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.