or two we then went inside and discussed what we found.   This included drawing the graphs of the various equations.

At the debrief, with the schools teachers I was asked, 

"Did you notice the girl at the back right who answer, or tried to answer all the questions? 

"Yes, I did"

"She has never answer a question in maths before"

"Lets disregard the fact that I am a Male teacher in an all girls school, and consider if she is a Visual/Kinesthetic Learner?"

This is just one example how a changed teaching style can empower and involve a student who may have been "turned off" for most of the time.

One size(approach) does not fit all 

 

Picturing a Dichotomy

 How do we find out about a New Class we have been given?  But at the same time acknowledging that each student has different Traits?

Were you aware that some people have attached ear lobes others unattached?

Were you aware that some people can roll their tongue while others cannot?

Were you aware that some people can flip their tongue while others cannot?

Were you aware that some people have a Widows Peak and others do not?

I have used that attached activity from AIMS (Activities in Math and Science-Fresno USA) with both students and teachers as a way to encourage interactions and to explore Traits that we are often not aware of.

Useful from about Year3/4 and above 

The attached is the full AIMS Activity with Teacher Notes and Student Focus questions/reflections.

If you use this activity it would be great to get your feedback below! 

 

Algebra Race

 In all the times I have used this activity the students have really got involved.  They enjoy working in Groups of Four and of course the competition!

 

Counting Shapes

 Counting various shapes helps students differentiate and look laterally.  Often they quickly count the obvious and say"I have finished!" without really delving into the not so obvious.

I often wonder if this is because we have tended to focus on answers (and usually "correct ones") rather than have the students explain how they reached their answers.  This sharing/justification does not always have to be with the Teacher but could be with a partner or within a group.  Often sharing will elp the student "self correct" whereas focusing on answers will give them a high or a low.

 

I shared this activity with a Senior recently(over 70) who wanted some maths puzzles.

The Senior sent an answer of 21, my response was well done but have you considered all the different sized squares?

I have always loved this puzzle of a cat.  Mainly because most people never find the "correct" answer the first time.

 Enjoy using these puzzles and get your students to create their own. Or you could ask "How Many Squares on a Chessboard?" .... 

NIM Games: Great for pattern developing and logical thinking.

 After being woken this morning, by what sounded like brief spurts of strong winds, realised it was the gas burning to keep a hot air balloon aloft.

This of course reminded me of a Maths NIM Activity (already on this Blog) BALLOONS OVER WAIRARAPA! so I wont republish it here.

Nim is an ancient mathematical game of strategy, likely originating in China and popular in Europe by the 16th century. Known for its simple "take-away" rules, Harvard mathematician Charles L. Bouton coined the name "Nim" (from German nimm, "take") 

There are many forms of NIM, I used extensively what I called 21, in my Advisory work.  I also used it when driving my son to Intermediate School, many years ago.

TWENTY ONE 

A game for two people or teams

Start with                                                             21

Individuals take turns to Take Away(Subtract)     3, or 2, or 1  from the running total

The Individual who subtracts 3 or 2 or 1 to make ZERO Wins.

            e.g.                                    21  -    3    =    18

                                                     18    -    1    =    17

                                                    17    -    2    =    15

                                                    15    -    3    =    12 .........

For younger players this could be written instead of working in the head

Pose the Question:  How can you win most of the time?

                                Encourage scenarios and then try them out (Dont do this until they have plated many games with different partners. 

                                Can also be played with taking away 1, 2, 3, or 4 !

                                                    Or adding to make a target number, say 25

 

 

         

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