= - The meaning behind the sign

One of the important elements of the scope and sequence is the intention to correct students' understanding of the equals sign, or hopefully even prevent the need for correction in the first place. For many children, the equals sign is mistakenly perceived as a directive to perform an operation, commonly interpreted as "add it up." This misunderstanding becomes evident when students encounter equations such as 5 + ? = 7. In these instances, many students mistakenly add five and seven, as they have been conditioned to see the equals sign mainly in its typical position—preceding the final result of an operation.

The Equals Sign: A Relational Symbol

What these students often miss is that the equals sign is fundamentally a symbol of balance and equivalence. It serves as a relational symbol, indicating that the quantities on either side of it are the same, or "equal." This concept is not being explicitly taught, leading children to fill in the gaps with the simplest interpretation: performing an operation.

Mathematics is fundamentally about understanding relationships. From the very beginning, children need ample opportunities to explore the relationships between quantities. This exploration should be supported with materials, images, and the use of procedures. Understanding the equals sign is crucial in this process, as it sets the foundation for more complex mathematical concepts later on.

Equality and Mathematical Relationships

The equals sign in an equation signifies a relationship of equality and balance. This understanding is foundational and integral to grasping more advanced mathematical concepts. When students comprehend this, they can also understand the relationship between the equals sign and other mathematical symbols like the less than and greater than signs.

In efforts to simplify learning, many educators resort to gimmicks, such as portraying the less than and greater than signs as "crocodile mouths." While these methods may seem helpful, they often lead to further confusion. Explicit teaching of these concepts is far more effective than relying on such gimmicks. When in doubt, clear and direct instruction is the best approach. Just tell them!

It wasn't until I wrote the scope and sequence five years ago that I truly began to reflect on the meaning of "equal." Over time, I've come to realise just how critical this foundational understanding is.

Last year, I introduced my Year 1 and 2 class to vertical algorithms. This method wasn't initially part of the scope and sequence, but it seemed a natural progression from our work on expanding larger numbers. It dawned on me then about the importance of the "equals line," reinforcing the relational aspect of equations—a simple yet often overlooked piece of knowledge.

In my current Year 1 and 2 class, most students initially perceived the equals sign as "add it up." This clearly indicates the necessity of addressing this misconception even earlier on.

By reinforcing the relational meaning of the equals sign, we can provide students with a more solid foundation in mathematics, preparing them for future learning and understanding.

By the end of last week, they were showing a great growing understanding, showing the relationship between the numerals we write and the Woodin patterns we learn.

I love this little guy when we are exploring equality, his mouth moves to show the relationship between amounts, I think this has been my best buy in many years!

Epidemic Alert - We are building a system that is just making things worse!

Addressing the Educational Epidemic

Recognising the Crisis - We are at tipping point

We are facing a significant educational epidemic that has been quietly developing over many years. Over a decade ago, when we first embraced play-based learning, we began to notice alarming declines in oral language skills among children entering school. Initially, it was just a few children; now, it affects more than half of a class.

Worsening Symptoms

This epidemic extends beyond oral language. Over time, we have witnessed a decline in social and emotional skills, and more recently, in motor skills—both fine and gross. Shockingly, children who arrive with movement skills, good social and emotional abilities, and a keen interest in learning, are now considered advanced. This was once the norm.

The Tipping Point

We have reached a critical tipping point. At least half of new entrants are unable to form sentences, lack social skills and emotional understanding, and struggle with basic motor skills like hopping, skipping, crawling, running, and jumping. Many children lack the hand strength to hold a pencil or open a container, and they often struggle with sitting due to poor abdominal strength.

Cry for Action

Despite advocacy on this issue by play based experts and those that understand the brain (myself included), it has only recently gained more prominent attention, but will those in power listen? 

Our children, chronologically five years old, are developmentally equivalent to 2.5 to 3-year-olds. The pervasive use of devices exacerbates these issues, impacting attention span, eyesight, and overall development. If a parent gave a child drugs, society would be outraged. Yet, allowing children hours on devices seems acceptable.

Misguided Government Policies

Regrettably, the government believes it is excelling at the basics by implementing structured literacy and math, allocating an hour a day to these subjects, and enforcing poorly conceived standardised tests. These measures ignore the fundamental problem.

Imagine assessing phonics after 20 weeks for a child who cannot form sentences, recognise letters in their name, or perform basic movements. Instead of spending money on ineffective overseas assessments and solutions, we must address the root issue.

The current mindset assumes that expecting more from children who are capable of less will solve everything. It won't. We need to eliminate politically driven initiatives and focus on implementing the actual basics brilliantly.

A Call to Action

1. Prioritise Movement: Recognise that movement is crucial for brain development. Children are more sedentary than ever, fixated on screens rather than running, climbing, jumping, and rolling. Ensure that new entrant classes embrace play for at least six months, if not the entire first year. Ensure that classes in the second and third year or school, also embrace an understanding of play and implement play alongside explicit teaching.

2. Eliminate Devices: Remove devices from all junior classrooms. Ensure that device use from Year 4 up has a clear purpose and is limited.

3. Invest in People: Our junior rooms require a 1:10 ratio, some as low as 1:5. Invest in teacher aides, relationships, and connections to prepare children's brains for academic learning.

4. Enhance Outdoor Spaces: Invest in areas that encourage movement. Movement skills are vital for preparing the brain for learning.

5. Support Developmental Engagement: Allow teachers time to engage with students developmentally and understand how to best work with them.

6. Rethink Assessments: Conduct phonics and number checks after two years at school.

7. Rethink Standardised Testing: If standardised tests are necessary, implement them at Year 5 and 6, not from Year 3 and make sure the information gained from them is worth the hassle of conducting them.

8. Support Junior Teachers: Understand the challenges faced by junior teachers and provide the support they need.

9. Educate whānau: Help families see how destructive devices are. Fund initiatives like ‘reading together’ however focus these on the importance of movement, play and the power of reading to and talking with children.

Aligning Realities

The reality in our schools must become the government's reality. Understanding the challenges we face and implementing strategies that genuinely help is crucial. Current policies often hinder our ability to perform effectively. Let us start by aligning our priorities with the real basics for genuine educational improvement.

Mind your language!

Language and communication are fundamental to how we gather information about our world and express our understanding. This blog post focuses on the significance of language in learning, particularly in the context of mathematics.

The Journey into Language

My interest in the role of language in learning began with a focus on oral language development. Over time, I’ve come to realise that language encompasses much more than just spoken words; it is a crucial component of all learning processes. During the 23 years at my School, I've observed that every child requiring Tier 2 or Tier 3 support has struggled with either expressive language, receptive language, or both. Despite its importance, language doesn't receive the attention it deserves. For instance, Developmental Language Disorder (DLD) is still not widely recognised in New Zealand, yet at least one child in every classroom may have DLD.

The Importance of Receptive Language and Vocabulary in Maths

Everything in education ties back to language. This post will particularly focus on receptive language and vocabulary understanding in mathematics. As someone who is self-diagnosed with dyscalculia, I've struggled with maths concepts such as quantity, directionality, and time. This in fact led to the development of a scope and sequence, aiming to prevent other children from having similar negative experiences. Through teaching myself with this framework, I've realised how effective explicit vocabulary instruction and connecting concepts can be in overcoming these challenges.

The Struggle with Mathematical Vocabulary

Many children struggle with mathematical vocabulary, just as I did. Fortunately, addressing this issue is relatively straightforward, but we must ensure that we don't take any term for granted. Here are some examples from my experience:

For years, I didn’t understand why multiplication was called "times tables." I had learned multiplication as "groups," which failed to help me make the necessary conceptual links. The term "times" didn't click for me until I realised it meant multiplying 'lots of times.'

I consistently mixed up "horizontal" and "vertical." It wasn't until I connected "horizontal" with "horizon" that I understood the term without needing to look it up again.  You can imagine how this impacted many aspects of mathematics in high school particularly.

As a child, I found terms like "whole numbers" and "natural numbers" perplexing. It wasn't until I began working with the scope and sequence that I understood what these terms meant.

I was confused about the difference between "equations" and "algorithms" until I associated "equation" with "equal" and "equivalent."

Many students face confusion due to inadequate vocabulary comprehension, which leads to fragmented understandings of mathematical concepts. This isn't limited to maths; language impacts all areas of learning. For children with language struggles, morphology becomes even more critical. Addressing these gaps with deliberate vocabulary instruction can significantly enhance comprehension and learning outcomes.

By focusing on explicit vocabulary instruction and fostering conceptual connections, we can better support students struggling with language and mathematical concepts, helping them build a cohesive understanding and improving their overall learning experience, hopefully we can put a stop to generations of children growing up believing that they are 'just not a maths person.'

This video on connections may be useful when thinking about language.

Along with this one on the crucial role of language

The Goldilocks Zone - The Scope And Sequence in 2025

 

I am currently in the process of reformatting the scope and sequence. This task has been more time-consuming than anticipated as I continue to incorporate all the wonderful additions that emerged quite spontaneously during sessions this year (I guess you could say I have been in my own Goldilocks zone, something I want for all teachers.)

It is incredibly heartwarming to witness an idea that began as a mere germ of an idea in 2020 flourish and strengthen over time. 

 What was that idea? To create a scope and sequence, structured in such a way that met the needs of my learners with dyscalculia, in turn meeting the needs of all.  I had seen the success of Structured Literacy and was driven to create that for maths, at the time, it was something I could not see being created well.  I wanted to make something even the most reluctant math teacher could pick up and grow from.  

This year has been particularly successful, primarily due to my growing understanding of teaching mathematics each year.  

Every year, part of our reporting process includes student voice.  Consistently, when I ask my class about their favourite subject, they overwhelmingly choose maths. While this is not unusual—maths is often a popular choice in my class—this year, the difference was in the children who expressed this preference. Many of the students who were initially uncertain about their abilities in maths have now listed it as their favourite, or at least as a subject they wish to continue improving in.  Some were really explicit about their next steps, expanding large numbers, multiplication, subtraction, change unknown, all areas they listed as wanting to improve in.

Many of those children who wanted to fade into the background during a math sessions, began pushing themselves to the fore.  

This led me to ponder: what made maths the most favoured subject for my students this year? What had I changed or improved upon?

In 2024, I developed a solid understanding of the importance of basic fact fluency and the instructional hierarchy. I experimented with retrieval practice techniques and achieved some success.

In 2025, I continued to focuson subitising (which my scope and sequence is based on) and the use of concrete materials. But my aim this year was to transition students more quickly to more pictorial and abstract thinking. This approach, guided by the instructional hierarchy to determine when to employ fact retrieval practice, has been very effective.  Thank you Brian Poncy, Sarah Powell, Anna Stokke and Amanda VanDerheyden to name a few.

The confidence my students display in maths can be attributed to engaging them in the 'Goldilocks zone'—working within their skill range while gently extending their abilities to bridge new concepts. The emphasis has been on achieving success, building robust foundations, and recognising when students are ready to be challenged or need more practice. I strive to ensure that no child is left behind, aiming for all students to 'get it.'

Operating within this zone fosters a sense of success, fun, and achievement, a dopamine hit! It allows children to connect new concepts and build strong schemas, through a scope and sequence designed to support, grow and connect, rather than rushing them through.

This year, I have observed my students thrive, eagerly expressing their love for maths and seeking more independent problem-solving opportunities, even in their own time. Parents have also shared their amazement at their children's progress and enthusiasm for maths.

The role of basic fact fluency—achieving automaticity (declaratively) in two seconds—has significantly influenced how my students perceive themselves as budding mathematicians. This approach of ensuring no child falls behind in whole-class instruction has benefitted everyone and made it easier to extend those who need it within the same conceptual framework.

I am admittedly biased, but I genuinely believe this scope and sequence is outstanding. With a sustained emphasis on teacher understanding, it holds the potential to provide our Year 1-3 children with exceptionally strong foundations in mathematics and not a workbook in sight!

PS- I thought the Goldilocks zone was something only I dwelled upon, but this podcast is fantastic to listen to.

 

When Did Balance Become a Dirty Word?

Bringing Balance Back to Education

I am currently working on rewriting my scope and sequence, striving to make it even more user-friendly. I know, I know, I can hear everyone saying, "Leslee, stop, take a break, give yourself some time!" I hear you all, and please understand, the chance to refine my scope and sequence so others can have a better experience using it, alongside the opportunity to write, is my idea of a break. In fact, it's a chance to finally release the thoughts and ideas that have been occupying my mind all year.

The Importance of Balance

Now, let's dive into the main topic of this post: balance. Balance is essential, right? We are constantly reminded to achieve a work-life balance, to eat a balanced diet, and to balance rest with exercise. Yet, when it comes to teaching and learning, the word "balance" has somehow become controversial, a dirty word.

When we started advocating for structured literacy, the word "balance" became closely associated with "balanced literacy." Unfortunately, as soon as anyone mentioned "balanced," they were met with criticism and thoroughly chastised.

The mere mention of "balanced" has, for some reason, come to imply that we are not committed to best practices, and thus, should be dismissed.

Reclaiming Balance

However, I am here to reclaim the concept of balance—not to advocate for balanced literacy per se, but to emphasise that balance is crucial if we are to succeed for our children. The current "prescribed" curriculum being promoted nationwide is, in my view, a sham—a placebo, if you will, reminiscent of the Emperor's New Clothes.

The disparagement of the word "balance" has led us to a narrow path, a path where, if we are not careful, we will discard all the good that makes schools places where children can truly thrive. This prescribed curriculum is turning us into fools, leaving us exposed, prancing around as if we were clothed.

This does not mean I am against getting the teaching right. The very existence of my scope and sequence (which can be taught across mixed levels) is a testament to my commitment to excellence. This blog also serves as further evidence of that commitment.

The Missing Element

Here's the kicker: what the government is missing is that they are eliminating the very elements that would make their touted teaching practices work effectively for all, not just a select few. They are pushing out play, relational practice, the arts, culture, time to connect, individuality, understanding—they are pushing out balance, the very things that we as human beings need to thrive.

Without the beautiful nuances that make a successful school truly successful—provision for play, developmentally informed practice, relational practice, local curriculum, the arts, neuroscience-informed practice, and people—the prescription they are offering leaves us vulnerable, balancing between the here and the upside down.

So, let's bring balance back. For those of us who have never let it go, hold on tight, because without it, we are nothing more than a foolish naked Emperor, prancing around proudly, too vain to admit we are getting it wrong.

Where Structure And I Part Ways

This blog has become a place to share my thoughts—thoughts that others may or may not read, thoughts others may or may not care about, but thoughts that very much reflect my journey.

I started this blog after my discovery of 'play' and my original Number Agent approach back in 2016. Saying it like that, that I discovered play, makes it sound like something new. Of course, others, far more expert than I, had unearthed the importance of play long before I stumbled upon its magic. However, that is how professional journeys work; we come to things in our own space and time.

Before I started my posts, I considered myself structured. Our school was structured. Academic achievement was really important to me, and it drove what I did in my new entrant class. I very much believed children needed to be ready for school, and I was often loudly wondering what on earth my ECE colleagues were doing. Children in my new entrant class were whisked quickly into formal learning, assessed for their alphabet on day one, and swiftly provided with literacy and numeracy goals. They were often expected to work in silence, and play was something that would happen in the form of choosing.

I make myself sound like a tyrant, but I wasn't. In fact, my class was fun and engaging, with lots of energy and excitement, but it was very teacher-led.

Gradually, I came to see and appreciate the need for play and have posted many times about how it all started with oral language. Very quickly, my blog and my world became about play.

In 2019, I stumbled across structured literacy (for want of a better term) and my interest turned to how I could mould this with my dedication to play. Following in the footsteps of this learning came 'structured maths', and this blog became more of an exploration of evidence-based practice and the merging of two worlds: structured and explicit, with genuine free-range, child-led play.

Over the last few years, I have advocated that there can be a wonderful balance, but the last year in this country has me worried. The curriculum being imposed on us and the rhetoric being spouted has all become a bit too much. We are losing the balance. I am all for effective teacher practice. I understand the role of explicit teaching and very much 'get' the role of a knowledge-rich approach, but I worry that it is taking over by stealth, overwhelming us into submission, slowly squeezing out the room to play and once again causing us angst about 'acceleration' and levelled achievement.

I admit, even I, who advocates for play, have been guilty of getting bogged down and perhaps 'zombie-ified' by the constant achievement-based focus. Getting caught up in the whirlwind of expectation that reeks of National Standards.

A few weeks ago, I was tired, exhausted, ready to throw it all in—the closest I have ever gotten to just feeling plain beaten down. I even cried in the staffroom (not a great look for the principal, lol).

But, I went back to where it all began, with play. We have a world in desperate need of good people, and I believe a commitment to childhood allows us to work towards that far more than a commitment to a man-made construct of a curriculum and its levels.

There is no getting away from the things we have to attend to. It is important for whānau to know where their child is at and if they need more support, but it is also important to embrace the importance of childhood.

So, as I stood in front of my community during prize-giving week, I reaffirmed our commitment to childhood. As I wandered around the playground, this was only further affirmed for me. Three boys, three tyres, and a hill—that was all it took for me to realise that while I can remain committed to strong pedagogical approaches and best practice, I also know where I need to get off this bus for the good of my children, before it seeps into everything that we are and everything that we do.

I have found my stop, and right now, it feels really good. Childhood is important. We can maintain structured approaches, but we also must hold childhood above that. It must be the most important thing we honour and cherish, because if it isn't, nothing else really matters.

What does it actually mean to strive for excellent academic outcomes for all?

The prevailing rhetoric of the current government suggests a return to the basics, with a keen focus on academic outcomes as the sole priority. Recently, a Minister even asserted that it is impossible to concentrate on more than one thing at a time.

It is deeply regrettable that those making these decisions often lack classroom experience and do not seek the perspectives of those who do. If they did, they would understand that it is indeed possible—and essential—to focus on multiple aspects simultaneously to achieve the academic outcomes they desire.

I have yet to meet a teacher who does not strive for the best for the children in their care. Indeed, no teacher wishes for their children to fail. Ironically, our current government is right now providing the very conditions within schools that mean many children and teachers are actually failing.

If this government truly aims for academic excellence for all, they must recognise that our focus cannot be singular but rather multifaceted:

1. Recognising the Whole Child: We must truly see each child. Understanding child development is crucial, as chronological age or year level often does not align with a child's developmental age. Embracing a pedagogy of play honours the natural ways in which children learn. It is possible to combine play and explicit teaching, in fact, it is the perfect balance.